aspen polymers+vol1v7 1-usr

Aspen Polymers

User Guide Volume 1

Version Number: V7.1 January 2009

Copyright (c) 1981-2009 by Aspen Technology, Inc. All rights reserved.

Aspen Polymers™, Aspen Custom Modeler®, Aspen Dynamics®, Aspen Plus®, Aspen Properties®, aspenONE, the aspen leaf logo and Plantelligence and Enterprise Optimization are trademarks or registered trademarks of Aspen Technology, Inc., Burlington, MA.

All other brand and product names are trademarks or registered trademarks of their respective companies.

This document is intended as a guide to using AspenTech's software. This documentation contains AspenTech proprietary and confidential information and may not be disclosed, used, or copied without the prior consent of AspenTech or as set forth in the applicable license agreement. Users are solely responsible for the proper use of the software and the application of the results obtained.

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Aspen Technology, Inc. 200 Wheeler Road Burlington, MA 01803-5501 USA Phone: (1) (781) 221-6400 Toll Free: (1) (888) 996-7100 URL: http://www.aspentech.com

Contents iii

Contents

Introducing Aspen Polymers ...................................................................................1 About This Documentation Set ......................................................................... 1 Related Documentation................................................................................... 2 Technical Support .......................................................................................... 3

1 Polymer Manufacturing Process Overview...........................................................5 About Aspen Polymers .................................................................................... 5 Overview of Polymerization Processes ............................................................... 6

Polymer Manufacturing Process Steps...................................................... 6 Issues of Concern in Polymer Process Modeling .................................................. 7

Monomer Synthesis and Purification ........................................................ 8 Polymerization ..................................................................................... 8 Recovery / Separation........................................................................... 9 Polymer Processing............................................................................... 9 Summary............................................................................................ 9

Aspen Polymers Tools ..................................................................................... 9 Component Characterization .................................................................10 Polymer Physical Properties ..................................................................10 Polymerization Kinetics ........................................................................10 Modeling Data.....................................................................................11 Process Flowsheeting ...........................................................................11

Defining a Model in Aspen Polymers.................................................................12 References ...................................................................................................14

2 Polymer Structural Characterization .................................................................15 Polymer Structure .........................................................................................15 Polymer Structural Properties .........................................................................19 Characterization Approach..............................................................................19

Component Attributes ..........................................................................19 References ...................................................................................................20

3 Component Classification ..................................................................................21 Component Categories...................................................................................21

Conventional Components ....................................................................22 Polymers............................................................................................22 Oligomers ..........................................................................................23 Segments ..........................................................................................24 Site-Based .........................................................................................24

Component Databanks...................................................................................25 Pure Component Databank ...................................................................25 Initiator Databank ...............................................................................26

iv Contents

Segment Databank..............................................................................26 Polymer Databank...............................................................................27

Segment Methodology ...................................................................................27 Specifying Components..................................................................................27

Selecting Databanks ............................................................................28 Defining Component Names and Types...................................................28 Specifying Segments ...........................................................................29 Specifying Polymers.............................................................................29 Specifying Oligomers ...........................................................................30 Specifying Site-Based Components ........................................................30

References ...................................................................................................31

4 Polymer Structural Properties ...........................................................................32 Structural Properties as Component Attributes ..................................................32 Component Attribute Classes ..........................................................................33 Component Attribute Categories......................................................................34

Polymer Component Attributes..............................................................34 Site-Based Species Attributes ...............................................................44 User Attributes ...................................................................................45

Component Attribute Initialization ...................................................................46 Attribute Initialization Scheme ..............................................................46

Component Attribute Scale Factors ..................................................................50 Specifying Component Attributes.....................................................................51

Specifying Polymer Component Attributes...............................................51 Specifying Site-Based Component Attributes ...........................................51 Specifying Conventional Component Attributes ........................................51 Initializing Component Attributes in Streams or Blocks .............................51 Specifying Component Attribute Scaling Factors.......................................52

References ...................................................................................................52

5 Structural Property Distributions ......................................................................53 Property Distribution Types ............................................................................53 Distribution Functions ....................................................................................54

Schulz-Flory Most Probable Distribution ..................................................54 Stockmayer Bivariate Distribution..........................................................56

Distributions in Process Models .......................................................................56 Average Properties and Moments...........................................................56 Method of Instantaneous Properties .......................................................58 Copolymerization ................................................................................61

Mechanism for Tracking Distributions ...............................................................62 Distributions in Kinetic Reactors ............................................................62 Distributions in Process Streams............................................................64 Verifying the Accuracy of Distribution Calculations ...................................65

Requesting Distribution Calculations ................................................................66 Selecting Distribution Characteristics......................................................66 Displaying Distribution Data for a Reactor ...............................................67 Displaying Distribution Data for Streams.................................................67

References ...................................................................................................68

6 End-Use Properties............................................................................................70 Polymer Properties ........................................................................................70

Contents v

Prop-Set Properties .......................................................................................71 End-Use Properties........................................................................................72

Relationship to Molecular Structure........................................................72 Method for Calculating End-Use Properties ........................................................73

Intrinsic Viscosity ................................................................................74 Zero-Shear Viscosity............................................................................74 Density of Copolymer...........................................................................75 Melt Index..........................................................................................75 Melt Index Ratio..................................................................................76

Calculating End-Use Properties........................................................................76 Selecting an End-Use Property ..............................................................76 Adding an End-Use Property Prop-Set ....................................................76

References ...................................................................................................76

7 Polymerization Reactions ..................................................................................78 Polymerization Reaction Categories..................................................................78

Step-Growth Polymerization..................................................................80 Chain-Growth Polymerization ................................................................80

Polymerization Process Types..........................................................................81 Aspen Polymers Reaction Models .....................................................................82

Built-in Models....................................................................................82 User Models........................................................................................83

References ...................................................................................................84

8 Step-Growth Polymerization Model ...................................................................85 Summary of Applications................................................................................85 Step-Growth Processes ..................................................................................86

Polyesters ..........................................................................................86 Nylon-6 .............................................................................................92 Nylon-6,6...........................................................................................94 Polycarbonate.....................................................................................96

Reaction Kinetic Scheme ................................................................................97 Nucleophilic Reactions..........................................................................97 Polyester Reaction Kinetics .................................................................101 Nylon-6 Reaction Kinetics ...................................................................107 Nylon-6,6 Reaction Kinetics ................................................................111 Melt Polycarbonate Reaction Kinetics....................................................118

Model Features and Assumptions...................................................................120 Model Predictions ..............................................................................120 Phase Equilibria ................................................................................122 Reaction Mechanism ..........................................................................122

Model Structure ..........................................................................................123 Reacting Groups and Species ..............................................................123 Reaction Stoichiometry Generation ......................................................128 Model-Generated Reactions ................................................................129 User Reactions..................................................................................134 User Subroutines...............................................................................136

Specifying Step-Growth Polymerization Kinetics...............................................152 Accessing the Step-Growth Model ........................................................152 Specifying the Step-Growth Model .......................................................152 Specifying Reacting Components .........................................................153 Listing Built-In Reactions....................................................................153

vi Contents

Specifying Built-In Reaction Rate Constants ..........................................154 Assigning Rate Constants to Reactions .................................................154 Including User Reactions ....................................................................154 Adding or Editing User Reactions .........................................................155 Specifying Rate Constants for User Reactions ........................................155 Assigning Rate Constants to User Reactions ..........................................156 Selecting Report Options ....................................................................156 Selecting the Reacting Phase ..............................................................156 Specifying Units of Measurement for Pre-Exponential Factors...................157 Including a User Kinetic Subroutine......................................................157 Including a User Rate Constant Subroutine ...........................................157 Including a User Basis Subroutine........................................................157

References .................................................................................................158

9 Free-Radical Bulk Polymerization Model..........................................................159 Summary of Applications..............................................................................159 Free-Radical Bulk/Solution Processes .............................................................160 Reaction Kinetic Scheme ..............................................................................161

Initiation..........................................................................................167 Propagation......................................................................................172 Chain Transfer to Small Molecules .......................................................174 Termination......................................................................................175 Long Chain Branching ........................................................................177 Short Chain Branching .......................................................................178 Beta-Scission....................................................................................179 Reactions Involving Diene Monomers ...................................................179

Model Features and Assumptions...................................................................182 Calculation Method ............................................................................182 Quasi-Steady-State Approximation (QSSA) ...........................................184 Phase Equilibrium..............................................................................184 Gel Effect .........................................................................................185

Polymer Properties Calculated.......................................................................187 Specifying Free-Radical Polymerization Kinetics ...............................................189

Accessing the Free-Radical Model ........................................................189 Specifying the Free-Radical Model........................................................190 Specifying Reacting Species................................................................190 Listing Reactions ...............................................................................190 Adding Reactions...............................................................................191 Editing Reactions...............................................................................191 Assigning Rate Constants to Reactions .................................................192 Adding Gel-Effect ..............................................................................192 Selecting Calculation Options ..............................................................192 Specifying User Profiles ......................................................................193

References .................................................................................................194

10 Emulsion Polymerization Model.....................................................................195 Summary of Applications..............................................................................195 Emulsion Polymerization Processes ................................................................196 Reaction Kinetic Scheme ..............................................................................196

Micellar Nucleation ............................................................................197 Homogeneous Nucleation ...................................................................200 Particle Growth .................................................................................202

Contents vii

Radical Balance.................................................................................203 Kinetics of Emulsion Polymerization .....................................................207

Model Features and Assumptions...................................................................211 Model Assumptions............................................................................211 Thermodynamics of Monomer Partitioning.............................................211 Polymer Particle Size Distribution ........................................................212

Polymer Particle Properties Calculated............................................................214 User Profiles .....................................................................................214

Specifying Emulsion Polymerization Kinetics....................................................215 Accessing the Emulsion Model .............................................................215 Specifying the Emulsion Model ............................................................215 Specifying Reacting Species................................................................216 Listing Reactions ...............................................................................216 Adding Reactions...............................................................................217 Editing Reactions...............................................................................217 Assigning Rate Constants to Reactions .................................................217 Selecting Calculation Options ..............................................................218 Adding Gel-Effect ..............................................................................218 Specifying Phase Partitioning ..............................................................218 Specifying Particle Growth Parameters .................................................219

References .................................................................................................219

11 Ziegler-Natta Polymerization Model ..............................................................220 Summary of Applications..............................................................................220 Ziegler-Natta Processes ...............................................................................221

Catalyst Types ..................................................................................221 Ethylene Process Types ......................................................................222 Propylene Process Types ....................................................................223

Reaction Kinetic Scheme ..............................................................................225 Catalyst Pre-Activation.......................................................................232 Catalyst Site Activation ......................................................................232 Chain Initiation .................................................................................232 Propagation......................................................................................233 Chain Transfer to Small Molecules .......................................................233 Site Deactivation...............................................................................234 Site Inhibition...................................................................................234 Cocatalyst Poisoning ..........................................................................235 Terminal Double Bond Polymerization...................................................235

Model Features and Assumptions...................................................................235 Phase Equilibria ................................................................................235 Rate Calculations ..............................................................................236

Polymer Properties Calculated.......................................................................236 Specifying Ziegler-Natta Polymerization Kinetics ..............................................237

Accessing the Ziegler-Natta Model .......................................................237 Specifying the Ziegler-Natta Model ......................................................237 Specifying Reacting Species................................................................237 Listing Reactions ...............................................................................238 Adding Reactions...............................................................................238 Editing Reactions...............................................................................239 Assigning Rate Constants to Reactions .................................................239

References .................................................................................................239

viii Contents

12 Ionic Polymerization Model ...........................................................................241 Summary of Applications..............................................................................241 Ionic Processes ...........................................................................................242 Reaction Kinetic Scheme ..............................................................................242

Formation of Active Species ................................................................246 Chain Initiation .................................................................................247 Propagation......................................................................................247 Association or Aggregation .................................................................248 Exchange .........................................................................................248 Equilibrium with Counter-Ion ..............................................................248 Chain Transfer ..................................................................................249 Chain Termination .............................................................................249 Coupling ..........................................................................................250

Model Features and Assumptions...................................................................250 Phase Equilibria ................................................................................250 Rate Calculations ..............................................................................250

Polymer Properties Calculated.......................................................................251 Specifying Ionic Polymerization Kinetics .........................................................252

Accessing the Ionic Model...................................................................252 Specifying the Ionic Model ..................................................................252 Specifying Reacting Species................................................................252 Listing Reactions ...............................................................................253 Adding Reactions...............................................................................253 Editing Reactions...............................................................................253 Assigning Rate Constants to Reactions .................................................254

References .................................................................................................254

13 Segment-Based Reaction Model ....................................................................256 Summary of Applications..............................................................................256

Step-Growth Addition Processes ..........................................................257 Polymer Modification Processes ...........................................................257

Segment-Based Model Allowed Reactions .......................................................258 Conventional Species .........................................................................259 Side Group or Backbone Modifications ..................................................260 Chain Scission ..................................................................................260 Depolymerization ..............................................................................260 Propagation......................................................................................261 Combination .....................................................................................261 Branch Formation..............................................................................261 Cross Linking....................................................................................261 Kinetic Rate Expression ......................................................................261

Model Features and Assumptions...................................................................263 Polymer Properties Calculated.......................................................................264

User Subroutines...............................................................................265 Specifying Segment-Based Kinetics ...............................................................276

Accessing the Segment-Based Model....................................................276 Specifying the Segment-Based Model ...................................................276 Specifying Reaction Settings ...............................................................277 Building A Reaction Scheme................................................................278 Adding or Editing Reactions ................................................................279 Specifying Reaction Rate Constants .....................................................279 Assigning Rate Constants to Reactions .................................................280

Contents ix

Including a User Rate Constant Subroutine ...........................................280 Including a User Basis Subroutine........................................................281

References .................................................................................................281

14 Steady-State Flowsheeting............................................................................282 Polymer Manufacturing Flowsheets ................................................................282

Monomer Synthesis ...........................................................................283 Polymerization ..................................................................................284 Recovery / Separations ......................................................................284 Polymer Processing............................................................................284

Modeling Polymer Process Flowsheets ............................................................284 Steady-State Modeling Features ....................................................................285

Unit Operations Modeling Features.......................................................285 Plant Data Fitting Features .................................................................285 Process Model Application Tools...........................................................285

References .................................................................................................285

15 Steady-State Unit Operation Models..............................................................286 Summary of Aspen Plus Unit Operation Models ................................................286

Dupl ................................................................................................288 Flash2 .............................................................................................290 Flash3 .............................................................................................290 FSplit ..............................................................................................291 Heater .............................................................................................291 Mixer...............................................................................................291 Mult ................................................................................................291 Pump ..............................................................................................292 Pipe ................................................................................................292 Sep .................................................................................................293 Sep2 ...............................................................................................293

Distillation Models .......................................................................................293 RadFrac ...........................................................................................293

Reactor Models ...........................................................................................294 Mass-Balance Reactor Models .......................................................................294

RStoic .............................................................................................294 RYield..............................................................................................295

Equilibrium Reactor Models...........................................................................296 REquil..............................................................................................296 RGibbs.............................................................................................296

Kinetic Reactor Models .................................................................................296 RCSTR.............................................................................................296 RPlug ..............................................................................................309 RBatch.............................................................................................319

Treatment of Component Attributes in Unit Operation Models ............................328 References .................................................................................................330

16 Plant Data Fitting ..........................................................................................331 Data Fitting Applications ..............................................................................331 Data Fitting For Polymer Models ....................................................................332

Data Collection and Verification ...........................................................333 Literature Review ..............................................................................333

x Contents

Preliminary Parameter Fitting..............................................................334 Preliminary Model Development...........................................................335 Trend Analysis ..................................................................................335 Model Refinement .............................................................................336

Steps for Using the Data Regression Tool .......................................................336 Identifying Flowsheet Variables ...........................................................338 Manipulating Variables Indirectly .........................................................339 Entering Point Data ...........................................................................341 Entering Profile Data..........................................................................342 Entering Standard Deviations..............................................................343 Defining Data Regression Cases ..........................................................343 Sequencing Data Regression Cases ......................................................344 Interpreting Data Regression Results ...................................................344 Troubleshooting Convergence Problems................................................345

17 User Models...................................................................................................351 User Unit Operation Models ..........................................................................351

User Unit Operation Models Structure...................................................351 User Unit Operation Model Calculations.................................................352 User Unit Operation Report Writing ......................................................357

User Kinetic Models .....................................................................................357 User Physical Property Models.......................................................................361 References .................................................................................................365

18 Application Tools...........................................................................................366 Example Applications for a Simulation Model ...................................................366 Application Tools Available in Aspen Polymers .................................................367

CALCULATOR....................................................................................367 DESIGN-SPEC...................................................................................368 SENSITIVITY ....................................................................................368 CASE-STUDY ....................................................................................368 OPTIMIZATION .................................................................................369

Model Variable Accessing..............................................................................369 References .................................................................................................371

19 Run-Time Environment..................................................................................372 Aspen Polymers Architecture.........................................................................372 Installation Issues .......................................................................................373

Hardware Requirements .....................................................................373 Installation Procedure ........................................................................373

Configuration Tips .......................................................................................373 Startup Files.....................................................................................373 Simulation Templates ........................................................................373

User Fortran...............................................................................................374 User Fortran Templates......................................................................374 User Fortran Linking ..........................................................................374

Troubleshooting Guide .................................................................................374 User Interface Problems .....................................................................374 Simulation Engine Run-Time Problems ................................................376

References .................................................................................................377

Contents xi

A Component Databanks ....................................................................................378 Pure Component Databank ...........................................................................378 POLYMER Databank .....................................................................................378

POLYMER Property Parameters ............................................................378 POLYMER Databank Components .........................................................379

SEGMENT Databank ....................................................................................382 SEGMENT Property Parameters ...........................................................382 SEGMENT Databank Components ........................................................383

B Kinetic Rate Constant Parameters...................................................................421 Initiator Decomposition Rate Parameters ........................................................421

Solvent Dependency ..........................................................................421 Concentration Dependency .................................................................422 Temperature Dependency...................................................................422 Pressure Dependency ........................................................................423

References .................................................................................................434

C Fortran Utilities ...............................................................................................435 Component Attribute Handling Utilities ...........................................................436

CAELID............................................................................................436 CAID ...............................................................................................436 CAMIX .............................................................................................437 CASPLT............................................................................................438 CASPSS ...........................................................................................438 CAUPDT ...........................................................................................439 COPYCA ...........................................................................................440 GETCRY ...........................................................................................440 GETDPN...........................................................................................441 GETMWN..........................................................................................442 GETMWW.........................................................................................443 GETPDI............................................................................................443 GETSMF...........................................................................................444 GETSWF ..........................................................................................445 LCAOFF............................................................................................446 LCATT..............................................................................................446 NCAVAR...........................................................................................447

Component Handling Utilities ........................................................................448 CPACK.............................................................................................448 IFCMNC ...........................................................................................449 ISCAT..............................................................................................449 ISINI...............................................................................................450 ISOLIG ............................................................................................450 ISPOLY ............................................................................................451 ISSEG .............................................................................................451 SCPACK ...........................................................................................452 XATOWT ..........................................................................................453 XATOXT ...........................................................................................453

General Stream Handling Utilities ..................................................................454 IPTYPE.............................................................................................454 LOCATS ...........................................................................................455 LPHASE ...........................................................................................456

xii Contents

NPHASE ...........................................................................................456 NSVAR.............................................................................................457 SSCOPY ...........................................................................................457

Other Utilities .............................................................................................458 VOLL ...............................................................................................458

D Input Language Reference..............................................................................460 Specifying Components................................................................................460

Naming Components..........................................................................460 Specifying Component Characterization Inputs........................................461

Specifying Component Attributes...................................................................464 Specifying Characterization Attributes ..................................................464 Specifying Conventional Component Attributes ......................................464 Initializing Attributes in Streams..........................................................465

Specifying Attribute Scaling Factors ...............................................................466 Specifying Component Attribute Scale Factors .......................................466

Requesting Distribution Calculations ..............................................................467 Calculating End Use Properties ......................................................................468 Specifying Physical Property Inputs................................................................470

Specifying Property Methods ...............................................................470 Specifying Property Data ....................................................................471 Estimating Property Parameters ..........................................................473

Specifying Step-Growth Polymerization Kinetics...............................................474 Specifying Free-Radical Polymerization Kinetics ...............................................482 Specifying Emulsion Polymerization Kinetics....................................................493 Specifying Ziegler-Natta Polymerization Kinetics ..............................................499 Specifying Ionic Polymerization Kinetics .........................................................510 Specifying Segment-Based Polymer Modification Reactions ...............................517 References .................................................................................................521

Index ..................................................................................................................522

Introducing Aspen Polymers 1

Introducing Aspen Polymers

Aspen Polymers (formerly known as Aspen Polymers Plus) is a general-purpose process modeling system for the simulation of polymer manufacturing processes. The modeling system includes modules for the estimation of thermophysical properties, and for performing polymerization kinetic calculations and associated mass and energy balances.

Also included in Aspen Polymers are modules for:

• Characterizing polymer molecular structure

• Calculating rheological and mechanical properties

• Tracking these properties throughout a flowsheet

There are also many additional features that permit the simulation of the entire manufacturing processes.

About This Documentation Set The Aspen Polymers User Guide is divided into two volumes. Each volume documents features unique to Aspen Polymers. This User Guide assumes prior knowledge of basic Aspen Plus capabilities or user access to the Aspen Plus documentation set. If you are using Aspen Polymers with Aspen Dynamics, please refer to the Aspen Dynamics documentation set.

Volume 1 provides an introduction to the use of modeling for polymer processes and discusses specific Aspen Polymers capabilities. Topics include:

• Polymer manufacturing process overview - describes the basics of polymer process modeling and the steps involved in defining a model in Aspen Polymers.

• Polymer structural characterization - describes the methods used for characterizing components. Included are the methodologies for calculating distributions and features for tracking end-use properties.

• Polymerization reactions - describes the polymerization kinetic models, including: step-growth, free-radical, emulsion, Ziegler-Natta, ionic, and segment based. An overview of the various categories of polymerization kinetic schemes is given.

• Steady-state flowsheeting - provides an overview of capabilities used in constructing a polymer process flowsheet model. For example, the unit

2 Introducing Aspen Polymers

operation models, data fitting tools, and analysis tools, such as sensitivity studies.

• Run-time environment - covers issues concerning the run-time environment including configuration and troubleshooting tips.

Volume 2 describes methodologies for tracking chemical component properties, physical properties, and phase equilibria. It covers the physical property methods and models available in Aspen Polymers. Topics include:

• Thermodynamic properties of polymer systems – describes polymer thermodynamic properties, their importance to process modeling, and available property methods and models.

• Equation-of-state (EOS) models – provides an overview of the properties calculated from EOS models and describes available models, including: Sanchez-Lacombe, polymer SRK, SAFT, and PC-SAFT.

• Activity coefficient models – provides an overview of the properties calculated from activity coefficient models and describes available models, including: Flory-Huggins, polymer NRTL, electrolyte-polymer NRTL, polymer UNIFAC.

• Thermophysical properties of polymers – provides and overview of the thermophysical properties exhibited by polymers and describes available models, including: Aspen ideal gas, Tait liquid molar volume, pure component liquid enthalpy, and Van Krevelen liquid and solid, melt and glass transition temperature correlations, and group contribution methods.

• Polymer viscosity models – describes polymer viscosity model implementation and available models, including: modified Mark-Houwink/van Krevelen, Aspen polymer mixture, and van Krevelen polymer solution.

• Polymer thermal conductivity models - describes thermal conductivity model implementation and available models, including: modified van Krevelen and Aspen polymer mixture.

Related Documentation A volume devoted to simulation and application examples for Aspen Polymers is provided as a complement to this User Guide. These examples are designed to give you an overall understanding of the steps involved in using Aspen Polymers to model specific systems. In addition to this document, a number of other documents are provided to help you learn and use Aspen Polymers, Aspen Plus, and Aspen Dynamics applications. The documentation set consists of the following:

Installation Guides

Aspen Engineering Suite Installation Guide

Aspen Polymers Guides

Aspen Polymers User Guide, Volume 1

Introducing Aspen Polymers 3

Aspen Polymers User Guide, Volume 2 (Physical Property Methods & Models)

Aspen Polymers Examples & Applications Case Book

Aspen Plus Guides

Aspen Plus User Guide

Aspen Plus Getting Started Guides

Aspen Physical Property System Guides

Aspen Physical Property System Physical Property Methods and Models

Aspen Physical Property System Physical Property Data

Aspen Dynamics Guides

Aspen Dynamics Examples

Aspen Dynamics User Guide

Aspen Dynamics Reference Guide

Help

Aspen Polymers has a complete system of online help and context-sensitive prompts. The help system contains both context-sensitive help and reference information. For more information about using Aspen Polymers help, see the Aspen Plus User Guide.

Third-Party

More detailed examples are available in Step-Growth Polymerization Process Modeling and Product Design by Kevin Seavey and Y. A. Liu, ISBN: 978-0-470-23823-3, Wiley, 2008.

Technical Support AspenTech customers with a valid license and software maintenance agreement can register to access the online AspenTech Support Center at:

http://support.aspentech.com

This Web support site allows you to:

• Access current product documentation

• Search for tech tips, solutions and frequently asked questions (FAQs)

• Search for and download application examples

• Search for and download service packs and product updates

• Submit and track technical issues

• Send suggestions

• Report product defects

http://support.aspentech.com/

4 Introducing Aspen Polymers

• Review lists of known deficiencies and defects

Registered users can also subscribe to our Technical Support e-Bulletins. These e-Bulletins are used to alert users to important technical support information such as:

• Technical advisories

• Product updates and releases

Customer support is also available by phone, fax, and email. The most up-to-date contact information is available at the AspenTech Support Center at http://support.aspentech.com.

http://support.aspentech.com/

1 Polymer Manufacturing Process Overview 5

1 Polymer Manufacturing Process Overview

This chapter provides an overview of the issues related to polymer manufacturing process modeling and their handling in Aspen Polymers (formerly known as Aspen Polymers Plus).

Topics covered include:

• About Aspen Polymers, 5

• Overview of Polymerization Processes, 6

• Issues of Concern in Polymer Process Modeling, 7

• Aspen Polymers Tools, 9

• Defining a Model in Aspen Polymers, 12

About Aspen Polymers Aspen Polymers is a general-purpose process modeling system for the simulation of polymer manufacturing processes. The modeling system includes modules for the estimation of thermophysical properties, and for performing polymerization kinetic calculations and associated mass and energy balances.

Also included in Aspen Polymers are modules for:

• Characterizing polymer molecular structure

• Calculating rheological and mechanical properties

• Tracking these properties throughout a flowsheet

There are also many additional features that permit the simulation of the entire manufacturing processes.

6 1 Polymer Manufacturing Process Overview

Overview of Polymerization Processes Polymer Definition

A polymer is a macromolecule made up of many smaller repeating units providing linear and branched chain structures. Although a wide variety of polymers are produced naturally, synthetic or man-made polymers can be tailored to satisfy specific needs in the market place, and affect our daily lives at an ever-increasing rate. The worldwide production of synthetic polymers, estimated at approximately 100 million tons annually, provides products such as plastics, rubber, fibers, paints, and adhesives used in the manufacture of construction and packaging materials, tires, clothing, and decorative and protective products.

Polymer Molecular Bonds

Polymer molecules involve the same chemical bonds and intermolecular forces as other smaller chemical species. However, the interactions are magnified due to the molecular size of the polymers. Also important in polymer production are production rate optimization, waste minimization and compliance to environmental constraints, yield increases and product quality. In addition to these considerations, end-product processing characteristics and properties must be taken into account in the production of polymers (Dotson, 1996).

Polymer Manufacturing Process Steps Polymer manufacturing processes are usually divided into the following major steps:

1 Monomer Synthesis and Purification

2 Polymerization

3 Recovery / Separation

4 Polymer Processing

The four steps may be carried out by the same manufacturer within a single integrated plant, or specific companies may focus on one or more of these steps (Grulke, 1994).

The four steps may be carried out by the same manufacturer within a single integrated plant, or specific companies may focus on one or more of these steps (Grulke, 1994).

The following figure illustrates the important stages for each of the four polymer production steps. The main issues of concern for each of these steps are described next.


Issues of Concern in Polymer Process Modeling There are modeling issues associated with each step in the production of polymers. The following table summarizes these issues along with the required tools:


Step Modeling Issues/Concerns Tools Required

Monomer synthesis and purification

Feedstock purity

Monomer degradation

Emissions

Waste disposal

Unit operations: separators

Reaction kinetics

Phase equilibria

Polymerization Temperature control

Molecular weight control, polymer specifications

Conversion yield

Reaction medium viscosity

Residence time

Reactor stability

Waste minimization

Characterization

Reaction kinetics

Phase equilibria

Heat transfer

Unit operations: reactors

Transport phenomena

Process dynamics

Process control

Recovery / Separation Solvent removal

Monomer recovery


Phase equilibria

Heat and mass transfer

Polymer processing Solvent removal

Solids handling

Heat and mass transfer


Monomer Synthesis and Purification During monomer synthesis and purification, the engineer is concerned with purity. This is because the presence of contaminants, such as water or dissolved gases for example, may adversely affect the subsequent polymerization stage by:

• Poisoning catalysts

• Depleting initiators

• Causing undesirable chain transfer or branching reactions

Another concern of this step is the prevention of monomer degradation through proper handling or the addition of stabilizers. Control of emissions, and waste disposal are also important factors in this step.

Polymerization The polymerization step is usually the most important step in terms of the economic viability of the manufacturing process. The desired outcome for this step is a polymer product with specified properties such as:

• Molecular weight distribution

• Melt index

• Composition

• Crystallinity/density

• Viscosity


The obstacles that must be overcome to reach this goal depend on both the mechanism of polymer synthesis (chain growth or step growth), and on the polymerization process used.

Polymerization processes may be batch, semi-batch or continuous. In addition, they may be carried out in bulk, solution, slurry, gas-phase, suspension or emulsion. Batch and semi-batch processes are preferred for specialty grade polymers. Continuous processes are usually used to manufacture large volume commodity polymers. Productivity depends on heat removal rates and monomer conversion levels achieved. Viscosity of polymer solutions, and polymer particle suspensions and mixing are important considerations. These factors influence the choice of, for example, bulk versus solution versus slurry polymerization. Another example is the choice of emulsion polymerization that is often dictated by the form of the end-use product, water-based coating or adhesive. Other important considerations may include health, safety and environmental impact.

Most polymerizations are highly exothermic, some involve monomers that are known carcinogens and others may have to deal with contaminated water.

In summary, for the polymerization step, the reactions which occur usually cause dramatic changes in the reaction medium (e.g. significant viscosity increases may occur), which in turn make high conversion kinetics, residence-time distribution, agitation and heat transfer the most important issues for the majority of process types.

Recovery / Separation The recovery/separation step can be considered the step where the desired polymer produced is further purified or isolated from by-products or residual reactants. In this step, monomers and solvents are separated and purified for recycle or resale. The important concerns for this step are heat and mass transfer.

Polymer Processing The last step, polymer processing, can also be considered a recovery step. In this step, the polymer slurry is turned into solid pellets or chips. Heat of vaporization is an important factor in this step (Grulke, 1994).

Summary In summary, production rate optimization, waste minimization and compliance to environmental constraints, yield increase, and product quality are also important issues in the production of polymers. In addition, process dynamics and stability constitute important factors primarily for reactors.

Aspen Polymers Tools Aspen Polymers provides the tools that allow polymer manufacturers to capture the benefits of process modeling.


Aspen Polymers can be used to build models for representing processes in two modes: with Aspen Plus for steady-state models, and with Aspen Dynamics or Aspen Custom Modeler™ for dynamic models. In both cases, the tools used specifically for representing polymer systems fall into four categories:

• Polymer characterization

• Physical properties

• Reaction kinetics

• Data

Through Aspen Plus, Aspen Dynamics and Aspen Custom Modeler, Aspen Polymers provides robust and efficient algorithms for handling:

• Flowsheet convergence and optimization

• Complex separation and reaction problems

• User customization through an open architecture

Component Characterization Characterization of a polymer component poses some unique challenges. For example, the polymer component is not a single species but a mixture of many species. Properties such as molecular weight and copolymer composition are not necessarily constant and may vary throughout the flowsheet and with time. Aspen Polymers provides a flexible methodology for characterizing polymer components (U.S. Patent No. 5,687,090).

Each polymer is considered to be made up of a series of segments. Segments have a fixed structure. The changing nature of the polymer is accounted for by the specification of the number and type of segments it contains at a given processing step.

Each polymer component has associated attributes used to store information on molecular structure and distributions, product properties, and particle size when necessary. The polymer attributes are solved/integrated together with the material and energy balances in the unit operation models.

Polymer Physical Properties Correlative and predictive models are available in Aspen Polymers for representing the thermophysical properties of a polymer system, the phase equilibrium, and the transport phenomena. Several physical property methods combining these models are available. In addition to the built-in thermodynamic models, the open architecture design allows users to override the existing models with their own in-house models.

Polymerization Kinetics The polymerization step represents the most important stage in polymer processes. In this step, kinetics play a crucial role. Aspen Polymers provides built-in kinetic mechanisms for several chain-growth and step-growth type polymerization processes. The mechanisms are based on well-established sources from the open literature, and have been extensively used and


validated against data during modeling projects of industrial polymerization reactors.

There are also models for representing polymer modification reactions, and for modeling standard chemical kinetics. In addition to the built-in kinetic mechanisms, the open-architecture design allows users to specify additional reactions, or to override the built-in mechanisms.

Modeling Data A key factor in the development of a successful simulation model is the use of accurate thermodynamic data for representing the physical properties of the system, and of kinetic rate constant data which provide a good match against observed trends.

In order to provide the physical property models with the parameters necessary for property calculations, Aspen Polymers has property parameter databanks available. These include:

• Polymer databank containing parameters independent of chain length

• Segment databank containing parameters to which composition and chain length are applied for polymer property calculations

• Functional group databank containing parameters for models using a group contribution approach is also included

This User Guide contains several tabulated parameters which may be used as starting values for specific property models. Property data packages are also being compiled for some polymerization processes and will be made available in future versions.

In addition to physical property data, Aspen Polymers provides users with ways of estimating missing reaction rate constant data. For example, the data regression tool can be used to fit rate constants against molecular weight data.

Process Flowsheeting Aspen Polymers provides unit operation models, flowsheeting options, and analysis tools for a complete representation of a process.

Models for batch, semi-batch and continuous reactors with mixing extremes of plug flow to backmix are available. In addition, other unit operation models essential for flowsheet modeling are available such as:

• Mixers

• Flow splitters

• Flash tanks

• Devolatilization units

Flowsheet connectivity and sequencing is handled in a straightforward manner.

Several analysis tools are available for applying the simulation models developed. These include tools for:

• Process optimization


• Examining process alternatives as case studies

• Analyzing the sensitivities of key process variables on polymer product properties

• Fitting process variables to meet design specifications

Defining a Model in Aspen Polymers In order to build a model of a polymer process you must already be familiar with Aspen Plus. Therefore, only the steps specific to polymer systems will be described in detail later in this User Guide. The steps for defining a model in Aspen Polymers are as follows:

Step 1. Specifying Global Simulation Options

The first step in defining the model is the specification of:

• Global simulation options, i.e. simulation type

• Units to be used for simulation inputs and results

• Basis for flowrates

• Maximum simulation times

• Diagnostic options

Step 2. Defining the Flowsheet

For a full flowsheet model, the next step is the flowsheet definition. Here you would specify the unit operation models contained in the flowsheet and define their connectivity.

Chapter 4 describes the unit operation models available for building a flowsheet.

Step 3. Defining Components

Most simulation types require a definition of the component system. You must correctly identify polymers, polymer segments, and oligomers as such. All other components are considered conventional by default.

Chapter 2 provides information on defining components.

Step 4. Characterizing Components

Conventional components in the system are categorized by type. Additional characterization information is required for other than conventional components. You must specify the:

• Component attributes to be tracked for polymers

• Type of segments present

• Structure of oligomers

• Type and activity of catalysts

In addition, you may wish to request tracking of molecular weight distribution.

Component characterization is discussed in Chapter 2.


Step 5. Specifying Property Models

You must select the models to be used to represent the physical properties of your system.

The Aspen Polymers User Guide, Volume 2, Aspen Polymers Physical Property Methods and Models, describes the options available for specifying physical property models.

Step 6. Defining Polymerization Kinetics

Once you have made selections out of the built-in polymerization kinetic models to represent your reaction system, you need to choose specific reactions from the sets available and enter rate constant parameters for these reactions.

Chapter 3 describes the models available and provides descriptions of the input options.

Step 7. Defining Feed Streams

For flowsheet simulations, you must enter the conditions of the process feed streams. If the feed streams contain polymers, you must initialize the polymer attributes.

Polymer attribute definition in streams is discussed in a separate section of Chapter 2.

Step 8. Specifying UOS Model Operating Conditions

You must specify the configuration and operating condition for unit operation models contained in the flowsheet. In the case of reactors, you have the option of assigning kinetic models defined in step 6 to specific reactors.

Chapter 4 provides some general information regarding the use of unit operation models.

Step 9. Specifying Additional Simulation Options

For a basic simulation the input information you are required to enter in steps 1-8 is sufficient. However, there are many more advanced simulation options you may wish to add in order to refine or apply your model. These include setting up the model for plant data fitting, sensitivity analyses, etc.

Many of these options are described in a separate section of Chapter 4.

Information for building dynamic models is given in the Aspen Dynamics and Aspen Custom Modeler documentation sets. Note that for building dynamic models, users must first build a steady-state model containing:

• Definition of the polymer system in terms of components present

• Physical property models

• Polymerization kinetic models

Note: Aspen Polymers setup and configuration instructions are given in Chapter 5.


References Dotson, N. A., Galván, R., Laurence, R. L., & Tirrell, M. (1996). Polymerization Process Modeling. New York: VCH Publishers.

Grulke, E. A. (1994). Polymer Process Engineering. Englewood Cliffs, NJ: Prentice Hall.

Odian, George. (1991). Principles of Polymerization (3rd Ed.). New York: John Wiley and Sons.

2 Polymer Structural Characterization 15

2 Polymer Structural Characterization

One of the fundamental aspects of modeling polymer systems is the handling of the molecular structure information of polymers. This chapter discusses the approaches used to address this issue in Aspen Polymers (formerly known as Aspen Polymers Plus).


• Polymer Structure, 15

• Polymer Structural Properties, 19

• Characterization Approach, 19

Included in this manual are several sections devoted to the specification of polymer structural characterization information.

• 3 Component Classification, 21

• Polymer Structural Properties, 32

• Structural Property Distributions, 53

• End-Use Properties, 70

Polymer Structure Polymers can be defined as large molecules or macromolecules where a smaller constituting structure repeats itself along a chain. For this reason, polymers tend to exhibit different physical behavior than small molecules also called monomers. Synthetic polymers are produced when monomers bond together through polymerization and become the repeating structure or segment within a chain. When two or more monomers bond together, a polymer is formed. Small polymer chains containing 20 or less repeating units are usually called oligomers.

The fact that identifiable segments are found repeatedly along a polymer chain, provides convenient ways to categorize polymers. Polymers can be classified based on segment composition or sequence:

• Homopolymers - containing one type of repeating unit which can be mapped into one segment

16 2 Polymer Structural Characterization

• Copolymers - which have two or more repeating units. Copolymers can be in a random, alternating, block, or graft configuration

If we consider the arrangement of a given chain, another classification arises. Polymers may be:

• Linear

• Branched (with short or long chains)

• Star

• Ladder

• Network

Another classification that results from polymer structure has to do with physical state. A solid polymer may be:

• Amorphous - when the chains are not arranged in a particular pattern

• Crystalline - when the chains are arranged in a regular pattern

A related classification divides polymers by thermal and mechanical properties into:

• Thermoplastics (may go from solid to melt and vice versa)

• Thermosets (remain solid through heating)

• Elastomers (which have elastic properties)

Finally, polymers can be categorized based on the form they are manufactured into: plastics, fibers, film, coatings, adhesives, foams, and composites.

Polymer Types by Physical Structure

The following figure illustrates the various polymer types based on chain structure:


Polymer Types by Property

The following table illustrates the various polymer types based on properties:

Classification Type Physical Property


Thermal / Mechanical properties

Thermoplastics

Thermosets

Elastomers

Can melt and solidify again

Remain solid through heating

Have elastic properties

Fabrication Plastics

Fibers

Coatings

Adhesives

Foams

Composites

Elastomers

Very versatile in terms of application

Most commonly used as textiles

Used for both decorative and protective purposes

Used for their bonding properties

Used as packaging, upholstery, insulation, etc.

Can be tailored to many applications

Used for their elastic properties

In addition to these classifications, polymers can be categorized based on the type of constituting atoms on the chains.

Homochains produced through chain-growth polymerization have only carbon atoms on the polymer backbone.

Heterochains produced through step-growth polymerization have other types of atom incorporated into the polymer backbone.

Polymer Categories by Chemical Structure

The following table lists various homochain and heterochain polymers based on the type of atoms on the polymer backbone or the substituted side groups:

Polymer Category Description Examples

Polymers with carbon-carbon backbone

Polyacrylics Ethylene backbone with one acrylic acid (or derivative) as side group per ethylene

Polyacrylic acid, polymethyl methacrylate, polyacrylonitrile, polyacrylamide

Polydienes One double bond per repeat unit Polybutadiene

Polyhalogen hydrocarbons

Fluorine or chlorine side group per ethylene

Polyvinyl fluoride, polyvinylidene fluoride, polyvinylchloride,

Polyolefins Alphatic or aromatic substituents Polyethylene, polypropylene, polyisobutylene, polystyrene

Polyvinyls From vinyl monomers Polyvinyl acetate, polyvinyl alcohol

Polymers with carbon-nitrogen backbone

Polyamides Amide group on backbone Nylon 6, nylon 6,6

Polyurethanes Urethane group on backbone Polyurethane foams

Polyureas Urea group on backbone Polyurea resins

Polymers with carbon-oxygen backbone

Polyacetals Acetal group on backbone Polyacetate

Polyethers Ether group on backbone Polyethylene oxide, polyphenylene oxide


Polymer Category Description Examples

Polyesters Ester group on backbone Polycarbonate polyethylene therephthalate, polybutylene therephthalate polylactide

Polymers with carbon-sulfur backbone

Polysulfides Sulfide group on backbone Polysulfide fibers

Polymer Structural Properties All the methods of categorizing polymers point to certain key characteristics that must be taken into account in order to fully define polymer molecules. Typical information needed to capture the structure and behavior of polymers includes:

• Chemical structure of segments: segment type, and configuration

• Chain size for the mixture of polymer chains

• Crystallinity

• Additional structural, thermal, and mechanical characteristics

Characterization Approach Aspen Polymers allows for the different types of chemical species that may be found in a polymer system:

• Monomers

• Solvents

• Catalysts

• Oligomers

• Polymers

Polymer segments are introduced to identify the chemical structure of the polymer or oligomer repeat unit. In addition, they are used as building blocks within polymerization reactions, and in the determination of thermodynamic properties.

More than the chemical structure of the segments is needed in order to define a polymer. Also needed is the segment composition of the chains. In addition, properties related to size are needed: degree of polymerization or number of segments.

Component Attributes Within Aspen Polymers, component attributes are used to define these structural characteristics. Component attributes are available to track segment composition, degree of polymerization, molecular weight, etc. Because the polymer is a mixture of chains, there is normally a distribution of


these structural characteristics. The component attributes are used to track the averages.

There are additional attributes used to track information about the distribution of chain sizes. These are the moments of chain length distribution. For detailed information about component attributes, see Polymer Structural Properties on page 32.

In addition to the component attributes, users have the option within Aspen Polymers to examine polymer molecular weight distribution. This feature is based on a method of instantaneous properties. For more information, see Method of Instantaneous Properties on page 58.

References Grulke, E. A. (1994). Polymer Process Engineering. Englewood Cliffs, NJ: Prentice Hall.

Munk, P. (1989). Introduction to Macromolecular Science. New York: John Wiley and Sons.

Odian, G. (1991). Principles of Polymerization (3rd Ed.). New York: John Wiley and Sons.

Rudin, A. (1982). The Elements of Polymer Science and Engineering. Orlando: Academic Press.

3 Component Classification 21

3 Component Classification

This section discusses the specification of components in a simulation model.


• Component Categories, 21

• Component Databanks, 25

• Segment Methodology, 27

• Specifying Components, 27

Component Categories When developing a simulation model in Aspen Polymers (formerly known as Aspen Polymers Plus), users must assign components present in process flow streams to one of the following categories:

• Conventional

• Polymer

• Oligomer

• Segment

• Site-based

The following figure illustrates the different categories of components and their input requirements:

22 3 Component Classification

Conventional Components Standard conventional components are molecular components such as water. These components have a fixed molecular structure and participate in phase equilibrium. Components falling into this category include:

• Monomers

• Initiators

• Chain transfer agents

• Solvents

• Catalysts

In order to fully specify conventional components, you need only specify pure component data required for the phase equilibrium calculations. This data may be entered or retrieved from component databanks.

Note: Ziegler-Natta catalysts and ionic initiators require additional characterization information.

Polymers In Aspen Polymers, polymer components represent a distribution of polymeric species. The average size and composition of the molecules in this distribution


can change throughout the simulation. Each polymer molecule is considered to be made up of repeating units or segments. Typically, the segments correspond to the monomers that are used to grow the polymer.

The structure of polymers depends on the number and type of segments they contain and the arrangement of segments in linear, branched, or cross-linked forms.

Component attributes are used to track polymer structural properties (U.S. Patent No. 5,687,090) such as:

• Segment composition

• Copolymer composition and average sequence length

• Degree of polymerization

• Molecular weight

• Branching

• Moments of molecular weight distribution

• Molecular architecture (physical arrangement of segments within the polymer molecule)

Segments are specified independently from polymers. For each polymer, you must select the types of component attributes to be included in the simulation model. If the polymer is present in the process feed streams, you must provide its properties by initializing the component attributes while specifying input data for these feed streams.

For more information on component attribute specification, see Polymer Structural Properties on page 32.

Oligomers By convention, oligomers are defined as components with two or more segments and a fixed molecular structure. They can be defined as volatile or non-volatile. Typically, the oligomer feature is used to allow users to track the loss of volatile short-chain polymers.

In order to specify oligomers, you must specify their composition in terms of the number and type of segments they contain. Oligomers do not require component attributes. For this reason, you may treat a polymer as an oligomer in cases where you want to process the polymer within a unit operation model which cannot handle polymer component attribute data.

When using oligomer components, you may specify addition properties through the following unary property parameters:

Parameter Definition Default

POLDP Number-average chain length

Calculated *

POLPDI Polydispersity index 1 **

POLCRY Mass fraction crystallinity

* Calculated from the number of segments in the oligomer as specified in the

Polymers form Oligomers subform.

** Used to calculate DPW and MWW.


Note: Not all kinetic models track oligomers as separate components. If a model does not provide fields for specifying oligomers on its input forms, then these components are not tracked.

Segments Segments are the structural units of a polymer or oligomer and are specified independently from these components. Their structure is fixed throughout a simulation. Segments typically correspond to the monomers used to grow the polymer. They are divided into types depending on their location on the polymer chain:

• Repeat units

• End groups

• Branch point (attached to three or four branches)

Site-Based Site-based components pertain to multisite reaction kinetic models (Ziegler-Natta and Ionic). Site-based components include Ziegler-Natta catalysts and ionic initiators.

Ziegler-Natta Catalysts Ziegler-Natta catalysts are often used to initiate polymer chain formation in chain-growth polymerization reactions. Catalysts can be treated as standard conventional components. Ziegler-Natta catalysts or metallocene catalysts involve one or more polymerization site types which may be in an activated or deactivated state.

In order to use Ziegler-Natta catalysts, you must specify the number of site types and the catalyst properties to be tracked, that is, the site activity.

Catalyst properties are defined as component attributes. You must initialize the catalyst properties while specifying input data for the streams containing the catalysts.

For more information on component attribute specification, see Polymer Structural Properties on page 32.

Ionic Initiators Ionic initiators are used in anionic and cationic polymerization. The ionic initiators can be treated as standard conventional components. The propagating species in ionic polymerization can be:

• Free-ions

• Ion-pairs

• Dormant esters


In Aspen Polymers, these different species are modeled as different sites of an ionic initiator. Three different site-based attributes are tracked for an ionic initiator. For more information, see Ionic Initiator Attributes on page 44.

Component Databanks The thermodynamic and transport property models needed to perform the physical property and phase equilibrium calculations during a simulation require pure component property data. These include:

• Molecular weight

• Heat capacity

• Heat of formation

• Heat of vaporization

• Vapor pressure

• Density

Enter that information while selecting and specifying physical property models. Normally, you would make use of the pure component databanks and retrieve data from them for each of the components present in the simulation model:

• Data for conventional components are retrieved from the Pure Component databank

• Data for free-radical initiators are retrieved from the INITIATOR databank

• Data for polymers are retrieved from the POLYMER databank

• Data for oligomers are retrieved either from the pure component databank or from the POLYMER databank

• Data for segments are retrieved from the SEGMENT databank

• Data for PC-SAFT are retrieved from the PC-SAFT databank

• Data for POLYPCSF are retrieved from the POLYPCSF databank

Descriptions of the databanks, and the parameters they contain are given in Appendix A.

Pure Component Databank In the Pure Component databank, components are named using a nomenclature developed for Aspen Plus. Each component is given an alias summarizing the number of each type of atom: C, H, O, N, P, S, CL, F, etc. (e.g. C2H4 for ethylene). For cases where the same alias matches several components, a counter is added to make the distinction (e.g. C2H4O2-1 for acetic acid).

Note: Catalysts are often solid components and may not be found in the PURE11 databank. Normally, you do not need a rigorous representation of these components.


An acceptable approach is to assign a monomer alias to the catalyst and then provide the correct molecular weight and certain parameters which will prevent the catalyst from vaporizing. If an activity coefficient model is being used for phase equilibrium representation, the catalysts can be assumed to be non-volatile by specifying -40 as the first Antoine parameter (PLXANT(1) = -40).

PC-SAFT Databank The PC-SAFT databank contains pure and binary parameters used with the PC-SAFT property method. The parameters are taken from the literature, including many normal compounds, polar compounds and associating compounds.

POLYPCSF Databank The POLYPCSF databank contains pure and binary parameters used with the POLYPCSF property method. The parameters are taken from the literature, including many normal compounds, but excluding polar compounds and associating compounds.

INITIATO Databank The INITIATO databank contains data for initiator components. Rate constants in this databank are derived from half-life data in vendor datasheets published on public web sites. These datasheets generally contain data at several temperatures, allowing the activation energy and prefactor to be determined. These rate constants depend on the reaction environment, and may vary between polar and non-polar solvents. Where multiple sets of data were available, the data from monomer or organic solvents were used in preference to data from aqueous solutions.

Molecular weight and other parameters are calculated from structure using estimation methods from Aspen Plus, except in those few cases where vapor pressure data was provided in the datasheets.

In the INITIATO databank, components are named using industry-standard acronyms. Each component is given an alias summarizing the number of each type of atom: C, H, O, N, P, S, CL, F, etc. For cases where the same alias matches several components, a counter is added to make the distinction (e.g. –1,-2, etc).

Segment Databank In the Segment Databank, a segment name comes from the name of the monomer from which it originates. Therefore, in this databank component names and aliases follow the same conventions as those for the Pure Component Databank.

A label is added to the monomer name to identify the segment as either a repeat unit,-R, an end group,-E, or a branch point, -B (e.g. for butadiene segments: C4H6−R−1or BUTADIENE−R−1 corresponding to the repeat unit –


CH2–CH=CH–CH2, C4H5−E−1 or BUTADIENE−E−1 corresponding to the end group –CH=CH–CH=CH2 and C4H5−B or BUTADIENE−B corresponding to the

branch segment CH2 CH CH CH ).

Polymer Databank The Polymer Databank does not follow the conventional nomenclature. The polymer aliases are the typical acronyms used in industry or academia, and the polymer names consist of the repeat unit name enclosed in parentheses and preceded by the prefix Poly (e.g. PS or POLY(STYRENE) for polystyrene).

Note: The MW property parameter used to store molecular weights in the component databanks is the true molecular weight for all component types except polymers. For polymers, the true polymer molecular weight is normally tracked as a component attribute only. The molecular weight stored in the databank is the apparent molecular weight calculated as the average segment molecular weight (See Appendix A).

Segment Methodology The segment approach to characterizing components is a fundamental methodology which affects almost every functionality within Aspen Polymers. Segments are used as the building blocks for polymers. Once you have specified the types of segments in the polymer, the segment composition and degree of polymerization defined as component attributes may be used to define the size and composition of the polymer.

For oligomers, although component attributes are not used, the number of each segment must be specified directly.

Most of the Aspen Polymers physical property models calculate polymer and oligomer properties from segment properties. This is done by taking into account the degree of polymerization and the segment composition. The calculated properties should be the same for both oligomers and polymers, assuming that the oligomer structure and molecular weight were specified correctly. Note that this is true for mass-based properties only. Mole-based properties will be different between polymer and oligomer if their apparent molecular weights are different.

Within the polymerization reaction models, segments also play a key role. As polymerization progresses, the models map the reacting monomers into the corresponding segments and return rates of change for the segment composition.

Specifying Components To specify components within your model you need to know the following:

Item For

Component types All the species in your system


Property parameter databank selections

The species in the system

IUPAC names All conventional components or you need their physical properties (molecular weight, boiling point, Antoine constants, etc.)

Segment structure All polymers and oligomers (define whether you want to include any end groups or branch points)

Polymer properties to be tracked

All polymers, that is, degree of polymerization, segment composition

Additional characteristics All additional characteristics for catalysts, or ionic initiators

Selecting Databanks For an Aspen Polymers simulation, you generally retrieve physical property data from the following databanks:

• Pure component databank (PURE12)

• Polymer databank (POLYMER)

• Polymer segment databank (SEGMENT)

• Initiator databank (INITIATOR)

You can also use other Aspen Plus databanks, user databanks, or in-house databanks. Appendix A provides descriptions of the polymer and segment databanks and the parameters they contain.

If you selected a polymer template to start your simulation, the correct databanks are already specified.

If you did not select a polymer template, or if you want to modify the databank selection:

1 From the Data Browser, click Components.

2 From the Components folder, click Specifications.

3 On the Selection sheet, click the Databanks tab to open the databank selection form.

Defining Component Names and Types You must specify a:

• Name and a type for each component in the simulation

• Component name or identifier

• Databank name or formula that sets the pure component properties for the component

• Component type that sets the category to which the component belongs and determines the treatment of that component

To access the components specifications input sheet:


2 From the Components folder, click Specifications.

3 On the Selection sheet, click the Databanks tab to set the databanks to be searched for pure component properties.


To define component names and types:

1 On the Selection sheet, in the Component ID field, specify an ID for each component.

This ID is used to refer to the component in all subsequent input, and is also used to identify the component in the simulation report.

2 For polymers, oligomers, and segments, specify the component type in the Type field.

By default, all components are assumed to be standard conventional components. For Aspen Polymers simulation you must correctly identify the component types:

Use For

Conventional Standard conventional components

Polymer Homo and copolymers

Oligomer Short chain polymer molecules

Segment Polymer or oligomer repeat units

3 If component property data is being retrieved from databanks, you must also supply either the databank component formula in the Formula field, or the databank name in the Component name field.

Specifying Segments The Type of each polymer or oligomer segment must be specified on the Polymer Characterization Segments sheet. Segments can be repeat units, end groups or branch points attached to three or four branches.

To access the segments definition input form:


2 From the Components folder, click Polymers.

3 From the Polymers folder, click Characterization.

To define segments:

• On the Segments sheet, assign a type to the segments from the Type field.

Specifying Polymers For each polymer you must define the component attributes to be tracked. All components specified Polymer in the Components Specifications folder require component attributes.

To access the polymer input specifications:




4 From the Characterization form, click the Polymers tab.

To specify component attributes for the polymers in your simulation:


1 In the Polymer ID field, select the polymer.

2 If you want to retrieve a predefined set of component attributes, in Built-in attribute group select a grouping. The attribute summary table is filled in.

For a complete discussion of Aspen Polymers component attributes, see Polymer Structural Properties on page 32.

− or − If you do not want to use a predefined set of attributes, or if you want to change the attribute selection for a given group, click the attribute table or click Edit to open the attribute list.

3 Click specific attributes to add or remove them from the list.

Repeat these steps for each polymer.

Specifying Oligomers For each oligomer you must specify an ID and a structure in terms of number and name of contained segments.

To access the oligomers definition input form:




4 From the Characterization form, click the Oligomers tab.

To define oligomers:

1 In the Oligomer field, select the oligomer.

2 In the Segment field, enter the name of a segment contained in the oligomer.

3 Repeat these steps for each oligomer.

You can define as many segments as needed for an oligomer.

Specifying Site-Based Components Specify the structure and activity of site-based catalytic species such as Ziegler-Natta catalysts and ionic initiators.

To access the site-based species definition form:




4 From the Characterization form, click the Site-Based Species tab.

To specify site-based species characteristics:

1 Select the component type: Ziegler-Natta catalyst, ionic initiator, etc.

2 In the Comp ID field, specify the component name.

3 Specify the number of site types in Number of sites for the component. For Ziegler-Natta catalysts, you must also specify the moles of sites per gram of catalyst.


4 Select the list of properties or component attributes to be tracked for that component. Click the attribute list table or Edit to open the attribute list.

5 Click specific attributes to add or remove them from the list for the component.

References Bailey, J., & Ollis, D. F. (1986) Biochemical Engineering Fundamentals (2nd Ed.). New York: McGraw-Hill.

Brandrup, J., & Immergut, E. H. (Eds.). (1989). Polymer Handbook (3rd Ed.). New York: John Wiley & Sons.

Danner R. P., & High, M. S. (1992). Handbook of Polymer Solution Thermodynamics. New York: American Institute of Chemical Engineers.

Kroschwitz, J. (Ed.). (1990). Concise Encyclopedia of Polymer Science and Engineering. New York: John Wiley and Sons.

32 4 Polymer Structural Properties

4 Polymer Structural Properties

This section discusses the use of component attributes for tracking polymer structural properties in a simulation model.


• Structural Properties as Component Attributes, 32

• Component Attribute Classes, 33

• Component Attribute Categories, 34

• Component Attribute Initialization, 46

• Component Attribute Scale Factors, 50

• Specifying Component Attributes, 51

Structural Properties as Component Attributes Component attributes provide a convenient framework to associate structural characterization data to components in a flow stream. They are carried throughout the flowsheet along with state and composition information, and effectively extend the stream structure.

Aspen Polymers (formerly known as Aspen Polymers Plus) uses component attributes as a vehicle for tracking important modeling information for polymers, ionic initiators and Ziegler-Natta catalysts (U.S. Patent No. 5,687,090). For example, there are component attributes to store:

• Segment composition (segment fraction or segment flow)

• Copolymer composition and average sequence length

• Degree of polymerization (number, weight, and z-average)

• Molecular weight (number, weight, and z-average)

• Degree of branching (long and short)

• Degree of cross-linking (cross-link density)

• Molecular architecture (physical arrangement of segments within the polymer molecule)

4 Polymer Structural Properties 33

• Live polymer properties

• Aggregate polymer properties

In the case of multi-site-type Ziegler-Natta catalyst polymerization, the attributes provide the structure to store the properties by site. Examples of catalyst attributes include the fraction of dead and potential sites. The catalyst attributes are used to track catalyst activity. There are also component attributes available to track user defined data.

The complete list of available attributes is given in the Polymer Component Attributes, Site-Based Species Attributes, and User Attributes sections of this chapter (pages 34 through 45).

Component Attribute Classes Component attributes are divided into classes to reflect the nature of various structural properties carried in process streams:

• Class 0 component attributes are derived quantities from other attributes. They are therefore recalculated from these attributes after they are updated. For example, number average degree of polymerization is a Class 0 component attribute. It is computed from the zeroth and the first moments of chain length distribution.

• Class 1 component attributes are structural properties per unit mass. They are not used for polymers.

• Class 2 component attributes are structural properties per unit time. Examples are zeroth and first moments of chain length distribution

The following table lists the differences between the Aspen Polymers component attribute classes:

Class Conserved Quantity

Convergence Treatment

Unit of Measurement Examples

0 N/A Recalculated Varies Degree of polymerization

1 Attribute × component mass

Direct substitution Attribute / component mass

None for polymers

2 Attribute Accelerated convergence

Attribute / time Segment flows, moments of chain length distribution

For a typical polymer process simulation, Class 0 and Class 2 component attributes are used. Since Class 0 component attributes are calculated from Class 2 attributes, users have the option of entering either of the two types for simulation models where polymer is present in the process feed streams. For this reason, an attribute initialization scheme has been designed. For more information, see Component Attribute Initialization on page 46.


Component Attribute Categories The main categories of component attributes available are:

• Polymer attributes

• Ziegler-Natta catalyst attributes

• Ionic initiator attributes

• User attributes

Polymer Component Attributes The polymer properties tracked as component attributes include:

• Segment fraction

• Segment flow

• Flow and fraction of segment dyads (pairs)

• Number-average degree of polymerization and molecular weight

• Weight-average degree of polymerization and molecular weight

• Z-average degree of polymerization and molecular weight

• Zeroth through third moment of chain length distribution

• Number of long and short chain branches

• Long and short chain branching frequency

• Number and frequency of cross-links

• Number-average block length (sequence length)

• Several aspects of molecular architecture, including tacticity, head-to-head insertions (orienticity)

• Flow and fraction of terminal double bonds

• Flow and fraction of cis-, trans-, and vinyl- isomers associated with diene segments (internal and pendent double bonds)

There are component attributes available to track most of these properties for dead polymer, live polymer, and aggregate polymer. You may want to track information for live polymers for cases of free-radical polymerization where the quasi-steady-state approximation (QSSA) is not used. Site based component attributes are also available to accommodate multi-site type Ziegler-Natta catalyst polymerization. Composite attributes are summed over all site types. They represent the average properties of the polymer.

Polymer Attribute Sets

In summary, there are six sets of polymer component attributes.

• Composite Polymer Set contains the basic attributes that may be used for any type of polymerization, including the minimum required set for all simulation models.

• Composite Live Polymer Set contains the attributes required to track the characteristics of live polymer chains in chain growth polymerization.


• Composite Aggregate Polymer Set contains the attributes required to track the characteristics of aggregate polymer chain in ionic polymerization.

• Site-Based Polymer Set contains attributes corresponding to the composite set, but structured to track information for each catalyst site type.

• Site-Based Live Polymer Set contains attributes corresponding to the composite live polymer set, structured to track information by catalyst site type.

• Site-Based Aggregate Polymer Set contains attributes corresponding to the composite aggregate polymer set, structured to track information by ionic site type.

The tables that follow list the component attributes available in each set. Attributes must be associated from these sets to each of your polymer components when building a simulation model. To simplify this, the attributes in the tables were grouped by model usage, or polymerization reaction type (for example, physical property simulation model, free-radical polymerization model). Select a grouping and all the attributes needed are retrieved automatically. A table of the minimum required attributes by model usage is also provided. Attribute Definitions – Composite Polymer Attribute Set

Name Symbol† Description Equation‡ Class Dimension Units

DPN D Pn Number-average degree of polymerization

DPn = λ λ1 0/ 0 1 Unitless

DPW DPw Weight-average degree of polymerization

DPw = λ λ2 1/ 0 1 Unitless

DPZ DPz Z-average degree of polymerization

DPz = λ λ3 2/ 0 1 Unitless

PDI PDI Polydispersity index PDI = DP /D Pw n 0 1 Unitless

MWN Mn Number-average molecular weight

M DP Mn n seg= 0 1 Unitless

MWW Mw Weight-average molecular weight

M DP Mw w seg= 0 1 Unitless

MWZ Mz Z-average molecular weight

M DP Mz z seg= 0 1 Unitless

MWSEG Mseg Average segment molecular weight

M F i Mseg p i=∑ ( ) 0 1 Unitless

ZMOM 0λ Zeroth moment of chain length distribution

---- 2 1 Mole flow

FMOM 1λ First moment of chain length distribution 1 1λ λ= ∑ ( )i 0 1 Mole

flow

SMOM 2λ Second moment of chain length distribution

---- 2 1 Mole flow

TMOM 3λ Third moment of chain length distribution

---- 2 1 Mole flow



SFLOW 1( )λ i Mole flow of segments of type i

---- 2 NSEG Mole flow

Attribute Definitions - Composite Polymer Attribute Set (continued)


SFRAC F ip( ) Mole fraction of segments of type i

F i ip( ) ( ) /= λ λ1 1 0 NSEG Unitless

EFRAC F ie( ) Fraction of chain end segments of type i

F i i ieends

( ) ( ) / ( )= ∑λ λ1 1 0 NEND Unitless

DYADFLOW ji,Θ Molar flow rate of

dyads composed of type I and j segments

---- 2 ( )2

2segseg NN + Mole

flow

DYADFRAC ji,θ Fraction of dyads

composed of type I and j segments

1,, /λθ jiji Θ= 0 ( )2

2segseg NN + Unitless

BLOCKN iBn Number-average block

length for segment i ii

i

i

iBnΘ−

=1

1

λλ

0 NSEG Unitless

Attributes Related to Branching and Terminal Double Bonds

LCB LCB Number of long chain branches

---- 2 1 Mole flow

SCB SCB Number of short chain branches

---- 2 1 Mole flow

FLCB FLCB Long chain branching frequency FLCB

LCB=

103

1λ

0 1 Unitless

FSCB FSCB Short chain branching frequency FSLB

SCB=

103

1λ

0 1 Unitless

TBDFLOW ( )i=0λ Mole flow of terminal

double bond segments of type i


TBDFRAC )(iFp=

Mole fraction of terminal double bond segments of type i

10 /)()( λλ iiFp== =

0 NSEG Unitless

Attributes Related to Molecular Architecture (Tacticity and Orienticity)

ATACFLOW atactic1λ Apparent mole flow of

atactic polymer ---- 2 1 Mole

flow

ATACFRAC atacticF Mass fraction of atactic polymer 11 /λλatacticatacticF = 0 1 Unitless

HTHFLOW HTHiiΘ Mole flow rate of i-I

dyads with head-to-head orientation


HTHFRAC HTHiiθ Fraction of i-I dyads

with head-to-head orientation

iiHTHii

HTHii ΘΘ= /θ 0 NSEG Unitless

Attribute Definitions - Composite Polymer Attribute Set (continued)



Attributes Related to Reactions with Diene Monomers

XFLOW XFLOW Number of cross links ---- 2 NSEG* Mole flow

XDENSITY XLρ

Cross-linking density

0λρ

nXL M

XLFLOW=

0 NSEG* Kmol/kg

CIS-FLOW cisi,1λ Flow rate of diene

segment i in cis configuration

---- 2 NSEG* Mole flow

TRANSFLO transi,1λ Flow rate of diene

segment i in trans configuration


VINYLFLO vinyli,1λ Flow rate of diene

segment i in vinyl configuration


CIS-FRAC cisif Fraction of diene

segment i in cis configuration

icisicisif 1

,1 /λλ= 0 NSEG* Unitless

TRANSFRA transif

Fraction of diene segment i in trans configuration

itransitransif 1

,1 /λλ=

0 NSEG* Unitless

VINYLFRA vinylif

Fraction of diene segment i in vinyl configuration

ivinylivinylif 1

,1 /λλ=

0 NSEG* Unitless

Attributes Related to Particle Size (Emulsion Polymerization)

PDV PDv Polydispersity for PSD (volume) PD V

Vvn

v=

0 1 Unitless

PSDZMOM ν0 Zeroth moment of the particle size distribution (volume)

---- 2 1 # /s

PSDFMOM ν1 First moment of the PSD (volume)

ν ρ1 = Mass / 0 1 m /s3

PSDSMOM ν2 Second moment of the PSD (volume)

---- 2 1 m /s6

PSDTMOM ν3 Third moment of the PSD (volume)

---- 2 1 m /s9

VOLN Vn Number average volume of the particles

Vn =νν

1

0

0 1 m3

VOLV Vv Volume average volume of the particles

Vv =νν

2

1

0 1 m3

VOLZ Vz Z-average volume of the particles Vz =

νν

3

2

0 1 m3

DIAV Dv Volume average diameter Dv = 3 6 1

0πνν

0 1 m


† i = Segment index

Moments of the chain length distribution are defined as ∑= nm

m Qnλ

Where:

m = 0-3

n = Chain length

Qn = Number of moles of polymer of length n.

‡ Equation for recalculating class 0 attributes only. Class 2 attributes are integrated.

* Although the dimension is NSEG, these attributes only apply to diene segments, other elements will be set to zero.

Attribute Definitions – Composite Live Polymer Attribute Set


LDPN DPnL Number average DP

of live polymer DPn

L = μ μ1 0/ 0 1 Unitless

LDPW DPwL Weight average DP of

live polymer DPw

L = μ μ2 1/ 0 1 Unitless

LPDI PDI L Polydispersity index of live polymer

PDI DP DPLwL

nL= / 0 1 Unitless

LMWN MnL Number average MW

of live polymer M DP Mn

LnL

segL= 0 1 Unitless

LMWW MwL Weight average MW

of live polymer M DP Mw

LwL

segL= 0 1 Unitless

LMWSEG MsegL Average segment

molecular weight of live polymer

M LF i MsegL

p i= ∑ ( ) 0 1 Unitless

LZMOM μ0 Zeroth moment of live polymer

μ μ0 0=∑ ( )i 0 1 Mole flow

LFMOM μ1 First moment of live polymer

μ μ1 1=∑ ( )i 0 1 Mole flow

LSMOM μ2 Second moment of live polymer

---- 2 1 Mole flow

LSFLOW μ1( )i Segment flow rates in live polymer


LSFRAC LF ip ( ) Segment mole fraction in live polymer

LF i ip ( ) ( ) /= μ μ1 1 0 NSEG Unitless

LEFLOW μ0( )i End segment flow rates in live polymer


LEFRAC LF ie( ) End segment mole fractions in live polymer

LF i ie( ) ( ) /= μ μ0 0 0 NSEG Unitless

LPFRAC Flp Fraction of polymer that is live Flp =

μλ

0

0

0 1 Mole fraction




Attribute Definitions – Composite Aggregate Polymer Attribute Set


ADPN DPnA Number average DP of

aggregate polymer DPn

A = ξ ξ1 0/ 0 1 Unitless

ADPW DPwA Weight average DP of

aggregate polymer DPw

A = ξ ξ2 1/ 0 1 Unitless

APDI PDI A Polydispersity index of aggregate polymer

PDI DP DPAwA

nA= / 0 1 Unitless

AMWN MnA Number average MW of

aggregate polymer M DP Mn

AnA

segA= 0 1 Unitless

AMWW MwA Weight average MW of

aggregate polymer M DP Mw

AwA

segA= 0 1 Unitless

AMWSEG MsegA Average segment

molecular weight of aggregate polymer

M AF i MsegA

p i= ∑ ( ) 0 1 Unitless

AZMOM ξ0 Zeroth moment of aggregate polymer

ξ ξ0 0= ∑ ( )i 0 1 Mole flow

AFMOM ξ1 First moment of aggregate polymer

ξ ξ1 1= ∑ ( )i 0 1 Mole flow

ASMOM ξ2 Second moment of aggregate polymer

ξ ξ2 2= ∑ ( )i 0 1 Mole flow

ASFLOW ξ1( )i Segment flow rates in aggregate polymer

ξ ξ1 1( ) ( , )i i j= ∑ 0 NSEG Mole flow

ASFRAC AF ip( ) Segment mole fraction in aggregate polymer

AF i ip( ) ( ) /= ξ ξ1 1 0 NSEG Unitless

AEFLOW ξ0( )i End segment flow rates in aggregate polymer

ξ ξ0 0( ) ( , )i i j= ∑ 0 NSEG Mole flow

AEFRAC AF ie( ) End segment mole fractions in aggregate polymer

AF i ie( ) ( ) /= ξ ξ0 0 0 NSEG Unitless

APFRAC Fap Fraction of polymer that is aggregate Fap =

ξλ

0

0

0 1 Mole fraction



Attribute Definitions – Site-Based Polymer Attribute Set


SDPN DP jn( ) Number average degree of polymerization at site j

DP j j jn( ) ( ) / ( )= λ λ1 0 0 NSITE Unitless

SDPW DP jw( ) Weight average degree of polymerization at

DP j j jw( ) ( ) / ( )= λ λ2 1 0 NSITE Unitless



site j

SDPZ DP jz ( ) Z-average degree of polymerization at site j

DP j j jz ( ) ( ) / ( )= λ λ3 2 0 NSITE Unitless

SPDI PDI j( ) Polydispersity index at site j

PDI j DP j DP jw n( ) ( ) / ( )= 0 NSITE Unitless

SMWN M jn ( ) Number-average molecular weight at site j

M j DP j M jn n seg( ) ( ) ( )= 0 NSITE Unitless

SMWW M jw ( ) Weight-average molecular weight at site j

M j DP j M jw w seg( ) ( ) ( )= 0 NSITE Unitless

SMWZ M jz ( ) Z-average molecular weight at site j

M j DP j M jz z seg( ) ( ) ( )= 0 NSITE Unitless

SMWSEG M jseg ( ) Average segment molecular weight at site j

M j F i j Mseg p i( ) ( , )=∑ 0 NSITE Unitless

SZMOM λ0( )j Zeroth moment of chain length distribution at site j

---- 2 NSITE Mole flow

SFMOM λ1( )j First moment of chain length distribution at site j

λ λ1 1( ) ( , )j i j=∑ 0 NSITE Mole flow

SSMOM λ2( )j Second moment of chain length distribution at site j


STMOM λ3( )j Third moment of chain length distribution at site j


SSFLOW λ1( , )i j Mole flow of segments of type I at site j

---- 2 NSEG, NSITE

Mole flow

SSFRAC F i jp ( , ) Mole fraction of segments of type I at site j

F i j i j jp ( , ) ( , ) / ( )= λ λ1 1 0 NSEG;

NSITE

Unitless

SEFRAC F i je ( , ) Fraction of chain end segments of type i at site j

F i j i j i jeends

( , ) ( , ) / ( , )= ∑λ λ1 1 0 NEND,

NSITE

Unitless

SLCB LCB j( ) Number of long chain branches at site j


SSCB SCB j( ) Number of short chain branches at site j


SFLCB FLCB j( ) Long chain branching frequency at site j

FLCB j LCB jj

( ) ( )( )

=103

λ1

0 NSITE Unitless

SFSCB FSCB j( ) Short chain branching frequency at site j

FSLB j SCB jj

( ) ( )( )

=103

λ1

0 NSITE Unitless



SPFRAC FSP j( ) Mass fraction of composite polymers at that site

0 NSITE Unitless


j = Site number


Attribute Definitions – Site-Based Live Polymer Attribute Set


LSDPN DP jnL( ) Number average

DP of live polymer

DP j j jnL( ) ( ) /= μ μ1 0( ) 0 NSITE Unitless

LSDPW DP jwL( ) Weight average

DP of live polymer

DP j j jwL( ) ( ) /= μ μ2 1( ) 0 NSITE Unitless

LSPDI PDI jL( ) Polydispersity index of live polymer

PDI j DP j DP jLwL

nL( ) ( ) /= ( )

0 NSITE Unitless

LSMWN M jnL( ) Number average

MW of live polymer

M j DP j M jnL

nL

segL( ) ( )= ( ) 0 NSITE Unitless

LSMWW M jwL( ) Weight average

MW of live polymer

M j DP j M jwL

wL

segL( ) ( )= ( ) 0 NSITE Unitless

LSMWSEG M jsegL ( ) Average segment

molecular weight of live polymer

M j LF i j MsegL

p i( ) ( , )= ∑ 0 NSITE Unitless

LSZMOM μ0( )j Zeroth moment of live polymer

μ μ0 0( ) ( , )j i j=∑ 0 NSITE Mole flow

LSFMOM μ1( )j First moment of live polymer

μ μ1 1( ) ( , )j i j=∑ 0 NSITE Mole flow

LSSMOM μ2( )j Second moment of live polymer


LSSFLOW μ1( , )i j Segment flow rates in live polymer

---- 2 NSEG,

NSITE

Mole flow

LSSFRAC LF ip ( ) Segment mole fraction in live polymer

LF i j i j jp ( , ) ( , ) / ( )= μ μ1 1 0 NSEG,

NSITE

Unitless

LSEFLOW μ0( , )i j End segment flow rates in live polymer

---- 2 NSEG,

NSITE

Mole flow

LSEFRAC LF i je( , ) End segment mole fractions in live polymer

LF i j i j je( , ) ( , ) / ( )= μ μ0 0 0 NSEG,

NSITE

Unitless



LSPFRAC F jlp ( ) Fraction of polymer that is live

F j jjlp ( ) ( )

( )=μλ

0

0

0 NSITE Mole fraction


j = Site number


Attribute Definitions – Site-Based Aggregate Polymer Attribute Set


ASDPN DP jnA( ) Number average

DP of aggregate polymer

DP j j jnA( ) ( ) /= ξ ξ1 0( ) 0 NSITE Unitless

ASDPW DP jwA( ) Weight average DP

of aggregate polymer

DP j j jwA( ) ( ) /= ξ ξ2 1( ) 0 NSITE Unitless

ASPDI PDI jA( ) Polydispersity index of aggregate polymer

PDI j DP j DP jAwA

nA( ) ( ) /= ( ) 0 NSITE Unitless

ASMWN M jnA( ) Number average

MW of aggregate polymer

M j DP j M jnA

nA

segA( ) ( )= ( ) 0 NSITE Unitless

ASMWW M jwA( ) Weight average

MW of aggregate polymer

M j DP j M jwA

wA

segA( ) ( )= ( ) 0 NSITE Unitless

ASMWSEG M jsegA ( ) Average segment

molecular weight of aggregate polymer

M j AF i j MsegA

p i( ) ( , )= ∑ 0 NSITE Unitless

ASZMOM ξ0( )j Zeroth moment of aggregate polymer

ξ ξ0 0( ) ( , )j i j= ∑ 0 NSITE Mole flow

ASFMOM ξ1( )j First moment of aggregate polymer

ξ ξ1 1( ) ( , )j i j= ∑ 0 NSITE Mole flow

ASSMOM ξ2( )j Second moment of aggregate polymer


ASSFLOW ξ1( , )i j Segment flow rates in aggregate polymer

---- 2 NSEG,

NSITE

Mole flow

ASSFRAC AF ip( ) Segment mole fraction in aggregate polymer

AF i j i j jp( , ) ( , ) / ( )= ξ ξ1 1 0 NSEG,

NSITE

Unitless

ASEFLOW ξ0( , )i j End segment flow rates in aggregate polymer

---- 2 NSEG,

NSITE

Mole flow

ASEFRAC AF i je( , ) End segment mole fractions in aggregate polymer

AF i j i j je( , ) ( , ) / ( )= ξ ξ0 0 0 NSEG,

NSITE

Unitless



ASPFRAC F jap( ) Fraction of polymer that is aggregate F j

jjap( )

( )( )

=ξλ

0

0

0 NSITE Mole fraction

DSEFLOW η0( , )i j End segment flow rates in dissociated (from aggregate) polymer

---- 2 NSEG,

NSITE

---

DSSFLOW η1( , )i j Segment polymer flow rates in dissociated (from aggregate) polymer

---- 2 NSEG,

NSITE

---

DSSMOM η2( )j Second moment of dissociated (from aggregate) polymer

---- 2 NSITE ---


j = Site number


The following table lists the minimum required component attributes by model:

Model Attributes

Property Models

MWN, DPN or both ZMOM and FMOM

SFRAC or SFLOW

Emulsion MWN, DPN or both ZMOM and FMOM

SFRAC or SFLOW

DIAV or both PSDZMOM and PSDFMOM

Other polymer particle attributes (optional)

Free-Radical MWN, DPN or both ZMOM and FMOM

SFRAC or SFLOW

Other composite attributes (optional)

Composite live attributes (optional)

Step-Growth MWN, DPN or both ZMOM and FMOM

SFRAC or SFLOW

Ziegler-Natta MWN, DPN or both ZMOM and FMOM

SFRAC or SFLOW

Other composite attributes (optional)

Composite live attributes (optional)

Site based component attributes (optional)

Site based live component attributes (optional)

Ionic SZMOM, LSEFLOW

ASEFLOW, DSEFLOW (if association reaction present)

LSSFLOW, SSFLOW

ASSFLOW, DSSFLOW (if association reaction


present)

Site-Based Species Attributes There are two types of site-based species attributes:

• Zielger-Natta catalyst attributes

• Ionic initiator attributes

Zielger-Natta Catalyst attributes Component attributes are used to track multi-site Ziegler-Natta catalyst site activity, in terms of mole flow and fraction of potential, inhibited, vacant, and dead sites. The occupied sites are not tracked since that information may be obtained from the live polymer zeroth moment of chain length distribution. The site types are defined as follows:

• Potential Sites - these are sites not yet activated.

• Vacant Site - these are activated sites without a growing polymer attached.

• Inhibited Sites - these are activated sites temporarily in an inactive state.

• Dead Sites - these are sites having permanently lost their catalytic activity.

• Occupied Sites - these are activated sites with a growing polymer attached.

The following table lists the catalyst component attributes:

Attribute Description Class Dimension

CPSFLOW Mole flow of potential sites 2 NSITE

CPSFRAC Mole fraction of potential sites 0 NSITE

CVSFLOW Mole flow of vacant sites of type k 2 NSITE

CVSFRAC Mole fraction of vacant sites of type k

0 NSITE

CISFLOW Mole flow of inhibited sites of type k 2 NSITE

CISFRAC Mole fraction of inhibited sites of type k

0 NSITE

CDSFLOW Mole flow of dead sites 2 NSITE

CDSFRAC Mole fraction of dead sites 0 NSITE

CMSFLOW Mole flow of metal hydride 2 NSITE

CMSFRAC Mole fraction of metal hydride 0 NSITE

Ionic Initiator Attributes The component attributes are used to track various states of ionic initiator (free ions, ion pairs, dormant esters) using a multi-site model.

The following table lists the three ionic component attributes:


Attribute Description Class Dimension

P0FLOW Mole flow of P0 2 NSITE

PT0FLOW Mole flow of PT 0 2 NSITE

CIONFLOW Mole flow of counter-ion CI

2 NSITE

For more information on ionic attributes, see Ionic Polymerization Model in Chapter 3.

User Attributes Generic component attributes are available for tracking user-specified data. These may be used to track additional properties not available through the pre-defined attributes.

User component attributes are available as Class 0 through Class 2 attributes. You must supply a Fortran subroutine to return rates of change for Class 2 attributes and recalculate Class 0 attributes. This would typically be a user kinetic routine.

User attributes DPSDN and DPSDW are designed to hold data related to particle size distributions of solid polymers or monomers. The number flow rates (DPSDN) have units of inverse time. Since particle flow rates are often very high the user may wish to apply appropriate scaling to define this attribute on a relative basis (for example use this attribute to track flow rates in trillions of particles/sec). The DPSDW attribute tracks the mass flow rate of each element of the distribution. User subroutines are required to use this advanced feature.

The following table lists the available user component attributes:

Attribute Description Unit Type Dimension

CACLASS0 Class 0 user attribute Unitless 10

CAUSR1…5 Class 1 user attributes Unitless 10

CAUSRA…E Class 2 user attributes Mole flow 10

DPSDN Discrete particle size distribution, particle number flow rates. Class 2.

Inverse time 50

DPSDW Discrete particle size distribution, particle mass flow rates. Class 2.

Mass flow 50


Component Attribute Initialization In cases where polymer is present in the process feed streams, values for the polymer component attributes must be specified. Enter this information while specifying the feed stream conditions.

Within Aspen Polymers, material streams are made up of substreams that carry the flow of material of different types:

• Conventional vapor/liquid flow goes into the “Mixed” substream type

• Solid polymer and other solid components which do not participate in phase equilibrium go into the “Cisolid” substream type

Most simulations only make use of the “Mixed” substream. In this substream, you would enter the conditions, such as temperature and pressure, the number of phases (2 if both vapor and liquid are present), and the composition in terms of component flows or fractions (along with the total stream flow).

If one of the components for which you enter composition data is a polymer or a catalyst, you must specify its component attributes. Because users are allowed to specify either Class 0 or Class 2 component attributes, an initialization mechanism had to be defined to calculate the corresponding Class 2. Remember that the Class 2 attributes are the ones which are converged upon during simulation.

Attribute Initialization Scheme The attribute initialization scheme performs several important functions. In addition to calculating the needed Class 2 attributes, it automatically calculates an expanded component attribute set from the minimum required and specified by the user. The minimum required attributes are:

• Segment flow rates (SFLOW), or segment fractions (SFRAC)

• Number average degree of polymerization (DPN), or both

• Zeroth and first moment of chain length distribution (ZMOM and FMOM)

From this set, several other attributes can be calculated using the definitions given in the attribute definition tables provided earlier in this chapter. The scheme uses priority rules to decide how to calculate each attribute.

The following table describes the calculation methods and order of priority. The initialization scheme is also used for recalculating Class 0 attributes during flowsheet convergence. Finally, it can be considered as a method of ensuring consistency between interrelated attributes.

The Aspen Polymers component attribute initialization methodology is:

Attribute Calculated from† Priority

Composite Bulk Polymer Attribute Set



SFRAC SFRAC

SFLOW / SUM (SFLOW)

1 / NSEG

1

2

3

ZMOM ZMOM

FMOM / DPN

FMOM*MWSEG / MWN

PDI*FMOM*FMOM / SMOM

1

2

3

4

FMOM SUM (SFLOW)

PMASS / MWSEG

1

2

SMOM SMOM

FMOM*DPW

FMOM*MWW / MWSEG

FMOM*FMOM*PDI / ZMOM

ZMOM

1

2

3

4

5

TMOM TMOM

SMOM*DPZ

SMOM*MWZ / MWSEG

1

2

3

LCB LCB

FMOM*FLCB / 1.E3

1

2

SCB SCB

FMOM*FSCB / 1.E3

1

2

PSDZMOM PSDZMOM 1

PSDFMOM PSDFMOM

PMASS / PDENS

1

2

PSDSMOM PSDSMOM 1

PSDTMOM PSDTMOM 1

VOLN VOLN

PSDFMOM / PSDZMOM

0.0

1

2

3

VOLV VOLV

PSDSMOM / PSDSMOM / PSDFMOM

0.0

1

2

3

VOLZ VOLZ

PSDTMOM / PSDSMOM

0.0

1

2

3

DIAV DIAV

(6.0*PSDFMOM / π / PSDZMOM)

0.0

1

2

3

PDV PDV

(PSDZMOM*PSDSMOM) / (PSDFMOM)

0.0

1

2

3



Composite Live Polymer Attribute Set

LSFRAC LSFRAC

LSFLOW / SUM (LSFLOW)

1 / NSEG

1

2

3

LZMOM LZMOM

LPFRA*ZMOM

LFMOM / LDPN

LFMOM*LMWSEG / LMWN

LPDI*LFMOM*LFMOM / LSMOM

1

2

3

4

5

LFMOM SUM (LSFLOW)

LZMOM*LDPN

LZMOM*LMWN / LMWSEG

LZMOM*LSMOM / LPDI

1

2

3

4

LSMOM LSMOM

LFMOM*LDPW

LFMOM*LMWW / LMWSEG

LFMOM*LFMOM*LPDI / LZMOM

1

2

3

4

Composite Aggregate Polymer Attribute Set

ASFRAC ASFRAC

ASFLOW / SUM (ASFLOW)

1 / NSEG

1

2

3

AZMOM AZMOM

APFRA*ZMOM

AFMOM / ADPN

AFMOM*AMWSEG / AMWN

APDI*AFMOM*AFMOM / ASMOM

1

2

3

4

5

AFMOM SUM (ASFLOW)

AZMOM*ADPN

AZMOM*AMWN / AMWSEG

AZMOM*ASMOM / APDI

1

2

3

4

ASMOM ASMOM

AFMOM*ADPW

AFMOM*AMWW / AMWSEG

AFMOM*AFMOM*APDI / AZMOM

1

2

3

4


Site Based Bulk Polymer Attribute Set

SSFRAC SSFRAC

SSFLOW / SUM (SSFLOW)

1 / NSEG

1

2

3



SZMOM SZMOM

SFMOM / SDPN

SFMOM*SMWSEG / SMWN

SPDI*SFMOM*SFMOM / SSMOM

1

2

3

4

SFMOM SUM(SSFLOW)

SPFRAC*PMASS / SMWSEG

1

2

SSMOM SSMOM

SFMOM*SDPW

SFMOM*SMWW / SMWSEG

SFMOM*SFMOM*SPDI / SZMOM

SZMOM

1

2

3

4

5

STMOM STMOM

SSMOM*SDPZ

SSMOM*SMWZ / SMWSEG

1

2

3

SLCB SLCB

SFMOM*SFLCB / 1.E3

1

2

SSCB SSCB

SFMOM*SFLCB / 1.E3

1

2

Site Based Live Polymer Attribute Set

LSSFRAC LSSFRAC

LSSFLOW / SUM (LSSFLOW)

1 / NSEG

1

2

3

LSZMOM LSZMOM

LSPFRA*SZMOM

LFSMOM / SLDPN

LSFMOM*LSMWSEG / SLMWN

LSPDI*LSFMOM*LSFMOM / LSSMOM

1

2

3

4

5

LSFMOM SUM (LSSFLOW)

LSZMOM*LSDPN

LSZMOM*LSMWN / LSMWSEG

DSQRT (LSZMOM*LSSMOM / LSPDI)

1

2

3

4

LSSMOM LSSMOM

LSFMOM*LSDPW

LSFMOM*LSMWW / LSMWSEG

LSFMOM*LSFMOM*LSPDI / LSZMOM

1

2

3

4

Site Based Aggregate Polymer Attribute Set

ASSFRAC ASSFRAC

ASSFLOW / SUM (ASSFLOW)

1 / NSEG

1

2

3



ASZMOM ASZMOM

ASPFRA*SZMOM

AFSMOM / SADPN

ASFMOM*ASMWSEG / SAMWN

ASPDI*ASFMOM*ASFMOM / ASSMOM

1

2

3

4

5

ASFMOM SUM (ASSFLOW)

ASZMOM*ASDPN

ASZMOM*ASMWN / ASMWSEG

DSQRT (ASZMOM*ASSMOM / ASPDI)

1

2

3

4

ASSMOM ASSMOM

ASFMOM*ASDPW

ASFMOM*ASMWW / ASMWSEG

ASFMOM*ASFMOM*ASPDI / ASZMOM

1

2

3

4

† PMASS is polymer mass, PDENS is polymer density

Component Attribute Scale Factors Aspen Plus uses numerical solvers to resolve flowsheet recycle streams and to solve the conservation equations in each of the kinetic reactor models (RCSTR, RPLUG, and RBATCH). The solver algorithms use scaled variables. Typically, the ideal scale factors for each type of variable should be on the same order of magnitude as the variable itself. In other words, the solvers work best when the scaled variables are all close to unity.

In Aspen Polymers, default scaling factors are defined for each type of component attribute variable. These defaults are designed to address a wide range of problems, however they may not be ideal for any particular problem. The Attr-Scaling form lets you view and change the default scaling factors for each type of component attribute.

Under some circumstances, you may be able to improve the reactor and/or flowsheet recycle stream convergence by optimizing the attribute scaling factors. For example, in a Ziegler-Natta polymerization process the live end flow rate (LEFLOW) and the related attributes LZMOM and LSZMOM are sensitive to the catalyst activity. Highly active catalysts result in very low live end flow rates. Further, the number of vacant and potential sites (CVSFLOW and CPSFLOW) may be very low for the catalyst.

The Attr-Scaling form can be used to specify more accurate scaling factors for the component attributes for polymers, catalysts, and other types of attributed components.

Reducing the scaling factors on this form tightens the tolerance on the selected variables. If the scaling factors are set too low, the tolerance will be unreasonably tight, leading to convergence problems or excessive CPU time. If the scaling factors are set too high, the problem may be loosely converged and the simulation accuracy may suffer.


The reactor models and flowsheet recycle convergence algorithms currently ignore the attribute upper bound limits that appear on this form.

Specifying Component Attributes There are several categories of components for which you can specify component attributes:

• Polymers

• Site-based components

• Conventional components

Specifying Polymer Component Attributes See Specifying Polymers on page 29.

Specifying Site-Based Component Attributes See Specifying Site-Based Components on page 30.

Specifying Conventional Component Attributes You can associate attributes to conventional components by selecting user attributes. Typically, you do this if you have a user subroutine to return values for these attributes.

To access the user component attribute selection form:


2 From the Components folder, click Attr-Comps.

To associate user attributes to conventional components:

1 On the Selection sheet, specify the component name in the Component field.

2 In the Attribute field, specify the attribute name.

3 Continue adding as many attributes as needed.

Initializing Component Attributes in Streams or Blocks If you have an attributed component present in a feed stream, you must specify component attribute values for that component.

To access the component attribute input form for a stream:


1 From the Process Flowsheet window, use the right mouse button to click the feed stream.

2 Click Input.

3 From the stream input specifications sheet, click the Component Attr. tab.

4 On the Component Attr. sheet, select the Component ID.

5 For each attribute, select the Attribute ID and enter the values for the attributes.

If you have an attributed component produced within a reactor, you can specify attribute values (product values or product value estimates) for that component. This is not available for all reactors.

For a description of the treatment of component attributes in reactors, see Steady-State Unit Operation Models in Chapter 4.

To access the component attribute input form for a reactor:

1 From the Process Flowsheet window, use the right mouse button to click the reactor.

2 Click Input. 3 From the reactor input specifications sheet, click the Component Attr.

tab.

4 On the Component Attr. sheet, select the Component ID.

5 For each attribute, select the Attribute ID and enter the values for the attributes.

Specifying Component Attribute Scaling Factors You can override default component attribute convergence parameters for polymer or catalyst components. Adjusting the scaling factor helps you improve flowsheet convergence and internal convergence in reactor models. Typically, the scaling factor should be the same order as the expected value of the variable.

To access the component attribute scaling form:


2 From the Components folder, click Attr-Scaling.

To adjust the default scaling factor and upper bound of defined attributes:

1 On the Input tab, specify the component name in the Component ID field.

2 In the Attribute field, specify the attribute name. 3 Continue adding as many attributes as needed.

4 Adjust the Scaling factor and/or Upper bound as needed.

References Aspen Plus User Guide. Cambridge, MA: Aspen Technology, Inc.

5 Structural Property Distributions 53

5 Structural Property Distributions

This section discusses the mechanism available in Aspen Polymers (formerly known as Aspen Polymers Plus) for tracking structural property distributions, in particular chain size distribution, for chain-growth polymerization processes (U.S. Patent No. 6,093,211).


• Property Distribution Types, 53

• Distribution Functions, 54

• Distributions in Process Models, 56

• Mechanism for Tracking Distributions, 62

• Requesting Distribution Calculations, 66

Property Distribution Types The common polymer structural properties for which distributions are typically considered include:

• Chain size - molecular weight or chain length

• Copolymer composition

• Degree of branching

• Polymer particle size

In order to accurately characterize a polymer component, and maintain control of polymer product properties, engineers must concern themselves with these distributions.

From a modeling standpoint, many theoretical and empirical functions have been developed to represent distributions. These functions tend to fall into categories derived from their formulation, or from their graphical representation.

For example, distributions that consider two dependent parameters simultaneously (for example, chain size and copolymer composition) are termed bivariate distributions.

54 5 Structural Property Distributions

Distributions that mimic the normal bell-shaped graphical representation are called unimodal distributions.

This is in contrast with distributions that reveal several peaks and are called bimodal or multimodal distributions. The following figure shows examples of unimodal and bimodal distributions:

Distribution Functions In the majority of cases, the distribution functions proposed in the literature are based on a statistical approach and use one of three types of mathematical functions: binomial, Poisson or Gaussian.

The parameters in these distribution functions can easily be calculated from the polymer average properties (degree of polymerization, polydispersity index, etc.). The following are the common distribution functions that have been applied to the calculation of polymer property distributions:

• Schulz-Flory Most Probable (Flory, 1936, 1953; Schulz, 1935, 1939)

• Schulz (Schulz, 1935, 1939)

• Weibull-Tung Generalized Exponential (Tung, 1956; Weibull, 1951)

• Normal (Biesenberger & Sebastian, 1983)

• Wesslau Logarithmic Normal (Wesslau, 1956)

• Lansing Logarithmic Normal (Lansing, 1935)

• Poisson (Biesenberger & Sebastian, 1983)

• Zimm (Zimm, 1948)

• Stockmayer Bivariate (Stockmayer, 1945)

In addition to these distribution functions, a method using the moments of distributions is also available (Tompa, 1976). Of these functions, two have greater importance for Aspen Polymers.

Schulz-Flory Most Probable Distribution Schulz and Flory developed a one-parameter equation to represent the distribution of polymers falling into one of the following categories:


• Addition polymers - formed by a constant rate of initiation, with invariant monomer concentration, with termination by disproportionation only, and with no chain transfer to monomer

• Linear condensation polymers - obeying the assumption of equal reactivities of chain ends or linear condensation polymers formed by random interchange of units

• Low molecular weight polymer - formed from a high molecular weight polymer by random scission

The Schulz-Flory distribution is also known as the Most-Probable distribution since it is dictated by the probability of random events, such as the location of a scission reaction on a long-chain molecule. The number or mole-fraction distribution and the weight fraction distribution are given by:

Mole-Fraction Distribution

F r p pr( ) ( )= −−1 1 (number distribution)

Weight-Fraction Distribution

W r rp pr( ) ( )= −−1 21 (weight distribution)

Where:

p = Extent of reaction

r = Size of the molecule or number of segments

For addition polymerizations p is the probability that a growing live polymer molecule will propagate. For step-growth reactions, p is the fractional conversion of monomer end groups.

From these distributions, the number, weight, and z-average degree of polymerization are:

DPpn = −

11( )

DP ppw =

+−

( )( )11

F r p pr( ) ( )= −−1 1

PDI p= +1

To generate the distribution, p can be calculated from degree of polymerization as:

pDPn

= −1 1

Note that the polydispersity approaches two as p → unity.


Stockmayer Bivariate Distribution There are cases where two polymer property distributions must be considered simultaneously, which are called bivariate. Stockmayer developed a distribution function to consider both chain size and composition distribution for example (Stockmayer, 1945).

This model may be extended to other combinations of polymer properties such as chain size and long chain branching distribution for the case of copolymers.

Distributions in Process Models There is a great demand to know the full molecular weight distribution, particularly for complex distributions that may have a shoulder, or are even bimodal. This information is needed for optimization of rheological and mechanical properties of the final polymer product.

Within Aspen Polymers a dual approach for determining polymer properties is used:

• Method of moments continues to be the preferred approach for calculating average properties.

• Method of instantaneous properties is used to calculate distributions. This method addresses the issue of data storage and computational complexity in tracking distributions.

Under special circumstances, the most general form of the instantaneous distribution function reduces to Flory’s most probable distribution. The instantaneous distribution functions are unimodal. However, the distribution functions for polymer accumulated in a multi-reactor system may be multimodal.

Average Properties and Moments It is convenient to examine polymer molecular properties in terms of averages instead of considering the complete distribution. Average properties must be determined from the actual distributions either through distribution moments or through instantaneous properties.

The average properties tracked for polymers were described in the Polymer Component Attributes section on page 34. These properties are calculated using the method of moments within kinetic models.

For a given property s, the property distribution may be described by a frequency function f s when the property is a discrete variable, and by a

density function f s( ) when the property s is continuous.

Therefore, f s and f s( ) represent the portion (for example, number, weight, volume, fraction) of the population whose property is exactly s (discrete) or whose property lies between s and s + ds.

The frequency and density distribution functions are respectively:


Frequency Function

F fS ss

S

= ∑0

and

Density Function

F S f s dss

S( ) ( )= ∫

0

Where:

s0 = Initial value of s

S = Arbitrary higher value (Biesenberger & Sebastian, 1983)

Distribution moments may be defined from the origin of the average property, i.e. property is equal to 0, or from the mean value of that property. The moments employed in Aspen Polymers use the first approach.

In this case, the generalized form of the relationship between distribution moment and distribution function is shown below:

( )μk

k

all ss

k

all s

s f

s f s ds≡

⎧

⎨⎪⎪

⎩⎪⎪

∑

∫

for the frequency function

for the density function

Where:

μ = Moment

k = Moment order (e.g. 0-3 for zeroth through third moment)

s = Property value (e.g. chain length, molecular weight, particle size, etc.)

f s = Frequency function

f s( ) = Density function

Average Properties

The average properties can be calculated as ratios of the moments. Number average is the ratio of first to zeroth moment,μ μ1 0/ . Weight or Volume

average is the ratio of second to first moment, μ μ2 1/ . Z-average is the ratio

of third to second moment, μ μ3 2/ .

For the case of chain length distribution the moment frequency distribution is given by:

λmm

nn Q= ∑


Where:

λ = Moment

m = Moment order

n = Chain length or degree of polymerization

Qn = Number of moles of polymer of length n

The average chain length properties are then:

DPn = λ λ1 0/

DPw = λ λ2 1/

DPz = λ λ3 2/

PDI = λ λ λ2 0 12/

A similar definition of moments for the frequency distribution can be applied to molecular weight. Typically, in Aspen Polymers it is applied to chain length. Then the average molecular weight values are determined using the average degree of polymerization and average segment molecular weight.

Method of Instantaneous Properties Applying the method of moments for the calculation of property distributions has several drawbacks. In addition to CPU requirements and computational complexity, a larger number of moments than currently calculated would be required. Knowledge of leading moments of a distribution does not permit one to unambiguously construct a complex distribution. One must therefore look beyond the method of moments for a more powerful method to predict these complex distributions.

A better approach for generating molecular weight distributions consists of storing reaction rate data throughout the kinetic calculations, and later using them to construct the full distribution of polymer accumulated in the reactor system. Such an approach was developed by Hamielec (Hamielec, 1992).

In the simplest case, linear polymerization in a single CSTR reactor, the ratios of termination and chain transfer reaction rates to propagation reaction rates are stored. The instantaneous chain length distribution is expressed as a function of these ratios and chain length.

For the case of two CSTRs in series, at steady-state, the outlet polymer distribution function is the weighted average of the distribution function in each CSTR taken separately. The case of a plug flow reactor can be approximated using multiple CSTRs, and similarly for a batch reactor.

By looking at the treatment of such reactor configurations, it can be deduced that the final polymer distribution is a result of the entire system of reactors. For this reason, the MWD implementation in Aspen Polymers needs to consider the proper data structure to track distribution parameters at every point in the flowsheet. Users should be able to request MWD from any point in the flowsheet, and from this point the Aspen Plus flowsheet connectivity information can be used to track polymerization history.


The calculation of chain length distribution for a batch reactor from reaction rate parameters for linear addition polymerization was described by Hamielec (Hamielec, 1992).

Consider the equations for the generation and consumption of free radicals. A similar approach may be used for other active centers (Ziegler-Natta, metallocene, etc.):

Radical Generation and Consumption Rates

[ ] ( ) ][][][][]][[]][[

otdtcfTfmp

ofT

ofmI

lo

RKKTKMKMKRTKRMKR

R++++

++=

[ ] ( ) ][][][][]][[ 1

otdtcfTfmp

ro

pr

o

RKKTKMKMKRMK

R++++

=−

Where:

[ ]R K f II d= 2 [ ] = Initiation rate

Instantaneous Distribution Parameters

Introducing two dimensionless parameters τ and β.

τ =+

=+ +R R

RK R K M K T

K Mtd f

p

tdo

fm fT

p

[ ] [ ] [ ][ ]

β = =RR

K RK M

tc

p

tco

p

[ ][ ]

Where:

R K R Mp po= [ ][ ] = Propagation rate

R K Rtd tdo= [ ]2 = Rate of termination by disproportionation

R K Rtc tco= [ ]2 = Rate of termination by combination

R K R M K R Tf fmo

fTo= +[ ][ ] [ ][ ] = Total rate of all chain transfer

reactions

If we assume that the stationary-state hypothesis holds, then the initiation rate is equal to the sum of the termination rates, R R RI td tc= + .

The equations for the rate of generation and consumption of radicals can be written as follows:

[ ] [ ]R Rol

o=+

+ +τ βτ β1

[ ] [ ]R Ror

or=

+ +−

11 1

τ β


Therefore:

[ ] [ ]( )R Ror

o r= +τ β Φ

Where:

Φ =+ +

11 τ β

The rate of production of polymer molecules of chain length r , R rFp( ) is

given by:

[ ]( ) [ ] [ ] [ ]( )[ ] [ ][ ]R rV

d V Pdt

K M K T K R R K R RFPr

fm fT tdo o

r tco

ss

ro

r s( ) = = + + +=

−

−∑1 12 1

1

Substituting [ ]Rfo gives:

[ ][ ]( ) ( )( )R r K R M rFP po r( ) = + + + −⎧

⎨⎩

⎫⎬⎭

τ β τβτ β

21 Φ

Instantaneous Weight Chain Length Distribution

Therefore, the instantaneous weight chain length distribution can be calculated from production rate of polymer molecules as follows:

( )

( )

( ) ( )( )( ) ( )( )W r

rR r

rR r

r rr rFP

FPr

r

r( ) = =+ + + −⎧

⎨⎩

⎫⎬⎭

+ += + + + −⎧

⎨⎩

⎫⎬⎭

=

∞+

∑1

121

1 21

τ β τβτ β

τ βτ β τ

βτ β

ΦΦ

In other words, W(r) is the weight chain length distribution of dead polymer chains produced in a small time interval t to t+dt, in a batch reactor. W(r) is also the weight chain length distribution of dead polymer chains produced in a CSTR operating at steady-state.

If β τ<< , which is the case when the polymer chains are formed by chain transfer or by termination by disproportionation, this equation reduces to:

W r r rrr

( ) = =+

⎛⎝⎜

⎞⎠⎟ +

⎛⎝⎜

⎞⎠⎟

+−

ττ

ττ

2 11 21

1 1Φ

Where:

1 1/ ( )+ τ = Probability of growth for a polymer radical

τ τ/ 1+ = Probability that a polymer radical stops growing

Chain Length distribution equation

Since r is usually large, W(r) in the original equation on page 60 can be approximated as a continuous function with small error:


( ) ( )( ) ( ){ }W r r r r( ) .exp≈ + + + −⎧⎨⎩

⎫⎬⎭

− +τ β τβ

τ β τ β2

1

For most free-radical polymerizations ( )τ β+ <<1 and is of the order

10 106 2− −− .

The weight-average chain length for polymer produced instantaneously is given by:

( ) ( )( ) ( )

P rW rwr

= =+ + + + +

+≈

+

+=

∞

∑ ( )1

2 22 3 2 3τ τ β β τ β

τ β

τ β

τ β

The instantaneous number-average chain length distribution is given by:

( )Pn W r

rr

=+ +

+⎛⎝⎜

⎞⎠⎟≈

+⎛⎝⎜

⎞⎠⎟

−

∞

∑1 1

2

1

21

( )τ β

τ β τ β

The polydispersity index for polymer produced instantaneously is given by:

( )( )

PDIPP

w

n= ≈

+ +⎛⎝⎜

⎞⎠⎟

+

2 3 22

τ β τ β

τ β

Copolymerization The chain length distribution equation on page 61 applies to both homo- and co-polymerization with two or more monomer types. When chain growth polymerizations are done with active center types other than radicals (Ziegler-Natta, metallocene, etc.) β = 0 in the equation, and the instantaneous chain length distribution becomes a single parameter τ distribution, which is Flory’s most probable distribution with a polydispersity index of 2.0.

This equation is the main expression used in Aspen Polymers to generate chain length distribution. Within the context of a polymerization reactor, this expression is valid for the case of linear chains of a homopolymer produced in a single CSTR at steady-state.

CSTR in Series

For the case of two CSTRs in series, the end product polymer distribution is a composite that is a weighted average of the distributions of polymer produced in the first and the second reactor:

W rmm

W rmm

W rout ( ) * ( ) * ( )= +11

22

Where:

m m m= +1 2 = Total mass of polymer produced in the first and second reactor per unit time


The distribution function in each reactor is given by the chain length distribution equation on page 61 with the τ and β, varying from reactor 1 to reactor 2, and independent of time under steady-state operation.

Plug Flow & Batch Reactors

A plug flow reactor can be divided into several volume elements and treated as a series of CSTRs. The τ, β, and polymer mass values are stored for each volume element and later used for the calculation of the composite chain length distribution function. A batch reactor is handled using a similar approach. In this case, the τ, β, and polymer mass values are stored for each time element.

For linear chains of a copolymer, the difference from the homopolymer case can be factored into the calculation of the reaction rates for propagation, termination, and transfer reactions, R R Rp tc td, , , and Rfm .

Mechanism for Tracking Distributions The method of instantaneous properties is used to generate chain length distributions in Aspen Polymers. This method is applied at two levels:

• Reactor level for determining the distribution of polymer newly produced within the vessel (local distribution), and

• Flowstream level for determining the distribution of polymer produced up to that point in the flowsheet (cumulative distribution)

Distributions in Kinetic Reactors Within kinetic reactors, the method of instantaneous properties is used to determine the distribution of newly produced polymer. The reaction models calculate the instantaneous properties τ and β using the respective equations on page 59. In addition, the polymer mass corresponding to these values is saved.

Calculating Distribution Increments The distribution increments are spaced in logarithmic steps between unity and the specified upper limit (Upper) using the following formula:

( )⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ×=

point

10logalog,maxN

upperiiri

Where i varies between one and the specified number of points Npoint, and upper is the user-specified upper bound of the distribution. This spacing provides good resolution over the entire spectrum of molecular weights, with emphasis on the low molecular weight species that are more likely to be lost in fractionation steps. To ensure accuracy, the upper bound should be set at


least five times higher than the observed weight-average degree of polymerization.

Calculating Local Distributions For CSTR reactors, the values of τ and β are stored during simulation. For multi-site kinetics (such as Ziegler-Natta kinetics), values of τ and β and polymer mass generation are stored for each site j. These parameters are used to calculate the local distribution for the CSTR reactor.

For single-site kinetics (free radical and emulsion):

( ) ( )( ) ( )[ ]βτβτβτβτ +×−⎥⎦⎤

⎢⎣⎡ −+++×= rrrW local

r exp12

For multi-site kinetics (Ziegler-Natta):

( ) ( )( ) ( )[ ]jjjjj

jjjlocal

jr rrrW βτβτβ

τβτ +×−⎥⎦

⎤⎢⎣

⎡−+++×= exp1

2,

∑∑ ×

=j j

jlocal

jrjlocalr m

WmW

,

For plug-flow reactors, the values of τ and β are calculated at each axial step during the numerical integration. The local distribution for the reactor is calculated by summing the instantaneous distributions (from either equations

for localrW given previously) at each step over all the steps from the reactor

inlet (z = 0) to the reactor outlet (z = L).

For single-site kinetics:

( ) ( )( ) ( )[ ]zzzzz

zzzzr rrrW βτβτβτβτ +×−⎥⎦⎤

⎢⎣⎡ −+++×= exp1

2,

∑

∑

=

=

×= L

zz

L

zzrz

localr

m

WmW

0

0,

For multi-site kinetics:

( ) ( )( ) ( )[ ]zjzjzjzjzj

zjzjzjzjr rrrW ,,,,,

,,,,, exp12

βτβτβ

τβτ +×−⎥⎦

⎤⎢⎣

⎡−+++×=

∑

∑

=

=

×= L

zzj

L

zzjrzj

localjr

m

WmW

0,

0,,,

,


The local composite distribution is calculated using the equation given

previously for localrW for multi-site kinetics.

The local site-based and composite distributions are stored in the reactor results form and can be viewed from the Reactor folder Results subfolder, Distributions sheet and plotted using the Aspen Plot Wizard.

Calculating Cumulative Distributions For a reactor with multiple feeds, the feed distribution is calculated as shown below:

∑

∑

=

=

×=

feeds

feeds

N

kk

N

kkrk

feedr

m

WmW

1

1,

The cumulative composite distribution is calculated by adding the feed distribution to the local composite distribution:

localfeed

localr

localfeedr

feedcomposite

r mmWmWm

W+

×+×=

The composite cumulative distribution is stored in the outlet stream of the reactor and can be viewed through the stream results form.

GPC Distributions If the user selects the GPC Distribution format, the distribution is calculated as rrW .

Distributions in Process Streams The polymer distribution calculated within kinetic reactors is transferred into the outlet stream. This allows flowsheeting of the cumulative distribution data, i.e. the data follows the polymer component throughout the flowsheet. The cumulative distribution is stored within the stream.

Aspen Plus provides several different vehicles for associating data with process streams. These include:

• Basic stream vector, which contains composition and state information

• Component attributes, which are a fundamental tool in Aspen Polymers

• Prop-Sets, which allow users to request additional properties for streams

• Other non-accessible storage space

The first two categories are processed during convergence calculations while the last two are not.

The information used for calculating the distributions is derived from converged quantities. There is no need for applying convergence calculations


to the distribution data itself. Therefore, the polymer distribution data is carried in non-accessible storage space.

The following figure illustrates the procedure followed to generate the distribution:

Verifying the Accuracy of Distribution Calculations The molecular weight distributions calculations involve round-off error associated with the discretization into a finite number of elements and truncation error due to the upper bound imposed on the distribution. The following expressions can be used to verify the accuracy of the distribution. These expressions calculate the area under the distribution curve and the number- and weight-average molecular weight of the polymer in the distribution.

For non-GPC curves:

( ) ⎟⎠⎞

⎜⎝⎛ +

−= ++ 2

11

iiiii

WWrrw

For GPC curves (distribution stores irW ):

( )⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=

+

++

i

i

i

iiii r

Wr

Wrrw1

11

2

Where:

iW = Y-axis value of distribution element i

ir = X-axis value of distribution element i

iw = Mass-fraction of polymer in the size range between ir and

1+ir


The total mass fraction of all elements in the distribution should sum to unity:

0.1pointsN

1≅∑

=iiw

If the calculated area is below unity, the specified upper bound of the distribution may be too low. If the calculated area is greater than one, the number of points in the distribution may need to be increased to improve the accuracy of the distribution calculations.

For chain-length distributions, the value r refers to the molecular size. The number average and weight average degree of polymerization can be calculated as:

( )

1N

1 121

points−

= +⎟⎟⎠

⎞⎜⎜⎝

⎛

+= ∑

i ii

in rr

wP ( )∑=

+ +=pointsN

112

1

iiiiw rrwP

For molecular-weight distributions, the term r refers to the molecular weight of each increment. The number and weight average molecular weights of the distributions are calculated as:

( )

1N

1 121

points−

= +⎟⎟⎠

⎞⎜⎜⎝

⎛

+= ∑

i ii

in rr

wM ( )∑=

+ +=pointsN

112

1

iiiiw rrwM

The area under the distribution curve and the number- and weight-average properties of the distribution can be generated by the plot wizard and displayed on the distribution plots.

For unit operation blocks, the number- and weight-average properties of the distribution may be verified against the local polymer results, displayed on the Polymer Results sheet for each reactor.

For streams, the number- and weight-average properties of the distribution may be verified against the polymer component attributes shown in the stream table.

Requesting Distribution Calculations In order to track distributions in your simulation, you must select the distribution characteristics. After the simulation is complete you must retrieve the distribution data for plotting. You can display and plot the distribution data for the polymerization reactor, or you can display a distribution table for a stream or for the entire flowsheet.

Selecting Distribution Characteristics To access the polymer distribution specifications:




3 From the Polymers folder, click Distributions.

The Selection sheet appears.

To request tracking of distributions, from the Selection sheet:

1 In the Polymer ID field, select the polymer for which you would like distributions tracked.

2 In the Distribution type frame, select the type of distribution.

3 Select the distribution plot characteristics: number of points for plot resolution, maximum for x-axis.

4 For a GPC distribution, select Perform GPC Distribution Calculations. The distribution is calculated as rW(r) vs. r where r is number-average degree of polymerization.

Displaying Distribution Data for a Reactor Once simulation calculations are complete, you can display and plot the distribution data for the polymerization reactor (RCSTR, RPLUG, or RBATCH) .

To display the distribution data for a polymerization reactor:

1 From the Process Flowsheet window, use the right mouse button to click the reactor.

2 Click Results.

3 From the reactor Results form, click the Distributions tab.

4 On the Distributions sheet, select the distribution to view.

To plot the distribution data:

1 From the Plot menu, select Plot Wizard.

2 Click Next. 3 Click a distribution plot sample, then click Next.

4 Change the plot settings as needed, then click Next or Finish to display the plot.

5 Click the plot graphics to change the plot configuration: reconfigure axes, legends, or change titles. If you requested the GPC distribution format, you must set the x-axis to a log scale for the plot to display properly.

Displaying Distribution Data for Streams To display a distribution data table for a stream:

1 From the Process Flowsheet window, use the right mouse button to click the feed stream.

2 Click Results.

3 From the Results form, click the Poly. Curves tab.

4 On the Poly. Curves sheet, select the distribution to view.

To display a distribution data table for the flowsheet:

1 From the Data Browser, click Results Summary.

2 From the Results Summary folder, click Streams.

3 From the Streams form, click the Poly. Curves tab.


4 On the Poly. Curves sheet, select the distribution to view.

To plot the distribution data:

1 From the Plot menu, select Plot Wizard.

2 Click Next. 3 Click a distribution plot sample, then click Next.

4 Change the plot settings as needed, then click Next or Finish to display the plot.

5 Click the plot graphics to change the plot configuration: reconfigure axes, legends, or change titles.

References Biesenberger, J. A., & Sebastian, D. H. (1983). Principles of Polymerization Engineering. New York: Wiley-Interscience.

Billmeyer, F. W. (1971). Textbook of Polymer Science. New York: Wiley-Interscience.

Flory, P. J. (1936). Molecular Size Distribution in Linear Condensation Polymers. J. Am. Chem. Soc., 58, 1877.

Flory, P. J. (1953). Principles of Polymer Chemistry. Ithaca, NY: Cornell University Press.

Hamielec, A. E. (1992). Polymerization Processes. In B. Elvers, S. Hawkins, & G. Schulz (Eds.), Ullmann’s Encyclopedia of Industrial Chemistry (5th Ed.) A21, (pp. 324-330). New York: VCH.

Lansing, W. D., & Kramer, E.O. (1935). Molecular Weight Analysis of Mixtures by Sedimentation Equilibrium in the Svedberg Ultracentrifuge. J. Am. Chem. Soc., 57, 1369.

Peebles, L. H., Jr. (1971). Molecular Weight Distribution in Polymers. New York: Wiley-Interscience.

Rodriguez, F. (1989). Principles of Polymer Systems. New York: Hemisphere Publishing.

Schulz, G. V. (1935). Uber die Beziehung zwischen Reaktionsgeschwindigkeit und Zusammensetzung des Reaktionsproduktes bei Makropolymerisationsvorgängen., Z. Physik. Chem., B30, 379.

Schulz, G. V. (1939). Uber die Kinetik der kettenpolymerisationen. V. Der Einfluss verschiedener Reaktionsarten auf die Polymolekularität. Z. Physik. Chem., B43, 25.

Stockmayer, W. H. (1945). J. Chem. Phys., 13, 199.

Tompa, H. (1976). The Calculation of Mole-Weight Distributions from Kinetic Schemes. In C.H. Bamford & C.F.H. Tipper (Eds.), Comprehensive Chemical Kinetics, 14A. New York: American Elsevier.

Tung, L. H. (1956). Fractionation of Polyethylene. J. Polymer Sci., 20, 495.

Weibull, W. (1951). A Statistical Distribution Function of Wide Applicability. J. Appl. Mech., 18, 293.


Wesslau, H. (1956). Die Molekulargewichtsverteilung einiger Niederdruckpolyäthelene. Makromol. Chem., 20, 111.

Zimm, B. H. (1948). Apparatus and Methods for Measurement and Interpretation of the Angular Variation of Light Scattering; Preliminary Results on Polystyrene Solutions. J. Chem. Phys., 16, 1099.

70 6 End-Use Properties

6 End-Use Properties

This section describes polymer end-use properties. First, an overview of the properties of interest for polymers is given, followed by methods available in Aspen Polymers (formerly known as Aspen Polymers Plus) for calculating these properties.


• Polymer Properties, 70

• Prop-Set Properties, 71

• End-Use Properties, 72

• Method for Calculating End-Use Properties, 73

• Calculating End-Use Properties, 76

Polymer Properties Polymer properties fall into many categories:

• Structural properties

• Thermophysical properties - which provide an indication of the thermodynamic behavior of polymers

• Thermochemical properties - which provide information on thermal stability

• Transport properties

• Processing and end-use properties - which provide information about processability and performance during end-use

Polymer structural properties do not provide a direct measure of the performance of the polymer product during processing or during its end use.

However, there is a relationship between polymer structural properties and the end use properties. For this reason, it is important to account for such properties within polymer process simulation models.

6 End-Use Properties 71

Prop-Set Properties A property set is a collection of thermodynamic, transport, and other properties that you can use in:

• Stream reports

• Physical property tables and Analysis

• Unit operation model heating/cooling curve reports

• Distillation column stage property reports and performance specifications

• Reactor profiles

• Design specifications and constraints

• Calculator and sensitivity blocks

• Optimization and Data-Fit blocks

Aspen Plus has several built-in property sets that are sufficient for many applications. The list of built-in property sets is determined by the Template you choose when creating a new run.

You can use a built-in property set and modify it to fit your needs, or you can create your own property sets. To see the built-in sets available or to select one, use the drop-down list on any property set list box. The list prompts describe the contents of each built-in property set.

For information on defining a property set, see the Aspen Plus User Guide.

The following table summarizes key property sets for the major thermophysical and transport properties of interest in polymer process simulations:

Valid Qualifiers Property Set Name Description Phase Comps. Temp. Pres.

CP Pure component heat capacity X X X X

CPMX Mixture heat capacity X X X

K Pure component thermal conductivity

X X X X

KMX Mixture thermal conductivity X X X

KINVISC Mixture kinematic viscosity X X X

MU Pure component viscosity (zero shear)

X X X X

MUMX Mixture viscosity (at zero shear) X X X

RHO Pure component density X X X X

RHOMX Mixture density X X X

TG Component glass transition temp. X X

TM Component melt transition temp. X X

TRUEFLOW

Component true mole flow rate X X

TRUEFRAC

Component true mole fraction X X

TRUEMW Component true molecular weight X


End-Use Properties The end-use or processing properties of interest for polymers include properties that describe their performance in the last stage of the polymer manufacturing process. Also of interest are properties relating to their performance when they reach the consumer.

The following table summarizes some end-use properties:

Category Property Availability in Aspen Polymers

Processing Melt index

Melt index ratio (I10/I2)

Moldability index

Zero-shear viscosity

Density of copolymer

Yes

No

No

Yes

Yes

Polymer product

Deformation

Toughness/hardness

Flammability

No

No

No

Relationship to Molecular Structure The end-use properties such as rheological and mechanical properties are functions of the polymer structural properties and processing history. For example, long chain branching raises low shear viscosity, increases shear thinning, delays melt fracture, and increases extrudate swell.

For example, one could relate end-use properties of polyethylene to density, molecular weight, or melt index (Foster, 1993). See the following table:

Properties Molecular Weight ↑

Melt Index ↑

Density ↑

Molecular weight ↑ ↓ ---

Melt Index ↓ ↑ ---

Impact strength ↑ ↓ ↓

Stress crack resistance ↑ ↓ ↓

Elongation ↑ ↓ ---

Tensile strength ↑ ↓ ↑

Melt strength ↑ ↓ ---

Orientation ↑ ↓ ---

Elasticity ↑ ↓ ---

Parision sag resistance ↑ ↓ ---

Distortion resistance ↓ ↑ ---

Weatherability ↔ ↔ ↔

Stiffness --- --- ↑

Heat Resistance --- --- ↑

Hardness --- --- ↑


Properties Molecular Weight ↑

Melt Index ↑

Density ↑

Permeation resistance --- -- ↑

Shrinkage --- --- ↑

Creep resistance --- --- ↑

Transparency --- --- ↓

Flexibility --- --- ↓

The basic structure-property relationship has attracted much research activity as the relationship is critical for product performance control. We recommended you follow the recent developments in structure-property relationship (Bicerano, 1996; Foster, 1993).

Method for Calculating End-Use Properties Few end-use properties of interest for polymers are currently available in Aspen Polymers. However, the method used for implementing the ones available is a good mechanism for users to incorporate additional ones if they have the necessary correlations to molecular structure and/or thermophysical properties.

Within Aspen Polymers, end-use properties are available as property sets (Prop-Set). A Prop-Set provides a method for calculating properties for components within process flowstreams or vessel contents.

A number of built-in Prop-Sets are available (See your Aspen Plus User Guide documentation). In addition, Prop-Sets allow the specification of a property set with add-on user correlations. When doing this, a Fortran subroutine is required to perform the calculations.

End-use polymer properties are available as user property sets. This is because the correlations available to calculate these properties are highly empirical and are often dependent on the type of polymer for which they are used.

User property sets can easily be modified. Users can directly change the property correlation in the associated Fortran subroutine.

User Property Sets

The following table summarizes the Prop-Set name and Fortran subroutine name for the built-in user property sets:

Property Prop-Set Name Fortran Subroutine

Melt index MI-KAR, MI-SIN USRPRP

Intrinsic viscosity IV USRPRP

Zero-shear viscosity ZVIS USRPRP

Density of copolymer DENS USRPRP


Intrinsic Viscosity The intrinsic viscosity is given as:

η = +K M JMw w

Where:

η = Intrinsic viscosity

Mw = Weight-average molecular weight

J and K = Correlation constants

Zero-Shear Viscosity For some ethyl branched paraffinic monodisperse polymers, Arnett and Thomas reported an empirical correlation for zero-shear viscosity as a function of molecular weight, number of branched sites per 1000 carbon atoms, and temperature (Arnett & Thomas, 1980):

( )ln ln ( )η0

31= +

++a M

d cnT

e B nwbn

Where:

η0 = Zero shear viscosity in Poise

Mw = Molecular weight

n = Number of branched sites per 1000 carbon atoms

a = 3.41

d = 3523

c = 0.832

b = 2.368

B(n) = Function of number of branches with:

B(0) = -35.78

B(0.02) = -37.04

B(0.069) = -38.11

B(0.13) = -40.88

B(0.183) = -43.54


Density of Copolymer Randall and Ruff presented an empirical correlation for semicrystalline copolymer density (Randall & Ruff, 1988):

( )ρ ρρ ρ

γ γ−−

= + −=∑a

c a

i

i

n

a b i12

1

Where:

ρ = Actual density

ρc = Crystalline density

ρa = Amorphous density

a and b = Correlation constants

n = Minimum crystallization run length of monomer

γ = Reaction probability that monomer is followed by similar monomer

Melt Index Karol and colleagues suggested a Quackenbos equation for high density polyethylene prepared with chromocene-based catalysts (Karol et al., 1973; Quackenbos, 1969):

( )MI a bM cMw nd

= +

Where:

MI = Melt index

a = 10 1018. ×

b = 0.2

c = 0.8

d = -3.9

Mw = Weight-average molecular weight

Mn = Number-average molecular weight

Sinclair suggested a simpler correlation (Sinclair, 1983):

MIa

Mw

b

=⎛⎝⎜

⎞⎠⎟

1

Where:

a = 111,525

b = 0.288


Melt Index Ratio The Quackenbos equation can also be used to correlate melt index ratio.

Calculating End-Use Properties End-use properties are calculated as Prop-Sets. You must first select which end-use property to include in the simulation, then you must define this property as a Prop-Set.

Selecting an End-Use Property To access end-use property Prop-Sets:

1 From the Data Browser, click Properties.

2 From the Properties folder, click Advanced.

3 From the Advanced folder, click User Properties.

4 From the User Properties object manager, click New.

5 If necessary, change the default ID for the user-property and click OK.

6 From the User Properties Specifications sheet, choose the standard property as the type (default), then provide the subroutine name.

Create one User-Property for each end-use property.

Adding an End-Use Property Prop-Set To access Prop-Sets:

1 From the Data Browser, click Properties.

2 From the Properties folder, click Prop-Sets.

3 From the Prop-Sets object manager, click New.

4 If necessary, change the default ID for the Prop-set and click OK.

5 From the Prop-Set Properties sheet, in the Physical Properties field, select the ID for the end-use property User-Property.

You can have as many User-Properties as needed.

References Arnett, R. L. & Thomas, C. P. (1980). Zero-Shear Viscosity of Some Ethyl Branched Paraffinic Model Polymers. J. Phys. Chem., 84, 649-652.

Aspen Plus User Guide. Cambridge, MA: Aspen Technology, Inc.

Bicerano, J. (1996). Prediction of Polymer Properties. New York: Marcel Dekker.

Foster, G.N. (1993). Short Course: Polymer Reaction Engineering. Ontario, Canada: McMaster Institute for Polymer Production Technology.



Hamielec, A. E. (1996), Polymer Reactor Modeling Technology (Course Notes). Cambridge, MA: Aspen Technology, Inc.

Karol, F. J., Brown, G. L., & Davison, J. M. (1973) Chromocene-Based Catalysts for Ethylene Polymerization: Kinetic Parameters. J. of Polymer Science: Polymer Chemistry Edition, 11, 413-424.

Quackenbos, H. M. (1969). Practical Use of Intrinsic Viscosity for Polyethylenes. J. of Applied Polymer Science, 13, 341-351.

Randall, J. C. & Ruff, C. J. (1988). A New Look at the 'Run Number' Concept in Copolymer Characterization. Macromolecules, 21, 3446-3454.

Rudin, A. (1982). The Elements of Polymer Science and Engineering. New York: Academic Press Inc., Harcourt Brace Jovanovich.

Sinclair, K. B. (1983). Characteristics of Linear LPPE and Description of UCC Gas Phase Process, Process Economics Report. Menlo Park, CA: SRI International.

78 7 Polymerization Reactions

7 Polymerization Reactions

This chapter discusses polymerization mechanisms and kinetics. Topics discussed in the introductory section include:

• Polymerization Reaction Categories, 78

• Polymerization Process Types, 81

• Aspen Polymers Reaction Models, 82

Following an introduction that provides background information of the subject, a separate section is devoted to each of the polymerization kinetic models available in Aspen Polymers (formerly known as Aspen Polymers Plus).

• Step-Growth Polymerization Model, 85

• Free-Radical Bulk Polymerization Model,

• Emulsion Polymerization Model,

• Ziegler-Natta Polymerization Model,

• Ionic Polymerization Model,

• Segment-Based Reaction Model,

Polymerization Reaction Categories Over the years, many classifications have been developed for polymerization reactions. One classification divides them into condensation and addition polymerization.

Condensation Polymerization

Condensation polymerization results in the elimination of a smaller molecule, water for example, through the reaction of bi- or polyfunctional monomers.

Addition Polymerization

Addition polymerization, on the other hand, does not produce small molecule byproducts. The repeating units within the polymer have the same structure as the monomers from which they originated.

7 Polymerization Reactions 79

The problem with this classification is that while it describes differences in the molecular structure of the resulting polymer, it does not fully capture the differences in the reaction mechanism. Furthermore, a given polymer can be made by more then one pathway, one which would result in an addition polymer, and one which would result in a condensation polymer, by this classification.

For example, Nylon-6 can be made through a caprolactam, and therefore be labeled an addition polymer, or through an ∈-aminohexanoic acid, and in this case be labeled a condensation polymer.

Step Growth and Chain Growth Polymerization

A classification that is more useful for capturing the difference in the mechanisms through which polymers are produced divides polymerization reactions into step-growth and chain-growth polymerization. The differences between step-growth and chain-growth polymerization are summarized in the following tables:

Step Growth Polymerization

Chain Growth Polymerization

Monomer type Bi-, polyfunctional No functionality

Reaction categories

Single intermolecular reaction

Several consecutive reactions for initiation, growth, and termination

Reacting species Any combination of monomers, oligomers, polymer chains

Monomers and active centers (free-radical, ion, polymer, catalyst end)

Elimination product

Small molecule elimination product for condensation polymerization only

None

Polymer growth rate

Slow, chain lifetime of the order of hours

Rapid, chain lifetime of the order of seconds

Polymer size High molecular weight at high conversion

High molecular weight at all conversion levels

Reaction Type

Active Center Initiation Growth Reaction

Step Growth

Condensation

Bi-, polyfunctional end groups

None Nucleophilic substitution

Pseudo condensation


None Nucleophilic addition

Ring Scission


Yes for ring opening

Nucleophilic addition or substitution

Chain Growth

Free-radical Free radical Chemical, thermal, radiative

Monomers add on to radical

Coordinatio Metal complex Catalyst Monomers insert into metal


n activation complex carbon bond

Ionic Anion or cation Dissociation Monomers add on at ion pair

Step-Growth Polymerization Step-growth polymerization retains the definition given for condensation polymers for the majority of cases. That is, monomers react with each other to eliminate small molecules. Step-growth polymers are formed through the same reaction type occurring between functional groups located on any combination of monomers, oligomers, or polymer chains. The polymer chains continue to grow from both ends as polymerization progresses. The reactions occur at a relatively slow rate and chains grow slowly.

Some examples of step-growth polymers include polyamides, polyesters, polycarbonates, and polyurethanes (See Polymer Structure in Chapter 2 for a discussion of polymer types based on molecular structure).

Step Growth Polymer Categories

Step-growth polymerization can be sub-categorized as condensation, pseudocondensation, and ring-opening or ring-scission depending on the chemical pathways through which the reactions occur. The following table lists typical commercial step-growth polymers:

Polymer (Trade Name)

Monomers Repeat Unit Reaction Type

Applications (Similar Polymers)

Polyamide

(Nylon 6,6)

Adipic acid Hexamethylene diamine

N H ( C H 2 ) 6 N H C ( C H 2 ) 4 C

O O

Dicarboxylic acid + diamines

Fiber, plastics (Lycra, Nylon 6)

Polyester (PET)

Terephthalic acid Ethylene glycol

C O

C O C H 2 C H 2 O O

Dicarboxylic onhydride + glycols

Fiber (PBT, Dacron, Nylon)

Polycarbonate (Lexan)

Bisphenol-A Phosgene

O C

C H 3

C H 3 O C

O

Dihydroxy reactant + Phosgene

Lenses, packaging (Merlon)

Polyurethane Toluene diisoyamate polyether diol

R N H C O O R 1

Diisocyanate + dialcohol

Foam, packaging

Chain-Growth Polymerization Chain growth polymers are formed through the addition of monomers to an active center (free-radical, ion, or polymer-catalyst bond), in a “chain” reaction, at a very fast rate. Furthermore, several different types of reaction occur to initiate, propagate, and terminate polymer growth. Examples of


chain growth polymers include various polyolefins, polyvinyls, and several copolymers (styrenic copolymers, for example).

Chain Growth Polymer Categories

Chain-growth polymerization can be categorized as free-radical, coordination complex, or ionic, depending on the type and method of formation of the active center. The following table lists typical commercial chain-growth polymers:

Polymer Monomers Repeat Unit Reaction Types Applications

Polyethylene Ethylene CH2 CH2

Bulk/solution (free-radical)

Coordination complex (Ziegler-Natta)

Film, packaging

Polystyrene Styrene CH2 CH

Bulk/solution/ suspension (free-radical)

Containers, packaging, insulation

Polypropylene Propylene CH2CH

CH3

Coordination complex (Ziegler-Natta)

Films, packaging, autoparts, sealants

Polyisobutylene Isobutylene CH2C

CH3

CH3

Ionic Films, plastic tubing

Polyvinyl chloride Vinyl chloride CH2 CH

Cl

Bulk/solution/ suspension (free-radical)

Floor coverings, pipes

Polymethalmethacrylate

Methyl Methacrylate

CH2 C

COOCH3

CH3

Bulk/solution (free-radical)

Lenses, plastics

Styrene butadiene rubber

Styrene Butadiene CH2 CH CH2 CH CH CH2

Emulsion (free-radical) Tires, belting, shoe soles

Polymerization Process Types Step Growth Reaction Sub-classes

In addition to chemical pathways, the environment or process conditions in which the polymerization reactions occur introduce more sub-classes of polymers. For example, step-growth reactions may take place as melt phase, solid-state, solution, or interfacial polymerization:

• Melt-phase processes are carried out above the melting point of the polymer

• Solid-state processes are carried out below the melting point of the polymer


• Solution processes are carried out in the presence of an inert solvent

• Interfacial processes are carried out in the interface between an organic phase and an aqueous phase

Chain Growth Reaction Sub-classes

Chain-growth polymerization may take place in bulk phase, solution, precipitation, suspension, or emulsion:

• Bulk polymerization is carried out in the bulk monomer phase without a solvent

• Solution polymerization is carried out in the presence of an inert solvent in which monomers and polymer are dissolved

• Precipitation polymerization is carried out using a solvent to precipitate out the polymer

• Suspension polymerization involves monomers suspended as droplets in a continuous phase (usually water) to which an oil-soluble initiator is added

• Emulsion polymerization involves monomers and micelles dispersed in a continuous water phase using surfactants. Initiator is added to the emulsion of partially water soluble monomers in the surfactant solution

There are additional process related classifications that have to do with reactor geometry. These are discussed in sections covering unit operation modeling later in this User Guide.

Aspen Polymers Reaction Models There are two types of reaction models available in Aspen Polymers:

• Built-in models

• User models

Built-in Models The polymerization reaction models available in Aspen Polymers are summarized in the following table:

Model Name Chemistry Processes Polymers

Step-growth

STEP-GROWTH Step-growth condensation Melt phase, solution, interfacial

PC, PBT, PET, Nylons

SEGMENT-BAS Step-growth addition Melt phase, solution, interfacial

Polyurethanes, polyimides, PPO, engineering plastics

Chain-growth

FREE-RAD Free-radical Bulk, solution

PS, PVAC, SAN, PMMA


Model Name Chemistry Processes Polymers

EMULSION Free-radical Emulsion SBR, SBA

ZIEGLER-NAT Ziegler-Natta / metallocene coordination complex

Bulk, solution

HDPE, PP, LLDPE

IONIC Anionic/Cationic group transfer

Solution PIB, SBR, PEO

Generic

SEGMENT-BAS Segment-based power-law reaction model

N/A PVA from PVAC

In addition to models for the chemistries and process types listed, there is one model available for generic polymer modification reactions. This model follows a standard power-law scheme and is used to represent reactions involving modifications to segments of polymers made through one of the conventional reaction schemes. One of the standard Aspen Plus reaction models can also be used in conjunction with the polymerization reaction models. The standard Aspen Plus reaction models are:

Model Name Description

LHHW Langmuir-Hinshelwood-Hougen-Watson reaction rate expressions

POWERLAW Power-law reaction rate expressions

USER Kinetic rate expressions supplied by user, kinetic rate computed in user supplied subroutine

For more information about these models, consult the Aspen Plus User Guide and Aspen Plus User Models.

User Models There are cases where the built-in models do not provide the features necessary to model specific polymerization kinetics. Some of the polymerization reaction models provide capabilities to incorporate user reactions. In addition, the USER reaction model provides the capabilities for defining user kinetic schemes.

The USER reaction model is structured to allow the specification of the reaction stoichiometry. In addition, there are vectors for entering user real and integer parameters. This input information along with the reaction vessel contents, in the form of the stream structure, is made available to a user supplied Fortran subroutine during calculations.

Note that component attributes are part of the stream structure. There is an update and initialization scheme to automatically process these attributes. The user supplied Fortran subroutine can return rates for components and component attributes.

From the subroutine, Aspen Plus utilities including physical property routines, math utilities, and stream handling utilities can be accessed. Some of these utilities are documented in Appendix C.


References Aspen Plus User Models. Cambridge, MA: Aspen Technology, Inc.


Dotson, N. A, Galván, R., Laurence, R. L., & Tirrell, M. (1996). Polymerization Process Modeling. New York: VCH Publishers.


Hamielec, A. E. (1992). Polymerization Processes. In B. Elvers, S. Hawkins, & G. Schulz (Eds.), Ullmann’s Encyclopedia of Industrial Chemistry (5th Ed.) A21, (pp. 324-330). New York: VCH.

Odian, G. (1991). Principles of Polymerization, 3rd Ed. New York: John Wiley & Sons.

Rudin, A. P. (1982). The Elements of Polymer Science and Engineering. Orlando, FL: Academic Press.

Sun, S. F. (1994). Physical Chemistry of Macromolecules. New York: John Wiley & Sons.

8 Step-Growth Polymerization Model 85

8 Step-Growth Polymerization Model

This section covers the step-growth polymerization model available in Aspen Polymers (formerly known as Aspen Polymers Plus). It begins with general background information on step-growth polymerization and covers some of the terms associated with these kinetics. Several industrial polymerization processes are examined in detail. A discussion of the model features and usage is also included.


• Summary of Applications, 85

• Step-Growth Processes, 86

• Reaction Kinetic Scheme, 97

• Model Features and Assumptions, 120

• Model Structure, 123

• Specifying Step-Growth Polymerization Kinetics, 152

The Aspen Polymers Examples & Applications Case Book illustrates how to use the step-growth model to simulate nylon-6 polymerization from caprolactam.

More detailed examples are available in Step-Growth Polymerization Process Modeling and Product Design by Kevin Seavey and Y. A. Liu, ISBN: 978-0-470-23823-3, Wiley, 2008.

Summary of Applications Step-growth polymerization can be used to model various polycondensation and specialty plastic processes. Some of the applicable polymers are described below:

• Aliphatic polycarbonates - Transesterification of diols with lower dialkyl carbonates, dioxolanones, or diphenyl carbonate in the presence of catalysts such as alkali metal, tin, and titanium compounds.

• Aromatic polycarbonates - Reaction product of bisphenols with carbonic acid derivatives. May be prepared by transesterification, solution polymerization, and, most often by interfacial polymerization.

86 8 Step-Growth Polymerization Model

• Polyesters - Produced commercially in two steps: monomer formation by ester interchange of diesters with diols or esterification of diacids with diols, followed by polycondensation by removing excess diols to promote chain extension. This is accomplished commercially on a simple two-vessel batch process or on large-scale multi-vessel continuous-polymerization process.

• Polyamides - Produced via direct amidation, reaction of acid chlorides with amines, ring-opening polymerization, reaction of diacids and diisocyanates, etc. Commercially prepared by melt polycondensation, ring-opening polymerization, and low temperature solution polymerization.

• Polyurethanes - Polyurethane isocyanates are usually produced commercially by the phosgenation of amines. Polyester polyols are prepared by step-growth polymerization.

Step-Growth Processes Several commodity polymers, including polyesters, nylons, and polycarbonate, are manufactured through step-growth polymerization processes. This section examines some of the major processes that can be represented using the step-growth polymerization kinetics model.

Polyesters

Continuous Polyethylene-Terephthalate Processes Polyethylene-terephthalate (PET) is produced by the step-growth polymerization of ethylene glycol, a diol, and either terephthalic acid, a diacid, or dimethyl terephthalate, a diester. Most processes are continuous although many older process lines operate in batch or semi-batch mode.

Direct Esterification

The direct esterification process involves the reaction of ethylene glycol with terephthalic acid. The terephthalic acid is mixed with excess ethylene glycol to form a solid-liquid paste. In the continuous process, the monomer paste is typically fed to a well-mixed reactor, the primary esterifier, which operates at temperatures of 250-290 °C and pressures ranging from one to several atmospheres. Typical residence times range from one to four hours in this stage of the process.

A solid at room temperature, terephthalic acid has limited solubility in the polymer solution, even at the relatively high process temperatures. Further, the dissolution rate of TPA may be limited by the solid-liquid mass transfer rate, especially if the average particle size is large, or when the reactor operates at high temperatures and pressures.

The following figure illustrates a continuous direct esterification process for PET:


Secondary Esterification

In most continuous plants, the primary esterifier is followed by secondary and, occasionally, a tertiary esterifier. These reactors range from single-tank CSTRs to a variety of multiple-stage CSTRs composed of vertical or horizontal vessels divided into two or more chambers by partitions. Secondary esterification reactors typically have residence times on the order of an hour, with temperatures similar to or slightly higher than the primary esterifier. The secondary esterification reactor is often run under atmospheric conditions, although slight positive pressure or vacuum pressures are also used in some processes.

Vapor from the esterification reactors flows to one or more distillation columns which separate ethylene glycol from the reaction by-products which include water and acetaldehyde. In some processes, spray-condenser loops are used to “wash” entrained TPA and vaporized low-molecular weight oligomers from the vapor stream to prevent oligomer build-up in the distillation columns.

Glycol Recovery

The ethylene glycol from the esterification distillation columns can be recycled directly to the esterification reactors, to the paste mixing tank, or, in the case of high-quality products, it can be collected for further processing to remove contaminants. The companies which license PET technology use a wide variety of glycol recovery and recycling schemes. All of these recycling schemes can be simulated using conventional distillation, flash, and heat exchanger models available in Aspen Plus.


Esterification Results

The product of the esterification reactors is composed of short-chain oligomers with some residual monomers. The main oligomer in the product is bis-hydroxyethyl-terephthalate (BHET), which is slightly volatile under typical operating conditions. The step-growth model includes an “oligomer” feature which can be used to account for evaporative loss of linear oligomers such as BHET.

Transesterification Process

In the transesterification process, dimethyl terephthalate (DMT) is used instead of terephthalic acid (TPA). One advantage of this process is the relatively high solubility of DMT, which eliminates the solid-liquid mass transfer problem in the first stage of the process. A second advantage is the low acidity of DMT, which reduces several of the side reaction rates and results in a higher quality polymer. The limitations of the transesterification process include increased monomer cost, production of methanol as a by-product (instead of water), and reduced reactivity in the finishing stages.

The transesterification process produces methanol as a reaction by-product. The methanol is distilled from ethylene glycol through distillation columns. Recovered glycol may be recycled to the reactor, the paste mixing tank, or accumulated for additional processing.

It is desirable to minimize the concentration of methylester ends in the feed to the polymerization section. Obtaining high conversions is very important in the DMT process because the reverse reaction of methanol with PET is more highly favored than the reaction of water and PET. A wide variety of proprietary reactors are used to effect high end-group conversion during the transesterification process.

Continuous Polymerization

The continuous polymerization process is the same for the direct esterification and transesterification processes. Typically, the polymerization section consists of one or more CSTR reactors (pre-polymerization reactors) followed by one or more horizontal “finishing reactors” (polymerization reactors). These reactors consist of a series of rotating blades or disks which lift polymer from a pool at the bottom of the reactor into a vapor space over the pool. The design criteria of these reactors are to maximize surface area generation while minimizing back-mixing. In polyester processes, the finishing reactors are almost always limited by the liquid-vapor mass transfer rates. In some cases, the pre-polymerization reactors are also limited by mass transfer.

The reactors in the polymerization section operate at increasingly higher temperatures and lower pressures to enhance the devolatilization of excess glycol and reaction byproducts such as water, methanol, and acetaldehyde. Reactor residence times range from thirty minutes to four hours depending on the number and type of reactors in the polymerization section.

Vapor from the polymerization section is scrubbed by spray-condenser loops composed of a contacting vessel, accumulation tank, pump, and heat exchanger. In most plants, vacuum is generated through venturi jets operated by steam or vaporized glycol. In some process configurations, the


condensed glycol and water mixture is recycled to the esterification columns. Otherwise, the condensate is accumulated and processed to recover glycol.

Operating Conditions

The esterification and transesterification sections of PET processes frequently operate below the melting point of the polymer. Under these operating conditions, the process can be considered solution polymerization. The polymerization reactors operate above the melting point of the polymer in a true melt-phase polymerization. The step-growth reaction model may be used for both modes of operation. In most cases, the same reaction kinetics apply to both solution- and melt-phase reaction processes.

Final Products

The continuous melt-phase PET processes generally produce polymer with an average intrinsic viscosity of approximately 0.6 dl/g, which corresponds to a number-average degree of polymerization near 100 units. This product may be directly spun as clothing fiber, partially oriented yarn (POY), film, or it may be cooled and chipped for on- or off-site use.

Recent increases in consumer recycling programs and consumer preference for unbreakable bottles has created a very large market for polyester bottles. These bottles are molded from a higher molecular weight polyester chip which is produced by a solid state process. Fundamentally, the step-growth model can apply to solid-state polymerization. However, at this time, Aspen Polymers does not include a solid-state polymerization (SSP) reactor model. Semi-rigorous SSP models can be developed using a series of CSTR reactors. Solid phase polymer solutions can be treated as a liquid phase in Aspen Polymers. The property system switches between liquid-phase property models and solid-phase property models when the temperature drops below the melting point of the polymer component.

Batch Polyethylene-Terephthalate Processes Polyethylene Terephthalate is also produced in batch and semi-batch processes, as shown in the following figure. Usually, the process consists of two batch reactors in series. The role of the first reactor is to reach high conversions of the terephthalate monomer while minimizing undesirable side reactions. The role of the second reactor is to raise the molecular weight of the polymer to appropriate levels.


The first reactor is coupled to a column which separates the volatile reaction by-products from excess ethylene glycol and evaporated oligomers. The heavy components are continuously returned to the reactor during most of the batch cycle. Towards the end of the cycle, the evaporated ethylene glycol and residual monomers are removed and accumulated for re-use in the next batch.

The batch esterification process commonly uses a semi-continuous feeding system for the solid TPA. In most batch esterification processes, the reaction rate is limited by the rate of dissolution of TPA. This is complicated by the relationship between the mass transfer rates and particle size.

To enhance TPA solubility, a portion of the polymer product is retained in the reactor at the end of the cycle. The recycled product is used to start the next batch. This design allows the cycle to start at a higher temperature, reducing the cycle time for each batch. The trade off between the batch cycle time and the quantity of recycle polymer is one of the most interesting problems to examine using simulation technology.

The batch transesterification process is typically operated in true-batch mode, without recycling polymer. In this process, the monomers, ethylene glycol and DMT, are charged to the reactor at the beginning of the cycle. The continuous removal of methanol from the batch reactor makes very high end-group concentrations possible.

This version of Aspen Plus does not include an appropriate reactor model to simulate batch polymerization reactors with overhead distillation columns. AspenTech’s Polyester Technology Package includes several modeling solutions for representing these types of batch processes in the Aspen Plus and Aspen Custom Modeler environments.


Second Batch Stage

The liquid product from the batch esterification or transesterification is charged to a second batch stage. In this stage, the reactor is evacuated as the temperature is increased. These operating profiles enhance the removal of excess ethylene glycol from the reaction mixture, allowing these highly reversible reactions to proceed.

As the polymer viscosity increases, the reactions become limited by the rate of mass transfer from the liquid phase to the vapor phase due to decreased surface renewal rates and reduced agitator speeds.

Other Polyester Processes Polybutylene-terephthalate (PBT) is an engineering plastic frequently used for machine parts, car body panels, and other applications. Polybutylene terephthalate is analogous to PET, except butylene glycol is used in place of ethylene glycol. Most PBT is manufactured from DMT through continuous transesterification processes, although batch processes and direct esterification processes are also found in industry.

In the PBT process, tetrahydrofurane, THF, is formed from butylene glycol end groups as an undesirable reaction by-product. The transesterification process is favored over direct esterification because the acid end groups in TPA catalyze the formation of THF.

Polypropylene-terephthalate (PPT) is used for carpet fiber and other applications. Like PET and PBT, PPT can be manufactured from terephthalic acid or dimethyl terephthalate. In the PPT process, propylene glycol is used as the diol monomer.

Polyethylene-naphthalate (PEN) manufacturing processes are under development by several polyester producers. This new product has a higher melting point than PET, and is aimed at specific demands, such as hot-fill bottles, which are not well satisfied by other polyesters. The dimethyl ester naphthalate monomer is much more expensive than TPA or DMT, so PEN is frequently produced as a copolymer with PET.

At this time, most PEN is produced in batch processes which are analogous to the batch PET process. Copolymers of PEN and PET are being used for some bottling applications already. The similarities in the chemical mechanism for PET and PEN make them relatively easy to copolymerize in various ratios, resulting in several product grades with properties intermediate between pure PET and pure PEN.

Polyester Technology Package Aspen Technology offers several solutions for polyester processes. The AspenTech Polyester Technology Package provides steady-state simulation of melt-phase continuous processes and also includes process models for batch polyester processes. The Polyester Technology Package is designed for PET and PBT, but can be easily modified for analogous polyesters such as PEN, PTT, etc.


Aspen PolyQuestSM, jointly developed with Hosokawa Bepex corporation, is a simulation package covering all varieties of solid-state PET processes. Aspen PolyQuest includes detailed and rigorous models for reaction kinetics, diffusion, heat transfer, and crystallization, as well as a library of detailed unit operation models for solid-state processing equipment. Aspen PolyQuest runs on the Aspen Custom Modeler platform. The underlying equation-based models can be used for dynamic or steady-state process simulation.

The models in these packages account for all the major side reactions in the process, such as thermal scission, aldehyde formation, DEG formation, and cyclic trimer formation. The reaction kinetic models consider the influence of several common catalysts and additives as well as acid catalysis and uncatalyzed side reactions. The package includes reactor models which consider solid-liquid mass transfer for the direct esterification process, and liquid-vapor mass transfer limited kinetics for the polymerization reactors.

The Polyester Technology Package includes models of several common process configurations, including both batch and continuous processes. The models predict various quality parameters such as the acid end group concentration (acid value), intrinsic viscosity, vinyl end content, DEG content, conversion, etc.

Contact your Aspen Technology sales representative for more information about the Polyester Technology Package, Aspen PolyQuest, and advanced consulting services.

Nylon-6 Nylon-6 is produced by ring-opening polymerization of ε-caprolactam. Water and caprolactam are fed to a primary reactor where the ring-opening reaction takes place. The primary reactor may be a single (liquid) phase tubular reactor, CSTR, or one of a variety of proprietary reactors.

The following figure illustrates a continuous melt-phase nylon-6 process:


VK Column

One of the most well known of these proprietary designs is the Vereinfacht Kontinuierliches (or VK) column. The VK column is a reactor with a high aspect ratio which is filled to relatively high liquid levels. The reacting mixture boils vigorously near the top of the VK column, resulting in considerable radial and axial mixing. Below this well-mixed zone is a plug-flow zone in which the hydrostatic pressure is sufficient to suppress boiling. Reactors of this type can be simulated using one or more two-phase CSTR reactors (model RCSTR) in series with a single liquid-phase plug flow reactor (model RPlug).

The top of the VK column typically operates near atmospheric pressure. Heat exchangers inside the upper section of the reactor bring the reactants to temperatures of 220-270°C. Typical residence times are in the order of three to five hours. A reflux condenser or distillation column over the reactor returns the monomer and most of the water back to the VK column.

Although the initial stages of Nylon-6,6 polymerization are catalyzed by water, the water must be removed in later stages to allow the condensation reactions to proceed to high conversion. Water removal is accomplished by carrying out the reaction in a series of stages at successively lower pressures. Secondary stages typically involve one or more CSTR reactors followed by vertical wiped-film evaporators. Inert gas may be used to strip water from the polymer melt.

For some products, chain terminators are used to control the molecular weight of the product. Acetic acid is commonly used, but any monofunctional acid or alcohol can be used to control molecular weight build-up.

Horizontal finishing reactors may be used to increase the polymer molecular weight and reduce the residual monomer and cyclic oligomer concentrations.


In these devolatilization stages, the evaporation of water, excess caprolactam, aminocaproic acid, and cyclic oligomers is limited by the rate of mass transfer from the liquid phase to the vapor phase.

Nylon-6,6 Nylon-6,6 is manufactured by two types of processes. In the most common process, dyadic nylon salt is first produced by mixing adipic acid (ADA) in an aqueous solution of hexamethylene diamine (HMDA). A newer process involves the direct melt polymerization of the two monomers.

Salt Preparation In the traditional salting process, the formation of nylon salt ensures stoichiometric ratios of the two monomers, allowing the production of high molecular weight polymers. In the salt solution process, solid adipic acid is dissolved in an aqueous solution of HMDA. The resulting aqueous salt solution is concentrated by further addition of the monomers and/or by partial evaporation.

An alternative salting process uses methanol as the primary solvent. Solutions of adipic acid and HMDA in methanol are prepared separately in continuously stirred heated tanks. These solutions are mixed in a reactor where the nylon salt is generated. Most of the nylon salt precipitates out of solution due to the low solubility of the nylon salt in methanol. A small amount of the salt, however, remains dissolved in the reactor, resulting in the generation of some short-chain oligomers. The salt slurry is centrifuged to remove the solid salt. Methanol is used as a washing solution in the centrifuge to further purify the salt. The methanol is purified in a distillation column and recycled. The solid nylon salt is dried and collected for use on- or off-site.

Polymerization from Aqueous Salt Solutions Most nylon-6,6 is produced in continuous processes made up of several stages. The primary stage operates at high pressures and temperatures to control the loss of volatile monomers and to accelerate the reactions. In the intermediate reactors, the operating pressure is reduced substantially and much of the excess water is evaporated. The finishing stages of the process are made up of one or more wiped-film evaporators which help to remove the remaining residuals.

A typical nylon-6,6 continuous process is shown here:


First Stage

In the first stage, aqueous salt solutions are fed to a reactor which operates at high temperatures (230-290°C) and pressures (> 250 psig). High temperatures are required to dissolve the salt and to accelerate the reaction rates. The high pressure is required to avoid excess loss of HMDA, which is generated by polymerization reactions. In the first reactor, the nylon salt dissolves and condensation reactions take place between molecules of the dissolved salt and between the dissolved salt and polymer end groups. Much of the water which enters with the salt and is generated by the condensation reactions is boiled off in the first stage due to the high operating temperature.

In some processes, the salt solution is fed to a column over the first reactor. As the solution flows down the column, excess water is driven off. Condensation reactions take place in the reactor at the bottom of the column as well as in the trays of the column. The column also condenses evaporated HMDA, returning it to the reactor vessel. Additives, such as titanium dioxide, are fed to the primary reactor vessel.

The reactor vessel is made up of two parts: a separation vessel and a heat exchanger tube-bank. The separator vessel is located at the bottom of the column, where it receives the reflux from the column. The liquid at the bottom of the separator is pumped through the tube-bank heat exchanger, which acts as the reboiler for the column. The high circulation rates through the heat exchanger section of the reactor keep the reactor contents well mixed.


Intermediate Stage

Liquid from the primary reactor must be throttled to lower pressures to remove water, which allows the reversible condensation reaction to proceed to higher conversions. The depressurization and devolatilization of the intermediate are carried out by several different techniques involving a series of degassing vessels connected by throttle valves. In some processes, a loop-type reactor is used to reduce the pressure.

Excess HMDA or adipic acid or monofunctional chain stoppers, such as acetic acid, may be added in the intermediate stages of the process to control the molecular weight build-up. Catalysts and thermal stabilizers are also added to the oligomer.

Final Stage

In the final stages of polymerization, wiped-wall evaporators are used to finish the reaction at high temperatures (up to 300°C) and medium vacuum pressures (760-200 torr). Typical finishing reactor residence times range from 20-60 minutes. The removal of water and excess monomers from the liquid phase may be limited by the mass transfer rate.

Melt-Phase Polymerization Recent developments in nylon-6,6 polymerization have led to the development of continuous melt-phase polymerization processes. Adipic acid and hexamethylene diamine solutions are fed to a tubular primary reactor, which operates at very high pressures (approximately 1000 psig), temperatures around 275°C, and residence times of 15-30 minutes. Under these conditions, boiling does not occur in the reactor.

The pressure is throttled down to 250-350 psig through a series of valves or tubes of successively larger diameter. The pressure profile must be adjusted to minimize cooling caused by the rapid evaporation of steam, which can cause the polymer solution to freeze.

In the final stage, the polymer is brought close to chemical equilibrium (with dissolved water and excess monomers) in a wiped film evaporator.

Polycarbonate Polycarbonate is a relatively strong polymer with good optical and mechanical properties. It is used in several applications including car body parts (frequently blended with PBT), specialty films, and laser disc media.

Historically, most polycarbonate was produced by interfacial polymerization of bisphenol-A (BPA) with phosgene. In the interfacial process, the reactions are relatively fast, but the reaction rate is limited by the mass transfer rates of the reactants from the bulk liquid phases into the swollen polymer phase.

A limited amount of polycarbonate is produced from BPA and phosgene in a solution polymerization process. The reaction is carried out by solution polymerization in pyridine. The pyridine solvent captures chlorine from the phosgene groups, resulting in pyridine chloride as a reaction by-product.


Recently, the melt-phase polymerization of bisphenol-A with diphenyl carbonate (DPC) has become an important industrial process. The melt polymerization process has a significant safety advantage over the interfacial process because phosgene is highly volatile and extremely toxic. A typical melt-phase polycarbonate process is shown here:

The monomers, BPA and DPC, are fed in a carefully controlled ratio to a series of CSTRs. Phenol, which is generated as a reaction by-product, is vaporized in the reactors and must be condensed and recycled. Distillation columns are used to recover residual monomers from phenol.

The CSTRs are followed by a series of wiped film evaporators and horizontal finishing reactors which operate at successively lower pressures to enhance the removal of residual monomers and phenol. These reactors are limited by the mass transfer rate of phenol from the melt.

Reaction Kinetic Scheme This section gives a general overview of nucleophilic reactions and reaction nomenclature, as well as specific information on polyester, nylon-6, nylon-6,6, and melt polycarbonate reaction kinetics.

Nucleophilic Reactions Step-growth polymerization involves reactions between monomers containing nucleophilic and electrophilic functional groups. Nucleophilic groups are electron-strong groups, typically alcohols (~OH), amines (~ NH 2 ), or water.


Electrophilic groups are electron-weak groups such as acids (~COOH), esters (~COO~), amides (~CONH~), and isocyanates (~NCO). When two chemical species react, the species with the strongest nucleophilic group is called the nucleophile; the other reactant bearing the strongest electrophilic group is called the electrophile.

Nucleophiles and electrophiles participate in bimolecular reactions. Depending on the types of functional groups in each reactant, the reaction mechanism may be nucleophilic substitution or nucleophilic addition.

Nucleophilic Substitution

In nucleophilic substitution reactions, a nucleophilic group from one reactant (the nucleophile) displace a nucleophilic group in the other reactant (the electrophile), resulting in two new products. (Note: Electrophilic groups are highlighted in each of the following figures.) Nucleophilic substitution reactions tend to be highly reversible.

CH3OH + CHOO

HOH + CCH3OO

NucleophilicSpecies

ElectrophilicSpecies

Forward Reaction Reverse Reaction


NucleophilicSpecies

Nucleophilic Addition

In nucleophilic addition reactions, the electrophile and nucleophile combine to form a new functional group. These reactions are typically irreversible.

CH3OH + NHCCH3OO

NCO


NucleophilicSpecies

Currently, the step-growth reaction generation algorithm is limited to condensation reactions. Pseudocondensation reactions must be defined through the user reaction feature or through the segment-based power-law reaction model.

In some reverse reactions and re-arrangement reactions, the electrophile may be a polymer or oligomer. These reactions occur at the bonds which link two segments together. To fully describe these reactions, the two segments in the electrophile must be identified. In this case, we refer to the electrophile as the “victim” reactant and the nucleophile as the “attacking” reactant. The victim reactant includes a nucleophilic segment and an electrophilic segment.

CH3OH + CO

CO(CH2)2OO

AttackingNucleophilic

Species

VictimNucleophilic

Species

VictimElectrophilic

Species

O(CH2)2OH + CCOO

CH3O

The following table lists the role of electrophiles and nucleophiles in several step-growth polymerization processes, as well as the typical reacting


functional groups, the characteristic repeat unit, and the by-product related to each polymerization process:

Polymer Class Nucleophile Electrophile Repeat Unit Condensate By-product

Polyester ~OH

~OH

~O(C=O)CH3

~COOH

~COOCH3 ~COOH

~(C=O)O~

~(C=O)O~

~(C=O)O~

H2OCH3OHCH3COOH

Polyamide ~NH2

~COOH ~(C=O)NH~ H2O Polyacetal

(Polycarbonate)

~OH

~OH

~O(C=O)Cl

~O(C=O)Oph

~O(C=O)O~

~O(C=O)O~

HCl

PhOH

Polyurethanes ~NH2

~OH

~(C=O)Cl

~N=C=O

~NH(C=O)O~

~NH(C=O)O~

HCl

none

Polyurea ~NH2 ~N=C=O ~NH(C=O)NH

~ none

Polyether ~OH OCH CH2

~OCH2C(OH)H~

none

Reaction Nomenclature Polymerization reactions are classified by chemical mechanism, by the number of reacting components, and by the influence a reaction has on the chain length distribution. This section describes the basic types of reactions found in step-growth polymerization and serves as a glossary of reaction nomenclature.

Intermolecular reactions involve two or more molecules.

Intramolecular reactions involve two sites on the same molecule.

Condensation reactions are polymerization reactions which produce a small molecule as a by-product. Typically, the condensate is a volatile compound such as water, methanol, acetic acid, or phenol. Step-growth reactions involving chlorine end groups result in hydrochloric acid or chlorinated hydrocarbon condensate products.

Reverse condensation reactions are where condensate molecules cleave an existing polymer chain, producing two smaller chains. Reverse condensation reactions near the end of a polymer molecule can generate free monomers.

Pseudocondensation reactions are nucleophilic addition reactions. These reactions involve rearrangement of atoms in two different functional groups, resulting in a new functional group. No by-products are produced by pseudocondensation reactions. Pseudocondensation reactions can involve two monomers, a monomer and a polymer end group, or two polymer end groups.

Addition reactions are reactions in which small molecules, including free monomers, dyadic salts, and cyclic monomers and dimers react with the end


of a growing polymer molecule. These reactions are responsible for the conversion of the monomers and most of the conversion of functional end groups.

Combination reactions involve reactions between the end groups of two polymer molecules. In most systems, combination reactions play an important role in molecular weight growth.

Rearrangement reactions occur between two polymer molecules, resulting in two new polymer molecules with different molecular weights. These reactions may involve the end group of one molecule and an internal site on another molecule, or they may involve internal sites on both molecules.

Ring opening reactions are intermolecular reactions between condensate or monomer molecules and cyclic monomers or oligomers. Condensate molecules or monomers react with cyclic compounds, opening the ring structure to produce linear oligomers or cyclic monomers.

Ring closing reactions are intramolecular reactions which occur between the two end groups of a linear molecule. Ring-closing reactions which occur between two end groups of a branched or network molecule are referred to here as intramolecular cyclization to differentiate them from reactions which form ring-shaped molecules.

Ring addition reactions are intermolecular reactions between polymer end groups and cyclic monomers or oligomers. The end group of the polymer links to the cyclic compound, opening the ring and lengthening the chain of the linear molecule.

Cyclodepolymerization reactions are intramolecular reactions in which a polymer end group reacts with a segment in the same molecule, forming a ring. The ring-shaped molecule is lost from the linear parent molecule, reducing the molecular weight of the parent.

Terminal monomer loss involves the loss of a monomer unit at the end of a polymer chain due to thermal degradation mechanisms.

Random scission involves the spontaneous cleavage of a polymer chain due to thermal degradation.

End group reformation reactions are those reactions which convert one type of end group into another without influencing the chain length.

The following table summarizes the reactions for step-growth polymerization:

Reaction Class Reaction Mechanism Reaction Type Reaction Scheme Included

Intermolecular


Condensation - Monomer Addition

M M P W+ → +2

P M P Wn n+ → ++1

Yes

Yes

Condensation - Polymer Addition

P P P Wn m n m+ → ++ Yes

Reverse Condensation - Terminal Monomer Loss

W P M M+ → +2

W P P Mn n+ → +−1

Yes

Yes

Reverse Condensation - Scission

W P P Pn n m m+ → +− Yes


Reaction Class Reaction Mechanism Reaction Type Reaction Scheme Included

Forward Polycondensation

P P P Mn m n m+ → ++ −1 Yes

Reverse Polycondensation

M P P Pn n m m+ → +− +1 Yes

Re-arrangement P P P Pn m n m q q+ → ++ − Yes

Ring Opening W C Pn n+ → No

Ring Addition P C Pn m n m+ → + No

Nucleophilic Addition (Pseudo-condensation)

Monomer Addition M M P+ → 2

P M Pn n+ → +1

No

No

Polymer Addition P P Pn m n m+ → + No

Intramolecular

Pseudo-condensation or Thermal mechanisms

Terminal Monomer Loss P M M2 → +

P P Mn n→ +−1

No

No

Scission P P Pn n m m→ +− No


Ring-Closing P C Wn n→ + No

Cyclodepolymerization P P Cn n m m→ +− No

Nucleophilic Addition Ring-Closing P Cn n→ No

Pn = Linear polymer with n segments

Cn = Cyclic polymer with n segments (C1 = cyclic monomer, such as caprolactam)

M = Monomer

W = Condensate

Polyester Reaction Kinetics In the direct esterification process, polyesters are produced by the reaction of diols, such as ethylene glycol, with diacids, such as terephthalic acid. The esterification reactions generate one mole of water for each mole of ester groups formed. The reactions are catalyzed by acid end groups in the polymer and diacid monomer.

Side Reactions

Several of the key side reactions are also acid-catalyzed. In the PET process, these reactions include the formation of diethylene glycol, or DEG, from ethylene glycol. The transesterification process does not involve acids, and substantially less DEG is produced.

An analogous reaction generates tetrahydrofurane (THF) in the PBT process. Like DEG formation, THF formation is accelerated by acid end groups. Since


THF poses environmental concerns, the generation of THF should be minimized. For this reason, PBT is usually produced by the transesterification route.

Metal acetate catalysts are used to accelerate the reaction rates in the later stages of the direct esterification process and throughout the transesterification process. These catalysts accelerate the main reactions and several side reactions including thermal scission and aldehyde formation.

In the transesterification process, acid end groups may be formed by thermal degradation reactions or by exchange reactions with water, which may be formed as a reaction by-product. These acid end groups participate in the reaction scheme, making transesterification kinetics a superset of esterification kinetics.

Polymerization Stage

The polymerization stage involves chain building reactions. There are two main growth mechanisms. Condensation reactions occur between two polymer end groups, releasing water or methanol. Polymerization reactions occur between diol end groups in different polymer molecules, generating a molecule of free glycol.

The polymer end group distribution and molecular weight distribution are randomized by redistribution reactions.

Polyester Production Final Stages

In the final stages of polyester production, high temperatures lead to thermal degradation reactions. In the PET process, these reactions degrade glycol end groups, producing acid ends and free acetaldehyde. Thermal scission reactions generate acid end groups and oxyvinyl end groups. Analogous reactions in the PBT process yield butenol and 1,4-butadiene. Additional side reactions involving these vinyl groups are the main source of color bodies in polyesters.

Cyclic compounds are formed by ring-closing and cyclodepolymerization reactions. Cyclic monomers, and some cyclic dimers do not form in terephthalic polyesters because of steric limitations. Trace amounts of larger cyclic oligomers, including trimers, tetramers, and pentamers, are commonly observed in terephthalate polyesters. These cyclic compounds reduce the quality of the polyester. Cyclic oligomers evaporate from the finishing reactors and condense in vapor vent lines, causing maintenance problems.

The reaction kinetics of terephthalate polyesters are summarized in the tables that follow.

The components involved in the reactions are:

Component ID

Databank ID

Component Structure Component Name

TPA C8H6O4-D3 CCOO

OHHO

Terephthalic acid

T-TPA C8H5O3-E CCOO

OH

Terephthalic acid end group


Component ID

Databank ID

Component Structure Component Name

B-TPA C8H4O2-R CCOO

Terephthalate repeat unit

DMT C10H10O4-D2 CC

OOOCH3CH3O

Dimethyl terephthalate

T-DMT C9H7O3-E CCOO

OCH3

Dimethyl terephthalate end group

MMT none CCOO

OCH3HO

Monomethyl terephthalate

H2O H2O H2O Water

MEOH CH4O CH3OH

Methanol

Components In Polyethylene Terephthalate Processes

EG C2H6O2 HO(CH2)2OH

Ethylene glycol

T-EG C2H5O2-E ~O(CH2)2OH

Ethylene glycol end group

B-EG C2H4O2-R ~O(CH2)2O~

Ethylene glycol repeat unit

DEG C4H10O3 HO(CH2)2O(CH2)2OH

Diethylene glycol

T-DEG C4H9O3-E ~O(CH2)2O(CH2)2OH

Diethylene glycol end group

B-DEG C4H8O3-R ~O(CH2)2O(CH2)2O~

Diethylene glycol repeat unit

T-VINYL C2H3O-E ~OCH=CH2 Oxyvinyl end group

C3 none

TG T

GTG

G = O(CH2)2OT = CC

OO

Cyclic trimer

Components In Polybutylene Terephthalate Processes

BD C4H10O2 HO(CH2)4OH

1,4 Butane diol

T-BD C4H9O2-E ~O(CH2)4OH

1,4 Butane diol end group

B-BD C4H8O2-R ~O(CH2)4O~

1,4 Butane diol repeat unit

T-BUTENOL C4H11O2-E ~O(CH2)2CH=CH2 Butenol end group

THF C4H8O-4 o

Tetrahydrofurane

The following table summarizes the step-growth reactions associated with terephthalate polyesters. For brevity, the table shows a subset of the reactions which actually occur - an analogous set of reactions involving DEG are also generated by the step-growth model.


Reaction Type Stoichiometric Reactions - Direct Esterification Route†

Condensation

CCOO

OHHOHO(CH2)xOH + CCOO

OHHO(CH2)xO + H2O

CCOO

OHO(CH2)xO+O(CH2)xOH CCOO

OHHO + H2O

CCOO

HOHO(CH2)xOH + CCOO

HO(CH2)xO + H2O

CCOO

HOO(CH2)xOH + CCOO

O(CH2)xO + H2O

12

34

56

78

Polymerization CCOO

OHO(CH2)xO+O(CH2)xOH + HO(CH2)xOHCCOO

OHHO(CH2)xO

CCOO

O(CH2)xO+O(CH2)xOH + HO(CH2)xOHCCOO

HO(CH2)xO

9101112

Rearrangement CCOO

O(CH2)xO+O(CH2)xOH + HO(CH2)xOCCOO

O(CH2)xO1314

Reaction Type Additional Reactions - Transesterification Route

Condensation 1516

1718

1920

2122

CCOO

OCH3CH3OHO(CH2)xOH + CCOO

OCH3HO(CH2)xO + CH3OH

CCOO

OCH3O(CH2)xO+O(CH2)xOH CCOO

OCH3CH3O + CH3OH

CCOO

CH3OHO(CH2)xOH + CCOO

HO(CH2)xO + CH3OH

CCOO

CH3OO(CH2)xOH + CCOO

O(CH2)xO + CH3OH

Polymerization 2324

CCOO

OCH3O(CH2)xO+O(CH2)xOH + HO(CH2)xOHCCOO

OCH3HO(CH2)xO

End-group Exchange

2526+ CC

OOCH3O + CH3OHCC

OOHOH2O

† x = 2 for polyethylene-terephthalate

x = 3 for polypropylene-terephthalate

x = 4 for polybutylene-terephthalate

The following table describes how to assign rate constants to each of the reactions listed in the previous table:

Reaction No.

Attacking Nucleophilic Species

Victim Electrophilic Species

Victim Nucleophilic Species

1 EG TPA none

2 H2O T-TPA T-EG


3 T-EG TPA none

4 H2O T-TPA B-EG

5 EG T-TPA none

6 H2O B-TPA T-EG

7 T-EG T-TPA none

8 H2O B-TPA B-EG

9 T-EG T-TPA T-EG

10 EG T-TPA B-EG

11 T-EG B-TPA T-EG

12 EG B-TPA B-EG

13 T-EG B-TPA B-EG

14 T-EG B-TPA B-EG

15 EG DMT none

16 MEOH T-DMT T-EG

17 T-EG DMT none

18 MEOH T-DMT B-EG

19 EG T-DMT none

20 MEOH B-TPA T-EG

21 T-EG T-DMT none

22 MEOH B-TPA B-EG

23 T-EG T-DMT T-EG

24 EG T-DMT B-EG

25 H2O T-DMT none

26 MEOH T-TPA none

Many of the side reactions in the polyester process are not included in the reaction generation scheme, and must be added to the model as “user reactions”. These reactions are:

Reaction Type Reaction Stoichiometry

DEG Formation U1HO(CH2)2OH + + H2OHO(CH2)2OH HO(CH2)2O(CH2)2OH

HO(CH2)2O(CH2)2OHO(CH2)2O + H2O+HO(CH2)2OH U2U3O(CH2)2OH + + H2OHO(CH2)2O O(CH2)2O(CH2)2O

Thermal Scission CC

OOO(CH2)2O CC

OOOH +

U4H2C CHO

Acetaldehyde Formation CC

OOO(CH2)2OH CC

OOOH + HCCH3

O

HCCH3

O+CC

OOOCH CH2O(CH2)2OH + CC

OOO(CH2)2O

U5

U6


Reaction Type Reaction Stoichiometry

Cyclic Trimer Formation

U7U8

TG T

GTG

G T GHTGHOT + H2O

U9U10

TG T

GTG

G T GHTGTHG + HO(CH2)2OH

U11U12

TG T

GTG

G T GHTGTG +O(CH2)2OH

The recommended power-law exponents for the reactants in the side reactions are:

Reaction No. Power-Law Exponents; Modeling Notes

U1 EG = 2 (Multiply group-based pre-exponential factor by 4.0)

U2 EG = 1, T-EG = 1 (Multiply group-based pre-exponential factor by 2.0)

U3 T-EG = 2 (Multiply group-based pre-exponential factor by 1.0)

U4 Reaction is first order with respect to polyester repeat units, assume concentration of repeat units is approximately equal to the concentration of B-TPA, set power-law exponents B-TPA = 1.0 B-EG = 1x10-8

U5 T-EG = 1

U6 T-EG = 1, T-VINYL = 1

U7 Reaction is first order with respect to linear molecule with the following segment sequence:

T-TPA: B-EG : B-TPA : B-EG : B-TPA : T-EG

option 1: assume this concentration = TPA concentration and use power-law constant TPA = 1*

option 2: use the following equation, based on the most-probable distribution, to estimate the concentration of this linear oligomer. This equation can be implemented as a user-rate constant correlation

[ ]PT EGNUCL

B TPAELEC

B EGNUCL

T TPAELEC

NUCL T EG T DEG B EGELEC T TPA B TPA2

2 2

0

2 22

=−⎛

⎝⎜⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

= − + − + − += − + −

[ ] [ ] [ ] [ ] [ ] [ ] *[ ] *[[ ] *[ ]

λ

U8 H2O = 1, C3 = 1 (Multiply group-based pre-exponential factor by 6.0)


T-EG : B-TPA : B-EG : B-TPA : B-EG : B-TPA : T-EG

option 1: assume this concentration = TPA concentration and use power-law constant TPA = 1*


[ ]PT EGNUCL

B TPAELEC

B EGNUCL

NUCL T EG T DEG B EG B DEGELEC T TPA B TPA2

2 3 2

0

2 22

=−⎛

⎝⎜⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

= − + − + − + −= − + −

[ ] [ ] [ ] [ ] [ ] *[ ] *[ ][ ] *[ ]

λ

U10 EG = 1, C3 = 1 (Multiply group-based pre-exponential factor by 12.0)




~B-EG : B-TPA : B-EG : B-TPA : B-EG : B-TPA : T-EG

option 1: assume this concentration = T-EG concentration and use power-law constant T-EG = 1*


[ ]PT EGNUCL

B TPAELEC

B EGNUCL

NUCL T EG T DEG B EG B DEGELEC T TPA B TPA2

3 3

0

2 22

=−⎛

⎝⎜⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

= − + − + − + −= − + −

[ ] [ ] [ ] [ ] [ ] *[ ] *[ ][ ] *[ ]

λ

U12 T-EG = 1, C3 = 1 (Multiply group-based pre-exponential factor by 6.0)

* To avoid numerical problems, set power-law exponents to 8101 −× for reactants

which do not appear in the rate expression

0λ = Concentration zeroth moment, mol/L (approximately=0.5*([T-TPA]+[T-

EG]+[T-DEG]+[T-VINYL])

Nylon-6 Reaction Kinetics Nylon-6 melt-phase polymerization reactions are initialized by the hydrolytic scission of caprolactam rings. The reaction between water and caprolactam generates aminocaproic acid. The reaction kinetics in the primary reactor are sensitive to the initial water concentration.

The carboxylic and amine end groups of the aminocaproic acid molecules participate in condensation reactions, releasing water and forming polymer molecules. The resulting acid and amine end groups in the polymer react with each other and with aminocaproic acid, releasing more water.

The amine end of aminocaproic acid and amine ends in polymer react with caprolactam through ring addition. This reaction is the primary growth mechanism in the nylon-6 process.

Cyclic Oligomers

As the reactions proceed, intramolecular reactions involving linear polymer molecules generate cyclic oligomers. Cyclic oligomers ranging from the dimer through rings ten units long are reported in the literature. The concentration of each successive cyclic oligomer (dimer, trimer, etc.) falls off sharply, in accordance with the most probable distribution.

Reactions involving cyclic compounds are not considered in the reaction generation algorithm in the step-growth model. These reactions, including ring opening, ring closing, ring addition, and cyclodepolymerization, must be specified as user reactions.


The following table summarizes key components in the nylon-6 melt polymerization process. The component names in this table are used in the tables that follow.

Component ID Databank ID Component Structure Component Name

CL C6H11NO

NH

O

ε-Caprolactam

ACA none (CH2)5 CH2N

OOH

Aminocaproic acid

T-NH2 C6H12NO-E-1 (CH2)5 CH2N

O

Amine end group segment

T-COOH C6H12NO2-E-1 (CH2)5 CNH

OOH

Acid end group segment

R-NY6 C6H11NO-R-1 (CH2)5 CNH

O

Nylon-6 repeat segment

CD none (CH2)5 CNHC NH(CH2)5O

O

Cyclic dimer

H2O H2O H2O Water

Major Reactions

The major reactions in the nylon-6 melt polymerization process are shown here:

Reaction Type User-Specified Reactions (Forward and Reverse Reactions Defined Separately)†

Ring Opening / Ring Closing

U1 H2O + CL ACA

U2 H2O + CD T-COOH : T-NH2 (=P2) Ring Addition / Cyclodepolymerization

U3 ACA + CL T-COOH : T-NH2 (=P2)

U4 T-NH2 + CL R-NY6 : T-NH2

U5 ACA + CD T-COOH : R-NY6 : T-NH2 (=P3)

R-NY6 : R-NY6 : T-NH2U6 T-NH2 + CD

Reaction Type Model-Generated Step-Growth Reactions (Define Nylon-6 Repeat Unit as EN-GRP)

Condensation 1. ACA + ACA T-COOH : T-NH2 + H2O

2. ACA + T-COOH T-COOH : R-NY6 + H2O

R-NY66 : T-NH2 + H2O3. T-NH2 + ACA4. T-NH2 + T-COOH R-NY66 : R-NY6 + H2O

Re-Arrangement

5. T-NH2 + T-NH2 : T-COOH T-NH2 : R-NY6 + ACA

6. T-NH2 + R-NY6 : T-COOH R-NY6 : R-NY6 + ACA

R-NY6 : R-NY6 + T-NH2 7. T-NH2 + R-NY6 : R-NY6


† In the reaction stoichiometry equations above, the colon (:) indicates connections between segments. Literature sources report re-arrangement reactions are insignificant, these reaction rates can be set to zero

The reactions U1-U6, which involve cyclic monomer and dimer, are not generated by the current version of the Step-Growth model. These reactions must be defined as user reactions. However, the stoichiometry of each of these reactions is shown.

Reactions 1-7 are considered in the reaction generation algorithm in the Step-Growth kinetics model. The rate constants for these reactions can be assigned according to the identifiers summarized here:

Reaction No.




1 forward ACA T-ACA none

2 forward ACA T-COOH none

3 forward T-NH2 ACA none

4 forward T-NH2 T-COOH none

5 forward T-NH2 T-NH2 T-COOH

6 forward T-NH2 T-NH2 R-NY6

7 forward T-NH2 R-NY6 R-NY6

1 reverse H2O T-NH2 T-COOH

2 reverse H2O R-NY6 T-COOH

3 reverse H2O T-NH2 R-NY6

4 reverse H2O R-NY6 R-NY6

5 reverse ACA T-NH2 R-NY6

6 reverse ACA R-NY6 R-NY6

7 reverse T-NH2 R-NY6 R-NY6

The suggested power-law exponents are shown here:


U1 forward

H2O = 1, CL = 1

U1 reverse

ACA = 1

U2 forward

H2O = 1, CD = 1 (Multiply group-based pre-exponential factor by 2.0)



U2 reverse

Reaction is first order with respect to linear dimer P2 with the following segment

sequence:

T-NH2 :T-COOH

option 1: assume P2 concentration = ACA concentration and use power-law constant

ACA = 1*

option 2: use the following equation, based on the most-probable distribution, to estimate concentration of P2 The denominator in this equation can be implemented

as a user rate constant, with first-order power-law constants for T-NH2 and T-COOH.

[ ]PT NH

T NH R NYT COOH

T COOH R NY2 0

22 6 6

=−

− + −⎛⎝⎜

⎞⎠⎟

−− + −

⎛⎝⎜

⎞⎠⎟

[ ][ ] [ ]

[ ][ ] [ ]

λ

U3 forward

ACA = 1, CL = 1

U3 reverse

See U2 reverse reaction

U4 forward

T-NH2 = 1, CL = 1

U4 reverse

T-NH2 = 1 (this approximation assumes most T-NH2 end groups are attached to repeat units)*

U5 forward

ACA = 1, CD = 1

U5 reverse

Reaction is first order with respect to linear trimer P3 with the following segment

sequence:

T-NH2 : R-NY6 : T-COOH

option 1: assume P3 concentration = ACA concentration and use power-law constant

ACA = 1*

option 2: use the following equation, based on the most-probable distribution, to estimate concentration of P3 The denominator in this equation can be implemented

as a user rate constant, with first-order power-law constants for T-NH2, R-NY6, and T-COOH.

[ ]PT NH

T NH R NYR NY

T COOH R NYT COOH

T COOH R NY2 0

22 6

66 6

=−

− + −⎛⎝⎜

⎞⎠⎟

−− + −

⎛⎝⎜

⎞⎠⎟

−− + −

⎛⎝⎜

⎞⎠⎟

[ ][ ] [ ]

[ ][ ] [ ]

[ ][ ] [ ]

λ

U6 forward

T-NH2 = 1, CD = 1

U6 reverse

T-NH2 = 1 (this approximation assumes most T-NH2 end groups are attached to repeat units)*

*

To avoid numerical problems, set power-law exponents to 8101 −× for reactants which do not appear in the rate expression

0λ = Concentration zeroth moment, mol/L (approximately = 0.5 * ([T-COOH] + [T-NH2])

The side reactions are thought to be catalyzed by acid end groups in aminocaproic acid and the polymer. A first-order power-law coefficient can be used to account for the influence of the acid groups in these components.


Alternately, a user rate-constant subroutine can be developed to account for the influence of the acid end groups.

Note that the forward and reverse terms of the reversible side reactions must be defined as two separate user reactions in the model.

Nylon-6,6 Reaction Kinetics The salt process involves a preliminary reaction to form the salt, which precipitates from solution. During the salt formation, some of the salt remains in solution, leading to higher polymers. For a rigorous model, it is a good idea to consider these oligomerization reactions, even in the salt precipitation reactor. Accounting for these reactions is important when using the model to optimize the temperature, pressure, and water content of the nylon salt crystallizer.

The model needs to consider three phase equilibrium (solid salt, liquid, and vapor). Three phase equilibrium can be considered in Aspen Plus using the electrolyte chemistry feature. In version 10.0, however, the CSTR model does not allow a component to appear simultaneously in chemistry reactions and kinetic reactions. Another way to represent the solid-liquid equilibrium is to define an equilibrium reaction between the components representing the dissolved and solid salt. Chemical equilibrium equations can be defined using the Power-Law reaction kinetics model in Aspen Plus. Apply the “mole-gamma” option to force the equilibrium equation to use the ratio of the molar activities as the basis of the equilibrium constant. By using this assumption, the equilibrium constant is the same as the solubility constant of the solid salt.

To model the reaction kinetics of the salt process, the dissolved salt should be considered as a component in the reaction model. The models described in the open literature do this by considering the salt as an “AB” type monomer. This treatment, however, fails to consider some of the reverse reactions which can occur during polymerization. This approach assumes that reverse condensation reactions and re-arrangement reactions always generate products with an equal number of adipic acid and HMDA units. In reality, polymer chains with an unequal number of units can be formed because the reactions can occur inside the repeat units which originally came from the reacting salts. Further, the reverse reactions can generate free adipic acid or HMDA when the reaction occurs at the end of a polymer chain.

Reverse Rate Constant

The models in the literature use a reverse rate constant which is twice the reverse rate constant experienced by an individual amine group. This factor of two accounts for the fact that each repeat unit has two amine groups. In the approach described here, the reverse rate constants used in the model should be the rate constant between two functional groups, for example between water and a single amine group.

Considering salt as a component, there are several reversible reactions which must be considered in the model. A number of condensation reactions occur including those between molecules of dissolved salt, dissolved monomers, and polymer end groups. These reactions can be implemented in the step-growth


model through the user reaction feature. The step-growth model will generate the reactions which do not involve the salt component.

The molecular weight distribution of nylon-6,6 is known to re-equilibrate when the polymer is exposed to HMDA under pressure. Further, as vacuum is applied, free HMDA appears to be generated. These facts indicate that rearrangement reactions are important in this process.

Modeling Approaches

There are two modeling approaches:

• Simplified

• Detailed

The component definitions for both modeling approaches are:

Component ID Databank ID Component Structure Component Name

Components Common to Simplified and Detailed Approach

ADA C6H10O4-D1 (CH2)4C

OHO C OH

O

Adipic acid

HMDA C6H16N2 (CH2)6 NH2H2N Hexamethylene diamine

DIS-SALT none (CH2)4C

OHO C

ONH (CH2)6 NH2

Dissolved nylon-6,6 salt

SOL-SALT none (CH2)4C

OHO C O-

O+H3N (CH2)6 NH2

Solid nylon-6,6 salt

MEOH CH4O CH3OH

Methanol

H2O H2O H2O Water

Segments In Simplified Salt Process Model

T-COOH none (CH2)4C

OHO C

ONH (CH2)6 NH

Acid end group segment

T-NH2 none (CH2)4C

OCO

NH (CH2)6 NH2

Amine end group segment

R-NY66 none (CH2)4C

OCO

NH (CH2)6 NH

Repeat unit segment

Segments In Detailed Salt Process Model and Melt-Process Model

T-ADA C6H9O3-E (CH2)4C

OC OHO

Adipic acid end group

B-ADA C6H8O2-R C (CH2)4 C

OO

Adipic acid repeat unit

T-HMDA C6H15N2-E (CH2)6 NH2HN HMDA end group

B-HMDA C6H14N2-R (CH2)6 NHHN HMDA repeat unit

Note: The component names used in this table are used in the successive tables to document the reactions.


In the simplified approach, the dissolved salt is treated as an “AB” monomer (a monomer with two different types of functional groups). This is accomplished by defining the repeat unit as an “EN-GRP” reactive group. The simplified approach is consistent with the modeling approach described in the open literature.

Using this approach, the Step-Growth model will generate all of the main reactions. The solid-liquid phase equilibrium can be represented as a chemical equilibrium reaction using the Power-Law model or as two side reactions in the step-growth model. The equilibrium constant of this reaction corresponds to the solubility constant of the salt.

The reactions for a simplified Nylon-6,6 salt process model are shown here:

Reaction Type Phase Equilibrium Reactions (Use Power-Law Reaction Kinetics Model)

Solid/Liquid Equilibrium

C1 DIS-SALT + H2O SOL-SALT

Reaction Type User-Specified Reactions (Forward and Reverse Reactions Defined Separately)

Salt formation U1 HMDA + ADA DIS-SALT + H2O

Reaction Type Model-Generated Step-Growth Reactions (Define Nylon-6,6 Repeat Unit as EN-GRP)†

Condensation

3. T-NH2 + DIS-SALT R-NY66 : T-NH2 + H2O

T-COOH : R-NY66 + H2O2. DIS-SALT + T-COOH

T-COOH : T-NH2 + H2O1. DIS-SALT + DIS-SALT

R-NY66 : T-NY66 + H2O 4. T-NH2 + T-COOH Re-Arrangement 5. T-NH2 + T-COOH : T-NH2 R-NY66 : T-NH2 + DIS-SALT

6. T-NH2 + T-COOH : R-NY66 R-NY66 : R-NY66 + DIS-SALT

R-NY66 : R-NY66 + T-NH2 7. T-NH2 + R-NY66 : R-NY66

† In the reaction stoichiometry equations above, the colon (:) indicates

connections between segments

The detailed modeling approach treats the HMDA and ADA segments as discreet molecular units. Using this assumption, the dissolved salt is a dimer made up of one hexamethylene diamine end group and one adipic acid end group. This approach is more rigorous because it considers every possible reverse reaction, including terminal monomer loss. To use this approach, define the HMDA repeat group as a bifunctional nucleophile (NN-GRP), and the ADA repeat group as a bifunctional electrophile (EE-GRP).

The solid-liquid phase equilibrium (reaction C1) is represented as previously described. The reactions involving the dissolved salt, U1-U6, must be defined as user reactions. Reactions 1-7, which do not involve the salt, are generated by the model automatically.

The reactions for a detailed Nylon-6,6 salt process model are shown here:

Reaction Type Phase Equilibrium Reactions (Use Power-Law


Reaction Kinetics Model)

Solid/Liquid Equilibrium

C1 DIS-SALT + H2O SOL-SALT

Reaction Type User-Specified Reactions (Forward and Reverse Reactions Defined Separately)†

Salt formation U1 HMDA + ADA DIS-SALT + H2O Condensation

U4 HMDA + DIS-SALT T-HMDA : B-ADA : T-HMDA + H2O

T-ADA : B-HMDA : T-ADA + H2OU3 DIS-SALT + ADA

T-HMDA : B-ADA : B-HMDA : T-ADA + H2OU2 DIS-SALT + DIS-SALT

T-ADA : B:HMDA : B-ADA + H2O U5 DIS-SALT + T-ADAU6 T-HMDA + DIS-SALT B-HMDA : B-ADA : T-HMDA + H2O

Reaction Type

Model-Generated Step-Growth Reactions (Define B-HMDA as NN-GRP, B-ADA as EE-GRP)

Condensation

2. HMDA + T-ADA T-HMDA : B-ADA + H2O

3. T-HMDA + ADA B-HMDA : B-ADA + H2O

B-HMDA + B-ADA + H2O 4. T-HMDA + T-ADA

T-HMDA : T-ADA + H2O1. HMDA + ADA

Re-Arrangement

5. T-HMDA + T-ADA : T-HMDA T-ADA : B-HMDA + HMDA

6. T-HMDA + B-ADA : T-HMDA B-ADA : B-HMDA + HMDA

B-ADA : B-HMDA + T-HMDA 7. T-HMDA + B-ADA : B-HMDA

† In the reaction stoichiometry equations above, the colon (:) indicates connections

between segments

Rate Constant Identifiers

The rate constants can be assigned to model-generated reactions in the simplified model using the identifiers summarized here:

Reaction No.




1 forward DIS-SALT DIS-SALT none

2 forward DIS-SALT T-COOH none

3 forward T-NH2 DIS-SALT none

4 forward T-NH2 T-COOH none

5 forward T-NH2 T-COOH T-NH2

6 forward T-NH2 T-COOH R-NY66

7 forward T-NH2 R-NY66 R-NY66

1 reverse H2O T-COOH T-NH2

2 reverse H2O T-COOH R-NY66

3 reverse H2O R-NY66 T-NH2


4 reverse H2O R-NY66 R-NY66

5 reverse DIS-SALT T-NH2 R-NY66

6 reverse DIS-SALT R-NY66 R-NY66

7 reverse T-NH2 R-NY66 R-NY66

A subset of these identifiers can be used to assign the same rate constant to several different reactions. For example, reactions 3-7 can be lumped together by specifying “T-NH2” as the attacking nucleophilic species and by leaving the victim species identifiers blank (unspecified).

Rate constants can be assigned to reactions 1-7 in the detailed model using the identifiers summarized here:

Reaction No. Attacking Nucleophilic Species



1 forward HMDA ADA none

2 forward HMDA T-ADA none

3 forward T-HMDA ADA none

4 forward T-HMDA T-ADA none

5 forward T-HMDA T-ADA T-HMDA

6 forward T-HMDA B-ADA T-HMDA

7 forward T-HMDA B-ADA B-HMDA

1 reverse H2O T-ADA T-HMDA

2 reverse H2O B-ADA T-HMDA

3 reverse H2O T-ADA B-HMDA

4 reverse H2O B-ADA B-HMDA

5 reverse HMDA T-ADA B-HMDA

6 reverse HMDA B-ADA B-HMDA

7 reverse T-HMDA B-ADA B-HMDA

A subset of these identifiers can be used to assign the same rate constant to several different reactions. For example, reactions 3-7 can be lumped together by specifying “T-HMDA” as the attacking nucleophilic species and by leaving the victim species identifiers blank (unspecified).

Each reaction involving the dissolved salt must be defined as a user-reaction in the Step-Growth model. The forward and reverse reactions are treated as two separate reactions. The stoichiometry of each reaction was shown previously in the reactions table for the detailed modeling approach. The power-law exponents are in the following table.

Several of the reverse reactions require a particular sequence of segments in order to occur. The concentration of molecules with these particular sequences can be assumed (for example, assume the linear trimer concentration is the same as the dissolved salt concentration) or they can be estimated from statistical arguments. The following table shows both techniques. The statistical approach is more rigorous, but it requires writing a


user rate-constant or user kinetic subroutine to perform the calculations as shown.

The power-law exponents for user-specified reactions in the detailed model are:


U1 forward

HMDA = 1, ADA = 1 Multiply group-based pre-exponential factor by 4.0

U1 reverse

H2O = 1, DIS-SALT = 1

U2 forward

DIS-SALT = 2

U2 reverse

Reaction is first order with respect to water and polymer molecule P4 with the

following segment sequence:

T-HMDA : B-ADA : B-HMDA : T-ADA

option 1: assume P4 concentration = DIS-SALT concentration and use DIS-SALT = 1,

H2O = 1*

option 2: set power-law exponent for H2O = 1 and use the following equation, based on the most-probable distribution, to estimate concentration of P4 (this equation can

be implemented as a user rate constant).

[ ]

0

4

][2][][

][2][][2

][2][][2

][2][][

λ⎟⎟⎠

⎞⎜⎜⎝

⎛−+−

−⎟⎟⎠

⎞⎜⎜⎝

⎛−+−

−

⎟⎟⎠

⎞⎜⎜⎝

⎛−+−

−⎟⎟⎠

⎞⎜⎜⎝

⎛−+−

−=

HMDABHMDATHMDAT

ADABADATADAB

HMDABHMDATHMDAB

ADABADATADATP

U3 forward

DIS-SALT = 1, ADA = 1, multiply group rate constant by 2.0

U3 reverse

Reaction is first order with respect to water and polymer molecule P aa3, with the


T-ADA : B-HMDA : T-ADA

option 1: assume P aa3, concentration = ADA concentration and use power-law

constants ADA = 1, H2O = 1*

option 2: set power-law exponent for H2O = 1 and use the following equation, based on the most-probable distribution, to estimate concentration of P aa3, (this equation

can be implemented as a user rate constant).

[ ]PT ADA

T ADA B ADAB HMDA

T HMDA B HMDAaa3

2

022

2,

[ ][ ] [ ]

[ ][ ] [ ]

=−

− + −⎛⎝⎜

⎞⎠⎟

−− + −

⎛⎝⎜

⎞⎠⎟λ

U4 forward

DIS-SALT = 1, HMDA = 1; multiply group rate constant by 2.0



U4 reverse

Reaction is first order with respect to water and polymer molecule P BB3, with the


T-HMDA : B-ADA : T-HMDA

option 1: assume P BB3, concentration=HMDA concentration and use power-law

constants HMDA=1, H2O=1*

option 2: set power-law exponent for H2O = 1 and use the following equation, based on the most-probable distribution, to estimate concentration of P BB3, (this equation

can be implemented as a user rate constant).

[ ]PT HMDA

T HMDA B HMDAB ADA

T ADA B ADAaa3

2

022

2,

[ ][ ] [ ]

[ ][ ] [ ]

=−

− + −⎛⎝⎜

⎞⎠⎟

−− + −

⎛⎝⎜

⎞⎠⎟λ

U5 forward

DIS-SALT = 1, T-ADA = 1

U5 reverse

H2O = 1, T-ADA = 1, set power law constants for B-ADA, B-HMDA to 1E-10 to avoid numerical problems

U6 forward

DIS-SALT = 1, T-HMDA = 1

U6 reverse

H2O = 1, T-ADA = 1, set power law constants for B-ADA, B-HMDA to 1E-10 to avoid numerical problems

*

To avoid numerical problems, set power-law exponents to 8101 −× for reactants which do not appear in the rate expression

0λ = Concentration zeroth moment, mol/L (approximately = 0.5 * ([T-ADA] + [T-

HMDA])


Melt-Phase Polymerization The best way to model the melt-phase polymerization of nylon-6,6 is to treat the HMDA and ADA segments as discreet molecular as shown in the components table on page 112.

The following table shows the main reactions in the melt-phase polymerization of nylon-6,6:

Reaction Type

Model-Generated Step-Growth Reactions (Define B-HMDA as NN-GRP, B-ADA as EE-GRP)†

Condensation 2. HMDA + T-ADA T-HMDA : B-ADA + H2O

3. T-HMDA + ADA B-HMDA : B-ADA + H2O

B-HMDA + B-ADA + H2O 4. T-HMDA + T-ADA

T-HMDA : T-ADA + H2O1. HMDA + ADA

Re-Arrangement

5. T-HMDA + T-ADA : T-HMDA T-ADA : B-HMDA + HMDA

6. T-HMDA + B-ADA : T-HMDA B-ADA : B-HMDA + HMDA

B-ADA : B-HMDA + T-HMDA 7. T-HMDA + B-ADA : B-HMDA



These reactions are generated by the Step-Growth model if the HMDA repeat group is defined as a bifunctional nucleophile (NN-GRP), and the ADA repeat group as a bifunctional electrophile (EE-GRP).

Side reactions that are not shown may be included in the model as “user reactions”.

Rate constants can be assigned to reactions 1-7 using the identifiers for the detailed model summarized on page 115.

A subset of these identifiers can be used to assign the same rate constant to several different reactions. For example, reactions 3-7 can be lumped together by specifying “T-HMDA” as the attacking nucleophilic species and by leaving the victim species identifiers blank (unspecified).

Melt Polycarbonate Reaction Kinetics There is little information regarding melt-phase polymerization of polycarbonate available in the public domain. From what is available, it is clear that the chemistry of the melt-polycarbonate process follows the typical pattern for step-growth condensation involving two dissimilar monomers. The bisphenol-A monomer behaves as a bifunctional nucleophile, and the diphenyl carbonate monomer behaves as a bifunctional electrophile. The reactions generate phenol as a by-product. In later stages of the process, rearrangement reactions regenerate small amounts of bisphenol-A monomer.

The following table summarizes the most convenient method for characterizing the components involved in the melt polycarbonate process:


Component ID

Databank ID Component Structure Component Name

Components Common to Simplified and Detailed Approach

DPC none CO

OO

Diphenyl Carbonate

T-DPC C7H5O2-E CO

O

Phenyl carbonate end group

B-DPC CO-R CO

Carbonate repeat unit

BPA C15H16O2 HO OH

Bisphenol-A

T-BPA C15H15O2-E O OH

Bisphenol-A end group

B-BPA C15H14O2-R O O

Bisphenol-A repeat unit

PHOH C6H6O OH

Phenol

The following table shows the main reactions in this process. These reactions are generated by the model if the carbonate group is defined as a bifunctional electrophile (EE-GRP) and the BPA group as a bifunctional nucleophile (NN-GRP) .

Reaction Type

Model-Generated Step-Growth Reactions (Define B-BPA as NN-GRP, B-DPC as EE-GRP)†

Condensation 2. BPA + T-DPC T-BPA : B-DPC + PHOH

3. T-BPA + DPC B-BPA : B-DPC + PHOH

B-BPA + B-DPC + PHOH4. T-BPA + T-DPC

T-BPA : T-DPC + PHOH1. BPA + DPC

Re-Arrangement

T-DPC : B-BPA + BPA5. T-BPA + T-DPC : T-BPA 6. T-BPA + B-DPC : T-BPA B-DPC : B-BPA + BPA

7. T-BPA + B-DPC : B-BPA B-DPC : B-BPA + T-BPA



The following table shows how to assign rate constants to each of the reactions shown in the previous table:

Reaction No. Attacking Nucleophilic Species



1 forward BPA DPC none

2 forward BPA T-DPC none

3 forward T-BPA DPC none


4 forward T-BPA T-DPC none

5 forward T-BPA T-DPC T-BPA

6 forward T-BPA B-DPC T-BPA

7 forward T-BPA B-DPC B-BPA

1 reverse PHOH T-DPC T-BPA

2 reverse PHOH B-DPC T-BPA

3 reverse PHOH T-DPC B-BPA

4 reverse PHOH B-DPC B-BPA

5 reverse BPA T-DPC B-BPA

6 reverse BPA B-DPC B-BPA

7 reverse T-BPA B-DPC B-BPA

Rate constants can be assigned to several by leaving some of the reaction identifiers unspecified. For example, the reverse reactions involving phenol can be lumped together by assigning phenol as the attacking nucleophilic species and by leaving the names of the victim species unspecified.

The open literature does not describe the side reactions involved in this process, although side reactions are certainly known to exist. These side reactions can be added to the model as “user reactions”.

Model Features and Assumptions

Model Predictions The step-growth model calculates the component reaction rates and the rate

of change of the zeroth and first polymer moments ( , )λ λ0 1i of the polymer

chain length distribution. The number average polymer properties (Pn, Mn) are calculated from the moments. These component attributes can be used to calculate secondary properties, such as polymer viscosity, melting point, end group concentrations, intrinsic viscosity, melt flow index, etc. Correlations relating secondary properties to the polymer moments can be implemented using a User Prop-Set Property subroutine, as described in the Aspen Plus User Guide.

The rate of change of polymer mass is calculated as follows:

RR Mw

Mwp

s i i

Nseg

p=∑ , *

1

This is the sum of the rates of change of segment masses.

Each segment type is assigned a value Ω, which indicates the number of “points of attachment” connecting the segment to other segments in the polymer chain:


Segment Type Ω

End 1

Repeat 2

Branch-3 3

Branch-4 4

The rate of change of the zeroth moment ( 0λ ) is calculated from the rate of change of the first moment ( 1λ ) and the segment type (Ω):

ttt ∂Ω∂

−∂∂

=∂∂

211 0 λλ

The factor of ½ accounts for the fact that each “connection” links two segments (without this correction the points of connection are counted twice). This method is best illustrated through these examples:

Valid Reaction Type† Stoichiometry† 1Δλ ½ΔΩ 0Δλ

Yes Initiation 2PMM →+ M + M → E + E +2 +1 +1

No Initiation 1PM → M → R +1 +1 0

Yes Propagation (addition) 1nn PMP +→+ E + M → R + E +1 +1 0

Yes Propagation (insertion)

*1n

*n PMP +→+ M → R +1 +1 0

Yes Combination mnmn PPP +→+ E + E → R + R 0 +1 -1

Yes Combination mnmn PPP +→+ E + E → R -1 +0 -1

Yes Branching 1nn PMP +→+ R + M → B3 + E +1 +1 0

Yes Branching mnmn PPP +→+ R + E → B3 + R 0 +1 -1

Yes Cross linking mnmn PPP +→+ R + R → B4 -1 +0 -1

† M = Monomer; E = End group segment; B3 = Branch-3 segment; B4 = Branch-4

segment

This method lets you specify most classes of reactions. However, special care must be taken to ensure that the reaction is defined in a manner that is consistent with the previous equation.

By default, the model solves the zeroth moment (ZMOM) and segment flow rates (SFLOW attributes) as independent variables. This can cause a discrepancy between these variables, especially in flowsheets with high polymer recycle flow rates. This discrepancy, in turn, can lead to convergence problems in downstream reactors.

To avoid this problem, you can force the model to calculate the zeroth moment directly from the segment flow rates by checking the “explicitly solve


zeroth moment” option on the step-growth Options form. When this option is selected, the model calculates the zeroth moment as:

Ω−= 21

10 λλ

This option cannot be invoked if two or more reaction models are referenced from a single reactor block.

Phase Equilibria The step-growth model can be used to simulate reactions in single-phase (vapor or liquid), two-phase (VL), or three-phase (VLL) systems. Each step-growth reaction model is associated with a particular reaction phase, specified on the Options sheet. The user can consider simultaneous reactions in multiple phases by referring to two or more reaction models in a reactor.

Typical applications of this model include melt-phase polymerization and solution polymerization. Slurry, suspension, and emulsion processes involving step-growth kinetics can also be simulated with this model.

Interfacial polymerization involves a solvent phase, an organic monomer phase, and a polymer phase. The reaction rate is usually limited by the rate of mass transfer of monomers from the organic phase to the reacting polymer phase. The mass-transfer limits across the liquid-liquid interface are not taken into account by the standard model. These systems can be simulated by developing a custom reactor model in Aspen Custom Modeler or Aspen Plus, or by writing an appropriate concentration basis subroutine for the step-growth model.

Solid-state polymerization involves crystalline and amorphous solid polymer phases and a vapor phase. The reaction kinetics may be limited by the rate of mass transfer of volatile reaction by-products from the amorphous solid phase to the polymer phase. None of the standard reactor models in Aspen Polymers are designed for solid-state polymerization. Solid-state polymerization models can be developed in Aspen Custom Modeler and interfaced to the step-growth polymerization model through the Aspen Custom Modeler / Aspen Polymers Interface.

Mass transfer limitations in thin-film or horizontal finishing reactors can be considered by customizing the Step-Growth model using the available concentration basis subroutine or by developing an appropriate user reactor model in Aspen Plus or Aspen Custom Modeler.

Reaction Mechanism The Step-Growth reaction model applies to condensation polymerization. In the future the model will be extended to cover pseudocondensation and ring-addition polymerization. The model accounts for any combination of monofunctional and bifunctional monomers. Cyclic monomers and multifunctional monomers, however, are not included in the standard reaction scheme.

User-defined stoichiometric reactions can be added to the model to account for reactions which are not included in the standard reaction scheme. These reactions use a power-law rate expression which can be extended to more


complex rate expressions through the application of a user-written Fortran subroutine.

Model Structure This section outlines the structure of the Step-Growth kinetics model. It examines the theoretical framework in detail. The assumptions and limits of the algorithms are documented.

Reacting Groups and Species The first step in the development of any process simulation model is to determine the list of components. In Aspen Polymers it is also important to decide how to characterize the polymer components. A polymer can be broken down into segments any number of ways. For example, the nylon-6 repeat unit can be treated as a segment, or it can be divided into two segments corresponding to the portions of the repeat unit which came from the diacid and diamine monomers.

Segments The preferred method of segmenting the polymer component is to define segments corresponding to the monomers which are used to produce the polymer. This technique has two distinct advantages. First, the property models in Aspen Polymers use the monomer as a reference point for molecular size. Second, the reaction kinetics usually involve adding monomers to the end of growing polymer chains. Defining segments corresponding to the monomers makes it easy to write reactions corresponding to monomers and segments, for example monomer “A” → segment “A”.

The Step-Growth model assumes that the polymer is segmented in this manner. For monadic polymers such as nylon-6, this technique is straightforward. This method of segmenting the polymer is a bit unusual for dyadic polymers, such as PET, because it treats them as alternating copolymers. Thus, a molecule of PET with 100 PET units is defined as having a degree of polymerization of 200 in this model (100 terephthalate units and 100 glycol units).

Monofunctional monomers, such as benzoic acid, always correspond to an end-group segment in the model. Bifunctional monomers can end up inside a linear polymer chain as a repeat unit, or may be located at the end of the chain as an end group. Each symmetric bifunctional monomer (diacids, diols, diamines, etc.) corresponds to one repeat segment and one end-group segment. Asymmetric bifunctional monomers (monomers with two different types of end groups) correspond to one repeat unit and two end-group segments. Multifunctional monomers can correspond to several segments, as shown:

Corresponding Segment Formulas Monomer Type

Monomer Formula

End-Groups Repeat Unit Branch-3 Branch-4


Corresponding Segment Formulas Monomer Type

Monomer Formula

End-Groups Repeat Unit Branch-3 Branch-4

Acid CO

OHR CO

R --- --- ---

Ester CO

OR'R CO

R --- --- ---

Amine R NH2 R NH --- --- ---

Alcohol R OH R O --- --- ---

Diacid CO

OHRCO

HO CO

OHRCO

CO

RCO

--- ---

Diester CO

OR'RCO

R'O CO

OR'RCO

CO

RCO

--- ---

Carbonate CO

ORRO CO

OR CO

--- ---

Diamine R NH2H2N R NH2HN R NHHN --- ---

Diol R OHHO R OHO R OO --- ---

Amino acid CO

OHRH2N CO

RH2N

CO

OHRHN

CO

RHN --- ---

Lactic acid CO

OHRHO CO

RHO

CO

OHRO

CO

RO --- ---

Branch agent R(OH)3 ~O-R(OH)2

~O-R(OH)O~ RO OO

---

Branch agent R(OH)4 ~O-R(OH)3

~O-R(OH)2O~ RO O

O

OH RO OO

O

Reacting Functional Groups The Step-Growth reaction model generates reactions based on the types of functional groups found in the reactants. The model includes a list of pre-defined group types, as shown:

Description Type Examples†

Nucleophilic repeat units have two electron-strong sites.

NN-GRP HO(CH2)X OH HO OH

Electrophilic repeat units have two electron-weak sites.

EE-GRP

HO CO

(CH2) C OHO

X Cl C ClO

Mixed repeat units have one electrophilic site and one nucleophilic site.

EN-GRP

HO CO

(CH2) OHX HO COHO


Nucleophilic leaving groups are electron-strong end groups.

N-GRP

XHO CO

(CH2) C OHO

Cl C ClO

Electrophilic leaving groups are electron-weak end groups.

E-GRP OHXHO(CH2) HO OH

Nucleophilic modifiers are groups with a single nucleophilic site.

NX-GRP OH OH

Electrophilic modifiers are groups with a single electrophilic site.

EX-GRP

COHO

COHO

† Highlighted portion of component is the named reacting functional group.

Each functional group in the model is assigned a name and type. The names are used to distinguish between different groups with the same chemical functionality.

The following table shows the types of functional groups found in common monomers and the condensate products:

Reacting Functional Groups

Leaving Groups Segment Groups Monomer Type

Monomer Formula

Structure Type Structure Type Structure Type

Acid CO

OHR ~OH N-GRP --- ---

CO

R EX-GRP

Ester CO

OR'R ~OR’ N-GRP --- ---

CO

R EX-GRP

Amine R NH2 ~H E-GRP --- --- R NH NX-GRP

Alcohol R OH ~H E-GRP --- --- R O NX-GRP

Diacid CO

OHRCO

HO ~OH N-GRP --- ---

CO

RCO

EE-GRP

Diester CO

OR'RCO

R'O ~OR’ N-GRP --- ---

CO

RCO

EE-GRP

Carbonate CO

ORRO ~OR N-GRP --- ---

CO

EE-GRP

Diamine R NH2H2N ~H E-GRP --- --- R NHHN NN-GRP

Diol R OHHO ~H E-GRP --- --- R OO NN-GRP

Amino acid CO

OHRH2N

~H (amine) E-GRP ~OH (acid) N-GRP CO

RHN EN-GRP

Lactic acid CO

OHRHO ~H (alcohol) E-GRP ~OH (acid) N-GRP

CO

RO EN-GRP

Reacting Functional Groups In Common Types of Condensate Products


Water H2O ~H E-GRP ~OH N-GRP

Alcohol RO-H ~H E-GRP ~OR N-GRP

Reacting Species Since polymer components do not have a fixed structure, polymerization reactions must be written in terms of the polymer segments. The segments and standard components that make up the step-growth reaction network are referred to as reacting species. Each of these reacting species is made up of one or more reacting functional groups.

Once the reacting groups are defined, the structure of each reacting species is specified by defining the number of each reacting group in each reacting species. It is not necessary to specify a zero when a particular group is not in the species being defined.

Species Structure Validity

The model checks the species structures to verify they are valid and to see if there are any missing species. Species structures are considered valid if they follow these rules:

• Species may not be oligomer or polymer components.

• Species may include one EE-GRP, NN-GRP, or EN-GRP, but no species may have more than one of these three group types. Species may not contain more than one of any of these three groups.

• Species which are end group segments must include one E-GRP or one N-GRP.

• Species which are repeat segments may not include an E-GRP or N-GRP.

• Species which are monomers must have a balanced number of electrophilic groups and nucleophilic groups.

• Structures are unique - no two species may have the same structure.

The model determines every valid combination of the specified functional groups. Any combination which is not represented by a species structure is assumed to be a missing component. The model reports a warning message describing the structure of the species which was not specified and drops all reactions which would have involved this component. You can choose to ignore this warning if the missing component is unimportant in the process being simulated.

Oligomer Fractionation You can choose to include one or more oligomer components in the model. When this feature is used, the model will fractionate the polymer distribution between the polymer component and the various oligomer components. The fractionation algorithm assumes that the polymer follows the most probable distribution. These assumptions are valid when the reactions are reversible


and when the rate of rearrangement reactions is faster than the rate of the condensation reactions.

The oligomer feature can be used to track the loss of volatile short-chain oligomers from the polymer solution or melt. It can also be used to estimate oligomer concentrations to calculate reaction rates for ring closing reactions or other reactions that require a particular sequence of segments. Tracking oligomers, however, does require more simulation time and may make the model more difficult to converge.

The Options form lets you adjust the tolerance for the oligomer fractionation calculations. When several oligomers are tracked simultaneously it may be necessary to reduce the tolerance to improve reactor convergence.

The logic of the step-growth oligomer fractionation algorithm is summarized here:

Assumptions

Polymer molecules consist of alternating nucleophilic and electrophilic segments

Repeat segments in AB polymers, which are made up of EN-GRP groups, act as both a nucleophile and an electrophile. The end groups act as either electrophilic or nucleophilic segments, depending on which leaving group is attached to the end.

The probability of a particular segment being in a given point in the segment sequence is determined by the concentration of that segment and the concentration of all other segments of that type (note: this assumption is equivalent to assuming the most-probable distribution).

Equation

Definition of probability factors used to determine probability of a given sequence of segments:

Pf N

f NP

f Ef Ea

a a

ii ib

b b

jj j

= =∑ ∑

Pa = Probability that nucleophilic segment a occupies the next nucleophilic position

in the chain

Pb = Probability that electrophilic segment b occupies the next electrophilic

position in the chain

fa = Number of similar points of attachment in nucleophilic segment a (= 2 for

repeat segments which are composed of an NN-GRP)

fb = Number of similar points of attachment in electrophilic segment b (= 2 for

repeat segments which are composed of an EE-GRP)

Na = Concentration of nucleophilic segment “a”

Eb = Concentration of electrophilic segment “b”

i = Index corresponding to list of all nucleophilic segments

j = Index corresponding to list of all electrophilic segments

Example 1: calculation of expected concentration of oligomer with a sequence “ab”

C =P P ab a bλ0

Cab = Expected oligomer concentration


λ0 = Concentration zeroth moment of polymer (concentration of all polymer

molecules)

Example 2: calculation of expected concentration of oligomer with a sequence “aBABa”

C =P P P aBABa a B A2 2

0λ

Reaction Stoichiometry Generation The model predicts the stoichiometry of each step-growth reaction based on the structure of each of the reactants. The step-growth reaction generation algorithm is summarized here:

Reaction Type Reaction Scheme Reaction Generation Algorithm

Condensation - Monomer Addition

M M P Wxa yb xy ab+ → +2,

P M P Wn xa yb n xy ab, ,+ → ++1

M P P Wxa n yb n yx ab+ → ++, ,1

Find every combination by which nucleophilic monomers, Mxa , or end

segments Pxa , can react with

electrophilic monomers, M yb , or end

segments, Pyb , to give a condensate

molecule, Wab

Condensation - Polymer Addition

P P P Wn xa m yb n m xy ab, , ,+ → ++ Find every combination by which nucleophilic end segments, Pxa , can

react with end segments, Pyb , to give a

condensate molecule, Wab

Reverse Condensation - Terminal Monomer Loss

W P M MW P P M

ab xy xa yb

ab n xy n xa yb

+ → +

+ → +−

2

1

,

, ,

Find every combination by which a condensate molecule, Wab , can react

with a polymer molecule at the boundary between a nucleophilic repeat segment, x, and an electrophilic end group segment, y

Reverse Condensation - Scission

W P P Pab n xy n m xa m yb+ → +−, , , Find every combination by which a condensate molecule, Wab , can react

with a polymer molecule at the boundary between a nucleophilic repeat segment, x, and an electrophilic repeat segment, y

Forward Polycondensation

P P P Mn za m yx n m yz xa, , ,+ → ++ −1

Find every combination by which a nucleophilic end group segment, Pza ,

can react with a polymer molecule at the boundary between a nucleophilic repeat segment, x, and an electrophilic end segment, y

Reverse Polycondensation

M P P Pza n yx n m yz m xa+ → +− +, , ,1

Find every combination by which a nucleophilic monomer, Mxa , can react

with a polymer molecule at the


boundary between a nucleophilic repeat segment, x, and an electrophilic end segment, y

Re-arrangement P P P Pn za m xy n m q yz q xa, , , ,+ → ++ −

Find every combination by which a nucleophilic end group segment, Pza ,

can react with a polymer molecule at the boundary between a nucleophilic repeat segment, x, and an electrophilic repeat segment, y

By default, the step-growth model generates all types of step-growth reactions described above. You may “turn off” the reaction generation for a particular class of reactions by clearing the reaction from the Reaction Options section of the Options form.

Model-Generated Reactions There are two steps required to assign rate constants to model generated reactions. First, the rate constant values are specified in the Step-Growth Rate Constant form (SG-RATE-CON sentence). Then each set of rate constants is assigned a number for identification. Once the rate constants sets are defined, they can be assigned to the generated reactions.

Rate Expression for Model Generated Reactions The Step-Growth reactions model uses a modified power law rate expression, shown here:

Equation

Tref specified [ ][ ] ( )rate Nucl Elec f f P C k eT

TU flagn e i io

EaRT T T

ref

b

ii

i

ref

i

=⎛

⎝⎜⎜

⎞

⎠⎟⎟

−−

⎛

⎝⎜⎜

⎞

⎠⎟⎟

∑1 1

Tref unspecified [ ][ ] ( )rate Nucl Elec f f P C k e T U flagn e i io

EaRT b

ii

ii=

−

∑

Nomenclature

Symbol Description

[Nucl] Concentration of the attacking nucleophilic species, mol/L*

[Elec] Concentration of the attacking electrophilic species, mol/L*

fn Number of electrophilic leaving groups in the attacking nucleophilic species. This factor is 2 for diol and diamine monomers.


fe In reactions involving two victim species, fe is the number of electrophilic

groups in the electrophilic species. This factor is 2 for repeat units which contain EE-GRP groups.

In reactions involving one victim species, fe is the number of nucleophilic

leaving groups in the electrophilic species. This factor is 2 for diacid, diester, and carbonate monomers.

P In reactions involving two victim species, P is the probability of the victim nucleophilic species being adjacent to the victim electrophilic species. This probability factor is calculated by the model assuming the most probable distribution:

Pf N

f Nvns vns

ii i

= ∑

where:

fvns = Number of similar points of attachment in victim nucleophilic segment

(= 2 for NN-GRP repeat segments, 1 for all others)

Nvns = Concentration of victim nucleophilic segment

i = Index corresponding to list of all nucleophilic segments

i Index corresponding to the rate constant set number. The summation is performed over the specified list of rate constant set numbers.

Symbol Description

Ci Catalyst concentration for rate constant set i. If the catalyst species is specified, this is the concentration of the species. If the catalyst group is specified, this the group concentration. If both species and group are specified, this is the concentration of the species times the number of the specified group in the specified species. If the catalyst is not specified, this factor is set to one.

ko Pre-exponential factor in user-specified inverse-time units*

Ea Activation energy in user-specified mole-enthalpy units (default =0)

b Temperature exponent (default = 0)

R Universal gas constant in units consistent with the specified activation energy

T Temperature, K

Tref Optional reference temperature. Units may be specified, and they are converted to K inside the model.

flag User flag for rate constant set i. This flag points to an element of the user rate constant array.

U User rate constant vector calculated by the optional user rate constant subroutine. The user flag indicates the element number in this array which is used in a given rate expression. When the user flag is not specified, or when the user rate constant routine is not present, this parameter is set to 1.0.

* The concentration basis may be changed to other units using the Concentration

basis field on the Options sheet or using the optional concentration basis subroutine.

The reactions follow second order kinetics: one order with respect to the nucleophilic reactant and one order with respect to the electrophilic reactant.


Catalysts may make the reaction third order (one order with respect to catalyst).

The rate constants for the model-generated reactions are assumed to be on a functional group basis. The model applies correction factors to account for the number of like functional groups in each of the reactants. For example, in a reaction between a diol monomer and a diacid monomer, the specified rate constant is multiplied by four to account for the two acid groups in the diacid and the two alcohol groups in the diol.

Some reactions occur inside polymer chains at the intersection of two segments. The model applies a probability factor to estimate the concentration of the given segment pair. This probability is based on the most probable distribution. It assumes that the segments in the polymer alternate between nucleophilic segments and electrophilic segments. Repeat segments composed of an EN-GRP functional group behave as both nucleophiles and electrophiles, so these segments can alternate with themselves.

The standard rate expression is modified using the optional user rate constant feature. The rate constant form includes a parameter called the “user flag” which identifies an element in an array of user rate constants. This array is calculated by a user-written Fortran subroutine. The standard rate expression is multiplied by the user rate constants.

Assignment of Rate Constants to Model-Generated Reactions Six qualifiers are used to assign each set of rate constants to internally-generated step-growth reactions, the:

• Attacking nucleophilic reactant name (A-NUCL-SPEC)

• Attacking electrophilic leaving group name (A-ELEC-GRP)

• Victim electrophilic reactant name (V-ELEC-SPEC)

• Victim nucleophilic group name (V-NUCL-GRP)

• Victim electrophilic species name (V-ELEC-SPEC)

• Victim electrophilic group name (V-ELEC-GRP)

The following table contains an example illustrating how these identifiers are used to distinguish between reactions. Note that the victim electrophilic species is only used for reactions which occur at the intersection of two segments in a polymer molecule.


COHCOO

O(CH2)2O+O(CH2)2OH COHHOCOO

+ H2O

CHOCOO

O(CH2)2OH + CCOO

O(CH2)2O + H2O

109

COCH3HOCOO

HO(CH2)2OH + COCH3COO

HO(CH2)2O + H2O

1211

COCH3HOCOO

HO(CH2)2OH + COHCOO

HO(CH2)2O + CH3OH

34

CHOCOO

HO(CH2)2OH + CCOO

HO(CH2)2O + H2O5678

12

COHHOCOO

HO(CH2)2OH + COHCOO

HO(CH2)2O + H2O

Reaction Identifiers

Attacking Species Victim Species

Reaction A-Nucl-Spec A-Elec-Grp V-Elec-Spec V-Elec-Grp V-Nucl-Spec V-Nucl-Grp

1 HO(CH2)2OH

~H in alcohol

COHHOCOO

CCOO

none ~OH in acid

2 H2O ~H

COHCOO

CCOO

~O(CH2)2OH

~O(CH2)2O~

3 ~O(CH2)2OH

~H in alcohol

COHHOCOO

CCOO

none ~OH in acid

4 H2O ~H

COHCOO

CCOO

~O(CH2)2O~

~O(CH2)2O~

5 HO(CH2)2OH

~H in alcohol COHC

OO

CCOO

none ~OH in acid

6 H2O ~H

CCOO

CCOO

~O(CH2)2OH

~O(CH2)2O~

7 ~O(CH2)2OH

~H in alcohol COHC

OO

CCOO

none ~OH in acid

8 H2O ~H

CCOO

CCOO

~O(CH2)2O~

~O(CH2)2O~

9 HO(CH2)2OH

~H in alcohol

COCH3HOCOO

CCOO

none ~OH in acid

10 H2O ~H

COCH3COO

CCOO

~O(CH2)2OH

~O(CH2)2O~

11 HO(CH2)2OH

~H in alcohol

COCH3HOCOO

CCOO

none ~OCH3

12 CH3OH

~H COCH3COO

CCOO

~O(CH2)2OH

~O(CH2)2O~

It is not necessary to specify all of the reaction identifiers. For example, the only time it is necessary to specify the attacking nucleophilic species and the attacking electrophilic group is when this species contains more than one type of group and the two groups are not equally reactive.


Sets of reactions may be grouped together by making more general specifications. For example, if the attacking electrophilic group and victim nucleophilic group are the only two identifiers specified, then the rate constants are assigned to all reactions involving the named groups.

When more than one reaction set is specified, the sets are processed in reaction set number order, for example, reaction set one is processed before reaction set two, three, etc. When a match is found for a given reaction, the rate constant assignment algorithm moves to the next reaction, ignoring the remaining reaction sets. The algorithm is designed to find the “special cases” first, and then move on to the general cases.

Several examples illustrating the concept of rate constant assignment follow. These examples are based on the set of reactions provided previously.

Reaction Identifiers

Rxn-Sets

RC-Sets

A-Nucl-Spec

A-Elec-Grp

V-Elec-Spec

V-Elec-Grp

V-Nucl-Spec

V-Nucl-Grp

Case 1 Assign rate constant sets 1 and 2 to all of the model-generated reactions

1 1, 2 unspecified unspecified unspecified unspecified unspecified unspecified

Case 2 Assign rate constant sets 1 and 2 to reactions between alcohol groups in ethylene glycol and any acid groups

Assign rate constant sets 3 and 4 to reactions between alcohol groups in the polymer and any acid groups

Assign rate constant set 5 to reverse reactions involving methanol

Assign rate constant set 6 to reverse reactions involving water

1 1, 2 HO(CH2)2OH

unspecified unspecified unspecified unspecified ~OH in acid

2 3, 4 ~O(CH2)2OH

unspecified unspecified unspecified unspecified ~OH in acid

3 5 H2O unspecified unspecified unspecified unspecified unspecified

4 6 CH3OH

unspecified unspecified unspecified unspecified unspecified

Case 3 Assign rate constant sets 1 and 2 to reactions between alcohol groups in ethylene glycol and terephthalic acid

Assign rate constant sets 3 and 4 to all other reactions involving acid groups

Assign rate constant set 5 to reactions between water and glycol end groups

Assign rate constant set 6 to all other reverse reactions involving water

Assign rate constant set 7 to reactions between ethylene glycol and the methylester end groups in the polymer

Assign rate constant 8 to all other reactions

1 1, 2 HO(CH2)2OH

unspecified COHHOCOO

unspecified unspecified unspecified

2 3, 4 unspecified unspecified unspecified unspecified unspecified ~OH in acid

3 5 H2O unspecified unspecified unspecified ~O(CH2)2OH

unspecified

4 6 H2O unspecified unspecified unspecified unspecified unspecified

5 7 HO(CH2)2OH

unspecified COCH3COO

unspecified unspecified ~OCH3


6 8 unspecified unspecified unspecified unspecified unspecified unspecified

User Reactions The model cannot predict all types of reactions based on the specified structures. Reactions which are not predicted by the model can be included as user-specified reactions. These can include thermal scission reactions, monomer or segment reformation, end-group modification, etc.

The user-specified reactions apply a modified power-law rate expression, as shown here:

Equation

Tref specified ( )iref

bTTR

Ea

o iiinet flagUTTekCatalyst k

i

ref

i

⎟⎟⎠

⎞⎜⎜⎝

⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛−

− 11

, ][

Tref unspecified ( )ibRT

Ea

o iiinet flagUTekCatalyst k i

i−

= ][,

Assign User Rate Constants is used: ( )∑∏=i inetj

ajmm kCactivity rate mj

,

Assign User Rate Constants is not used: ( ) i)(mkC rate inetj

ajm

mj == ∏ ,

Nomenclature

Symbol Description

m User reaction number

i Rate constant set number

j Component number

Π Product operator

Cj Concentration* of component j, mol/L

iα Catalyst order term for catalyst i (default = 1)

mjα Power-law exponent for component j in reaction m

ko Pre-exponential factor in user-specified inverse-time and concentration units*

i,netk Net rate constant for set i




T Temperature, K

Tref Optional reference temperature. Units may be specified, they are converted to K in the model.


U User rate constant vector calculated by the optional user rate constant subroutine. The


user flag indicates the element number in this array which is used in a given rate expression. When the user flag is not specified, or when the user rate constant routine is not present, this parameter is set to 1.0.

* The concentration basis may be changed to other units using the Concentration

basis field on the Options sheet or using the optional concentration basis subroutine.

You can modify the standard rate expression using the optional user rate constant feature. The rate constant form includes a parameter called the “user flag” which identifies an element in an array of user rate constants. This array is calculated by a user-written Fortran subroutine. The standard rate expression is multiplied by the user rate constants as shown.

Assignment of Rate Constants to User Specified Reactions • There are two options for assigning rate constants to user-specified

reactions. By default, the model assumes there is exactly one set of rate constants for each reaction (for example, rate constant set “i” is used for reaction “i”).

Alternately, you may use the Assign User Rate Constant sheet to assign one or more sets of rate constants to each reaction. This feature is convenient in two situations:

• Models with a large number of user side reactions when the rate constants of the various reactions are equal or are related to each other algebraically.

• Reactions catalyzed by several catalysts simultaneously.

Conventional and Power-Law Components

Conventional components and segments can appear as reactants or products in the reaction stoichiometry. Each reaction must be mass balanced (the mass of the products must be equal to the mass of the reactants).

The power-law components can include conventional components, segments, or oligomers. Power-law coefficients can be specified for components which do not appear in the reaction stoichiometry, such as catalysts or inhibitors.

The model allows the reactants to have power-law constants of zero, but this is not recommended because it can lead to numerical problems in the reactor models. For example, if a reaction “A→B” is zeroth order with respect to component “A”, the reaction could have a positive rate even when component “A” is not present. This causes “non-negativity violation” integrator errors in RPlug and RBatch and causes convergence errors in RCSTR. To avoid these problems, specify a very small power-law coefficient, such as 1 10-8× .

A user-specified reaction can be accelerated by several different catalysts. In this situation, use the Assign User Rate Constants form to link multiple sets of rate constants to each reaction. Each set of rate constants may be associated with a particular catalyst.


When the side reaction kinetics are complicated, it can be easier to write the kinetics in the context of the available user kinetic subroutine. This subroutine is called from the Step-Growth reaction model. The argument list for this user-written Fortran subroutine includes the step-growth rate constants, user rate constants, species concentrations, group concentrations, species structures (number of each group in each species), and others.

User Subroutines The Step-Growth model can be customized by applying user-written subroutines. There are three types of subroutines available. The concentration basis for the model can be changed through a user basis subroutine. This subroutine can also be used to calculate the volume (RCSTR and RBatch) or area (RPlug) of the reacting phase. A user rate-constant subroutine can be used to extend the standard rate expression for model-generated or user-specified reactions. A user kinetics routine can be used to add reactions to the model which are too difficult to represent using the power-law approach, or to calculate user attributes for polymer characteristics which are not tracked by Aspen Polymers. These routines can be used together in any combination.

User Basis Subroutine The user basis subroutine can be used to calculate the component concentrations and the reacting-phase volume (area) basis used in the component and attribute conservation equations. Use this subroutine when rate constants are available in unusual concentration units not found in Aspen Polymers, or when the reacting phase volume or area calculated by the reactor model is not consistent with the real reactor (for example, in plug flow reactors with fixed liquid level).

This subroutine can also be used in conjunction with Fortran blocks and user component attributes to calculate mass-transfer rates and to account for the influence of mass-transfer limitations on the component concentrations in the reacting phase.

The argument list for the user basis routine is provided here. This argument list is prepared in a Fortran template called USRMTS.F, which is delivered with Aspen Polymers.

User Subroutine Arguments

SUBROUTINE USRMTS 1 SOUT, NSUBS, IDXSUB, ITYPE, XMW, 2 IDSCC, NPO, NBOPST, NIDS, IDS, 3 NINTB, INTB, NREALB, REALB, NINTM, 4 INTM, NREALM, REALM, NIWORK, IWORK, 5 NWORK, WORK, NCPM, IDXM, X, 6 X1, X2, Y, DUM1, FLOWL, 7 FLOWL1, FLOWL2, FLOWV, FLOWS, VLQ, 8 VL1, VL2, VV, VSALT, VLIQRX, 9 VL1RX, VL2RX, VVAPRX, VSLTRX, RFLRTN, * IFLRTN, CRATES, NTCAT, RATCAT, CSS, 1 VBASIS, IPOLY, NSEG, IDXSEG, AXPOS, 2 TIME )


Argument Descriptions Variable Usage Type Dimension Description

SOUT Input REAL*8 (1) Stream vector

NSUBS Input INTEGER Number of substreams in stream vector

IDXSUB Input INTEGER NSUBS Location of substreams in stream vector

ITYPE Input INTEGER NSUBS Substream type vector

1=MIXED

2=CISOLID

3=NC

XMW Input REAL*8 NCC Conventional component molecular weights

IDSCC Input HOLLERITH 2,NCC Conventional component ID array

NPO Input INTEGER Number of property methods

NBOPST Input INTEGER 6, NPO Property method array

NIDS Input INTEGER Number of reaction model IDs

NINTB Input INTEGER User-specified length of INTB array

INTB Retention INTEGER NINTB Reactor block integer parameters (See Integer and Real Parameters, page 151)

NREALB Input INTEGER

User-specified length of REALB array

REALB Retention REAL*8 NREALB Reactor block real parameters (See Integer and Real Parameters, page 151)

NINTM Input INTEGER User-specified length of INTM array

INTM Retention INTEGER NINTM User subroutine integer parameters (See Integer and Real Parameters, page 151)

NREALM Input INTEGER User-specified length of REALM array

REALM Retention REAL*8 NREALM User subroutine real parameters (See Integer and Real Parameters, page 151)

NIWORK Input INTEGER Length of user subroutine integer work vector

IWORK Work INTEGER NIWORK User subroutine integer work vector (See Local Work Arrays, page 151)

NWORK Input INTEGER Length of user subroutine real work vector

WORK Work REAL*8 NWORK User subroutine integer work vector (See Local Work Arrays, page 151)

NCPM Input INTEGER Number of components present in the mixed substream (See Packed Vectors, page 151)

IDXM Input REAL*8 NCPM Component sequence numbers (See Packed Vectors, page 151)

X Input REAL*8 NCPM Overall liquid mole fractions

X1 Input REAL*8 NCPM First liquid mole fractions

X2 Input REAL*8 NCPM Second liquid mole fractions

Y Input REAL*8 NCPM Vapor phase mole fractions

Dum1 Dummy REAL*8 (1) Argument reserved for future application

FLOWL Input REAL*8 Total liquid flow rate, kmol/sec


Variable Usage Type Dimension Description

FLOWL1 Input REAL*8 First liquid flow rate, kmol/sec

FLOWL2 Input REAL*8 Second liquid flow rate, kmol/sec

FLOWV Input REAL*8 Vapor flow rate, kmol/sec

FLOWS Input REAL*8 Salt flow rate, kmol/sec

VL Input REAL*8 Total liquid molar volume, m3/ kmol

VL1 Input REAL*8 First liquid molar volume, m3/ kmol

VL2 Input REAL*8 Second liquid molar volume, m3/ kmol

VV Input REAL*8 Vapor molar volume, m3/ kmol

VSALT Input REAL*8 Salt molar volume, m3/ kmol

VLIQRX Input REAL*8 Volume* of liquid in reactor, m3

VL1RX Input REAL*8 Volume* of first liquid in reactor, m3

VL2RX Input REAL*8 Volume* of second liquid in reactor, m3

VVAPRX Input REAL*8 Volume* of vapor in reactor, m3

VSLTRX Input REAL*8 Volume* of salt in reactor, m3

RFLRTN Retention REAL*8 (3, 1) Real retention for FLASH

IFLRTN Retention INTEGER (3, 1) Integer retention for FLASH

CRATES Output REAL*8 NCC Component rates of change, kmol/m3-sec

NTCAT Input INTEGER Number of component attributes

RATCAT Output REAL*8 NTCAT Component attribute rates of change, cat/m3-sec

CSS Output REAL*8 NCC Concentration vector for the active phase

VBASIS Output REAL*8 Holdup basis used to calculate reaction rates*

IPOLY Input INTEGER Reacting polymer component index

NSEG Input INTEGER Number of segment components

IDXSEG Input INTEGER NSEG Segment component index vector

AXPOS Input REAL*8 RPlug only: axial position, m

TIME Input REAL*8 RBatch only: time, sec

* When using molar concentrations, this parameter is volume of the reacting phase

in 3m in RCSTR and RBatch or the cross-sectional area of the reacting phase in m3 in RPlug.

Example 1 illustrates how to use the user basis routine to convert the concentration basis from the standard molar concentration basis (mol/L) to a mass concentration basis (mol/kg). (Note: the current version of Aspen Polymers supports several concentration basis through the CONC-BASIS keyword located on the Options form, we retain this example as a demonstration). Using these units, the reaction rates are calculated in units of mol/kg-sec. These rates are multiplied by the holdup basis (VBASIS) for the reactor in the Step-Growth model. For this reason, the holdup basis must be consistent with the concentration basis, e.g., it must be in kg. The holdup basis pertains to the reacting phase, it does not include the phases which do not react.


Example 1: A User Basis Routine For the Mass-Concentration Basis

CX

Mii

Liquid=

Ci = Mass-concentration of component i

Xi = Mole fraction of component i

M Liquid = Average molecular weight of components in the liquid phase

CALL PPMON_VOLL( TEMP, PRES, X, NCPMX, IDXM, 1 NBOPST, GLOBAL_LDIAG, 1, VLQ, DVS, KER) C-unpack the mole fraction vector into the molar concentrations... CALL SHS_UNPACK ( X , NCPMX, IDXM, CSS ) C --------------------------------------------------------------- C C concentration (mole/kg)=(mole I / mole liquid )*( mole liquid/kg) C C --------------------------------------------------------------- DO 10 I = 1, NCOMP_NCC CSS(I) = CSS(I) * 1.D3 / STWORK_XMWL 10 CONTINUE C --------------------------------------------------------------- C C reacting phase basis must be consistent with concentration basis (kg) C liquid mass inventory = liquid volume * density C C --------------------------------------------------------------- VBASIS = VLIQRX * STWORK_XMWL * 1.D-3 / VLQ RETURN

Note: This excerpt does not include the argument list and declarations section of the user basis routine.

The plug flow reactor model in Aspen Plus assumes that the vapor and liquid move at the same velocity through the reactor (e.g., no-slip conditions). This assumption is not consistent with the physical reality of polymer finishing reactors or wiped-film evaporators. The subroutine in Example 2 gets around the no-slip assumption in RPlug, allowing you to specify the volume occupied by the liquid phase. In this example, the user specifies the first integer argument in the RPlug block as “1” and specifies the first real argument as the volume fraction of the reactor occupied by the liquid phase.

Example 2: A User Basis Routine to Specify Liquid Volume in RPlug

UFRAC = 1.D0 IF ( REALB(1) .NE. RGLOB_RMISS ) UFRAC = REALB(1) IF ( INTB(1).EQ.1 ) THEN


C - unpack the mole fraction vector into the molar concentrations... CALL SHS_UNPACK ( X , NCPMX, IDXM, CSS ) C - concentration = mole fraction divided by molar volume of phase DO 20 I = 1, NCOMP_NCC CSS(I) = CSS(I) / VLQ 20 CONTINUE C - multiply total reactor volume by user-specified volume fraction - VBASIS = ( VLIQRX + VVAPRX ) * UFRAC C - this line makes RPlug calculate liquid residence time (not L+V) SOUT(NCOMP_NCC+8)=(SOUT(NCOMP_NCC+9)/ SOUT(NCOMP_NCC+6)) / VLQ RETURN END IF


User Rate-Constant Subroutine The user rate constant subroutine can be used to modify rate constant parameters for model-generated and user-specified reactions. Use this routine to modify the standard power-law rate expression for non-ideal reaction kinetics.

The user rate constant feature can be used to modify the standard power-law rate expression. This subroutine returns a list of real values which are stored in an array “RCUSER”. The length of this array is defined by the keyword NURC (number of user rate constants) in the user rate constant subroutine form (USER-VECS secondary keyword). Each of the elements in the user rate constant array can store a different user rate constant. The USER-FLAG keyword in the SG-RATE-CON and RATE-CON forms is used to specify which user rate constant is used with a particular set of rate constants.

Elements 1-NURC of RCUSER are calculated by a user rate-constant subroutine. The standard rate expression is multiplied by the USER-FLAGth element of the user rate constant vector RCUSER. By default, the USER-FLAG keyword is set to zero. The zeroth element of the RCUSER array is set to a value of 1.0, so the rate expression remains unmodified unless the USER-FLAG keyword is specified.

The argument list for the subroutine is provided here. This argument list is prepared in a Fortran template called USRRCS.F, which is delivered with Aspen Polymers.



SUBROUTINE USRRCS

1 SOUT, NSUBS, IDXSUB, ITYPE, XMW,

2 IDSCC, NPO, NBOPST, NIDS, IDS,

3 NINTB, INTB, NREALB, REALB, NINTR,

4 INTR, NREALR, REALR, NIWORK, IWORK,

5 NWORK, WORK, NCPM, IDXM, X,

6 X1, X2, Y, DUM1, VL,

7 VL1, VL2, VV, VSALT, IPOLY,

8 NSEG, IDXSEG, NOLIG, IDXOLI, NSGOLG,

9 NGROUP, IDGRP, NSPEC, IDXSPC, NFGSPC,

* CSS, CGROUP, TEMP, PRES, NURC,

1 RCUSER, CATWT )






1=MIXED

2=CISOLID

3=NC


IDSCC Input HOLLERITH 2, NCC Conventional component ID array


NBOPST Input INTEGER 6, NPO Property method array (used by FLASH)


IDS Input HOLLERITH 2,NIDS Reaction model ID list:

i,1 reactor block ID

i,2 reactor block type

i,3 reaction block ID

i,4 reaction block type

i,5 user subroutine ID



NREALB Input INTEGER User-specified length of REALB array


NINTR Input INTEGER User-specified length of INTM array

INTR Retention INTEGER NINTR User subroutine integer parameters (See Integer and Real Parameters, page 151)



NREALR Input INTEGER User-specified length of REALM array

REALR Retention REAL*8 NREALR User subroutine real parameters (See Integer and Real Parameters, page 151)












VL Input REAL*8 Total liquid molar volume, m3/kmol

VL1 Input REAL*8 First liquid molar volume, m3/kmol

VL2 Input REAL*8 Second liquid molar volume, m3/kmol

VV Input REAL*8 Vapor molar volume, m3/kmol

VSALT Input REAL*8 Salt molar volume, m3/kmol




NOLIG Input INTEGER Number of oligomer components

IDXOLI Input INTEGER NOLIG Oligomer component index vector

NSGOLG Input INTEGER NSEG, NOLIG

Segment frequency vector: contains number of each segment in each oligomer

NGROUP Input INTEGER Number of functional groups

IDGRP Input HOLLERITH NGROUP Functional group ID vector

NSPEC Input INTEGER Number of reacting species

IDXSPC Input INTEGER NSPEC Reacting species component index vector

NFGSPC Input INTEGER NSPEC, NGROUP

Group frequency vector: contains number of each functional group in each species

CSS Input REAL*8 NCC Concentration vector for reacting species

CGROUP Input REAL*8 NGROUP Concentration vector for reacting groups

TEMP Input REAL*8 Temperature, K

PRES Input REAL*8 Pressure, Pa



NURC Input INTEGER Number of user rate constants (See User Rate-Constant Subroutine, page 140)

RCUSER Output REAL*8 NURC User rate constant vector (See User Rate-Constant Subroutine, page 140)

CATWT Input REAL*8 Catalyst weight, kg (in RPLUG, weight/length)

Example 3 illustrates how to use this subroutine to implement complex rate expressions in the Step-Growth model.

Example 3: Implementing a Non-Ideal Rate Expression

Suppose a side reaction Q→Z is first order with respect to component Q and first order with respect to a catalyst C. The effectiveness of the catalyst is reduced by inhibitor I according to the following equation:

[ ] [ ][ ]C

Ca bT Ieff

actual=+ +1 ( )

Where:

[ ]Ceff = Effective catalyst concentration, mol/L

[ ]Cactual = Actual catalyst concentration, mol/L

[ ]I = Inhibitor concentration, mol/L

T = Temperature, K

a,b = Equation parameters

The net rate expression can thus be written as:

[ ][ ]rate Q

Ca bT I

k eactualo

ER T Tref=

+ +

−−

⎛

⎝⎜⎜

⎞

⎠⎟⎟

[ ]( )

*

1

1 1

Where:

ko = Pre-exponential factor, (L/mol)/sec

E* = Activation energy

R = Gas law constant

Tref = Reference temperature for ko

[Q] = Concentration of component Q, mol/L

The standard rate expression for side reactions is:

rate k e C U jo

ER T T

ii

ref i=⎛⎝⎜

⎞⎠⎟

−−

⎛

⎝⎜⎜

⎞

⎠⎟⎟

∏*

* ( )1 1

α


Where:

∏ = Product operator

Ci = Concentration of component i

αi = Power-law exponent for component i

U = User rate constant

j = User rate-constant flag

Suppose the rate constant for the uninhibited reaction is 3 10 3× − (L/mol)/min at 150°C, with an activation energy of 20 kcal/mol, and the inhibition rate constants are A=0.20 L/mol, B=0.001 L/mol-K. The stoichiometric coefficients and power-law exponents are specified directly in the Stoic and PowLaw-Exp keywords. The Arrehnius rate parameters and reference temperature are also specified directly in the model.

The parameters for the user rate constant equation can be specified using the optional REALRC list. Including the parameters in the REALRC list allows the model user to adjust these parameters using the standard variable accessing tools, such as Sensitivity, Design-Specification, and Data-Regression.

The resulting model input is summarized below:

USER-VECS NREALRC=2 NUSERRC=1 REALRC VALUE-LIST=0.2D0 0.001D0 STOIC 1 Q -1.0 / Z 1.0 POWLAW-EXP 1 Q 1.0 / C 1.0 RATE-CON 1 3D-3<1/MIN> 20.000<kcal/mol> TREF=150.0<C> URATECON=1

The power-law term from this equation is:

[ ][ ]rate k e C Qo

ER T Tref=

−−

⎛

⎝⎜⎜

⎞

⎠⎟⎟

* 1 1

Where:


[C] = Catalyst concentration, mol/L

ko = Pre-exponential factor

Thus, the required user rate constant is:

U ja bT I

( )( ( )[ ]

= =+ +

11

1

Where:

[I] = Inhibitor concentration, mol/L

T = Temperature, K

a, b = Equation parameters

An excerpt from the user rate constant subroutine for this equation is shown below:


C - Component Name - INTEGER ID_IN(2) DATA ID_IN /'INHI','BITO'/ C ====================================================================== C EXECUTABLE CODE C ====================================================================== C - find location of inhibitor in the list of components - DO 10 I = 1, NCOMP_NCC IF ( IDSCC(1,I).EQ.ID_IN(1).AND.IDSCC(2,I).EQ.ID_IN(2) ) I_IN=I 10 CONTINUE C - get the concentration of the inhibitor - C_IN = 0.0D0 IF ( I_IN .GT.0 ) C_IN = CSS( I_IN ) C ---------------------------------------------------------------------- C Parameters: each REALR element defaults to zero if not specified C ---------------------------------------------------------------------- A = 0.0D0 IF ( NREALR .GT. 0 ) A = REALR( 1 ) B = 0.0D0 IF ( NREALR .GT. 1 ) B = REALR( 2 ) C ---------------------------------------------------------------------- C User rate constant #1 U(1) = 1 / ( 1 + (A+BT)[I] ) C ---------------------------------------------------------------------- IF ( NURC.LT.1 ) GO TO 999 RCUSER(1) = 1.0D0 / ( 1.0D0 + ( A + B*TEMP ) * C_IN ) END IF 999 RETURN

User Kinetics Subroutine The user kinetics subroutine is used to supplement the built-in kinetic calculations. Use this subroutine when the side reaction kinetics are too complicated to represent through the user rate constant routine, or when previously written Fortran routines are to be interfaced to the Step-Growth model.

The argument list for this subroutine is provided here. The argument list and declarations are set up in a Fortran template called USRKIS.F, which is delivered with Aspen Polymers.



SUBROUTINE USRKIS( 1 SOUT, NSUBS, IDXSUB, ITYPE, XMW, 2 IDSCC, NPO, NBOPST, NIDS, IDS, 3 NINTB, INTB, NREALB, REALB, 4 NINTK, INTK, NREALK, REALK, NIWRK, 5 IWRK, NWRK, WRK, NCPMX, IDXM, 6 X, X1, X2, Y, DUMXS, 7 FLOWL, FLOWL1, FLOWL2, FLOWV, DUMFS, 8 VLQ, VLQ1, VLQ2, VVP, VOLSLT, 9 VLIQRX, VL1RX, VL2RX, VVAPRX, VSLTRX, * IPOLY, NSEG, IDXSEG, NOLIG, IDXOLI, 1 NSGOLG, NGROUP, IDGRP, NSPEC, IDXSPC, 2 NFGSPC, CSS, CGROUP, TEMP, PRES, 3 RFLRTN, IFLRTN, CRATES, NTCAT, RATCAT, 4 NRC, PREEXP, ACTNRG, TEXP, TREF, 5 IUFLAG, NURC, RCUSER )






1=MIXED

2=CISOLID

3=NC











i,5 user subroutine ID





NINTK Input INTEGER User-specified length of INTM array

INTK Retention INTEGER NINTK User subroutine integer parameters (See Integer and Real Parameters, page 151)

NREALK Input INTEGER User-specified length of REALM array



REALK Retention REAL*8 NREALK User subroutine real parameters (See Integer and Real Parameters, page 151)












FLOWL Input REAL*8 Total liquid flow rate, kmol / sec

FLOWL1 Input REAL*8 First liquid flow rate, kmol / sec

FLOWL2 Input REAL*8 Second liquid flow rate, kmol / sec

FLOWV Input REAL*8 Vapor flow rate, kmol / sec

FLOWS Input REAL*8 Salt flow rate, kmol / sec














NOLIG Input INTEGER Number of oligomer components

IDXOLI Input INTEGER NOLIG Oligomer component index vector

NSGOLG Input INTEGER NSEG, NOLIG

Segment frequency vector: contains number of each segment in each oligomer

NGROUP Input INTEGER Number of functional groups

IDGRP Input HOLLERITH 2,NGROUP Functional group ID vector



NSPEC Input INTEGER Number of reacting species

IDXSPC Input INTEGER NSPEC Reacting species component index vector

NFGSPC Input INTEGER NSPEC, NGROUP

Group frequency vector: contains number of each functional group in each species


CGROUP Input REAL*8 NGROUP Concentration vector for reacting groups


PRES Input REAL* Pressure, Pa

RFLRTN Retention REAL*8 3,(1) Real retention for FLASH

IFLRTN Retention INTEGER 3,(1) Integer retention for FLASH

CRATES Output REAL*8 NCC Component rates of change, kmol / m3 - sec

NTCAT Input INTEGER Total number of component attributes

RATCAT Output REAL*8 NTCAT Component attribute rates of change,

cat / m3 - sec

NSGRC Input INTEGER Number of sets of step-growth rate constants

PREEXP Input REAL*8 NSGRC Pre-exponential factors, 1/sec (See Step-Growth Rate Constants, page 149)

ACTNRG Input REAL*8 NSGRC Activation energies, J/kmol-K

TEXP Input REAL*8 NSGRC Temperature exponents, unitless

TREF Input REAL*8 NSGRC Reference temperatures, K

IUFLAG Input Integer*8 NSGRC User rate constant flags (See User Rate-Constant Subroutine, page 140)


NURC Input INTEGER Number of user rate constants


* Area in RPlug

The user kinetic subroutine returns the rate of change of the reacting species and the Class 2 component attributes (zeroth moment and segment flow rates). The subroutine may be applied to calculate user component attributes (CAUSRA etc.) to track color or other polymer properties which are related to the thermal history of the polymer.

Example 4 illustrates how the concentration of a color body can be tracked through user kinetics routine. The example assumes that the polymer color is proportional to the amount of unknown color bodies which are generated by side reactions. These unknown side reactions are sensitive to the thermal history of the polymer, according to an Arrehnius rate expression. The activation energy and pre-exponential factors of this expression are stored as the first and second REAL parameters for the user kinetics model.


Example 4: Tracking Polymer Color Using User Attributes in a Step-Growth User Kinetics Model

INTEGER IDUSRA(2) DATA IDUSRA /'CAUS','RA '/ C.....GAS CONSTANT IN KCAL/MOL-K... RGASKC = 1.987D-3 C.....locate CAUSRA attribute: LUSRA points to location in SOUT... LUSRA = SHS_LCATT( 1, IPOLY, IDUSRA ) C.....LURAT points to this attribute in the RATCAT vector... LURAT = LUSRA - NCOMP_NVCP C ---------------------------------------------------------------------- C Get the rate constants from the list of REAL parameters in the C user-kinetics section of the Step-Growth Subroutine form C REAL(1) A_CF Color Formation pre-exponential, 1/min C REAL(2) E_CF Color Formation activation energy, kcal/mol-K C ---------------------------------------------------------------------- A_CF = 0.D0 E_CF = 0.D0 IF ( NREALK .GT. 1 ) THEN IF ( REALK( 1 ) .GE. RGLOB_RMISS ) REALK( 1 ) = 0.D0 IF ( REALK( 2 ) .GE. RGLOB_RMISS ) REALK( 2 ) = 0.D0 A_CF = REALK( 1 ) / 60.D0 E_CF = REALK( 2 ) END IF C Calculate color formation rate in color-units/cubic-meter/second RATCAT( LURAT ) = A_CF * DEXP( -E_CF / ( RGASKC*TEMP ) ) RETURN

Step-Growth Rate Constants The step-growth reaction rate constants can be applied in the user kinetics subroutine. The rate constants are passed to this model as a set of arrays which are stored in rate constant set number order (the element number of the array corresponds to the reaction set number). These parameters are stored in SI units. The concentration basis for the pre-exponential factors are in molar concentration (mol/L) units. When a user concentration basis subroutine is used, the pre-exponential factors are assumed to be in units which are consistent with the user-calculated concentrations.

The user rate constants are also passed to the user kinetic subroutine. These parameters can be used “as is”, or they can be used with the step-growth rate constants to build rate expressions consistent with those used by the standard model. The array “UFLAG” is used to designate which user rate constant (if any) is assigned to a given set of step-growth rate constants. For example, if IUFLAG(2) = 1, then user rate constant 1 is assigned to step-growth rate constant set 2, and the pre-exponential factor can be adjusted accordingly. Example 5 illustrates how to apply user rate constants and step-growth rate constants in a user kinetics model.

Example 5: How to Apply User Rate Constants and Step-Growth Rate Constant in a Step-Growth User Kinetics Model


C set work space to calculate net rate constants LPREEX = 0 LNETRC = LPREEX + NSGRC C ---------------------------------------------------------------------- C Multiply step-growth pre-exponential factors by user rate constants C and store the results in the work array. C ---------------------------------------------------------------------- DO 10 IR = 1, NSGRC IRCU = IUFLAG( IR ) IF ( IRCU .EQ. 0 ) THEN WORK( LPREEX + IR ) = PREEXP( IR ) ELSE WORK( LPREEX + IR ) = PREEXP( IR ) * RCUSER( IRCU ) END IF 10 CONTINUE C ---------------------------------------------------------------------- C Calculate the net rate constants C ---------------------------------------------------------------------- DO 20 IR = 1, NSGRC IF ( TREF(IR) .EQ. 0 ) THEN TTERM1 = 1/TEMP TTERM2 = TEMP**TEXP(IR) ELSE TTERM1 = 1/TEMP - 1/TREF(IR) TTERM2 = ( TEMP / TREF )**TEXP(IR) END IF ETERM = DEXP( -ACTNRG(IR) * TTERM1 / PPGLOB_RGAS ) WORK( LNETRC+ IR ) = WORK( LPREEX+ IR ) * ETERM * TTERM2 20 CONTINUE

Note: The work array is used to store intermediate results in the calculations. The size of the work array must be specified in the subroutine form and must be large enough to avoid overwriting the end of the array.

INCL-COMPS List The reactor models in Aspen Polymers use mass-balance equations for each reacting component. In order to make the reactor models fast, components which do not appear in the reactions are excluded from these calculations.

The list of reacting components is automatically generated by the Step-Growth model. This list includes the polymer component, listed oligomers, components which appear in the list of reacting species, components which appear as products or reactants in the user-specified reactions, and components in the INCL-COMPS component list.

When user concentration basis or user kinetics subroutines are applied in a model, these subroutines can include reactions involving components which do not otherwise appear in the list of reacting components. These components should be added to the INCL-COMPS list to ensure they appear in the mass-balance equations.


Integer and Real Parameters Each user model has two sets of integer and real parameters. The first set comes from the subroutine form of the reactor block. The second set comes from the subroutine form of the step-growth reactions model. Each of these parameters are retained from one call to the next, thus these parameters can be used as model inputs, outputs, or retention.

The reactor block integer and real parameters can be used to specify data which are specific to a particular unit operation, such as reactor geometry, mass transfer coefficients, etc. The integer and real parameters in the subroutine forms can be used to specify global parameters, such as rate constants or physical property parameters.

Local Work Arrays You can use local work arrays by specifying the model workspace array length on the STEP-GROWTH Subroutine form. These work areas are not saved from one call to the next. All three user subroutines share a common work area, so you must zero out the work space at the start of each subroutine.

Packed Vectors Aspen Plus frequently uses a technique called “packing” to minimize simulation time. The user models previously described use packed vectors to track the mole fractions of each phase (vectors X, X1, X2, and Y). These vectors contain NCPM elements (Number of Components Present in the Mixed substream). The component index associated with each element is listed in the vector “IDXM”. All other vectors used by the model, including the rates vectors and the component concentration vectors, are unpacked.

Example 6: Calculating Unpacked Component Concentrations

Calculate unpacked component concentrations of the first liquid phase given the packed mole fractions of the first liquid phase and the molar volume of the first liquid phase.

IF ( VL1 .GT. 0.D0 .AND. FLOWL1.GT.0.D0 ) THEN DO 10 I = 1, NCPM CSS(I) = X1( IDXM( I ) ) / VL1 10 CONTINUE END IF

Note: NCPM steps were required to load the concentration vector. Since NCPM is always less than or equal to NCC (total number of conventional components), there is a reduction in the required number of steps to perform the operation.


Specifying Step-Growth Polymerization Kinetics

Accessing the Step-Growth Model To access the Step-Growth polymerization kinetic model:

1 From the Data Browser, click Reactions.

2 From the Reactions folder, click Reactions.

3 The Reactions object manager appears.

4 If the kinetic model already exists, double-click the desired Reaction ID in the object manager or click Edit to get to the input forms.

5 To add a new model, from the Reactions object manager, click New. If necessary, change the default ID for the reaction.

6 Select Step-Growth as the reaction type and click OK.

Specifying the Step-Growth Model The Step-Growth model input forms are divided into two folders: Specifications and User Subroutines.

Use the Specifications forms to define reacting species and functional groups, enter reaction rate constant parameters, and include user side reactions.

Use this sheet

To

Species Define reacting species and functional groups

Specify the name of the polymer being produced

Specify the names for linear oligomers (optional)

Reactions Generate and display model-generated reactions

Rate Constants Specify reaction rate constants for model-generated reactions

User Reactions Specify reaction stoichiometry and enter rate constants for user-specified reactions

User Rate Constants

Specify catalysts and reaction rate constants for user-specified reactions

Assign User Rate Constants

Assign one or more sets of rate constants to each user-specified reaction

Options Specify the reacting phase and concentration basis.

Change reaction convergence parameters.

Select report options.

Use the User Subroutines forms to specify the names and parameters for optional user subroutines.

Use this sheet To


Kinetics Specify the name of the user kinetics routine and give the integer and real arguments for the user arrays for this routine

Rate Constants Specify the name of the user kinetics routine, the number of user rate constants calculated by the routine, and to give the integer and real arguments for the user arrays for this routine

Basis Specify the name of the user concentration and reacting phase volume basis routine and give the integer and real arguments for the user arrays for this routine

Specifying Reacting Components You must specify the reacting species and functional groups on the Step-Growth Specifications Species sheet.

First specify the polymers and oligomers produced:

1 In the Polymer field, specify the polymer produced.

2 In the Oligomers field, list oligomers that you want the model to track.

3 In the species definition table, specify the functional groups contained in each reacting species and define each group type.

The structure of reacting species in terms of the reactive functional groups they contain must be defined. To do this:

1 In the Group field specify an ID name for each functional group type present in the reacting species.

2 For each group, select a type from the group type field.

3 List the species in the Species field.

These species can be monomers, condensates, or segments.

The resulting form is a spreadsheet, with each column representing a functional group and each row representing a reacting species. The cells in the spreadsheet correspond to the number of each functional group in each species.

4 In the number field for each species, specify the number of each defined functional group contained in that species.

Unspecified fields are interpreted as zeros.

Listing Built-In Reactions The step-growth model generates reactions based on the functional group definition of reacting species. You can view the system-generated reactions, by clicking the Generate Reactions button on the Specifications Reactions sheet.

In the Reaction summary listing for each reaction, the first column indicates the reaction type. The second column lists the reactants, and the last column lists the products. The Data Browser window can be resized to better view the reaction listing.


Specifying Built-In Reaction Rate Constants You can define the catalysts and rate constants for system-generated reactions. The model applies a modified power-law rate expression, which can be customized through a user-written rate constant subroutine. By default, the model assumes concentrations are in mol/liter. Another concentration basis can be applied through a user-written basis subroutine.

To specify rate constants:

1 Go to the Rate constants sheet.

2 In the reaction No. field, assign a unique integer identifier for a set of rate constant parameters.

3 In the Catalyst Species field, specify the name of a catalyst species associated with the rate constant set.

You can leave this field unspecified if the reaction is uncatalyzed, or if the catalyst is defined as a functional group.

4 In the Catalyst Group field, specify the name of a catalyst functional group associated with the rate constant set.

You can leave this field unspecified if the reaction is uncatalyzed, or if the catalyst is defined as a species.

5 Enter the rate constant parameters: ko for Pre-exponential factor, Ea for Activation energy, b for Temperature exponent, Tref for Reference temperature.

6 Request any user rate constant expression in the User flag field.

7 Repeat these steps as needed to specify the list of rate constant parameters.

Assigning Rate Constants to Reactions You can assign rate constants to individual reactions using the reaction stoichiometry, or you can assign rate constants to sets or reactions using the appropriate reaction identifiers.

To assign the rate constants set:

1 Click the Assign Rate Constants button on the Specifications Rate constants sheet.

2 Click the Global tab to assign rate constants to a set of reactions or use the Individual sheet to assign rate constants to individual reactions.

3 Go to the Rate Constant Sets field, select from the list of pre-defined rate constant sets for each reaction.

Including User Reactions You can add user reactions to the built-in set. For this you must specify a reaction stoichiometry and the associated rate constants. The model applies a modified rate expression, which can be customized through a user-written rate constant subroutine.

To add user reactions use the following options found on the Specifications User Reactions sheet:


Click To

New Add new reactions to the scheme

Edit Specify reaction stoichiometry and power-law exponents

Rate Constants Specify reaction rate constant parameters for the reactions

Click to select a reaction. Click a reaction then Control-Click to include additional reactions for multiple selections. Double-click to edit a reaction.

In addition, you can use the following buttons:

Click To

Hide/Reveal Exclude/Include a reaction from the calculations

Delete Permanently remove a reaction from the model

Adding or Editing User Reactions In the User Reactions sheet, to add a new reaction to the scheme or edit an existing reaction, open the Edit subform. When you open the Edit subform, a unique number is assigned in the Reaction no. field, to the reaction being added.

To add or edit your reaction:

1 On the Edit subform, specify the Component ID and stoichiometric Coefficient for the reactants.

Reactants must have a negative coefficient.

2 Specify the Component ID and stoichiometric Coefficient for the products.

Products must have a positive coefficient.

3 Click to check the Completion Status

− or − Click Close to return to the reaction summary.

Specifying Rate Constants for User Reactions All the rate constants for user-specified reactions are summarized in a grid on the User Rate Constants tab:

1 In the ko field, enter the pre-exponential factor.

2 In the Ea field, enter the activation energy.

3 In the b field, enter the temperature exponent.


4 In the Tref field, enter the reference temperature.

Note: Use the Catalyst Species field to associate a rate constant with a particular catalyst. If you leave this field blank the model drops the catalyst term from the rate expression. Use the Catalyst Order field to specify the reaction order with respect to the catalyst (the model assumes first order by default).

Assigning Rate Constants to User Reactions By default, the model assumes one set of rate parameters for each reaction. (For example, rate constants in row 1 apply to user reaction 1). Alternately, you may assign one or more rate constants to each reaction using the Assign User Rate Constants form.

When several rate constants are assigned to a reaction the model calculates a net rate constant by summing all of the listed rate constants and multiplying the sum by a specified activity.

To assign rate constants to user reactions:

1 On the Assign User Rate Constants form, use the Activity field to specify the activity factor.

2 In the Rate Constant Sets field, select from the list of pre-defined rate constant sets for each reaction.

Selecting Report Options You can select which format to use for the step-growth reactions in the report file. On the Options sheet, go to the Report frame to request a reaction report. Then, select a Summary or Detailed format.

Selecting the Reacting Phase The Options form lets you specify the phase in which the reactions occur.

Select the appropriate phase from the list in the Reacting Phase field. All of the reactions in a particular step-growth object are assumed to take place in the same phase.

Note: You must specify the Valid Phases keyword for each reactor model referencing the kinetics to ensure the specified reacting phase exists.

If the Reacting Phase option is set to Liquid-1 or Liquid-2 the model assumes two liquid phases exist. When the named phase is not present, the model prints a warning message and sets the reaction rates to zero. There are two options for handling phase collapse:

• Select the Use bulk liquid phase option to force the model to apply the specified reaction kinetics to the bulk phase when the named phase disappears.

• Select the Suppress warnings option to deactivate the warning messages associated with phase collapse.


These options are especially convenient when modeling simultaneous reactions in two liquid phases using two step-growth models. In this situation, you would typically select the Use bulk liquid option for one phase and not the other (to avoid double-counting reactions when one phase collapses).

Specifying Units of Measurement for Pre-Exponential Factors Reaction rates are defined on a molar basis (moles per volume per time) . The time units for the pre-exponential factors are specified directly on the Rate Constant forms.

By default, the concentration units are presumed to be in SI units (kmole/m3 or mole/L).

You change the concentration basis to other units using the Concentration Basis field of the Options sheet. Alternately, you may apply a user basis subroutine.

Including a User Kinetic Subroutine Use the User Subroutines Kinetics form to specify parameters for user kinetics calculations:

1 In subroutine Name, enter the name of the Fortran subroutine.

2 Specify the size of vectors for Integer, Real in Number of parameters, and Length of work arrays.

3 Enter integer and real parameter values in Values for parameters columns.

4 Click Include Comps to specify components to be included in material balance convergence.

Including a User Rate Constant Subroutine Use the User Subroutines Rate Constants form to specify parameters for user rate constants calculations:


2 Specify the size of vectors for Integer, Real and No. const. in Number of parameters.

3 Specify the size of vectors of Integer and Real in Length of work arrays.


Including a User Basis Subroutine Use the User Subroutines Basis form to specify parameters for basis calculations:



2 Specify the size of vectors for Integer and Real in the Number of parameters and Length of work arrays.


References Billmeyer, F. W. (1971). Textbook of Polymer Science. New York: Wiley.

Gupta, S. K, & Kumar, A. (1987). Reaction Engineering of Step-Growth Polymerization. New York: Plenum.

Jacobsen, L. L., & Ray, W. H. (1992). Unified Modeling for Polycondensation Kinetics. J. Macromol. Sci.-Rev. Macromol. Chem. Phys.

Kaufman, H. S., & Falcetta, J. J. (Eds). (1977). Introduction to Polymer Science and Technology: An SPE Textbook. New York: Wiley.

McKetta, J. J. (Ed.). (1992). Encyclopedia of Chemical Processing and Design, 39 & 40. New York: Marcel Dekker.

Rodriguez, F. (1989). Principles of Polymer Systems. New York: Hemisphere.

9 Free-Radical Bulk Polymerization Model 159

9 Free-Radical Bulk Polymerization Model

This section covers the free-radical bulk/solution polymerization model available in Aspen Polymers (formerly known as Aspen Polymers Plus).



• Free-Radical Bulk/Solution Processes, 160



• Polymer Properties Calculated, 187

• Specifying Free-Radical Polymerization Kinetics, 189

Several example applications of the free-radical bulk/solution polymerization model are given in the Aspen Polymers Examples & Applications Case Book.

The Examples & Applications Case Book provide process details and the kinetics of polymerization for specific monomer-polymer systems.

Summary of Applications The free-radical bulk/solution polymerization model is applicable to bulk and solution polymerization processes. Some examples of applicable polymers are:

• General purpose polystyrene - Made by polymerization of styrene monomer with or without solvent fed continuously to reactor.

• High impact polystyrene - Made by polymerization of an unsaturated rubber dissolved in styrene in a solution process. Also produced in mass-suspension processes.

• Poly(vinyl chloride) - Produced in bulk polymerization using monomer-soluble free radical initiators. Most of the homopolymers and copolymers of vinyl chloride, however, are produced by suspension polymerization.

• Poly(vinyl acetate) - Produced industrially by the polymerization of vinyl acetate in bulk or solution processes. Also produced in suspension and emulsion processes. Both batch and continuous processes are used.

160 9 Free-Radical Bulk Polymerization Model

• Poly(vinyl alcohol) - Poly(vinyl acetate) is converted into the corresponding poly(vinyl alcohol) by direct hydrolysis or catalyzed alcoholysis. The reaction can be catalyzed by strong acids or strong bases.

• Poly(methyl methacrylate) - The vast majority of commercially prepared acrylic polymers and methacrylic polymers are copolymers. Commercially they are prepared by solution polymerization. They are also produced by emulsion polymerization and suspension polymerization.

• Low density polyethylene - Made by high pressure, free radical processes in either a tubular reactor or a stirred autoclave. Typical commercial processes include staged compression, initiator injection, partial conversion of ethylene to polymer, separation of ethylene from polymer, extrusion of molten polymer, and cooling of ethylene.

• The Free-Radical model may also be used to simulate suspension polymerization processes in which the polymer is completely soluble in the organic (monomer) phase. Two reaction models can be applied together to represent reactions in each liquid phase. An example of this process is:

• Poly(styrene) - Poly(styrene) may be produced in a continuous suspension process in a series of CSTR type reactors.

Free-Radical Bulk/Solution Processes Free-radical polymerization accounts for a large proportion (more than 40% by weight) of the commodity grade polymers. It is employed in the synthesis of countless homo- and copolymers using monomers that are either monosubstituted ethylenes ( )RHC CH= 2 or 1,1-disubstituted ethylenes

( )R R C CH1 2 2= .

Free-radical polymerization usually takes place with the monomer in the liquid phase. Several types of processes are used. A solvent or suspending medium may be used, and the polymer formed may be soluble, insoluble, or swelled by the monomer and solvent. Commercially important processes for free-radical polymerization include bulk, solution, suspension, and emulsion polymerization.

Bulk and Solution Polymerization

Bulk and solution polymerization processes are characterized by the fact that the reactions proceed in a single phase. Typically the monomers are fed to a reactor with or without a solvent. A small amount of initiator is also fed. At the reaction temperature, the initiator decomposes to form radicals that initiate the polymerization reactions. The polymer formed is usually soluble in the monomer/solvent mixture. However, in some systems, such as PVC, the polymer is insoluble and forms a separate phase.

The most commonly used reactor types include batch, semi-batch, continuous stirred-tank and tubular reactors. Flowsheets consisting of several reactors in series are common. The main technical challenges with bulk/solution polymerization processes are heat removal, handling of the highly viscous


liquid, and recovery of residual monomer/solvent. Several modes of heat removal can be employed, including jacket cooling, internal cooling coils/baffles, external heat exchangers and reflux condensors.

Reaction Kinetic Scheme Most free-radical polymerizations have at least four basic reaction steps:

• Initiation

• Propagation

• Chain transfer to a small molecule (i.e. monomer, solvent or transfer agent)

• Termination

These reactions occur simultaneously during the polymerization. For branched polymers additional reactions for long and short chain branching can also be present. A comprehensive kinetic scheme for the free-radical homo- and copolymerization of up to N m monomers has been built into Aspen Polymers. The scheme includes most of the reactions commonly used for modeling free-radical polymerization. The model also includes several optional reactions:

• Terminal double bond polymerization

• Pendent double bond polymerization (for diene monomers)

• Head-to-head propagation (for asymmetric monomers)

• Cis- and trans- propagation (for diene monomers)

• Primary and secondary decomposition of bifunctional initiators

Reactions such as depropagation and random chain scission are not included in the current model. These reactions may be added to the built-in scheme in the future.

The main reactions in the current built-in free-radical kinetic scheme is shown here :


Built-in Free-Radical Polymerization Kinetic Scheme

The nomenclature used in the free-radical kinetic scheme is shown here:

Symbol Description


Symbol Description

Symbols Used in the Population Balance Equations

Ak Chain transfer agent of type k

21 , BB Reaction by-products (optional for some reactions)

Ck Coinitiator or catalyst of type k

Dn Dead polymer chain of length n ( , , ... )= n n nm1 2

jknD Polymer chain of length n containing an undecomposed bifunctional

initiator fragment of type k attached to penultimate segment of type j =i

nD Polymer chain of length n containing a terminal double bond of type i

)(vinylinD Polymer chain of length n reacting at an internal double bond of type i

(e.g., a diene segment of type i in the vinyl configuration) ij

TDBf Fraction of reactions between species i and j resulting in the formation of a terminal double bond of type i

Ik Standard initiator of type k

BkI Bifunctional initiator of type k

M j Monomer of type j

Pni

Live polymer chain of length n having an active segment of type i

)(cisinP Live polymer chain of length n having an active diene segment of type i

in the cis configuration. )(transi

nP Live polymer chain of length n having an active diene segment of type i in the trans configuration.

R•

Primary radicals

Sk Solvent of type k (for solution polymerization)

Xk Inhibitor of type k

21 ,αα Stoichiometric coefficients for reaction by-products B1, B2

kε Initiator efficiency factor for initiator k

Ak Chain transfer agent of type k

21 , BB Reaction by-products (optional for some reactions)

Ck Coinitiator or catalyst of type k

Dn Dead polymer chain of length n ( , , ... )= n n nm1 2

Symbol Description

Symbols Used in Reaction Rate and Moment Balance Equations

a b c, , Coefficients for the induced (thermal, radiation) initiation rate

C Concentration of a reacting non-polymeric species. The following


Symbol Description

subscripts are used to identify the component:

Ak Chain transfer agent k

Ck Catalyst or coinitiator k

Ik Initiator or bifunctional initiator k

Mi Monomer i

Sk Solvent k

Xk Inhibitor k

k Net rate constant (see Equation 3.1 on page 166 ). The following subscripts are used to identify the reaction types:

bs Beta scission

bid Bifunctional initiator primary decomposition

cis Cis-propagation

ic Catalyzed initiation

id Standard initiator decomposition

hth Head-to-head propagation

p Propagation (polymerization)

pdb Pendent double bond polymerization

pi Primary chain initiation

scb Short chain branching

si Special initiation (induced initiation)

sid Secondary decomposition of bifunctional initiator

tc Termination by combination

td Termination by disproportionation

tdbp Terminal double bond polymerization

tra Chain transfer to agent

trans Trans-propagation

trm Chain transfer to monomer

trp Chain transfer to polymer (long chain branching)

trs Chain transfer to solvent

x Inhibition

N Number of (A=agents, BI=bifunctional initiators, C=catalysts, CI=coinitiators, I=standard initiators, M=monomers, S=solvents, X=inhibitors)

krN Number of radicals (1 or 2) formed from the decomposition of initiator of

type k

21 ,αα Stoichiometric coefficients for reaction by-products B1, B2

kε Initiator efficiency factor for initiator k

ijTDBf Fraction of reactions between species i and j resulting in the formation of

a terminal double bond of type i i0μ Zeroth moment of live polymer with respect to active segment of type i

j1μ First moment of live polymer with respect to segment j

λ0 Zeroth moment of bulk polymer (live + dead)


Symbol Description

j1λ First moment of bulk polymer (live + dead) with respect to segment j

λ2 Second moment of bulk polymer (live + dead)

=jaλ Moment a (a=0, 1, 2, etc) of polymer molecules with terminal double

bond of type j

ji,θ Flow rate of dyads consisting of i and j segments (these values are stored in the DYADFLOW attribute)

iφ Molar fraction of diene segment i in the vinyl configuration (zero for non-diene segments) (related to VINYLFRA attribute)

kψ Concentration of undecomposed initiator fragment k in the bulk polymer (live + dead) (related to FRAGFLOW attribute)

In the discussion that follows, a polymer chain is considered to be made up of monomer units or segments derived from the propagating monomers. Typically there will be one segment type associated with each monomer. However, it is possible to define several segment types associated with a single monomer. This may be necessary, for example, for modeling the tacticity of a polymer, or head-to-head versus head-to-tail incorporation of an asymmetric monomer ( )RHC CH= 2 .

Polymer Chain Terms

The term live polymer chain ( )Pni refers to growing polymer chains containing

n segments, with a radical attached to a segment of type i, i.e., segment formed from monomer i. The term dead polymer chain ( )Dn refers to terminated polymer chains that do not have an attached radical. The term bulk polymer chain is used to refer to the sum of the live and dead polymer chains. The subscript n refers to the chain length in terms of the number of segments or monomer units incorporated in the polymer chain. Live chains are reactive and can participate in the polymerization reactions while dead chains are usually considered inert, except when long chain branching reactions are important.

The radical attached to one end of a live polymer chain is considered to be mobile and moves away from the initiator fragment with every addition of a monomer molecule. It is believed that after a few monomer additions the chemistry of the initiator fragment and developing chain microstructure will not have a strong influence on the mode of monomer addition.

The free-radical kinetic model assumes that the reactivity of a live polymer chain depends only on the active segment containing the radical, and is independent of the polymer chain length and other structural properties. This assumption was used in writing the rate expressions for the reactions shown in the Built-in Free-Radical Polymerization Kinetic Scheme figure on page 162.

For example, in the propagation reaction, the rate of propagation ( )Rpij is

independent of the polymer chain length. It depends only on the concentration of monomer j and the concentration of live polymer chains with active segments of type i. Models using this assumption are referred to as terminal models in the polymerization literature.


For copolymerization, the built-in kinetics routine allows the user to specify the number of monomers used. Similarly, the user has the flexibility to specify the number of each type of reactive species used in the polymerization, e.g. initiators, chain transfer agents, solvents and inhibitors. The user can easily setup the built-in kinetics to model a specific free-radical polymerization by selecting a subset of the reactions shown in the Built-in Free-Radical Polymerization Kinetic Scheme figure on page 162. It is necessary that the subset include a chain initiation and a propagation reaction. Frequently, at least one termination, chain transfer, or inhibition reaction to produce dead polymer is also selected.

The rate constants for each reaction in the built-in kinetics is calculated at the reaction temperature and pressure using the modified Arrhenius equation shown below with user specified parameters: pre-exponential (or frequency) factor, activation energy, activation volume, and reference temperature:

Rate Constant

gref

o fTTR

VPREakk

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛ Δ

−−

=11exp (3.1)

Where:

ko = Pre-exponential factor in l/sec for first order reactions,

and m kmol s3 / − for second order reactions

Ea = Activation energy in mole-enthalpy units

ΔV = Activation volume in volume/mole units

P = Reaction pressure

R = Universal gas constant

refT

= Reference temperature

gf

= Gel effect factor from optional built-in or user-defined gel effect correlation

The second term in the exponential function contains an activation volume that is important for high pressure polymerization systems. For low to moderate pressures, the activation volume is typically set to default value of zero. This term is used to account for the pressure dependence of the reaction rate constant.

The free-radical model allows the rate expression to be modified by a gel

effect term, gf. The gel effect term can be calculated using one of several

built-in correlations or it can be calculated by an optional user-defined gel effect subroutine.

The model allows any number of bifunctional initiators, however the maximum number of unique bifunctional initiators (used throughout the flowsheet) must be specified on the Polymers, Options subform. This parameter is used to dimension the FRAGFLOW polymer component attribute, which is used to track the flow rate of undecomposed initiator fragments. The FRAGFLOW attribute must be included in the attribute list in the Polymers,


Polymers subform. Bifunctional and standard initiators can be used in the same model.

Initiation The initiation step involves the generation of reactive free-radicals followed by the addition of a monomer molecule (chain initiation) to form chain radicals of

unit length ( )Pi1 . The non-chain or primary radicals ( )R• may be generated by

the thermal decomposition of a chemical initiator, a catalyzed initiation reaction involving electron transfer from ions, or by thermal/radiation induced mechanisms. Three types of standard initiation reactions are included in the built-in kinetics:

• Initiator decomposition reaction

• Induced initiation reaction

• Catalyzed initiation reaction

The initiator decomposition reaction accounts for primary radical generation from the thermal decomposition of chemical initiators.

The induced initiation reaction can be configured to account for the generation of radicals by thermal and radiation induced mechanisms from the monomers themselves, with or without the use of a coinitiator or promoter.

The catalyzed initiation reaction can be used to account for redox initiation, which has found wide application in aqueous emulsion polymerization systems.

The most commonly used radical generation method is the thermal decomposition of chemical initiators (usually peroxide or azo compounds) which decompose to form radicals when heated to an appropriate temperature. Only small amounts of the chemical initiator (less than 1 wt. % based on monomer) are needed. However, due to their high activation energies chemical initiators have a relatively narrow useful temperature range (approx. 30°C) over which the decomposition rates are neither too fast nor too slow.

Some processes, notably bulk polystyrene polymerization, use initiators with two active sites. These bifunctional initiators decompose in two stages, providing greater control over the molecular weight distribution of the product.

The free-radical model includes two reactions associated with bifunctional initiators:

• Bifunctional initiator decomposition (primary decomposition)

• Secondary initiator decomposition (primary decomposition)

• The primary decomposition reaction generates a pair of radicals, an undecomposed initiator fragment, and optional by-products. The undecomposed fragment is tracked using the FRAGFLOW polymer component attribute.

• The initiator fragment decomposes in the secondary decomposition reaction, generating a free radical and a polymeric radical.


Initiator Decomposition Reaction

The initiator decomposition reaction is modeled as a first order thermal decomposition reaction:

Ikkid

kidkkrkkk CkRBBRNI =++→ •

2,21,1 ααε

This rate expression )( kidR describes the rate for the thermal decomposition of

standard initiator k. The symbols 1B and 2B represent optional user-specified reaction by-products. This feature lets you track the formation of low-molecular weight decomposition by-products, such as carbon dioxide, which may be generated as the initiators decompose. The byproduct formation rates are determined by:

IkkidkkBIk

kidkkB CkRCkR ,2,,1, 21

αα ==

For mass balance purposes, the polymer mass generation rate is incremented by the initiator mass consumption rate, less the mass formation rate of by-products.

The rate expression for the formation of primary radicals from the thermal decomposition of standard initiators is given by:

∑=

=IN

kIk

kidk

kr

radid CkNR

1ε

There are a number of user specifiable parameters associated with this reaction. The user can specify more than one initiator to model systems where multiple initiators with different half-lives are used to control the initiation rate over the course of the polymerization. Depending on the initiator, either one or two primary radicals may be formed, hence the parameter Nrk should be set to 1 or 2. Bifunctional initiators, which can produce up to four radicals, are handled explicitly using another set of reactions described below. A fraction of the radicals generated by decomposition undergo radical recombination in the radical-cage, leading to stable byproducts. The initiator efficiency factor, kε , is used to specify the

fraction of radicals which are not destroyed by the cage effect. The efficiency factor can be adjusted using an efficiency gel effect correlation as described later in the text.

The rate constant kidk is calculated using a modified Arrhenius equation

(Equation 3.1 on page 166) with three parameters: pre-exponential factor, activation energy and activation volume. As noted previously, the activation volume accounts for the pressure dependence of the rate constant. This parameter is typically non-zero only at high pressures. Appendix B lists initiator decomposition rate constant parameters (pre-exponential factor and activation energies) for many commonly used initiators. These rate parameters are included in the INITIATOR databank and are automatically loaded into the model each time the reaction network is generated.

The standard rate expression can be modified using an optional built-in or user-defined gel effect correlation as described later in the text.


Induced Initiation Reaction

Free-radicals can also be generated from some monomers by thermal, radiative (UV, electron beam or gamma rays) or induced mechanisms. For example, styrene at temperatures above 120°C has a significant thermal initiation rate. The thermal initiation mechanism for styrene is believed to be 3rd-order in monomer (Hui & Hamielec, 1972). This reaction results in the formation of significant amounts of cyclic dimers and trimers which have to be removed during devolatilization. Hence, thermal initiation is not favored commercially.

Radiation initiation has been used mainly for polymer modification to induce branching, crosslinking or grafting reactions. The induced initiation reaction, shown below, can be configured to model both these initiation mechanisms:

)(h C C k = R P C + M cjbjM

ajCksisi2211

j1kj j

ναα kjkjkjkj BB ++→

For thermal initiation, the rate should be bjMj

jsi

jsi CkR = (set a cj j, to zero).

For radiation initiation, the rate should be cjbjMj

jsi

jsi hCkR )( ν= (set ja to zero)

The induced initiation reaction can also account for the effects of using an initiator or promoter )( kC to increase the rate of radical generation.

The parameters 1α and 2α are optional stoichiometric coefficients related to

by-products 1B and 2B . The byproduct formation rates are determined by:

cjbjMj

ajCk

jsi

kjkjB

cjbjMj

ajCk

jsi

kjkjB hCCkRhCCkR )()( 2211 νανα ==

The molar consumption rate of the monomer is equal to kjsiR . If a promoter is

specified in the reaction, its molar consumption rate is also set to kjsiR . The

mass generation rate of the polymer is set equal to the mass consumption rate of the monomer ( jM ) and promoter ( kC ).

The special initiation reactions generate live polymer directly, thus this reaction does not contribute to radical generation.

Catalyzed Initiation Reaction

The catalyzed initiation reaction is similar to the initiator decomposition reaction except that a catalyst concentration term is included in the reaction rate expression:

CjIkkjci

kjcikjkjjrkkjjk CCkRBBCRNCI =+++→+ •

2,21,1 ααεThis rate

expression )( kjciR describes the rate of consumption of initiator k. The catalyst

rate is set to zero, assuming that the catalyst is not consumed by this reaction. The corresponding rate expression for the formation of primary radicals is given by:

∑∑= =

=I CIN

k

N

jCjIk

kjic

kjrkj

radic CCkNR

1 1ε


The parameters 1α and 2α are optional stoichiometric coefficients related to

by-products 1B and 2B . The byproduct formation rates are determined by:

CjIkkjic

kjkjBCjIk

kjic

kjkjB CCkRCCkR 2211 αα == For mass balance purposes, the

polymer mass generation rate is incremented by the initiator mass consumption rate, less the mass formation rate of by-products.

Primary Chain Initiation

To complete the initiation process, the reactive primary radicals ( )R• react with monomer by the primary chain initiation reaction to form polymer chain radicals of unit length. The chain initiation reaction is shown below:

R M P R k C Rjj

pij

pij

Mj• •+ → =1

The chain radicals grow by successive addition of monomer molecules to form long chain polymer molecules. It is common practice to set the chain initiation rate constants equal to the propagation rate constant each monomer.

The primary chain initiation reaction consumes primary radicals:

∑=

−=MN

iMi

ipi

radpi RCkR

1

Bifunctional Initiator Primary Decomposition Reaction

The bifunctional initiator decomposition reaction is modeled as a first order thermal decomposition reaction:

Ikkbid

kbidkkkkk

Bk CkRBBRRI =+++→ ••

2,21,1 ααεε

This rate expression )( kbidR describes the rate for the primary decomposition

of bifunctional initiator k. Each primary decomposition reaction generates an undecomposed fragment. The generation rate of undecomposed fragments is equal to the initiator decomposition rate:

IkkbidkF CkR =)(

The symbols 1B and 2B represent optional user-specified reaction by-products. This feature allows you to track the formation of low-molecular weight decomposition by-products, such as carbon dioxide, which may be generated as the initiators decompose. The byproduct formation rates are determined by:

IkkbidkkBIk

kbidkkB CkRCkR ,2,,1, 21

αα ==

For mass balance purposes, the polymer mass generation rate is incremented by the bi-initiator mass consumption rate, less the mass formation rate of by-products.

The rate expression for the formation of primary radicals from the primary thermal decomposition of bifunctional initiators is given by:


∑=

=BIN

kIk

kbidk

kr

radbid CkNR

1ε

The user can specify more than one bifunctional initiator to model systems where multiple initiators with different half-lives are used to control the initiation rate over the course of the polymerization.

The model assumes that the each site in the bifunctional initiator generates two radicals. A fraction of the radicals generated by decomposition undergo radical recombination in the radical-cage, leading to stable byproducts. The initiator efficiency factor, kε , is used to specify the fraction of radicals which

are not destroyed by the cage effect. This factor can be adjusted using a built-in or user-defined efficiency gel effect correlation.

The rate constant kbidk is calculated using a modified Arrhenius equation

(Equation 3.1 on page 166) with three parameters: pre-exponential factor, activation energy and activation volume. As noted previously, the activation volume accounts for the pressure dependence of the rate constant. This parameter is typically non-zero only at high pressures.

The rate expression can be modified using an optional built-in or user-defined gel effect correlation as described later in the text.

To complete the initiation process, the reactive primary radicals ) ,( ••kRR

react with monomer by the chain initiation reaction to form polymer chain radicals of unit length. Note that the undecomposed initiator fragment k is

conserved in the polymer chain )( ,1

kjP . This fragment is eventually destroyed by the secondary decomposition reaction described in the next sub-section. The chain initiation reactions are shown below:

R M P R k C Rjj

pij

pij

Mj• •+ → =1

•

=→+• kMjjpi

jpi

kjjk RCkRPMR ,

1

The chain radicals grow by successive addition of monomer molecules to form long chain polymer molecules.

Bifunctional Initiator Secondary Decomposition Reaction

The secondary bifunctional initiator decomposition reaction is modeled as a first order thermal decomposition reaction:

kksidkFkk

jnkk

kjn kRBBPRD ψααεε =+++→ •

)(2,21,1,

This rate expression )( )(kFR describes the rate for the decomposition of

bifunctional initiator fragment k. In this equation ( )kψ is the concentration of

undecomposed fragments of type k, which is calculated from the FRAGFLOW polymer attribute.

The model assumes that the secondary decomposition reaction generates a primary radical and a live end group (polymer radical). A fraction of the radical pairs generated by decomposition recombine in the radical-cage,


leading to stable byproducts. The initiator efficiency factor, kε , is used to

specify the fraction of radicals which are not destroyed by the cage effect. This factor can be adjusted using a built-in or user-defined efficiency gel effect correlation.

The generation rate of primary radicals from this reaction can be written as:

∑=

=BIN

kk

ksidk

radsid kR

1ψε

Each fragment decomposition event generates a new live end. The model assumes that the fragments are randomly distributed across the bulk polymer molecules and that the penultimate segment attached to the fragment becomes a live end. The generation rate of live ends of type i from the decomposition of initiator fragment k can be written as:

1

1

0

0 )(λλ

λψεμ j

kksidk k

dtjd=

The byproduct formation rates are determined by:

kksidkkBk

ksidkkB kRkR ψαψα ,2,,1, 21

==

The mass generation rate of polymer is adjusted to account for mass lost in the form of reaction by-products.

The user can specify more than one bifunctional initiator to model systems where multiple initiators with different half-lives are used to control the initiation rate over the course of the polymerization.

The rate constant ksidk is calculated using a modified Arrhenius equation

(Equation 3.1 on page 166) with three parameters: pre-exponential factor, activation energy and activation volume. As noted previously, the activation volume accounts for the pressure dependence of the rate constant. This parameter is typically non-zero only at high pressures.

The rate expression can be modified using an optional built-in or user-defined gel effect correlation as described later in the text.

Propagation The chain radicals grow or propagate by the addition of monomer molecules

to form long polymer chains ( )Pni . The propagation reaction is represented

by:

P M P R k C Pni

j nj

pij

pij

Mj ni+ → =+1

where monomer j is being added to a polymer chain of length n, with an active segment of type i. The resulting polymer chain will be of length n+1 and the active segment will be of type j. The active segment type usually represents the last monomer incorporated into the polymer chain.

For copolymerization, there will be N Nm m* propagation reactions having different reactivities. For example, with two monomers, the monomer being


added could be monomer 1 or monomer 2 while the active segment type could be segments from monomer 1 or monomer 2. Hence there will be four rate constants ( , , , )k k k k11 12 21 22 where the first subscript refers to the active segment type while the second subscript refers to the propagating monomer type. For the terminal model the rate of propagation is dependent only on the active segment and propagating monomer concentrations.

This copolymerization scheme can be adapted for modeling the stereoregularity (isotactic, syndyotactic or atactic) of monomer addition in homopolymerization.

Head-to-Head Propagation

When reactions occur between substituted vinyl monomers or 1,3 dienes, the repeat units usually join the chain in a head-to-tail configuration, as shown below (here HTT = head-to-tail). A portion of the monomers may join the chain in the head-to-head configuration, as shown in the second reaction below. Head-to-head unions can also result from termination by combination as described later.

R

HC CH2*

R

+HTT Propagation H

CH2C

R

HC CH2*

R

R

CH2

CH* +HTH Propagation

CH2

HC

HC CH2*

RR R

head-to-tail dyad

head-to-head dyad

The head-to-head dyads disturb the normal regularity of the chain. As a result, the head-to-head fraction of the polymer can have a strong influence on the crystallinity of the polymer, and thus influence the mechanical properties of the final product.

The model can track head-to-head additions using the optional HTH Propagation reaction. The polymer attributes HTHFLOW and HTHFRAC (head-to-head flow and fraction) must be included in the list of attributes on the Polymers, Polymers subform.

The model does not explicitly track normal head-to-tail additions. Instead, the standard propagation reaction is used to track the total (head-to-head and head-to-tail) propagation rate. The head-to-head propagation reaction explicitly tracks the head-to-head propagations. This design allows the user to fit the overall propagation rate first, and then refine the model by adding head-to-head additions.

The HTHFLOW attribute is a scalar value. The overall rate of change of the head-to-head flow hthR is calculated by summing the head-to-head additions

across all pairs of monomers. Termination by combination also generates head-to-head pairs as discussed later. The net rate expression for head-to-head dyads can be written as:


( )[ ]∑ ∑= =

++=Nmon

i

Nmon

j

ijtcji

jihth

iMj

ijhth

jMihth kkCkCR

1 100 μμμμ

Chain Transfer to Small Molecules Chain transfer to small molecules such as monomer, solvent or chain transfer agent usually involves the abstraction of hydrogen from the small molecule by the chain radical and leads to the termination of the live chain. At the same time, a new primary transfer radical is formed which can start chain polymerization. The effect of chain transfer on the polymerization kinetics depends on the reactivity of the transfer radical. When the transfer radical is very reactive, as is the case when the chain initiation rate constant is greater than the propagation rate constant, chain transfer will not lower the polymerization rate or conversion, but will reduce the molecular weight of the polymer. However, if the transfer radical is less reactive than the monomer-based propagating radical, as in the case of low chain initiation rate constant, both the conversion and molecular weight of the polymer will be lowered.

Chain Transfer to Solvent or Agent

Chain transfer to solvent and chain transfer to a transfer agent have the following rate expressions:

P A D R R k C Pni

k n traij

traij

A ni

k+ → + =•

P S D R R k C Pni

k n trsij

trsij

S ni

k+ → + =•

For transfer to agent or solvent the transfer radicals are assumed to have the same reactivity as the primary radicals formed by initiation. The case where the transfer radical has a different reactivity than the primary radical may be added in a future version.

Chain Transfer to Monomer – Generation of Terminal Double Bonds

In the chain transfer to monomer reaction, the live polymer end )( nP

abstracts a hydrogen from a monomer molecule, resulting in a dead polymer chain )( nD . The monomer, which loses a hydrogen, becomes a live polymer

end group with an unreacted double bond )( 1=P . Subsequent propagation reactions generate long-chain polymer radicals with a terminal double-bond segment at the opposite end of the chain ( )=nP . These initial reaction steps

are shown below:


·

Pn + M Dn + P1=

·

P1=

·Propagation

+ n-1 M

Pn=

Terminaldouble bondsegment

Chain Transfer Terminaldouble bondsegmentto Monomer

·

The terminal double bond segments can react with live end groups through terminal double bond polymerization reactions as described later in this section. These reactions lead to the formation of a molecule with a long chain branch.

The model optionally tracks terminal double bonds using the polymer component attribute TDBFLOW, which contains one element for each type of segment.

The chain transfer to monomer reaction does not always generate a terminal double bond. The terminal segment may undergo a re-arrangement reaction, which destroys the double bond site. The model parameter “TDB fraction” ( )ij

TDBf can be used to specify the fraction of chain transfer to monomer reactions that generate a terminal double bond.

The reaction rate of the chain transfer to monomer reaction is defined as: ( ) i

nMjijtrm

ijtrm

jijTDB

jijTDBnj

in PCkRPfPfDMP =−++→+ = 1 11

Where ( )ijtrmR is the rate of consumption of monomer j and live polymer end

groups of type i and the generation rate of live ends of type j. The generation

rate of terminal double bonds of type j ( )=jtrmR is defined by:

inMj

ijtrm

ijTDB

jtrm PCkfR ==

Chain transfer to polymer, which is also included in the kinetic scheme, is discussed in the section that follows on Termination.

Termination Bimolecular termination of radicals may involve primary radicals ( )R• and

chain radicals ( )Pnj . However, the concentration of primary radicals is usually

much lower than the concentration of chain radicals. Hence, only bimolecular termination involving chain radicals is included in the built-in kinetic scheme. In termination, the chain radicals are destroyed and live chains are converted to dead polymer chains.

Intermolecular termination occurs by one of two mechanisms, combination (coupling) or disproportionation. Many monomers (e.g. MMA) show both types


of termination while other monomers (e.g. styrene) terminate predominantly by combination. The mode of termination has a strong influence on the average polymer chain length and chain length distribution, especially when chain transfer is not significant. When the combination reaction is dominant, the polydispersity (in a single CSTR) will approach 1.5. The polydispersity approaches 2.0 when disproportionation is dominant.

Termination by Combination

In termination by combination, two live polymer end groups react with each other, forming a single dead chain with a head-to-head segment pair. Each of these reactions, on average, doubles the molecular weight of the polymer. The figure below shows an example for poly(styrene).

PnCH2

CH + CH2

HC CH2

HC C

H2

HC

PmDn+m

The reaction rate depends on the concentration of the live end groups:

P P D R k P Pni

mj

n m tcij

tcij

nj

ni+ → =+

The formation of head-to-head segment dyads can be tracked by including the optional HTHFLOW and HTHFRAC (head-to-head flow and head-to-head fraction) attributes in the attribute list on the Polymers, Polymers subform. Head-to-head sequences can contribute to thermal instability and may cause degradation during storage or subsequent processing.

Termination by Disproportionation

In disproportionation reactions, the radical at the end of one chain attacks a hydrogen atom at the second-to-last carbon atom in the second chain, forming two dead polymer molecules with no net change in molecular weight. Disproportionation results in one of the dead chains having a saturated end-group while the other will have an end-group with a terminal double bond. For example:

CH C

CH3

C O

OCH3

H

+ CH2C

CH3

C

OCH3

O

CH

C

CH3

C O

OCH3

+ CH2HC

CH3

C

OCH3

O

Pn Pm Dn= Dm

The reaction rate depends on the concentration of the live end groups:

( ) in

jn

ijtd

ijtdmn

ijTDB

in

ijTDB

jm

in PPkRDDfDfPP =+−+→+ = 1

The formation of terminal double bonds can be tracked by including the TDBFLOW and TDBFRAC (terminal double bond flow and fraction) in the list


of attributes on the Polymers, Polymers subform. Terminal double bonds can contribute to thermal instability and may cause degradation, branching and gelation during storage or subsequent processing.

The chain transfer to monomer reaction does not always generate a terminal double bond. The terminal segment may undergo a re-arrangement reaction, which destroys the double bond site. The model parameter “TDB fraction” ( )ij

TDBf can be used to specify the fraction of chain transfer to monomer reactions that generate a terminal double bond. The generation rate of

terminal double bonds of type i by disproportionation ( )=itdR is defined by:

jn

in

ijtd

ijTDB

itd PPkfR ==

Inhibition

Inhibition is included as an additional termination mechanism. This involves reaction between a chain radical and a small molecule (inhibitor or impurities) to form a dead chain:

inXk

ikx

ikxnk

in PCkRDXP =→+

The model assumes that the inhibitor is consumed by the reaction; the polymer mass generation rate is adjusted accordingly.

Gel effect in Termination

Bimolecular termination reactions between chain radicals become diffusion controlled at high polymer concentration or high conversion. This leads to an increase in the polymerization rate and molecular weight. This condition is known as the gel effect or Trommsdorff effect. At high conversions the increased viscosity of the reaction medium imposes a diffusional limitation on the polymer chains, leading to lower effective termination rates. Eventually at high enough conversions, even the propagation, initiation, and chain transfer rates may be affected by the diffusional limitation.

The diffusional limitation is modeled by multiplying the low conversion reaction rate coefficients by a gel-effect factor that will lower their effective value with increasing conversion. The free-radical model includes an option to modify the reaction rate expressions using a built-in or user-defined gel-effect correlation, as described later in this chapter.

Long Chain Branching

Chain Transfer to Polymer

The polymer radical in one chain can transfer to a repeat unit in a second chain. This chain transfer to polymer reaction always generates a long chain branch, since subsequent propagation from the live site causes the backbone molecule to grow a new branch.

The chain transfer to polymer reaction can be written as:

P D D P R k m D Pni

m n mj

trpij

trpij

j m ni+ → + =


Each transfer reaction generates one long chain branch. The optional polymer component attributes LCB and FLCB are used to track the molar flow rate of long chain branches and the long chain branching frequency (branch point per thousand repeat units).

Terminal Double Bond Polymerization

Polymer chains with terminal double bonds are formed by several reactions, including chain transfer to monomer, termination by disproportionation, beta-scission and beta-hydride elimination.

These terminal double bond groups can participate in propagation reactions in much the same manner as a monomer molecule. The resulting terminal double bond propagation reactions generate a long chain branch since the propagation reaction goes “through” the terminal double bond, leaving the polymer molecule attached to the TDB group attached to the backbone of the growing live polymer molecule.

Dn=

·

+

Terminal Double BondPolymerization

·

· Propagation + Termination

Molecule withlong-chain branch

Pn+mPm

Each terminal double bond propagation reaction generates one long chain branch. This reaction can also transfer the live end from one type of segment to another (e.g., from segment i to segment j).

The optional polymer component attributes LCB and FLCB are used to track the molar flow rate of long chain branches and the long chain branching frequency (branch point per thousand repeat units).

The rate of terminal double bond polymerization, ijtdbpR between live end i and

terminal double bond segment j can be written as:

=+

= =→+ jm

in

ijtdbp

ijtdbp

jmn

jm

in DPkRPDP

The concentration of terminal double bond segments is calculated from the optional polymer component attribute TDBFLOW.

Short Chain Branching The radical in a live end group can undergo a “backbiting” reaction in which the radical in live end segment i is transferred to a hydrogen atom in segment j in the same chain, forming a short chain branch. Short chain branches, typically five or six carbon atoms in length, are quite morphologically different than long chain branches, which are formed by a number of reactions.

The backbiting reaction leads to short chain branches if the backbone radicals are stable and can continue propagation. The total rate of short chain


branching, SCBR , depends on the live end group concentrations, iμ , and the

rate constants for the short chain branching reaction, iscbk :

∑=→i i

iscbSCB

jn

in kRPP μ

Short chain branching is tracked by the optional polymer component attribute SCB. The short chain branching frequency (short chain branches per thousand repeat units) is reported in the optional polymer attribute FSCB.

For some polymers (e.g. polypropylene) the backbone radical can be highly unstable and will result in the scission of the chain into a dead polymer chain with a terminal double bond and a short live chain one to six carbon atoms long. Use the beta scission reaction (see below) to track these types of reactions.

Beta-Scission A simplified beta-scission reaction is included in the built-in kinetics. It is limited to reactions where a live chain undergoes scission to form a dead chain of the same length and a primary radical:

in

ibs

ibsn

iTDB

in

iTDB

in PkRRDfDfP =+−+→ •= )1(

This reaction can be used to simulate backbiting reactions which form short-chain polymer radicals (see Short Chain Branching).

The beta scission reaction usually generates a terminal double bond corresponding to the live end i. In some special cases, the double bond may not form or may be unstable. The “terminal double bond fraction” parameter,

iTDBf , can be used to specify the fraction of beta-scission reactions which

generate a terminal double bond (by default, this parameter is unity). Thus, the rate of generation of terminal double bonds from the beta-scission

reaction, =itdR , can be defined as:

jn

in

ijtd

ijTDB

itd PPkfR ==

Reactions Involving Diene Monomers

Cis and Trans Propagation

Propagation reactions involving 1,3-diene monomers, such as butadiene or isoprene, can generate three types of repeat segments as shown below.


* +CH2

* +

* +CH2

C C

CH2*

H

H

CH2

C C

H

CH2*

H

Normal Propagation

Cis Propagation

Trans Propagation

CH* Vinyl Configuration

Cis Configuration

Trans Configuration

Although these segments may exhibit different physical properties, it is convenient to lump them together as a single repeat segment, and track the various segment configurations using the optional polymer component attributes CIS-FLOW and TRANSFLO. Likewise, the three types of propagation reactions are lumped together under the standard propagation reaction. Optional Cis-Propagation and Trans-Propagation reactions are used to specify the rate parameters for reactions that generate segments with the cis- or trans- configurations.

This design is intended to keep the model development process as simple as possible. The user can add cis/trans/vinyl accounting a working model without changing any of the existing rate parameters.

The new CIS-FLOW and TRANSFLO attributes are dimensioned NSEG and correspond to the bulk polymer. The flow rate of each diene segment in the vinyl configuration can be calculated by taking a mole balance across the various configurations taken by diene segments. The optional polymer attributes CIS-FRAC, TRANSFRA, and VINYLFRA report the molar fraction of each type of diene segment in each of the three configurations (an additional cross link configuration is also tracked as discussed later).

The rate of formation of segments of type j with cis configuration, jcisR , is

calculated by summing over all types of live end groups i:

∑=→+ + ii

Mjijcis

jcis

cisjnj

in CkRPMP 0

)(1 μ

Likewise, the rate of formation of segments of type j with trans configuration, j

transR , is calculated by summing over all types of live end groups i:

∑=→+ + ii

Mjijtrans

jtrans

transjnj

in CkRPMP 0

)(1 μ

In the equations above, ijcisk and ij

transk are, respectively, the net rate

constants for cis and trans propagation of monomer j onto a chain with a live end i. The standard reaction scheme does not include any reactions which consume the cis and trans end groups. Further, the model does not constrain the cis and trans reaction rates in any manner; the model user must ensure that the cis and trans propagation rates are lower than the net propagation rate.


Pendent Double Bond Polymerization

Diene segments in the vinyl configuration contain a pendent double bond that “hangs” off the main polymer chain. Live chains can react with these double bonds in a “pendent double bond polymerization” reaction, analogous to normal propagation. These reactions generate a short cross-link between two long linear chains, as shown below.

* +CH2Propagation

Reaction Pathway

*

PDB Polymerization

*

Cross-linked molecule

CH*

Pendent double bond

The pendent double bond polymerization rate ( ijPDBR ) depends on the

concentration of live ends of type i ( i0μ ) and the concentration of pendent

(vinyl) double bonds of type j in the bulk polymer phase ( )(1

vinyljλ ):

)(10

)( vinyljiijpdb

ijPDB

jmn

vinyljm

in kRPDP λμ=→+ +

The model assumes the reaction generates a new live segment of type j. The reaction model does not distinguish between subsequent propagation from this new live site from normal propagation reactions involving live end groups.

Each pendent double bond polymerization reaction involving diene segment j generates a new cross-link of type j. The flow rate of cross-links is tracked by the optional polymer component attribute XLFLOW. The cross-linking density is (moles of links per mass of polymer) is tracked by polymer attribute XDENSITY.

The concentration of vinyl groups (pendent double bonds) is determined by a mole balance. The flow of pendent double bonds of type i ( )(iPDB ) is calculated by subtracting the concentration of other possible configurations (cis, trans, or cross-link):

))()()(_()()( iXFLOWiTRANSFLOiFLOWCISiSFLOWiPDB ++−=

This flow rate is used to determine the concentration of pendent groups.

When the degree of cross-linking is extensive, the polymer can form a gel phase. The current version of the Free-Radical kinetics model does not account for gelation. This limits the model to situations with a low degree of cross-linking.


Model Features and Assumptions Following are the model features and assumptions used in the free-radical polymerization model available in Aspen Polymers.

Calculation Method In the Aspen Polymers free-radical bulk/solution polymerization model, the polymer chain length distribution averages and molecular structure properties are calculated using the population balance and method of moments approach, based on the built-in kinetics shown in the Built-in Free-Radical Polymerization Kinetic Scheme figure on page 162.

Population balance equations are used to account for the concentration of live polymer chains and combined polymer chains of length n. The f-th live and combined polymer chain length distribution moments are defined as follows:

μ fj f

nj

nn P=

=

∞

∑0

λ ff

nj

nj

N

nn P D

m

= +⎛

⎝⎜

⎞

⎠⎟

==

∞

∑∑10

For homopolymerization the index f is a scalar variable and the active segment superscript j may be dropped for the live polymer moment definition as there is only one segment type. Hence, for homopolymerization there will be one zeroth moment, one first moment, one second moment and so on for the live and combined polymer. However, for copolymerization, the index f will be a vector whose elements denote the monomer with respect to which the moment is defined. For copolymerization with respect to every active segment, there will be one zeroth moment, Nm first moments,

mm mN N N -

+( )12

second moments and so on.

For example, for copolymerization with three monomers, the vector index f can have the following values for the first moment:

f = , ,

1

0

0

0

1

0

0

0

1

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

representing the first moment with respect to segment one, two and three respectively. The application of the moment definitions to the live and bulk polymer population balance equations yields the live and bulk polymer chain length distribution moment equations. The general moment equations are listed in the following figures. The various zeroth, first, second, etc. moment


equations can be generated from these by substituting the appropriate values for the index f.

The live polymer chain length distribution moment equation is shown here:

( )[ ] ⎟⎟⎠

⎞⎜⎜⎝

⎛++−= ∑∑

==

•CI

jkjkjkM N

k

cbMj

aCk

jksi

N

i

iMj

ijtrmMj

jpi

fif hCCkCkRCkjn

dtd

110 )( νμδδ

μ

∑=

+BIN

k

ki

fksidk k

1 0

0

1

1

λψ

λλλε

( ) jf

jjf

N

i

N

iMi

jip

f

a

ia

afjMj

ijp

M M

Ckaf

Ck μαμμδ −−⎟⎟⎠

⎞⎜⎜⎝

⎛+∑ ∑∑

= ==

−

1 10

∑∑==

+ −+MM N

i

jf

ijitrp

N

i

ijf

ijtrp kk

11

10 μλμλ δ

∑∑==

−+MM N

i

jf

jiscb

N

i

if

ijscb kk

11μμ

( )∑=

+−MN

i

jf

iijtc

ijtd kk

10μμ

∑∑ ∑=

=

= =−

= −⎟⎟⎠

⎞⎜⎜⎝

⎛+

MM N

i

jf

ijitdb

N

i

f

a

iaf

ja

ijtdb k

af

k1

01 0

μλμλ

∑∑ ∑== =

− −⎟⎟⎠

⎞⎜⎜⎝

⎛+

MM N

i

jf

ijipdb

N

i

f

a

iafa

jijpdb k

af

k1

11 0

μλφμλφ

where α j contains some terms for reactions leading to the formation of dead polymer

⎟⎟⎠

⎞⎜⎜⎝

⎛+++++= ∑∑∑∑∑

=====

XSAMM N

kXk

jkx

N

kSk

jktrs

N

kAk

jktra

N

i

ijitrp

N

iMi

jitrm

jbs

j CkCkCkkCkk1111

11

λα

The moments with respect to terminal double bonds are approximated:

... 0

202

0

101 etciiii

λλλλ

λλλλ ==== ≈≈

In the final term of the equation, the symbol iφ represents the molar fraction of diene segment i in the vinyl configuration (attribute VINYLFRA). This term is zero for all segments that are not dienes.

The term k0ψ represents the concentration of polymer molecules containing

an undecomposed initiator fragment associated with bifunctional initiator k.

The bulk polymer chain length distribution moment equation is shown here:


( )[ ] ( )∑ ∑= =

•⎟⎟⎠

⎞⎜⎜⎝

⎛++−=

M MN

j

N

i

cjbjMj

ajC

jsi

iMj

ijtrmMj

jpi

ff hCCkCkRCkjndt

d

1 10 νμδδ

λ

( )( ) ∑∑ ∑== =

− −⎟⎟⎠

⎞⎜⎜⎝

⎛+

MM N

i

jfMi

jip

N

j

f

a

ia

afMj

ijp Ckj

af

Ck11 0

μμδ

∑ ∑∑∑= = =

−=

⎟⎟⎠

⎞⎜⎜⎝

⎛+−

M MMN

i

N

i

f

a

jaf

ia

ijtc

jf

iN

j

ijtc k

af

k1 1 0

01 2

1 μμμμ

∑∑∑∑∑∑ ∑= =

=

= =

=

= = =

=− −−⎟⎟

⎠

⎞⎜⎜⎝

⎛+

M MM MM M N

i

N

j

jf

iijtdb

N

i

N

j

jif

ijtdb

N

i

N

j

f

a

ia

jaf

jitdb kk

af

k1 1

01 1

01 1 0

λμλμλμ

∑∑∑∑∑∑ ∑= =

+= == = =

+− −−⎟⎟⎠

⎞⎜⎜⎝

⎛+

M MM MM M N

i

N

j

jf

iijpdb

N

i

N

j

jif

ijpdb

N

i

N

j

f

a

ia

jaf

jipdb kk

af

k1 1

101 1

11 1 0

1 φλμφλμφλμ

For copolymers, segment-segment dyad rate equation is:

( ) jitcjiMi

jjipMj

iijp

ji kCkCkdt

d00,00

, μμμμθ

++=

Quasi-Steady-State Approximation (QSSA) Users may invoke the Quasi-Steady-State Approximation (QSSA) for the live moment equations. Invoking QSSA converts the live moment differential equations (ODE) to algebraic equations, which are solved internally in the kinetics routine. Assuming QSSA is equivalent to assuming that the live moments attain their steady-state values instantaneously. This approximation makes the system of ODEs much easier to integrate by reducing stiffness.

Comparison of the results with and without QSSA for most free-radical polymerization systems, where the chain lifetimes are short compared to the residence time, show negligible differences. Therefore it is usually reasonable to use the QSSA. However, users should check the validity of this approximation by running cases with the QSSA switch set to YES and NO for their particular system. By default the QSSA is turned off (QSSA switch is set to NO). Users have the option of invoking the QSSA for all the live polymer moment equations, or selectively for only the zeroth, first, or second moment of live polymer.

Phase Equilibrium The polymerization model currently considers a single-phase system (vapor or liquid), two-phase system (vapor and liquid), or three-phase (VLL) system when calculating concentrations for the reaction kinetics. For single-phase systems, the reacting phase may be either vapor or liquid. In multi-phase systems, reactions can occur in one or more phases simultaneously. Each reaction object is associated with a single reacting phase, identified on the options form.


By default the reacting phase is assumed to be the liquid phase (for VLL systems, the reacting phase must be specified). Several reaction models can be referenced from a single reactor block to account for reactions in each phase.

Gel Effect Bimolecular termination reactions between chain radicals become diffusion controlled at high polymer concentrations or high conversion leading to an initial increase in the polymerization rate and molecular weight. This condition is known as the gel effect or Trommsdorff effect. At high polymer concentrations, the increased viscosity of the reaction medium imposes a diffusional limitation on the polymer chains, which leads to lower effective termination rates. Typically the termination rate coefficients are affected first by the gel effect because they involve diffusion of two bulky polymer radicals. Eventually at high enough conversions, even the propagation, initiation, chain transfer reactions, and the initiator efficiency are lowered by the gel effect. Hence, in general it may be necessary to allow gel/glass effects for all the polymerization reactions in the built-in kinetic scheme.

Diffusional Limitation

The diffusional limitation is usually modeled by multiplying the low conversion reaction rate coefficients, ko , by a gel effect factor, GF, that decreases with increasing conversion. Hence the effective rate coefficient for a reaction is given by:

k k GFeff o=

Several empirical and semi-empirical correlations relating the gel effect factor to conversion and operating conditions are available in the literature. Currently two of these have been implemented as built-in correlations. Users will be able to use these gel effect correlations simply by specifying the correlation number and the parameters. The built-in correlations are:

Correlation Number 1:

GF aa X p

a=+

1

21 3

Where:

X p = Weight fraction of polymer

This correlation has three user specified parameters, a a1, , 2 and a3 .

Correlation Number 2:

( )[ ]GF Aa X

BX CX DXp

p p p

a

=−

− + +⎛

⎝⎜⎜

⎞

⎠⎟⎟1 9

2 310

exp

With:

A a a T= +1 2


B a a T= +3 4

C a a T= +5 6

D a a T= +7 8

Where:

X p = Weight fraction of polymer

T = Temperature in Kelvin

This correlation has ten user specified parameters, a1 to a10 .

Users may also include their own gel effect correlation by specifying a correlation number greater than the number of built-in gel effect correlations (currently two) . In this case, users must provide the correlation for the gel effect factor in the form of a Fortran subroutine. The user gel effect subroutine argument list is documented here:

User Gel Effect Subroutine Arguments

Subroutine USRGEL ( ICORR, MAXGP , GPAR ,WFTFRP , GF,

+ SOUT ,NSUBS ,IDXSUB,ITYPE ,

+ NINTK ,INTK ,NREALK,REALK ,

+ NPO ,NBOPST,IDS ,NCK ,

+ NITG ,ITG ,NREA ,REA )

Argument Descriptions Variable I/O Type-Spec Dimension Description

ICORR I I Gel effect correlation number

MAXGP I I Maximum number of gel effect parameters

GPAR I R MAXGP Gel effect parameters

WTFRP I R Weight fraction of polymer

GF O R Gel effect factor

SOUT I R Outlet stream

NSUBS I I Number of substreams

IDXSUB I I NSUBS Location of substreams in stream vector

ITYPE I I NSUBS Substream type vector

1 = MIXED

2 = CISOLID

3 = NC

NINTK I I Number of integers for model

INTK I/O I NINT Integer array for model

NREALK I I Number of reals for model

REALK I/O R NREAL Real array for model

NPO I I Number of property methods


Variable I/O Type-Spec Dimension Description

NBOPST I I 6, NPO Property method array

IDS I I 2, 13 Block IDs

i, 1 Block ID

i, 2 to i, 4 used by system

i, 5 kinetic subroutine name

NCK I I Total number of components

NITG I I Length of integer array for kinetics

ITG I I NITG Integer array for kinetics

NREA I I Length of real array for kinetics

REA I R NREA Real array for kinetics

Polymer Properties Calculated The following variables can be calculated by the built-in kinetics routine based on the polymer attributes and the subset of the built-in kinetics used for a specific simulation:

• Zeroth, first and second moments for the combined polymer

• Zeroth and first moments for the live polymer

• Number, weight and z-average degree of polymerization and polydispersity index for the combined polymer (DPN, DPW, DPZ, PDI)

• Number, weight and z-average molecular weight for the combined polymer (MWN, MWW, MWZ)

• Average molecular weight of segments in combined polymer (MWSEG)

• Copolymer segment composition for combined polymer (SFLOW, SFRAC)

• Mole fraction of combined polymer chains that are live (LDFRAC)

• Number average degree of polymerization for live polymer (LDPN)

• Live polymer active segment composition (LEFLOW, LEFRAC)

• Copolymer segment composition for live polymer (LSFLOW, LSFRAC)

• Copolymer dyad flow rates (DYADFLOW), fractions (DYADFRAC), and the number-average block length with respect to each type of monomer (BLOCKN).

• Total number of short and long chain branches (SCB, LCB)

• Short and long chain branching frequencies (FSCB, FLCB)

• Flow rate and fraction of head-to-head dyads (HTHFLOW, HTHFRAC)

• Flow rate of cis-, trans-, and cross-link segments configurations corresponding to each type of diene monomer (CIS-FLOW, TRANSFLO, XLFLOW)

• Fraction of diene segments in the cis-, trans-, and vinyl configuration (CIS-FRAC, TRANSFRA, VINYLFRA)

These parameters are stored as component attributes defined in Chapter 2.

These variables, except for the branching frequencies, are related to the moments by the relationship shown here:


DPNi

i

Nm

= =∑λ

λ

11

0

( ) LDPN

i

j

i

N

i

N

m

m= =

=

∑

∑

μ

μ

11

01

( )

( )

SFRAC I i

ii

Nm( ) ( )

( )=

=∑λ

λ

1

11

LSFRAC I i

ii

Nm( ) ( )

( )=

=∑μ

μ

1

11

PDI

ii

Nm

=⎛

⎝⎜⎜

⎞

⎠⎟⎟

=∑

λ λ

λ

2 0

1

2

1( )

LPFRACj

j

Nm

= =∑μ

λ

01

0

( )

LEFRAC I j

jj

Nm( ) ( )

( )=

=∑μ

μ

0

01

The branching frequencies are calculated from the rate of chain transfer to polymer and the rate of backbiting reactions. The branching frequencies are reported in terms of number of branches per thousand segments in the polymer.

Structural Properties

Frequently some of the polymer properties are reported in terms of other properties that are related to these structural properties. These include properties such as melt flow rate or melt index, viscosity numbers, or K-values, etc. User-property subroutines can be set up for calculating some of these polymer properties from the polymer moments and structural properties.

User Profile Properties

In addition to the polymer properties reported through the component attributes, additional results are reported through User Profile variables. The following user profile variables are currently available in the built-in free-radical kinetics routine:

Profile Number

Profile Type Units

1 Conversion of monomer to polymer Fraction

2 Rate of polymerization (propagation) KMOL/S/CUM

3 Heat of polymerization KCAL/S/CUM

4 Reacting phase volume (or volume flow)

CUM or CUM/S

5 Reacting phase total moles KMOL or


Profile Number

Profile Type Units

(or mole flow) KMOL/S

6 Reacting phase average molecular weight

KG/KMOL

7 Rate of chain termination by combination

KMOL/S/CUM

8 Rate of chain termination by disproportionation

KMOL/S/CUM

9 Rate of chain termination by inhibition KMOL/S/CUM

10 Rate of initiation of radicals KMOL/S/CUM

11 Rate of induced initiation KMOL/S/CUM

12 Rate of chain transfer to monomers KMOL/S/CUM

13 Rate of chain transfer to polymer KMOL/S/CUM

14 Rate of chain transfer to agents KMOL/S/CUM

15 Rate of chain transfer to solvents KMOL/S/CUM

16 Rate of beta scission KMOL/S/CUM

17 Rate of short chain branching KMOL/S/CUM

18 Concentration of initiators KMOL/CUM

19 Concentration of catalysts KMOL/CUM

20 Concentration of coinitiators KMOL/CUM

21 Concentration of monomers KMOL/CUM

22 Concentration of transfer agents KMOL/CUM

23 Concentration of solvents KMOL/CUM

24 Concentration of inhibitors KMOL/CUM

25 Concentration of polymer KMOL/CUM

For more information, see Adding Gel-Effect on page 192.

Rates and Concentrations

The rates and concentrations reported via the user profiles can be used to calculate additional information, such as the kinetic chain length and fraction of dead chains with terminal double bond segments. These user profile variables can only be accessed if you are calling the free-radical kinetics from a batch reactor (RBatch) or a plug flow reactor (RPlug).

Specifying Free-Radical Polymerization Kinetics

Accessing the Free-Radical Model To access the Free-Radical polymerization kinetic model:




The Reactions object manager appears.



5 Select Free-Rad as the reaction type and click OK.

Specifying the Free-Radical Model The Free-Radical model input forms are listed below:

Use this sheet To

Species Define reacting species

Reactions Specify reactions and rate constant parameters

Rate Constants Summarize rate constant parameters

Options Specify reacting phase and select additional options

Gel Effect Supply gel-effect correlation parameters

Specifying Reacting Species You must specify the reacting species in the Species sheet:


2 In the Monomers field, list the reacting monomers. For each monomer, in the goes to → field, specify the polymer segment that the monomer converts to.

3 Continue listing other types of reacting species, e.g. solvents, transfer agents, etc.

4 Select the Generate Reactions option if you want the reactions to be generated automatically.

After going through the reaction generation once, it is recommended that you turn off this feature. Otherwise, the reaction generation is performed repeatedly.

Listing Reactions The Free-Radical model generates reactions based on the list of reacting species. You can view the system-generated reactions, then assign rate constant parameters to these reactions.

You can view a list of the system-generated reactions on the Reactions sheet. In the Reaction summary listing for each reaction, the first column indicates the reaction type. The second column lists the reactants, and the last column lists the products. The Data Browser window can be resized to better view the reaction listing. Use the following options:

Click To



Edit Edit the current reaction indicated by the row selector




Click To



Adding Reactions To add a new reaction to the scheme click New to open the Add Reaction subform:

1 In Reaction type, select a type for the new reaction. The Reaction scheme for that type is displayed.

2 In the reactant fields (for example, Initiator, Catalyst) enter the reactants of the categories allowed for that reaction type.

3 Where applicable, specify reaction by-products and stoichiometric coefficients.

4 Click Cancel to discard the new reaction

− or − Click New to add a new reaction

− or −

Click to check the Completion status

− or − Click Done to return to the reaction summary.

Editing Reactions To edit a reaction, click Edit to open the Edit Reaction subform:

1 Modify the Reaction type as needed.

The Reaction scheme for that type is displayed.

2 Modify reactants as needed.

3 Click to check the Completion status



Assigning Rate Constants to Reactions To assign rate constants to user reactions, click Rate Constants to open the Rate Constant Parameters subform. Alternately, move to the Rate Constants summary form for a grid-style form displaying rate constants for all reactions. For each reaction, enter:



3 In the ΔV field, enter activation volume.

4 In the Tref field, enter reference temperature.

5 In the Efficiency field, enter initiator efficiency for initiation reactions.

6 In the No. radicals field, enter the number of primary radicals formed in initiation reactions.

7 In the TDB frac field, enter the fraction of reactions that generate a terminal double bond.

8 In the Gel Effect field, specify the number of the gel-effect sentence number associated with the specified reaction rate.

9 In the Efficiency Gel Effect field, specify the number of the gel-effect sentence associated with initiator efficiency.

10 Click the stoichiometry list and select a new reaction. Enter rate constants for the new reaction. You can use the Prev and Next buttons to select the previous or next reaction in the list (or move to another row when using the Rate Constants summary form).



Adding Gel-Effect Use the Gel-Effect sheet to add gel effect to reactions:

1 To activate the form, click Use Gel Effect. 2 In Sentence ID, enter a unique integer identifier.

3 In the Corr. No. field, specify a gel effect correlation number (use a number greater than 100 for user-defined gel effect correlations).

4 In Parameters, list the parameters for the gel effect correlation.

When the specified correlation number is larger than the number of built-in correlations, you must also enter the gel-effect subroutine name in the Subroutine box.

5 To repeat steps 1-4 for additional gel-effect correlations, in the Sentence ID field, click New.

Selecting Calculation Options You can select additional simulation options for the model such as QSSA, special initiation options, and gel-effect on the Options sheet.

Option Field Description


QSSA Apply the quasi-steady-state approximation.

This activates additional options in the Apply QSSA to frame on the right side of the form. Inside this frame, select the moments for which you would like to apply the QSSA approximation.

Special Initiation

Activate the Special Initiation Parameters frame at the bottom of the form.

In this frame, list the monomers affected, and enter the special initiation coefficients and radiation intensity.

Reacting Phase Specify the phase in which reactions occur.

All of the reactions in the free-radical reaction object are assumed to take place in the same phase. You can use two (or more) free-radical models in the same reactor to account for simultaneous reactions in multiple phases (see the SuspensionEPS example).

If the Reacting Phase option is set to Liquid phase 1 or Liquid phase 2 the model assumes two liquid phases exist. When the named phase is not present, the model prints a warning message and sets the reaction rates to zero. There are two options for handling phase collapse:



Note: You must specify the Valid Phases keyword for each reactor model referencing the kinetics to ensure the reactor models are consistent with the reaction models.

Specifying User Profiles User profiles may be tabulated in RBatch and RPlug reactors. To specify user profiles, go the reactor’s User Subroutine form User Variables sheet:

1 In the Number of user variables field, enter the number of user variable profiles to be tabulated.

For a list of user profiles available in the free-radical model, see Polymer Properties Calculated on page 1188.

2 In the Variable No. field, list the profile numbers in order.

You must enter the profiles sequentially, without omissions.

3 For each profile, enter a profile Label and a Units Label. Although these labels are displayed, the reactor model does not perform unit conversions on the user profiles. The user profile variables are totals. For example, the reported propagation rate is summed over all propagation reactions.

4 To view user profile results, go to the User Variables sheet of the reactor’s Profiles form.


References Arriola, D. J. (1989). Modeling of Addition Polymerization Systems, Ph.D. Thesis. University of Wisconsin-Madison, WI.

Biesenberger, J. A., & Sebastian, D. H. (1983). Principles of Polymerization Engineering. New York: Wiley.

Billmeyer, F. W. (1971). Textbook of Polymer Science. New York: Wiley-Interscience.

Choi, K.Y. & Kim, K.J. (1987). Steady State Behavior of a Continuous Stirred Tank Reactor for Styrene Polymerization with Bifunctional Initiators. Chemical Engineering Science.

Choi, K.Y., Liang, W.R., and G.D. Lei (1988). Kinetics of Bulk Styrene Polymerization Catalyzed by Symmetrical Bifunctional Initiators. Journal of Applied Polymer Science Vol. 35, 1547-1562.

Choi, K.Y., & Lei, G.D. (1987). Modeling of Free-Radical Polymerization of Bifunctional Initiators. AICHE Journal Vol. 33 No. 12, 2067-2076.

Friis, N., & Hamielec, A. E. (1976). Gel-Effect in Emulsion Polymerization of Vinyl Monomers. ACS Symp. Ser., 24.

Ham, G. E. (Ed.). (1967). Vinyl Polymerization Volume 1. New York: Marcel Dekker.

Hui, A. E., & Hamielec, A. E. (1972). Thermal Polymerization of Styrene at High Conversion and Temperatures. An Experimental Study. J. of Applied Polym. Sci., 16, pp. 749-769.

Kim, K.J., and Choi, K.Y. (1989). Modeling of Free Radical Polymerization of Styrene by Unsymmetrical Bifunctional Initiators. Chemical Engineering Science, Vol. 44 No. 2, pp. 297-312.

Lenz, R. W. (1968). Organic Chemistry of Synthetic High Polymers. New York: Wiley-Interscience.

Marten, F. L., & Hamielec, A. E. (1979). High Conversion Diffusion Controlled Polymerization. ACS Symp. Ser., 104.

Ray, W. H., & Laurence, R. L. (1977). Polymerization Reaction Engineering. In Chemical Reactor Theory. New Jersey: Prentice-Hall.

Villalobos, M.A., Hamielec, A.E., and P.E. Wood (1991). Kinetic Model for Short-Cycle Bulk Styrene Polymerization through Bifunctional Initiators. Journal of Applied Polymer Sciene V 42, 629-641.

10 Emulsion Polymerization Model 195

10 Emulsion Polymerization Model

This section covers the emulsion polymerization model available in Aspen Polymers (formerly known as Aspen Polymers Plus).



• Emulsion Polymerization Processes, 196



• Polymer Particle Properties Calculated, 214

• Specifying Emulsion Polymerization Kinetics, 215

The Aspen Polymers Examples & Applications Case Book illustrates how to use the emulsion model to simulate styrene butadiene copolymerization.

Summary of Applications The emulsion polymerization model is applicable to emulsion polymerization processes where nucleation occurs by both the micellar and homogeneous mechanisms or to seeded polymerization. Some of the applicable polymers are described below:

• Styrene - A component of synthetic rubber and paper coating

• Butadiene - Synthetic rubber, impact modifier in ABS and HIPS

• Tetrafluroethylene - Polytetrafluroethylene (PTFE), fluoropolymers Viton

• Vinylacetate - Polyvinylacetate (PVA) adhesives, paint formulation

• Methylmethacrylate - Surface coating applications.

• Acrylic Acid - Minor component in paints

• 2-chloro-1,3-butadiene (chloroprene) - Neoprene rubber

• Butyl Acrylate - Surface coatings

• Butyl Methacrylate - Comonomer in surface coatings

• Vinyl Chloride - PVC used in floor covering and coatings

196 10 Emulsion Polymerization Model

A wide variety of processes are used in emulsion polymerization. The processes that can be modeled using the Aspen Polymers emulsion polymerization model are those that follow micellar, homogeneous, or seeded polymerization.

An example of a process that follows micellar nucleation and subsequent growth is the production of SBR latex in semi-batch reactors for paper coating applications. The following lists polymeric products made by emulsion polymerization:

• Emulsion paints, made from a number of monomers (styrene, butadiene, acrylates, etc.) and a variety of other ingredients

• Adhesives, from slightly plasticized poly(vinyl acetate) and poly(ethylene-co-vinyl acetate) - a pressure sensitive adhesive

• SBR, for carpet backing and for coating paper and card board along with china clay, thus facilitating printing on surfaces

• Non-woven fabrics, which have their fabrics pre-coated with polymer and then heat pressed (these are termed “thermoformable” felts)

• ABS (Acrylonitrile-Butadiene-Styrene), used in high impact strength material made by swelling of a polybutadiene latex with a mixture of styrene and acrylonitrile and polymerizing further. HIPS (High-Impact PolyStyrene) made from bulk polymerized polystyrene in the presence of polybutadiene

Emulsion Polymerization Processes Emulsion polymerization is an industrially important process for the production of polymers used as synthetic rubber, adhesives, paints, inks, coatings, etc. The polymerization is usually carried out using water as the dispersion medium. This makes emulsion polymerization less detrimental to the environment than other processes in which volatile organic liquids are used as a medium.

In addition, emulsion polymerization offers distinct processing advantages for the production of polymers. Unlike in bulk or solution polymerization, the viscosity of the reaction mixture does not increase as dramatically as polymerization progresses. For this reason, the emulsion polymerization process offers excellent heat transfer and good temperature throughout the course of polymer synthesis. This process is always chosen when the polymer product is used in latex form.

Reaction Kinetic Scheme In emulsion polymerization, free-radical propagation reactions take place in particles isolated from each other by the intervening dispersion medium. This reduces termination rates, giving high polymerization rates, and simultaneously makes it possible to produce high molecular weight polymers.


One can increase the rate of polymerization without reducing the molecular weight of the polymer. Emulsion polymerization has more recently become important for the production of a wide variety of specialty polymers.

Particle Formation

To appreciate the complexities of emulsion polymerization, a basic understanding of the fundamentals of particle formation and of the kinetics of the subsequent particle growth stage is required. A number of mechanisms have been proposed for particle formation. It is generally accepted that any one of the mechanisms could be responsible for particle formation depending on the nature of the monomer and the amount of emulsifier used in the recipe.

The two common mechanisms for particle formation are:

• Micellar nucleation

• Homogeneous nucleation

With micellar nucleation, micelles, which are aggregates of emulsifier molecules, act as the site of nucleation.

With homogeneous nucleation, the radicals produced in the aqueous phase polymerize with dissolved monomer and precipitate out to form precursor particles. The precipitated precursor particles coagulate with each other until a stable particle is formed.

Micellar Nucleation Micellar nucleation is considered to be the primary mechanism for particle formation (Harkins, 1945; Smith & Ewart, 1948) in those emulsion polymerization systems for which the monomer is very sparingly soluble in water, and where the concentration of emulsifier is above the critical micelle concentration (CMC). As the name implies, the micelles, which are formed when the emulsifier concentration is above the CMC, act as the site for particle nucleation.

The reaction mixture consists of water, monomer, emulsifier and a water-soluble initiator. The monomer is dispersed in the form of droplets in the water by agitation. The droplets formed are stabilized by the emulsifier molecules which are adsorbed on the droplet surface. In addition to the droplets, monomer is also found dissolved in the aqueous medium and solubilized inside the micelles.

Similarly, the emulsifier is found in three locations: in the micelles, dissolved in the aqueous medium, and adsorbed on the monomer droplets. Since a water soluble initiator is used, the initiator molecules will be mainly found dissolved in the water medium.

When a typical emulsion polymerization recipe is heated, the initiator dissociates in the aqueous medium and produces initiator radicals. Upon propagating with monomer in the water phase the initiator radicals form oligomeric radicals and enter the micelles, which are aggregates of emulsifier molecules inside which a small amount of monomer is entrapped. The capturing of a radical by micelle and reaction with the entrapped monomer signifies the formation of a particle from a micelle. As the propagation takes


place in the newly created particle, a thermodynamic potential difference is created for the diffusion of the monomer from the monomer droplets into the growing particles.

As the particles grow, some of the micelles disintegrate and cover the growing particles to stabilize them. Therefore, the micelles are not only consumed in the formation of polymer particles, but also in the stabilization of growing polymeric particles. In fact, approximately one percent of the micelles are used in the formation of particles. When no micelles remain in the reaction mixture, micellar nucleation ceases.

Stage I

The time required for particle nucleation to be complete is also called the nucleation time or the nucleation period, and usually lasts 10-15 minutes in conventional polymerization systems. This is commonly referred to as the seed stage, or Stage I, in the emulsion polymerization industry. After the nucleation or seed stage, the number of particles in the reaction mixture remains constant if particles do not agglomerate.

Stage II

The stage following the seed stage is called the growth stage or Stage II of the emulsion polymerization. In Stage II, the polymer particles grow through a steady diffusion of monomer from the monomer droplets to the particles. Since the number of particles remains constant and the particles are saturated with monomer, this stage is marked by a constant rate of polymerization and could easily be observed on a conversion vs. time plot. Stage II is considered complete when the monomer droplets are totally depleted.

Stage III

In Stage III, the monomer finishing stage, the reaction mixture consists of the monomer swollen polymer particles and the aqueous medium. Further polymerization of the monomer in the particles takes place. This results in a decrease of the particle size due to higher density of the polymer compared to the monomer. During Stage III, the concentration of monomer dissolved in the aqueous phase falls rapidly, as does the concentration in the polymer particles. The final product obtained at the end of Stage III is called latex.

The following figure illustrates the stages in a micellar nucleation emulsion polymerization reaction:


Particle Number and Nucleation Time

The number of particles, usually in the range of 1016 to 1018 per liter of latex, is an important parameter in emulsion polymerization. Smith and Ewart have derived mathematical expressions for the number of particles under the following assumptions (Smith & Ewart, 1948):

• Particles as well as micelles are equally effective in capturing radicals from the aqueous phase

• Temperature of the reaction is constant

• Volumetric growth rate of polymer particles is constant

With these assumptions, the particle number and nucleation time are given by the following equations:


( ) 6.04.0

sv37.0 EANRN s

aIp ⎟⎟

⎠

⎞⎜⎜⎝

⎛= (3.2)

tA E

R Nnucs

I a=

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟0 65

1 0 4 0 6

.. .

v (3.3)

R NI a is the rate of generation of radicals in the water phase, and v s is the volumetric growth rate of swollen polymer particles. They are determined from the following equations:

R fk II d= 2 (3.4)

vs =k M n

NMW

dp p

a

m

p p

1ϕ

(3.5)

Where:

f = Initiator efficiency

kd = Rate constant for initiator dissociation

I = Initiator concentration

Na = Avogadro's number

kp = Propagation constant

M p = Monomer concentration inside the particles

n = Average number of radicals per particle

MWm = Molecular weight of the monomer

d p = Density of polymer

ϕ p = Volume fraction of polymer in the particle phase

Homogeneous Nucleation Homogeneous nucleation is the mechanism for particle formation when monomers are more water soluble and level of emulsifier is not high enough for the formation of micelles in the recipe.

The following figure shows a detailed picture of kinetic events that take place during particle formation by homogeneous nucleation:


When the reaction mixture is heated the initiator molecules dissolved in the water medium dissociate and produce the initiator radicals. These initiator radicals react with the dissolved monomer and quickly propagate into an oligomeric radical in the water phase.

As the size of the oligomeric radical increases it becomes insoluble in water and precipitates out of the water phase. This event signifies the formation of a primary polymer particle from the growing oligomeric radical in the water phase. However, these primary particles are not stable, and, hence, coagulate with each other until enough surface charge is developed to stabilize the particles. These surface charges are provided by the ionic end of the initiator molecules. In addition, the coagulated particles are also stabilized by ionic and non-ionic emulsifier added to the emulsion recipe.

Once a stabilized particle is formed, it grows by getting a steady supply of monomer from monomer droplets by diffusion. As the particles grow and


become large, the oligomeric radicals that are formed in the water phase are directly absorbed by the particles. After sufficient number of particles are formed that are able to absorb all of the radicals in the water phase, no new particles are formed in the water phase and the number of particles becomes constant. Also in homogeneous nucleation the particle number reaches a constant value, as in micellar nucleation. The subsequent growth stage is similar to the growth stage in the micellar nucleation.

Particle Formation Rate

The rate of particle formation by homogeneous nucleation can be derived by considering the water phase kinetics and rate of precipitation of the polymers at an assumed critical chain length (jcr). Assuming the aggregation number ( )Nagg for the formation of stable particles from the precipitated precursor

particles, the rate of particle formation by homogeneous nucleation is given by:

( )R

dNdt

N k nN NN

k Mk M k R k A k A

a i de a

agg

pw w

pw w tw w ap p am m

jcr

homo = =+

+ + +

⎛

⎝⎜⎜

⎞

⎠⎟⎟•

+ρ /

1

In the above equation Rw• refers to the concentration of live radicals in the

water phase and is given by:

( )R

k nN Nk M k R k A k Aw

i de a

pw w tw w ap p am m

jcr•

•

+

=+

+ + +−−

⎛⎝⎜

⎞⎠⎟

ρ ββ

/ 11

1

Where:

β =+ + +•

k Mk M k R k A k A

pw w

pw w tw w ap p am m

Refer to the table of page 204 for the explanation of the symbols in the above equations.

Particle Growth Stage II, the growth stage, starts after the completion of the seed stage in the in situ seed process . In the in situ seed process, the micelles are used for the generation of the seeds. In the case of an external seed process, a well characterized seed is used as the starting material for emulsion production. If quality control tests indicate that the particle number and particle size distribution of the seed particles will not result in the desired end-product specifications, the batch is normally terminated. Therefore, in the growth stage it can be assumed that the desired number of particles, with the desired particle size distribution has already been formed.

It is generally agreed that the growth process is a well understood process and amenable to control. The growth reaction is responsible for developing molecular properties (molecular weights, composition, etc.) and morphology (core-shell, particle size distribution). Since the growth reaction lasts about


10-12 hours, there is great potential for optimizing the reaction time by increasing temperature or by keeping the particles saturated with monomer.

Once inside a particle, radicals induce the usual free-radical polymerization steps such as propagation, termination, chain transfer, etc. A growing radical can escape from a particle and return to the aqueous medium to participate in an aqueous phase termination reaction or enter into another particle. During Stage II, monomer continuously diffuses from the monomer droplets into the particle phase, providing a steady monomer supply for the growing polymer particle.

As the particles grow, the emulsifier molecules are continuously adsorbed onto or desorbed from the particles to maintain thermodynamic equilibrium. This dynamic exchange between various phases when added to the regular polymerization kinetics makes emulsion polymerization a more complex process than bulk or solution polymerization processes. The following figure illustrates the transport processes and reactions in a latex particle:

Radical Balance The radical balance in the aqueous phase is controlled by the kinetic events that are responsible for the radical generation and the radical consumption in


that phase. Radicals are generated in the dispersant phase by two kinetic events:

• Initiator decomposition in the aqueous phase

• Desorption of radicals from the particle phase into the aqueous phase

Radicals are depleted from the aqueous phase by two kinetic events:

• Termination of a live radical with another live radical in the aqueous phase

• Diffusion of a radical from the aqueous phase into a particle or a micelle

Aqueous Phase Rate

The rate of production of radicals in the aqueous phase is considered equal to the rate of depletion of the radicals from the aqueous phase. This is an application of the stationary state hypothesis or quasi-steady-state approximation (QSSA):

k N n R N k R N k R Nde p I a a w a tw w a+ = +• •2 2 (3.6)

The previous equation can also be written as:

α α α= ′ + −mn Y 2 (3.7)

With:

••

=ρ′=ρ′

=α watpp

awa

tpp

as RkkNNRk

kNN vv 22

(3.8)

′ =αR NN kI s a

p tp

v 2

(3.9)

mk N

kde s a

tp=

v (3.10)

YN k kk N

p tp tw

a s a=

22 2v

(3.11)

The emulsion polymerization model nomenclature is shown here:

Symbol Description

am Area of a single micelle (m3)

ap Area of a single particle (m3)

Am Area of micelles (m2/m3 of aqueous phase)

Ap Area of particles (m2/m3 of aqueous phase)

As Area coverage by emulsifier (m2/kmol)

d p Density of polymer (kg/m3)

E Emulsifier concentration (kmol/m3)

F t( , )v Volume density function for particle size distribution (m-3)


Symbol Description

f Initiator efficiency

[ ]I Initiator concentration in the aqueous phase (kmol/m3)

ka Absorption constant for particles (s-1)

jcr Critical chain length

ϕ p Volume fraction of polymer in polymer particle

kd Initiator dissociation constant (s-1)

kde Rate constant for the desorption of radicals from the particles (m3/s)

kam Rate constant for the absorption of radicals by micelles (m/s)

kap Rate constant for the absorption of radical by the particles (m/s)

kp Rate constant for propagation in particle phase (m3/kmol-s)

kpw Rate constant for propagation in the aqueous phase (m3/kmol-s)

kactij Rate constant for activated initiation (m3/kmol-s)

koxij Rate constant for oxidation (m3/kmol-s)

kreij Rate constant for reduction (m3/kmol-s)

ktw Rate constant for the termination in the aqueous phase (m3/kmol-s)

Kipm Partition coefficient for the i-th component between polymer

particles and monomer droplets

M p Concentration of monomer in the polymer phase (kmol/m3)

Mwm Molecular weight of monomer (kg/kmol)

Mw Monomer concentration in aqueous phase (kmol/m3)

n Average number of radicals per particle

N p Number of particles per unit volume of aqueous phase (no./m3)

Na Avogadro number

Nagg Aggregation number

Nn Number of particles containing n radicals per unit volume (no./m3-s)

Rhomo Rate of particle generation by homogeneous nucleation (no./m3-s)

Rw• Radical concentration in the aqueous phase (kmol/m3)

RI Rate of initiator dissociation (kmol/m3-s)

tnuc Nucleation time(s)

v Volume of a single unswollen particle (m3)


Symbol Description

vm Volume of a single micelle (m3)

vh Volume of a single particle formed by homogeneous nucleation (m3)

v Volumetric growth rate of a single particle (m3/s)

v s Volume of a swollen particle (m3)

v s Volumetric growth rate of a swollen particle (m3/s)

′ρ Rate of radical absorption by N p particles (Kmol/s)

ρi Total rate of radical generation (Kmol/s- m3)

ν0 Zeroth moment of the particle size distribution (no./m3 of aqueous phase)

ν1 First moment of the particle size distribution (m3/m3 of aqueous phase)

ν2 Second moment of the particle size distribution (m6/m3 of aqueous phase)

ν3 Third moment of the particle size distribution (m9/m3 of aqueous phase)

Particles containing n radicals are produced by three kinetic events:

• Absorption of a radical from the aqueous phase by a particle containing (n-1) radical. The total rate of this event is given as:

p

n

NN ρ′−1

• Radical desorption from a particle containing (n+1) radicals. The total rate of this event is given as:

1)(n+ k N de1n+

• Termination in a particle containing (n+2) radicals. The total rate of this reaction is given as:

v)]1)(2[(2 +++ nnkN tpn

Particle Phase

Particles containing n free-radicals are depleted in the particle phase in three analogous ways. By equating the rate of formation to the rate of depletion of particles containing n free-radicals the recurrence formula is obtained:

( ) ( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛ −++′=⎟⎟

⎠

⎞⎜⎜⎝

⎛ +++++′ ++− v

)1(/v

)1)(2(1/ 211a

tpdepana

tpndenpan NnnknkNNN

NnnkNnkNNNN ρρ

(3.12)

This recurrence formula was first developed by Smith and Ewart, in a slightly modified form (Smith & Ewart, 1948). Equation 3.12 can be solved for the


average number of radicals per particle, n . The general solution as given by O'Toole is as follows (O'Toole, 1965):

n aI aI am

m=

× −

( )( )4 1

(3.13)

In Equation 3.13, I am( ) and I am−1( ) are modified Bessel functions of the first kind with parameters m and a. Equation 3.10 gives the definition of m. a is calculated as a function of α, defined in Equation 3.8, according to:

a = 8α (3.14)

The simultaneous solution for n (Equation 3.13) and the stationary steady state equation for the radical balance in the aqueous phase (Equation 3.6) completely define the kinetics of the emulsion polymerization.

Kinetics of Emulsion Polymerization A general emulsion polymerization kinetics scheme involves simultaneous free-radical polymerization taking place in the dispersant phase, particle phase and the monomer droplet phase. However, in general the monomer droplet phase is regarded as an inert phase supplying monomer to the particle phase during reaction. In conventional emulsion polymerization, initiator decomposition takes place in the dispersant phase and the initiator radicals enter the polymer particle phase.

The polymer particle phase is considered to be the site for all the polymerization reactions. There is a dynamic exchange of radicals between the particle phase and the dispersion phase. The average number of radicals per particle is dependent on the steady state that is reached as a result of this exchange. The free-radical kinetics scheme used in the model is that used in the free-radical polymerization model.

In addition to the kinetics previously described in the free-radical Reaction Kinetic Scheme section on page 161, emulsion polymerization can also handle activated initiation, redox initiation, absorption and desorption.

Activated Initiation

The mechanism for activated initiation is given as:

I A n R xk jk

kjactkj

+ ⎯ →⎯ +• *

Where:

Ik = Initiator molecule

Aj = Activator molecules which promote the dissociation of the initiator molecules

R• = Primary radical produced in the initiation reaction

x * = Waste products that do not participate in the polymerization reactions


In emulsion polymerization water soluble persulfate initiators are normally employed as initiators. In addition, water soluble sodium bisulfite is used as an activator in many emulsion polymerization reactions for accomplishing activated initiation of persulfates.

For the above given mechanism, Ractkj , the radical generation rate for

activated initiation, is given by the following equation:

RdRdt

n f k C Cactkj

kj kj actkj

I Ak j= =

•

Where:

kactkj = Rate constant for activated initiation

CIk = Concentration of initiator in the aqueous phase

CAj = Concentration of activator in the aqueous phase

nkj = Number of radicals produced per initiator molecules

fkj = Efficiency factor

Redox Initiation

The mechanism for redox initiation is given as:

*YFeRnFeI kk

k

kox ++⎯→⎯+ +++•++ (oxidation—slow)

*xFeReFe rek +⎯→⎯+ +++++ (reduction—fast)

Similar to activated initiation, redox initiation is used in emulsion polymerization reactions to promote decomposition of initiators at a much lower temperature. For example, redox initiation is employed in cold rubber production. It is also used in emulsion polymerization reactions where high radical flux is needed.

kI (the initiator, oxidant, or sometimes catalyst) decomposes in the presence

of the reduced (ferrous) ions, Fe++, to form one free radical, R•

, and the oxidized (ferric) ion, Fe+++. The reductant, Re, reacts with the ferric Fe+++ ion reducing it to ferrous Fe++. x* and Y* are inactive byproducts of the reactions.

The activator system (or redox couple), a Ferrous salt (e.g. ferrous sulfate heptahydrate) plus a reductant (e.g. SFS, Sodium Formaldehyde Sulphoxylate), activates the initiator and regenerates the ferrous ion as previously shown.

Multiple initiators are common: for example, KPS (Potassium persulfate) and tBHP (tert -butyl hydroperoxide). KPS is used initially. At high conversion, the

monomer concentration in the polymer phase is low and the −42OS radicals

cannot diffuse into the polymer phase because they are hydrophyllic. tBHP,


on the other hand, partitions into both the aqueous and the polymer phases and is, therefore, used for finishing in redox systems.

In the case of two initiators, two oxidation reactions and one reduction reaction should be specified.

As the ferrous and ferric ions get regenerated in the redox reaction, it is assumed that the total iron concentration remains constant in the reaction. As the rate of reduction is much faster than the rate of oxidation, a stationary state hypothesis is assumed for the ferrous and ferric ions.

Assuming stationary state hypothesis for the ferric and ferrous ion concentration in the redox initiation mechanism, one can derive an equation for the rate of generation of the radicals by the redox initiation as follows:

Re

Re

CkCkCkfnCCk

dtdR

redk Ikox

k IkoxkkFered

k

kt

+=

∑∑•

Where:

CFet = Total concentration of the iron in the aqueous phase

koxk = Rate constant for oxidation step of initiator k

redk = Rate constant for reduction step

CIk = Concentration of initiator k in the aqueous phase

ReC = Concentration of reductant in the aqueous phase

kn = Number of radicals produced per initiator molecule, k (default=1)

kf = Efficiency factor for initiator k (default=1)

In thermal decomposition, typically each initiator molecule produces two radicals. The cage effect is when the radicals annihilate each other before they are able to diffuse out of the cage into the aqueous phase. This effect is captured by the radical efficiency term for thermal decomposition.

In redox initiation, only one radical is generated from the initiator. Consequently, there is no cage effect because there is only one radical in the cage. Therefore, in redox initiation, there is typically no need for the two parameters: kn (number of radicals per initiator molecule) and kf (radical

efficiency). However, these parameters are provided and defaulted to a value of 1 to provide additional handles for the user to fit their model to plant data.

Absorption and Desorption

In addition, there is an exchange of radicals between the aqueous phase and the polymer phase. Radicals generated in the aqueous phase are absorbed by the micelles during micellar nucleation and by the particle during nucleation and subsequent growth. Radicals in the polymer phase can desorb from the


particle and enter the aqueous phase. The kinetics of absorption and desorption are described as follows:

Absorption by particles:

R N Nj ik

iap•

++ ⎯ →⎯ 1 R k a C Cap ap p N Ri j= •

Absorption by micelles:

R N Nj mkam• + ⎯ →⎯ 1 R k a C Cam am m N Rm j

= •

Desorption:

N N Rik

ide⎯ →⎯ +−

•1 R k iCde de Ni

=

Where:

am = Area of a single micelle

ap = Area of a single particle

Nm = Number of micelles with i radicals per cubic meter of aqueous phase

Ni = Number of particles with i radicals per cubic meter of aqueous phase

Reaction Rate Constant

The rate constant for each reaction in the built-in kinetics is calculated at the reaction temperature and pressure using the modified Arrhenius equation with user specified parameters for frequency factor, activation energy, activation volume, and reference temperature:

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛ Δ

−−

=ref

o TTRVP

REakk 11exp

Where:

ko = Pre-exponential factor in l/sec for first order reactions,

and m kmol s3 / − for second order reactions

Ea = Activation energy in mole-enthalpy units

ΔV = Activation volume in volume/mole units

P = Reaction pressure


T = Reaction temperature

refT

= Reference temperature

The second term in the exponential function contains the activation volume and is important for high pressure polymerization systems. For detailed


information of the reactions, see the free-radical Reaction Kinetic Scheme section on page 161.

Rate constants related to absorption by particles, absorption by micelles and desorption from particles are given by the Arrhenius expression as:

k kEa

RTo=−⎛

⎝⎜⎞⎠⎟exp

assuming zero activation volume.

Model Features and Assumptions Following are the model features and assumptions used in the emulsion polymerization model available in Aspen Polymers.

Model Assumptions The emulsion polymerization process is extremely complex and involves phenomena for which a complete theoretical understanding has not been reached. Important assumptions are made in the emulsion polymerization model:

• The reaction mixture is perfectly mixed

• Particles are formed by the micellar or the homogeneous mechanism

• No agglomeration or breakage of particles occurs

• No secondary nucleation occurs

• All particles have the same average number of radicals and hence the same volumetric growth rate

• The particle size distribution is unimodal, with moments of PSD sufficient to describe the PSD

• There are no mass transfer limitations on the polymerization reactions

• Molecular weight is controlled by chain transfer reactions

Thermodynamics of Monomer Partitioning Modeling of the kinetics involved in emulsion polymerization is complicated by the fact that the reaction mixture is multiphase. It is important to account for partitioning of the components among various phases. Up to four coexisting phases may be present in the reaction mixture. After the consumption of the monomer droplets, only three phases will remain in the system.

A short-cut partition coefficient methodology was used to handle the four phases. One benefit of using this approach is that NRTL parameters are not required for the polymer or its segments. The method assumes the polymer solubility is zero in the monomer, aqueous, and vapor phases and performs a rigorous 3-phase flash calculation to yield:

• Vapor phase - if present, contains water and monomers


• Dispersion phase - contains water, initiators, emulsifiers, activators and some dissolved monomer

• Monomer phase - contains monomer and some dissolved water

The user provides a partition coefficient for each component that may be present in the polymer phase. Following the rigorous 3-phase flash, an iterative algorithm calculates the amount of each component to transfer from the monomer phase, if present, and the aqueous phase to the polymer phase in order to satisfy the partition coefficient constraints. As monomer is transferred to the polymer phase, water is transferred from the monomer phase to the aqueous phase so that its concentration in the monomer phase is the saturation concentration calculated by the rigorous flash.

The user-supplied partition coefficients are provided as either:

• Monomer (L1) basis

iipi xkx 11 ∗=

• Aqueous (L2) basis

iipi xkx 22 ∗=

In either case, the partition coefficients are on a mass basis.

This scheme works equally well for monomer starved or monomer saturated situations. When the monomer phase collapses, the algorithm transfers monomer from the aqueous phase to the polymer phase. If the user provided partition coefficients on a monomer basis, the partition coefficient with respect to the aqueous phase is calculated as:

LLiii kkk /12 =

LLik values are only available when there is sufficient monomer present in the

swollen polymer particles to form a separate monomer phase if polymer were removed. If the 3-phase flash does not detect a separate monomer phase,

LLik values will not be available, and the algorithm will transfer all monomer

from the aqueous phase to the polymer phase.

In addition, there are two rigorous phase equilibrium approaches to handle the thermodynamics of monomer partitioning. The first rigorous approach assumes the presence of two liquid phases. The distribution of water, monomers, and polymers is determined by isofugacity relationships, and the fugacities of various species are computed by the physical property option set chosen for the system. The second approach performs rigorous four phase (vapor-liquid-liquid-polymer) flash calculations based on a newly available flash algorithm.

Polymer Particle Size Distribution Polymer particle size and size distribution, among other factors, determine the rheological properties of the latex . Although actual particle size distribution is important, it is often measured in terms of certain averages such as number average and weight average diameters. Further, rigorous tracking of the particle size distribution by discrete methods is computationally expensive.


In conventional emulsion polymerization where unimodal distributions are normally encountered, the moments of the particle size distribution give sufficient information about the nature of the particle size distribution. The particle size distribution can be described in terms of different independent variables such as diameter or volume of the particle. Since volumetric growth rate of the particle in emulsion polymerization remains almost constant in Stage I and Stage II of the process, the population balance equation is formulated in terms of the volume of the particles.

General Population Balance Equation

The general population balance equation for the emulsion polymerization is given as follows:

( ) ( )( ) [ ] ( ) ( )∂∂

∂∂

δ δF t

tF t

k A N R Ram m a w m hv v v

vv v v v

, ,+ = − + −•

homo (3.15)

In Equation 3.15 the right-hand side represents the nucleation of particles from miceller and homogeneous nucleation. Refer to the table on page 204 for an explanation of the variables used. The volumetric growth rate is v for a single unswollen particle (Equation 3.5):

v =k M n

NMW

dp p

a

m

p (3.16)

The general population balance equation can be converted to the equivalent moment equations. The j-th moment of the particle size distribution is given as:

ν ν ν νjj F j d=

∞

∫ ( , )0

(3.17)

Applying moment definition in Equation 3.17 to the general population balance equation in Equation 3.15, the first four moments of the particle size distribution are given as:

ddt

k A N R Ram m a wν0 = +•[ ] homo (3.18)

ddt

k A N R Rm am m a w hν

ν10= + +•[ ]v v v homo (3.19)

ddt


ν21

2 22= + +•[ ]v v v homo (3.20)

ddt


ν32

3 33= + +•[ ]v v v homo (3.21)

Where:

kam = Kinetic constant for the absorption of the oligomeric radicals into the micelles

Am = Area of the micelles


Rhomo = Rate of particle formation by homogeneous nucleation

Polymer Particle Properties Calculated The emulsion model is designed to generate the following results that are of interest for the emulsion polymerization process:

• Copolymer composition

• Number average molecular weight

• Particle size distribution averages for unswollen particles

The results are available as component attributes under the names listed here:

Name Symbol Description Class Units

PSDZMOM ν0 Zeroth moment of the particle size distribution (volume)

2 no./s

PSDFMOM ν1 First moment of the PSD (volume)

0 m3/s

PSDSMOM ν2 Second moment of the PSD (volume)

2 m6/s

PSDTMOM ν3 Third moment of the PSD (volume)

2 m9/s

VOLN Vn Number average volume of the particles

0 m3

VOLV Vv Volume average volume of the particles

0 m3

VOLZ Vz Z-average volume of the particles

0 m3

DIAV Dv Volume average diameter

0 m

PDV PDv Polydispersity for PSD (Volume)

0 ---

SFRAC --- Copolymer composition

0 ---

MWN --- Number average molecular weight

0 kg/kmol

User Profiles In addition to the polymer properties reported through the component attributes, other model calculations are reported through User Profile variables. The following user profile variables may be requested from the model:


• Glass transition temperature of the polymer (°C)

• Average number of radicals per particle

• % Soap coverage of the polymer particles

• Volume of the monomer droplet phase (m3)

• Concentration of monomers in the monomer droplets (kmol/m3)†

• Volume of the aqueous phase (m3)

• Monomer concentration in the aqueous phase (kmol/m3)†

• Volume of the polymer particle phase (m3)

• Monomer concentration in the polymer particles (kmol/m3)†

• Monomer conversion

† One profile is reported for each monomer.

User profiles are only accessible if the reaction model is called from a batch reactor (RBatch) or a plug flow reactor (RPlug). The user profiles are returned in the order shown. A label must be provided to differentiate the profile variables. For the monomer concentrations in the aqueous, monomer, and polymer phases one profile is returned for each monomer.

Specifying Emulsion Polymerization Kinetics

Accessing the Emulsion Model To access the Emulsion polymerization kinetic model:






5 Select Emulsion as the reaction type and click OK.

Specifying the Emulsion Model The Emulsion model input forms are divided into two folders: Specifications and Phases.

Use the Specifications forms to define reacting species and enter reaction rate constant parameters. Use the following options:

Use this sheet To





Options Select additional options

Gel Effect Gel-effect correlation parameters

Use the Phases forms to enter information related to phase partitioning and particle growth. Use the following options:

Use this sheet To

Phase Equilibria Specify component phase split

Particles Specify emulsifiers and define particle radical exchange information

Specifying Reacting Species You must specify the reacting species in the Specifications Species sheet:

1 In the Polymer field, specify the polymer produced. Also specify Dispersant and the Redox couple (ferrous salt and reductant) if redox initiation is used.

2 In the Monomers field list the reacting monomers. For each monomer, in the goes to → field, specify the polymer segment that the monomer converts to.

3 Continue listing other types of reacting species, e.g. initiators, transfer agents, etc.



Listing Reactions The Emulsion model generates reactions based on the list of reacting species. You can view the system-generated reactions, then assign rate constant parameters to these reactions.

You can view a list of the system-generated reactions on the Specifications Reactions sheet. In the Reaction summary listing for each reaction, the first column indicates the reaction type. The second column lists the reactants, and the last column lists the products. The Data Browser window can be resized to better view the reaction listing. Use the following options:

Click To







Click To



Adding Reactions To add a new reaction to the scheme, click New to open the Add Reaction subform:

1 In Reaction type, select a type for the new reaction.


2 In other reactant (for example, Initiator, Catalyst) fields, enter the reactants of the categories allowed for that reaction type.



− or −









Assigning Rate Constants to Reactions To assign rate constants to user reactions, click Rate Constants to open the Rate Constant Parameters subform:

1 In the Ko field, enter the pre-exponential factor.


3 In the ΔV field, enter activation volume.


5 In the Efficiency field, enter initiator efficiency for initiation reactions.


6 In the No. radicals field, enter the number of primary radicals formed in initiation reactions.

7 Click the stoichiometry list and select a new reaction. Enter rate constants for the new reaction. You can use the Prev and Next buttons to select the previous or next reaction in the list.

8 Click the Summary tab to see a listing of all the rate constant parameters.



Selecting Calculation Options You can select additional simulation options for the model, such as gel-effect, on the Options sheet.

For Gel effect, you need to specify parameters on the Gel Effect sheet.

Adding Gel-Effect Use the Gel-Effect sheet to add gel effect to reactions:

1 Enter a unique integer identifier in No.

2 In the Reaction field, specify the reaction to which you would like to apply gel effect.

3 In the Corr. No. field, specify a gel effect correlation number.

4 In Parameters, list the parameters for the gel effect correlation.

Specifying Phase Partitioning Use the Phases Phase Equilibria sheet to specify phase partitioning for the components in the emulsion system:

1 If you select a Rigorous approach, specify a Method.

2 If you select the Partition Coefficients approach, in the Basis field select the phase partitioning basis, for example, MONOMER or AQUEOUS

3 For each component present in the polymer phase (except the polymer), specify the split fraction using the Component and Coefficient fields.


Specifying Particle Growth Parameters Use the Phases Particles sheet to specify data for particle generation and particle related events:

1 Define Emulsifier, and specify critical micelle concentration, CMC, and surfactant Area.

2 For homogeneous nucleation, specify Aggregat no. and Critical length.

You must specify radical absorption and desorption rate constant parameters for micelles and particles.

References Barton, J., & Capek, I. (1994). Radical Polymerization in Disperse Systems. New York: Ellis Harwood.

Blackley, D. C. (1975). Emulsion Polymerization: Theory and Practice. London: Applied Science Publishers Ltd.

Gilbert, R. G. (1995). Emulsion Polymerization: A Mechanistic Approach. Boston: Academic Press.

Hamielec, A. E., & Tobita, H. (1992). Polymerization Processes. In Ullmans Encyclopedia of Industrial Chemistry, A21, 305. New York: VCH Publishers.

Harkins, W. D. (1945). J. Chem. Phys., 13, 301.

Odian, G. (1991). Principles of Polymerization, 3rd. Ed. New York: John Wiley & Sons.

O’Toole, J. T. (1965). Kinetics of Emulsion Polymerization. J. Appl. Polym. Sci., 9, 1291.

Poehlein, G. W. (1986). Emulsion Polymerization. In H.F. Mark, N. M. Bikales, C. G. Overberger, and G. Menges, (Eds.). Encyclopedia of Polymer Science & Technology, 6, 1. New York: Wiley-Interscience.

Ponnuswamy, S. R., & Hamielec, A. E. (1997). Emulsion Polymerization: Theory and Practice. Lecture notes for intensive short course on polymer reaction engineering held at Burlington, ON, Canada, April 28-30.

Smith, W. V., & Ewart, R. H. (1948). J. Chem. Phys., 16, 592.

220 11 Ziegler-Natta Polymerization Model

11 Ziegler-Natta Polymerization Model

This section covers the Ziegler-Natta polymerization kinetic model available in Aspen Polymers (formerly known as Aspen Polymers Plus). The term Ziegler-Natta polymerization is used here to describe a variety of stereospecific multi-site and single site catalyzed addition polymerization systems including the traditional Ziegler-Natta catalyzed systems, chromium based catalyzed systems (Phillips type) and the more recent metallocene based catalyzed systems.



• Ziegler-Natta Processes, 221




• Specifying Ziegler-Natta Polymerization Kinetics, 237

Several example applications of the Ziegler-Natta polymerization model are given in the Aspen Polymers Examples & Applications Case Book. Additionally, the Examples & Applications Case Book provides process details and the kinetics of polymerization for specific monomer-polymer systems.

Summary of Applications The Ziegler-Natta polymerization model is applicable to processes utilizing coordination catalysts for the production of stereospecific polymers.

Some examples of applicable polymers are:

• Linear low density polyethylene - Ethylene is copolymerized with an alpha-olefin, such as 1-butene, 1-hexene, or 1-octene. Commercial processes include low pressure, slurry-phase processes, solution-phase processes, low pressure, gas phase processes.

• High density polyethylene - Ethylene homopolymers or copolymers with

high alpha olefins with density 0.940 g / cm3 and higher. Commercial

11 Ziegler-Natta Polymerization Model 221

processes include solution, slurry or suspension, and gas phase polymerization.

• Ethylene-propylene elastomers - Polymerization proceeds by solution or slurry processes. Both are operated continuously in liquid-phase back-mixed reactors.

• Polypropylene - Commercial processes include liquid pool, diluent slurry, and gas phase polymerization.

Ziegler-Natta Processes Ziegler-Natta polymerization accounts for a significant fraction of the polyethylene polymers and all the polypropylene homopolymers and copolymers produced commercially. The commercial production of these polyolefins is done exclusively by continuous processes using several different processes and reactor types operating over a wide range of conditions.

High density polyethylene (HDPE) and linear low density polyethylene (LLDPE) are produced via catalyzed polymerization processes. The operating conditions for the catalyzed processes are relatively less severe compared to the high pressure processes for LDPE production. The pressure generally ranges from 10-80 atm while the temperatures range from 80-110°C. The pressure and temperature may be as high as 200 atm and 250°C in some of the solution polymerization processes.

Catalyst Types There is a variety of catalysts used for ethylene polymerization including supported and unsupported heterogeneous catalyst systems and homogeneous catalyst systems. The Ziegler-Natta transition metal (Ti) based catalysts are the most widely used.

However, there are numerous variations of these catalysts. Some vanadium based catalysts are also used. Chromic oxide on silica catalysts are used in the Phillips loop reactor process, while the Union Carbide Unipol process may use either Ziegler-Natta (Ti) or chromium compounds on silica catalysts.

More recently, several manufacturers have been developing commercial processes using metallocene based catalysts, mainly zirconium and titanium. These catalysts are believed to be single site catalysts that are capable of producing high yields, combined with narrow molecular weight and copolymer composition distributions.

All commercial isotactic polypropylene homopolymer (PP) is manufactured using heterogeneous Ziegler-Natta catalyst systems. The catalyst consists of a solid transition metal halide, usually TiCl3 , with an organoaluminum

compound cocatalysts, such as diethylaluminum chloride (DEAC), or a MgCl2

supported TiCl AlEt4 3. catalyst.


Ethylene Process Types There are three types of catalyzed ethylene polymerization processes in commercial use today:

• Liquid slurry

• Solution

• Gas-phase

A partial list of HDPE and LLDPE processes, along with a summary of their characteristics is shown here:

Process Reactor Diluent / Solvent

Catalyst Temp. (°C)

Press. (atm)

Residence Time (hr)

Company

Liquid slurry

Loop i-butane

n-hexane

Supported Ti or Cr

80-100 30-35 1.5-2.5 Phillips Solvay

CSTR n-hexane Supported Ti

80-90 8-35 2.0-2.7 Dow

Hoechst

Nissan

Mitsubishi

Montedison

Solution CSTR n-hexane cyclohexane

Ti/V 130-250

30-200 0.08-0.17 Dow

Dupont

Stamicarbon

Gas Stirred bed

--- Supported Ti or Cr

70-110 20-35 3-5 AMOCO

BASF

Fluidized bed

--- Supported Ti or Cr

85-100 20-30 3-5 BP

Union Carbide

In the slurry process, a hydrocarbon diluent is used, typically a C C4 7− paraffin, isoparaffin or cycloparaffin. Under the conditions used the polyethylene is essentially insoluble in the diluent. As a result a slurry is formed.

In the solution process, the conditions used are such that the polyethylene is completely dissolved in the solvent.

In gas-phase processes, gaseous ethylene and comonomers are contacted with a polymer-catalyst powder. Polymerization occurs in the monomer-swollen polymer particles which contain embedded catalyst fragments with active sites.

Ethylene polymerization processes have been reviewed extensively. More detailed descriptions of these processes are available in the open literature (Albright, 1985; Choi & Ray, 1985a; Nowlin, 1985; Short, 1983).


Propylene Process Types There are three types of catalyzed polypropylene homopolymerization processes in commercial use today:

• Liquid slurry

• Liquid pool (bulk)

• Gas-phase

A partial listing of propylene homopolymerizatio processes, along with a summary of their characteristics is shown here:

Process Reactor Diluent / Solvent

Catalyst Tacticity (%)

Temp. (°C)

Press. (atm)

Residence Time (hr)

Company

Bulk

(Liquid Pool)

Loop Liquid monomer

Supported Ti Up to 99 60-80 30-40 1-2 Himont

Mitsui

CSTR Liquid monomer

Unsupported or supported Ti

Up to 98 60-75 30-40 2 Dart

El Paso

Montedison

Sumitomo

Diluent Slurry

CSTR n-hexane,

n-heptane

Unsupported or supported Ti

Up to 98 60-80 15-20 3-4 Montedison

Gas Fluidized bed N2 Supported Ti Up to 98 60-80 20 3-5 Sumitomo

Union Carbide

Vertical stirred bed

--- Unsupported or supported Ti

Up to 98 70-90 20 4 BASF

ICI

USI

Horizontal compartmented stirred bed


Up to 98 70-90 20 4 AMOCO

In the slurry process, a hydrocarbon diluent, typically butane, hexane or heptane, is used at operating temperatures of 70-90°C. Under these conditions the isotactic polypropylene is essentially insoluble in the diluent. As a result a slurry is formed.

In the liquid pool process, liquid propylene is used in place of the diluent. In this process also, the polypropylene is insoluble in the liquid propylene and a slurry is formed. The higher monomer concentrations in this process allow for smaller reactors and lower operating temperatures compared to the slurry process.

In the gas-phase processes, gaseous propylene is contacted with a polymer-catalyst powder. Polymerization occurs in the monomer-swollen particles which contain embedded catalyst fragments with active sites.


Propylene polymerization processes have been reviewed extensively in the literature. More detailed descriptions of these processes are available in the open literature (Albright, 1985; Brockmeier, 1983; Choi & Ray, 1985b).

Besides polypropylene homopolymer (PP), high impact polypropylene (HIPP) and some ethylene-propylene (EP) copolymers are produced by including an additional reaction stage to the polypropylene homopolymerization process. A summary of catalyst processes for propylene copolymerization is shown here:

Press. (atm)

Process Reactor Diluent / Solvent Catalyst

Temp. (°C)

Stage 1

Stage 2

Resi-dence Time (hr)

Co-monomers Company

Bulk

(Liquid Pool)

+

Second Stage

Loop - fluid bed

--- Supported Ti 60-80 30-40 20 1-2 Ethylene & others

Himont

Mitsui

CSTR - CSTR

--- Supported Ti 60-75 30-40 30-40 2 Ethylene Sumitomo

CSTR - stirred horizontal bed


40-75 30-40 20 2-5 Ethylene Dart

El Paso

Diluent Slurry

CSTR Liquid monomers & diluents

Ti/V 0-20 5-20 --- 1 Ethylene, Butene, dienes

Montedison

Dutral

Multistage Gas

Fluid bed - fluid bed

--- Supported Ti 60-80 20 20 3-5 Ethylene & others

Sumitomo

Union Carbide

Vertical stirred bed - stirred bed

--- Unsupported of supported Ti

70-90 20 20 4 Ethylene & others

BASF

ICI

USI

Horizontal stirred bed - horizontal stirred bed

--- Supported Ti 70-90 20 20 4 Ethylene & others

AMOCO

Chisso

In the EP process, last reaction stage is designed to introduce the desired amount of EP copolymer into the PP product. For example, the Himont spheripol process uses liquid pool loop reactors followed by a gas-phase fluidized bed reactor for the copolymerization stage. The residence time distribution of the polymer particles leaving each stage should be as narrow as practical to ensure that the weight ratio of EP to PP for particles leaving the second stage is as uniform as possible. The Amoco/Chisso process has largely met this requirement.


Reaction Kinetic Scheme The built-in catalyst/polymerization kinetic scheme represents the typical scheme described in the open literature (Xie et al., 1994). Although a number of reaction mechanisms have been proposed to describe stereospecific Ziegler-Natta polymerization, there is still no definitive reaction mechanism to completely describe the kinetic behavior of these complex catalyst/polymerization systems.

Most of the proposed mechanisms include a detailed set of reactions. However, not all of these reactions apply to every catalyst system nor can they be verified. The kinetic scheme for chromium and metallocene catalyzed systems can be considered to be a subset of a comprehensive Ziegler-Natta kinetic scheme.

Reaction Steps

There are a few key elementary reactions that apply to almost all catalyzed addition polymerization systems. These include the three basic reaction steps:

• Chain initiation

• Propagation

• Chain transfer (spontaneous and to small molecules such as monomer, solvent and chain transfer agents)

For chromium and metallocene catalyst systems, additional reactions for long chain branching via terminal double bond polymerization must also be included.

In addition to the polymerization reactions, there are reactions affecting the catalyst active sites on which the polymerization reactions take place. These include catalyst site activation, inhibition and deactivation. The catalyst reactions and the polymerization reactions occur simultaneously during the polymerization.

A comprehensive kinetic scheme for the catalyzed multi-site homo- and copolymerization of any number of monomers has been built into Aspen Polymers.

Catalyst States

The multi-site catalyst states and the types of reactions affecting them are shown here:


In setting up a simulation, the user specifies the catalyst flow rate for the feed streams, and a catalyst parameter, the moles of sites per unit mass of catalyst. This parameter together with the catalysts flow rate is used to compute the total moles of sites.

The total moles of sites are made up of potential sites, active sites of different reactivities, and dead sites. Site activation reactions convert potential sites to active sites, while site deactivation reactions convert active sites to dead sites. There are several different site activation/deactivation reactions built into the kinetic scheme and these are discussed later in this section.

Site Types

In the figure, potential sites and dead sites are considered to be independent of site type. The user specifies the number of site types to be included for a particular simulation.

• A vacant site is an active site that does not have a polymer or other molecule attached to it.

• A propagation site has a growing polymer molecule attached to it.

• Inhibited sites have small molecules such as hydrogen or poisons attached, temporarily blocking it from becoming propagation sites. The small molecule may dissociate from an inhibited sited, which then becomes a vacant site once again. Therefore, the site inhibition reaction is considered reversible.


When a vacant site is involved in a chain initiation reaction it is converted to a propagation site. When a propagation site is involved in a chain transfer reaction, a vacant site and a dead polymer molecule are formed.

The built-in scheme includes most of the reactions commonly used for modeling Ziegler-Natta polymerization. Reactions such as depropagation, internal double-bond polymerization with diene comonomers, and site transformation reactions (Debling et al., 1994; Xie et al., 1994) have not been included in the current model. These reactions may be added to the built-in scheme in the future. The current built-in Ziegler-Natta catalyst and polymerization kinetic scheme is shown here:

Built-In Ziegler-Natta Catalysts and Polymerization Kinetic Scheme (continued)



continued



Kinetic Scheme Nomenclature

The nomenclature used in the Ziegler-Natta polymerization kinetic scheme is given here:

Symbol Description

Am Cocatalysts m

Em Electron donor m


Cds Dead catalyst sites

Cps Potential catalyst sites

Cisk Inhibited catalyst sites of type k

Dnk Dead polymer chain of length n ( , , ..., )= n n nm1 2 for

copolymerization produced from a catalyst site of type k

H2 Hydrogen

M j Monomer j

Nm Number of monomers

Nsites Number of active site types

Ok Reaction order for the non-polymer component at site type k

Pk0 Vacant catalyst sites of type k

Pn ik, Live polymer chain of length n having an active segment

of type i attached to a active site of type k

Sm Solvent m (for solution or slurry polymerization)

Tm Chain transfer agent m

Xn Inhibitor n

0,ikμ Zeroth moment of live polymer with respect to active

segment of type i and active site of type k

In the following discussion:

• A polymer chain is considered to be made up of monomer units or segments derived from the propagating monomers

• Live chain ( ),Pn ik refers to growing polymer chains containing n segments

or monomer units, with an active segment of type i attached to a catalyst active site of type k

• Dead chain ( )Dnk refers to a terminated polymer chain

• The superscript k refers to the active site type from which the dead polymer chain was formed

• The subscript n refers to the chain length in terms of the number of segments or monomer units incorporated in the polymer chain

Live chains are reactive and can participate in the polymerization reactions while dead chains are usually considered inert, except in cases where long chain branching reactions are important.

Polymerization Mechanism

The catalyst active site is attached to one end of a live polymer chain via a metal-carbon bond. It is generally accepted that polymerization proceeds via a two-step mechanism. In the first step, monomer is complexed to the transition metal site. The second step is the coordinated insertion of the


monomer into the metal-carbon bond. As a result, the polymer chain and the previously added segments grow away from the active site with every addition of a monomer molecule.

It is believed that the chain microstructure will not have a strong influence on the mode of monomer addition. For this reason, the built-in kinetic model assumes that the reactivity of a live polymer chain depends only on the active segment and the active site type, and is independent of the polymer chain length and other structural properties. Meaning in the propagation reaction, the rate of propagation Rp ij

k, is independent of the polymer chain length. It

depends only on the concentration of monomer j, and the concentration of live polymer chains with active segments of type i attached to an active site of type k. Models using this assumption are referred to as terminal models in the polymerization literature.

Copolymerization Mechanism

For copolymerization, the built-in kinetic scheme allows the user to specify the number of monomer types used. Similarly the user has the flexibility to specify the number of each type of reactive species present in the polymerization: catalysts, cocatalysts, chain transfer agents, solvents, etc. The user is able to tailor the built-in kinetics to model a specific catalyzed polymerization system by selecting a subset of the reactions shown in the Built-In Ziegler-Natta Catalysts and Polymerization Kinetic Scheme figure on page 227. However, it is important that the subset include a chain initiation, propagation, and at least one chain transfer or active site deactivation reaction to produce dead polymer.

Rate Expressions

The rate expression for each reaction is generally written as a product of the rate constant and the concentrations of the reacting species. In many of the reactions, one of the reacting species is a polymer chain while the other is a small molecule such as monomer, chain transfer agent, cocatalyst, etc. A reaction order with respect to the small reacting molecule is included for some of the reactions. This reaction order has a default value of one.

The rate constants for each reaction at sites of type k are calculated at the reaction temperature using the Arrhenius equation shown below. The user

specified rate constant parameters are pre-exponential factor ( )kok , activation

energy ( )Eak at sites of type k, and the reference temperature.

Rate Constant

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−

ref

kko

k

TTRaE -expk = k

11

Where:

ko = Pre-exponential factor in 1/sec for first order reactions


and m kmol3 / sec− for second order reactions

Ea = Activation energy in mole enthalpy units


refT = Reference temperature in Kelvin

Catalyst Pre-Activation Some of the chromium catalysts used in these processes exhibit slow activation with induction period. This slow activation can be modeled by catalyst preactivation reaction. The precatalyst goes to catalyst that further undergoes site activation, initiation and propagation.

Catalyst Site Activation The catalyst site activation step involves the generation of reactive vacant active sites from potential sites. Depending on the catalysts system, the activation may be done before the catalyst is fed to the reactor or within the reactor.

There are several different site activation reactions included in the built-in kinetic scheme. They include site activation by cocatalyst, by electron donors, by hydrogen, by monomer, and spontaneous site activation. Different catalyst systems tend to be activated by a different subset of the reactions in this scheme. For example, TiCl3 catalyst systems are usually activated with an organoaluminum cocatalyst such as diethylaluminum chloride (DEAC), in the reactor. Chromic oxide catalysts are calcined by heating with air for several hours at temperatures of 400°C to 975°C and cooled in dry air. Some of these catalysts may be activated with a reducing agent before introduction into the reactor, while others are activated within the reactor.

Site Activation Reactions

Some of the site activation reactions (activation by monomer, electron donor, hydrogen) have been proposed to explain the observed rate enhancement behavior in different catalyst systems. For example, the activation of additional sites by comonomer has been proposed to explain the rate enhancement observed with the addition of a comonomer to ethylene and propylene homopolymerization reactors.

Chain Initiation Chain initiation involves the reaction of a monomer molecule at a vacant active site to form a live polymer molecule of unit length at that site. This reaction converts a vacant active site to a propagation site. The chain initiation reaction is shown below:

( )P M P R k P Cok

ii

cik

cik

ok

MiOMi

k

+ → =1


The rate of chain initiation at site type k ( )Rcik is dependent on the

concentration of vacant sites of type k and the concentration of monomer i. The user can also specify the reaction order with respect to the monomer concentration. The live polymer chains grow by successive addition of monomer molecules to form long polymer molecules.

Propagation The live polymer at each active site type grow or propagate through the addition of monomer molecules to form long polymer chains. The propagation reaction is represented by:

kinMj

kijp

kijp

kjnj

kin PCkRPMP ,,,,1, =→+ + (main propagation)

Where monomer j is being added to a polymer chain of length n, with an active segment of type i at an active site of type k. The resulting polymer chain will be of length n+1 and the active segment will be of type j. The active segment type usually represents the last monomer type incorporated into the polymer chain.

For copolymerization, there will be N N Nm m site* * propagation reactions that may have different reactivities. For example, with two monomers and three site types, the monomer being added could be monomer 1 or monomer 2 while the active segment type could be segments from monomer 1 or monomer 2 at each site type.

As a result, there will be twelve rate constants ( ),kp ijk , where the subscript i

refers to the active segment type while the second subscript j refers to the propagating monomer type. The superscript k refers to active site type. For the terminal model the rate of propagation is dependent only on the concentration of live polymer with active segment i at active site k and the concentration of the propagating monomer j.

In Aspen Polymers Version 3.0 and higher, another propagation reaction has been added to account for formation of atactic polymer. This reaction has the same form as the main propagation reaction:

( ) kpaMiO

Mik

jkpaij

kpaij

kiinj

kin CkRPMP ,0,, μδ =→+ + (atactic propagation)

but uses a different rate constant ( )kpaijk . When the atactic propagation

reaction is included in the simulation, the main propagation reaction should be considered to account for the formation of all polymer whether it is isotactic or atactic. Hence the main propagation reaction is also termed the total propagation. The atactic propagation reaction only accounts for the formation of atactic polymer. The atactic content of the polymer is then calculated from the ratio of atactic to total polymer.

Chain Transfer to Small Molecules Chain transfer to small molecules such as monomer, solvent or chain transfer agent usually involves the extraction of hydrogen from the small molecule by the active site and leads to the termination of the live chain. At the same


time, a new vacant site is formed which can undergo chain initiation to start polymerization. The effect of chain transfer on the polymerization kinetics depends on the reactivity of the transfer sites.

When the transfer site is very reactive, as is the case when the chain initiation rate constant is greater than the propagation rate constant, chain transfer will not lower the polymerization rate or conversion, but will reduce the molecular weight of the polymer. However, if the transfer site is less reactive, as in the case of low chain initiation rate constant, both the conversion and molecular weight of the polymer will be lowered.

In the built-in kinetics, chain transfer to hydrogen, cocatalysts, solvent, transfer agent, electron donor, monomer and spontaneous chain transfer are included as shown in the Built-In Ziegler-Natta Catalysts and Polymerization Kinetic Scheme figure on page 227.

Chain Transfer to Monomer

For chain transfer to monomer a new polymer chain of unit length is generated while for the other transfer reactions a vacant site of that type is generated. The dead polymer chain formed by some of the chain transfer reactions will have an end-group with a terminal double bond. In addition to the rate constant parameters and the reaction order, the user may also specify a parameter to track the fraction of dead polymer chains with terminal double bonds that are generated from the chain transfer reactions. The default value for this parameter is zero.

Site Deactivation The catalyst site deactivation step involves the deactivation of active sites, vacant and propagation, to form dead sites. Depending on the catalyst system and operating conditions, the deactivation rate may be high or low.

There are several different site deactivations reactions included in the built-in kinetic scheme. They include site deactivation by cocatalyst, by electron donors, by hydrogen, by monomer, by poisons, and spontaneous site deactivation. Different catalyst systems tend to be deactivated by a different subset of the reactions.

The deactivation rate constants are assumed to be dependent only on the site type and not on the polymer segment attached to a site. Therefore, the same rate constant is applied to both vacant and propagation sites of the same type. Note that deactivation rates shown in the Built-In Ziegler-Natta Catalysts and Polymerization Kinetic Scheme figure on page 227 are per unit of active (vacant and propagation) site concentration.

Site Inhibition Inhibited sites have small molecules such as hydrogen or poisons attached. As a result, inhibited sites are temporarily blocked from becoming propagation sites. The site inhibition reaction is considered reversible. Therefore, the small molecule may dissociate from an inhibited site which then becomes a vacant site once again. The user must specify rate constant


parameters for both the forward (inhibition) and reverse (dissociation) reactions.

Cocatalyst Poisoning For some catalyst systems, additional amounts of cocatalysts are fed to the reactor to counteract the effect of any poisons present . This is modeled as a cocatalyst poisoning reaction in the built-in kinetics. The product of this reaction is designated as a byproduct in the list of reactive species. The byproduct is considered to be inert and does not participate in any reaction.

Terminal Double Bond Polymerization For some catalyst systems, primarily metallocene, polymer chains with long chain branches are formed. However, the long chain branching frequency is usually small. The long chain branches are believed to be due to propagation reactions involving a live chain and a terminal double bond on a dead polymer chain. Polymer chains with terminal double bonds are formed by some of the chain transfer reactions. To form long chain branches, the metal center must be open to provide a favorable reactivity ratio for the macromonomer.

The concentration of terminal double bond (TDB) end-groups on the dead polymer chains are tracked through an additional segment called the TDB-Segment. TDB-Segments are generated through the chain transfer reactions and are consumed through the TDB polymerization reaction. When the TDB reaction is used, one additional segment needs to be defined in the Components form for the TDB-Segment. Typically, for a copolymerization system with N monomers, N repeat segments would be defined in the Components form. However, with the TDB polymerization reaction, N repeat segments and one end segment should be defined in the Component form. The end segment must be specified as the TDB-Seg species in the Species folder of the Ziegler-Natta kinetics.

Model Features and Assumptions Following are the model features and assumptions used in the Ziegler-Natta polymerization model available in Aspen Polymers.

Phase Equilibria The polymerization model currently considers a single-phase system (vapor or liquid), two-phase system (vapor and liquid), or three-phase (VLL) system when calculating concentrations for the reaction kinetics. For single-phase systems, the reacting phase may be either vapor or liquid. In multi-phase systems, reactions can occur in one or more phases simultaneously. Each reaction object is associated with a single reacting phase, identified on the options form.



Rate Calculations The Ziegler-Natta polymerization kinetic model supplies to the reactor models the reaction rates for the components and the rate of change of polymer attributes (e.g. the chain length distribution moments) . The component reaction rates are computed from the kinetic scheme by summing over all reactions that involve the component. The site based moment rates are derived from a population balance and method of moments approach similar to that described in the Calculation Method section on page 182.

Polymer Properties Calculated The following variables can be calculated by the built-in kinetics routine based on the polymer attributes selected, and the subset of the built-in kinetics used for a specific simulation:

• Zeroth, first and second moments for the composite and site based combined polymer

• Zeroth and first moments for the composite and site based live polymer

• Number and weight degree of polymerization and polydispersity index for the composite and site based bulk polymer (DPN, DPW, PDI and SDPN, SDPW, SPDI)

• Number and weight average molecular weight for the composite and site based bulk polymer (MWN, MWW and SMWN, SMWW)

• Copolymer segment composition for composite and site based bulk polymer (SFRAC and SSFRAC segment mole fractions)

• Total number long chain branches (LCB)

• Long chain branching frequencies (FLCB)

• Mole fraction of live bulk polymer chains (LPFRAC and LSPFRAC)

• Number average degree of polymerization for live polymer (LDPN and LSDPN)

• Copolymer segment composition for live polymer (LSFRAC and LSSFRAC)

• Live polymer active segment composition (LEFRAC and LSEFRAC)

These variables are stored as component attributes (See Chapter 2). It is assumed that attributes needed for the kinetic scheme are selected. The specification of the Ziegler-Natta Model is described later in this section.

In many cases, users may need to know polymer product properties related to the above structural properties. For example, users may be interested in melt flow rate or melt index, viscosity, density, etc. These properties can be calculated in user-supplied Fortran subroutines which take the polymer moments and structural information and return the desired property. An example use of a user supplied subroutine to return melt index is shown in the HDPE section of the Aspen Polymers Examples & Applications Case Book.


Specifying Ziegler-Natta Polymerization Kinetics

Accessing the Ziegler-Natta Model To access the Ziegler-Natta polymerization kinetic model:






5 Select Ziegler-Nat as the reaction type and click OK.

Specifying the Ziegler-Natta Model The Ziegler-Natta model input forms are as listed below. Use these forms to define reacting species and enter reaction rate constant parameters.

Use this sheet To




Options Specify the reacting phase

Specifying Reacting Species You must specify the reacting species on the Species sheet:


2 In the Monomers field list the reacting monomers. For each monomer, in the goes to → field, specify the polymer segment that the monomer converts to.

3 If you select the terminal double bond polymerization reaction, in the T.D.B.-Seg field, list TDB segment that is formed by the chain transfer reactions and is consumed by the terminal double bond polymerization reaction. Otherwise, go to step 4.

Note: The TDB segment should be of type end segment and should not be used as a repeat segment for a particular monomer (see Step 2).

4 Continue listing other types of reacting species, for example, solvents, transfer agents, etc.




Listing Reactions The Ziegler-Natta model generates reactions based on the list of reacting species. You can view the system-generated reactions, then assign rate constant parameters to these reactions.

You can view a list of the system-generated reactions on the Reactions sheet. In the Reaction summary listing for each reaction, the first column indicates the reaction type. The second column lists the reactants, and the last column lists the products. The Data Browser window can be resized to better view the reaction listing. Use the following options:

Click To






Click To






2 In other reactant (for example, Initiator, Catalyst) fields, enter the reactants of the categories allowed for that reaction type.



− or −


− or −


Click Done to return to the reaction summary.








1 In the Site No. field, enter the site number.



4 In the Order field, enter the order for component in reaction.

5 In the Fraction field, enter terminal double bond fraction.






References Albright L. F. (1985). Processes for Major Addition-Type Plastics and Their Monomers, 2nd Ed. Florida: Krieger Pub.

Brockmeier, N. F. (1983). Latest Commercial Technology for Propylene Polymerization. In R.P. Quirk (Ed.), Transition Metal Catalyzed Polymerizations - Alkenes and Dienes. New York: Academic Pub.

Choi, K-Y, & Ray, W. H. (1985a). Recent Developments in Transition Metal Catalyzed Olefin Polymerization - A Survey. I. Ethylene Polymerization. J. Macromol. Sci. Rev. Macromol. Chem. Phys., C25 (1), 1.


Choi, K-Y, & Ray, W. H. (1985b). Recent Developments in Transition Metal Catalyzed Olefin Polymerization - A Survey. II. Propylene Polymerization. J. Macromol. Sci. Rev. Macromol. Chem. Phys., C25 (1), 57.

Debling, J. A., Han, G. C., Kuijpers, F., Verburg, J., Zacca, J., & Ray, W. H. (1994). Dynamic Modeling of Product Grade Transition for Olefin Polymerization Processes. AIChE J., 40, No. 3, 506.

Nowlin, T. E. (1985). Low Pressure Manufacture of Polyethylene. Prog. Polym. Sci., 11, 29.

Short, J. N. (1983). Low Pressure Ethylene Polymerization Processes. In R.P. Quirk (Ed.), Transition Metal Catalyzed Polymerizations - Alkenes and Dienes. New York: Academic Pub.

Xie, T., McAuley, K.B., Hsu, J. C. C., & Bacon, D. W. (1994). Gas Phase Ethylene Polymerization: Production Processes, Polymer Properties, and Reactor Modeling. Ind. Eng. Chem. Res., 33, 449.

12 Ionic Polymerization Model 241

12 Ionic Polymerization Model

This section covers the ionic polymerization kinetic model available in Aspen Polymers (formerly known as Aspen Polymers Plus). The cationic, anionic and group transfer addition polymerization kinetics can be modeled using this model.



• Ionic Processes, 242




• Specifying Ionic Polymerization Kinetics, 252

Summary of Applications Some examples of applicable polymers are given in below:

• Polystyrene - Anionic polymerization is used to produce narrow molecular weight distribution polystyrenes in small quantities. Cationic polymerization is used to produce low molecular weight polystyrenes for coatings and glues. Block copolymers of styrene and butadiene are produced commercially with anionic polymerization.

• Polyisobutylene - Low-to-medium molecular weight poly isobutylene is produced commercially by polymerization of high purity isobutylene in isobutane or hexane diluent using aluminum chloride or hexane trifluoride as a catalyst.

• Polybutene - Polybutenes are produced in solution by copolymerizing isobutylene and n-butene using aluminum chloride or hexane trifluoride as a catalyst.

• Polybutadiene - Block copolymers of styrene and butadiene are produced commercially with anionic polymerization.

• Polyoxides - Examples are poly ethylene oxide (PEO) and poly propylene oxide (PPO). Continuous tubular or column reactors or semibatch

242 12 Ionic Polymerization Model

autoclaves are used. The polymerization can be carried out with different mechanisms: anionic (base catalysis), cationic (acid catalysis), or coordinate.

Ionic Processes Many specialty polymers are manufactured by ionic polymerization processes. For the description of a specific ionic process, refer to the References section. Ionic polymers fall in the category of addition polymers, i.e., the reactive species grow in length by continuous addition of monomer units. However, there are several features that distinguish the ionic polymerization processes from other addition polymerization processes like free-radical and Ziegler-Natta:

• Different propagating species are often present in ionic processes. These species may be free ions, tight ion pairs, loose ion pairs, dormant esters, etc. Moreover the propagating species are often in equilibrium.

• Association or aggregation phenomena is common in BuLi type of initiators for anionic polymerization. The associated initiator is not reactive and is in equilibrium with its dissociated form. The association phenomena also takes place with growing polymer chains, which reduces the actual number of chains growing at any given time. This phenomena affects both the conversion and polymer properties.

• Exchange reaction takes place between live and dormant polymer. The active species transfer from one polymer to another. This reaction controls the molecular weight distribution of the final polymer. If the exchange reaction rate constant >> propagation rate constant, then for increasing monomer conversion the polydispersity approaches a limiting value of 1.0.

• Ionic reactions are a strong function of solvent, initiator and operating conditions and are susceptible to poisons.

• Chain transfer and termination reactions may be negligible or absent in certain polymerization processes thus leading to formation of living polymers.

Reaction Kinetic Scheme In the following sections, the general chemistry of ionic polymerization and the built-in initiator / polymerization kinetic scheme are described. The kinetic scheme is based on literature survey of ionic polymerization mechanisms. Ionic kinetic scheme can model either cationic, anionic or group-transfer polymerization. The ionic kinetic scheme in Aspen Polymers is a super-set of all the above mentioned reactions.

Reaction Steps

There are a few key elementary reactions that apply to all ionic polymerization systems. These include the three basic reaction steps:

• Formation of active species

• Chain initiation


• Propagation

There is almost no chain transfer in living polymerization. There are additional reactions for each chemistry which will be discussed later. There can be different forms of propagating species, e.g., free-ions, ion-pairs, and dormant esters. A given ionic polymerization system can have different combinations of these propagating species.

To account for different propagating species, the same framework is used as the Ziegler-Natta multi-site kinetics model. In the ionic model, each site refers to a unique type of active species. To model three propagating species for an initiator, the model will have three sites with each site corresponding to the unique propagating active species type. In this framework, the polymer produced by dormant esters will be stored in live polymer attributes for the selected dormant ester site.

Polymer Molecules Tracked

There are three different types of polymer molecules tracked by ionic kinetic scheme:

• Pn,ki - live polymer molecule chains of length n with active segment k

attached to the active center of type i.

For example, free-ions can be site 1, ion-pairs as site 2 and dormant esters as site 3. The propagation rate constant for dormant esters ( k p for

site 3) may be zero.

• inQ - associated (or aggregate) polymer molecule chains of length n

formed by association of propagating species of type i.

The site based aggregate polymer attributes contain the information about polymer formed by association of different propagating species. For example, only the ion pairs propagating species may associate in case of BuLi type of initiators.

• inD - dead polymer molecule chains of length n formed by active

propagating species of type i.

The site based bulk polymer attributes contain information about the bulk polymer which is a sum of live, aggregate and dead polymer.

Initiator Attributes

The initiator in ionic model has three attributes which are solved along with moment equations:

P P Ci t iIi

0 0= = =P0FLOW; PT0FLOW; CIONFLOW,

These variables are provided as attributes so that they can be used in user

kinetics to add side reactions. For example, a transfer species ( )Pt, i0 may

undergo a side reaction with other components; addition of a salt with same

counter ion ( )CIi may tilt the polymerization in one direction by allowing

counter-ion to be in equilibrium with ion concentrations from other salts. The

initiator decomposition reactions (involving Pi0 or Im ) can also be modeled in


Aspen Plus as user reactions which can be solved simultaneously with built-in ionic kinetics in Aspen Polymers.

The built-in initiator and polymerization kinetic scheme is shown in here :

Built-In Ionic Polymerization Kinetic Scheme


The nomenclature used in the ionic polymerization kinetic scheme is shown here:

Symbol Description

Am Chain transfer agent, m

AIm Associated initiator, m

bFC Coefficient (= 0 when catalyst does not participate in the reaction)

bTCI Coefficient (= 0 when C-ion does not participate in the reaction)

CIi Counter ion (C-ion) corresponding to active species of

type i

Cn Catalyst, n

Dni Dead polymer chain length of n produced by active

species of type i

dEQL Coefficient (= 0 when C-ion does not participate in the reaction)

dEXA Coefficient (= 0 when Po does not participate in the reaction)

dFC Coefficient (= 0 when C-ion does not participate in the reaction)

dI 2 Coefficient (= 0 when C-ion is not formed in the reaction)

I p Initiator, p

M j Monomer, j

nm,p Association number for initiator dissociation reaction

Pi0 Active species of type i (chain length 0)

Pt,i0 Transfer active species of type i (chain length 0)

P j,j

i

δ Active species of type i with active segment j (chain length

1)

Pn,ki Growing species chain of length n of type i with active

segment k

Qn, ki Associated polymeric species of chain length n with active

segment k

Tm Terminating agent, m

Xm Exchange agent, m

The ionic model is a terminal model, implying that the rate constants are functions of only terminal segment of the polymer chain.


Copolymerization

For copolymerization, the built-in kinetic scheme allows the user to specify the number of monomer types used. Similarly the user has the flexibility to specify the number of each type of reactive species present in the polymerization:

• Associated initiators

• Initiators

• Catalysts

• Exchange agents

• Chain transfer agents

• Termination agents

The user is able to tailor the built-in kinetics to model a specific polymerization system by selecting a subset of the reactions shown in the Built-in Ionic Polymerization Kinetic Scheme figure on page 244.

The rate constants for each reaction for active species of type i are calculated at the reaction temperature using the Arrhenius equation shown below. The

user specified rate constant parameters are pre-exponential factor ( )koi and

the activation energy ( )Eai at active species of type i:

Rate Constant

ioi

i

refk k -

EaR T T

= −⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟exp

1 1

Where:

ko = Pre-exponential factor in 1/sec for first order reactions and m3/kmol-sec for second order reactions

Ea = Activation energy in mole enthalpy units

R = Universal constant

T = Reaction temperature in Kelvin

Tref = Reference reaction temperature in Kelvin (default is

1E38)

Formation of Active Species The active species are the initiator in dissociated form:

AI n Imm,p

p⇔

The association and dissociation of initiator is observed in alkyl-Lithium type of initiators in nonpolar solvents for anionic polymerization. n-butyl-Li exists as hexamer whereas s-BuLi and t-BuLi exist as tetramers for styrene polymerization. The dissociated initiator further reacts with monomer to form growing polymer with unit chain length in chain initiation step. This reaction can also be used to represent self-ionization of some strong acids


(AlCl , AlBr , TiCl )3 3 3 in cationic polymerization, with nm,p being the degree of

ionization:

I + b C P + d Cm FC ni

FC Ii⇔ 0

The active species Pi0 is formed by this reaction. Several initiators

(KNH , NaNH2 2 ) decompose to form an active species (or dissociate into

ions) in anionic polymerization ( , )b dFC FC= =0 1 . Polystyrene is

manufactured using KNH2 initiator.

With no reverse reaction, the electron transfer initiation with light (electrochemical initiation) is also a special case of the above scheme for anionic polymerization. Initiator and catalyst are used in cationic polymerization with no counter-ion ( )dFC = 0 . In case of anionic polymerization, a starter may be used to generate an active species.

For polyether polyols (polypropylene oxide), initiator is ROH and catalyst is KOH (weak base) and the reaction is only in forward direction.

The above scheme can also represent donar-accepter equilibria and self

dissociation of acids in cationic initiation ( )A+B A +B- +⇔ .

Chain Initiation The active species incorporate monomer to form propagating species with unit chain length:

P M Pij j,j

i0 + →

δ

The initiator (in dissociated form) directly reacts with monomer to form propagating species with unit chain length. A counter-ion may be formed ( )dI 2 1= :

I + M P + d Cm j j,ji

I Ii→ δ 2

The transfer active species incorporate monomer to form propagating species with unit chain length:

P M Pt,ij j,j

i0 + →

δ

Propagation The growing polymer with an active species at the end of the chain may grow or propagate through the addition of monomer molecules to form long polymer chains. The propagation reaction is represented by:

P M Pn,ki

j n+ j , ji+ → δ

where monomer j is being added to a polymer chain of length n, with an active segment of type k and active species of type i. The resulting polymer chain will be of length n+1 and the active segment will be of type j. The


active segment type usually represents the last monomer type incorporated into the polymer chain.

Copolymerization

For copolymerization, there will be N N Nm m site* * propagation reactions that may have different reactivities. For example, with two monomers and three site types, the monomer being added could be monomer 1 or monomer 2 while the active segment type could be segments from monomer 1 or monomer 2 at each site type. As a result, there will be twelve rate constants ( ),k p kj

i , where the subscript k refers to the active segment type while the

second subscript j refers to the propagating monomer type. The superscript i refers to active species type.

For the terminal model the rate of propagation is dependent only on the concentration of live polymer with active segment k on active species i and the concentration of the propagating monomer j.

Association or Aggregation The propagating species initiated by alkyl-Lithium type of initiators in anionic polymerization also exhibit the association phenomena like the initiator. The association of live polymeric species is usually dimeric in nature. The

associated polymer Qn m, ki+ is tracked as a separate polymer and does not

participate in any other reactions:

P +P Qn, ki

m, ki

n m, ki⇔ +

Exchange Exchange reactions exchange the growing active species between two different growing polymers. If both free ions and ion pairs are growing, then the counter-ion can exchange between the two polymeric species. There can be exchange reaction between dormant polymer (with ester as growing species which does not propagate) and ion pairs/free ions. The exchange reaction can also take place between an exchange agent (e.g., alcohol end group in solvent or starter) and a growing polymer. If exchange reaction with a small molecule does not produce a P0 species, then dEXA = 0. The exchange between growing species and dormant species takes place in polyether polyols (propylene oxide). The dormant species can be an alcohol:

P + P P + Pn,ki

m,pj

n,kj

m,pi⇔

P X P d Pn,ki

m n,kj

EXAi+ ⇔ + 0

Equilibrium with Counter-Ion The following reaction represents the equilibrium between free ions and ion pairs, hence the name equilibrium with counter-ion ( )dEQL = 1 . The


spontaneous ionization reaction can also be represented by this reaction when dEQL = 0 :

P P d Cn,ki

n,kj

EQL Ij⇔ +

Chain Transfer There are four types of chain transfer reactions:

• Spontaneous

• Monomer

• Dormant polymer formation

• Chain transfer agent

Spontaneous chain transfer can lead to formation of a dead polymer molecule and an active species caused by proton loss, e.g., cationic polymerization of poly isobutylene:

Spontaneous P D + Pn,ki

ni i→ 0

Chain transfer to monomer can take place with hydride abstraction from an olefin, for example, cationic polymerization of polyisobutylene and butyl rubber:

Monomer P + M D + P n,ki

j ni

j, j i→ δ

Chain transfer to monomer in polyethers (propylene oxide) can form dormant species (alcohol) . The dormant species is modeled as a live polymer with a different site type but it does not have the usual chain initiation and propagation reactions. This dormant polymer can participate in exchange reactions:

Form dormant polymer P + M P + P n,ki

p n,kj

p, pi→ δ

The growing polymer chain can also be transferred to a chain transfer agent, A, leading to formation of a transfer active species of the same type, i. The reaction rate order wrt. to chain transfer agent can be specified by the user:

Chain transfer agent P + A D + Pn,ki

m ni t,i→ 0

Chain Termination The growing polymer chain with ion pairs as active species can be spontaneously terminated by combination with counter ion ( )bTCI = 0 , e.g., cationic polymerization of polystyrene, tetrahydrofuran, polyisobutylene. A growing free ion active species can terminate by reacting with its own counter ion ( )bTCI = 1 :

Counter-ion P + b C Dn,ki

TCI Ii

ni→

The chain can terminate after reacting with a chain terminating agent to form a dead polymer. Any small molecule can act as a chain terminating agent.


The reaction rate order wrt. to terminating agent can be specified by the user:

Terminating agent P +T Dn,ki

m ni→

Coupling Coupling reactions are encountered in thermo-plastic elastomer production. For example, to make styrene-butadiene-styrene (SBS) TPE, styrene is added first, and then half of the butadiene is added. Introducing a coupling agent to this reaction system will form SBS polymer. In this example i=j=1 and k=2.

kmn

jm

in PPP +↔+

Another mechanism represented by this reaction is higher order association of polymeric chain. Dimeric association can be modeled by the association reaction, but the coupling reaction should be used to model higher order association of polymer chains. In a given simulation, the coupling and association reactions are mutually exclusive.

Model Features and Assumptions Following are the model features and assumptions used in the ionic polymerization model available in Aspen Polymers.

Phase Equilibria The polymerization model currently considers a single-phase system (vapor or liquid), two-phase system (vapor and liquid), or three-phase (VLL) system when calculating concentrations for the reaction kinetics. For single-phase systems, the reacting phase may be either vapor or liquid. In multi-phase systems, reactions can occur in one or more phases simultaneously. Each reaction object is associated with a single reacting phase, identified on the options form.


Rate Calculations The ionic polymerization kinetic model supplies to the reactor models the reaction rates for the components and the rate of change of polymer attributes (e.g. the chain length distribution moments) :

• The component reaction rates are computed from the kinetic scheme by summing over all reactions that involve the component.


• The site based moment rates are derived from a population balance and method of moments approach similar to that described in the Calculation Method section on page 182.

Additionally, the moment definitions are modified to include the aggregate polymer as separate and as a part of bulk polymer. The attributes calculate and report up to third moments of live, aggregate and bulk polymer. The moment definitions are:

Polymer Moment Definition

Live Polymer, Pn,ki

μ f ki f

n ki

nn P, ,=

∞

∑

Aggregate Polymer, Qn,ki

ξ f ki f

n ki

nn Q, ,=

∞

∑

Dissociated Aggregate

Polymer, Qn m ki+ , η f k

i fn m ki

mnn Q, ,= +

∞∞

∑∑

Bulk Polymer

{ }λ

μ

fi f

kn ki

n ki

k

Nseg

ni

f ki

k

Nseg

f ki

k

Nsegf

ni

n

n P Q D

n D

= + +⎡

⎣⎢

⎤

⎦⎥

= + +

∞

∞

∑ ∑

∑ ∑ ∑

, ,

, ,ξ

Polymer Properties Calculated The following variables can be calculated by the built-in kinetics routine based on the polymer attributes selected, and the subset of the built-in kinetics used for a specific simulation:

• Zeroth, first and second moments for the composite and site based bulk polymer

• Zeroth and first moments for the composite and site based live polymer and aggregate polymer

• Number and weight degree of polymerization and polydispersity index for the composite and site based bulk polymer (DPN, DPW, PDI and SDPN, SDPW, SPDI)

• Number and weight average molecular weight for the composite and site based bulk polymer (MWN, MWW and SMWN, SMWW)

• Copolymer segment composition for composite and site based bulk polymer (SFRAC and SSFRAC segment mole fractions)

• Mole fraction of bulk polymer chains that are live (LPFRAC and LSPFRAC)

• Mole fraction of bulk polymer chains that are aggregated (APFRAC and ASPFRAC)

• Number average degree of polymerization for live polymer (LDPN and LSDPN)

• Number and weight average degree of polymerization for aggregate polymer (ADPN, ADPW, ASDPN and ASDPW)


• Copolymer segment composition for live and aggregate polymer (LSFRAC, ASFRAC, LSSFRAC and ASSFRAC)

• Live polymer active segment composition (LEFRAC and LSEFRAC)

These variables are stored as component attributes. See Chapter 2 for a description of these component attributes. It is assumed here that attributes needed for the kinetic scheme are selected. For each live polymer attribute, there is also a corresponding aggregate polymer attribute.

Specifying Ionic Polymerization Kinetics

Accessing the Ionic Model To access the Ionic polymerization kinetic model:






5 Select Ionic as the reaction type and click OK.

Specifying the Ionic Model The Ionic model input forms are as listed below. Use these forms to define reacting species and enter reaction rate constant parameters:

Use this sheet To




Options Specify the reacting phase

Specifying Reacting Species You must specify the reacting species on the Species sheet:


2 In the Monomers field, list the reacting monomers.

For each monomer, in the goes to → field, specify the polymer segment that the monomer converts to.

3 Continue listing other types of reacting species, for example, solvents, transfer agents, etc.


Listing Reactions You can build a list of reactions on the Reactions sheet. In the Reaction summary listing for each reaction, the first column indicates the reaction type. The second column lists the reactants, and the last column lists the products. The Data Browser window can be resized to better view the reaction listing. Use the following options:

Click To






Click To






2 In other reactant (for example, Initiator, Catalyst) fields enter the reactants of the categories allowed for that reaction type.



− or −



Editing Reactions To add or edit a reaction, click Edit to open the Edit Reaction subform:








1 In the ko(fwd) or (rev) field, enter the pre-exponential factor for forward or reverse reaction.

2 In the Ea(fwd) or (rev) field, enter the activation energy for forward or reverse reaction.


4 In the Order field, enter the order.

5 In the Asso. No. field, enter the polymer association number.

6 In the Coeff. b and Coeff. d fields, enter coefficients b and d.





References Biesenberger, J. A., & Sebastian, D. H. (1983). Principles of Polymerization Engineering. New York: Wiley.

Bikales, M., Overberger, & Menges. (1985). Encyclopedia of Polymer Science and Engineering, 2nd Ed. New York: Wiley Interscience.

Chang, C. C., Miller, J. W., & Schorr, G. R. (1990). Fundamental Modeling in Anionic Polymerization Processes. J. of Appl. Pol. Sci., 39, 2395-2417.

Chang, C. C., Halasa, A. F., & Miller, J. W. (1993). The Reaction Engineering of the Anionic Polymerization of Isoprene. J. of Appl. Pol. Sci., 47, 1589-1599.

Compton, R. G. (Ed.). (1992). Mechanism and Kinetics of Addition Polymerizations. Comprehensive Chemical Kinetics, 31.

Fathi, H., Hamielec, A. E., & Davison, E. J. (1996). Modelling of Anionic Solution Polymerization of Butadiene - The Effects of Chain Termination and Long Chain Branching on Molecular Weight Distribution Development. Polymer Reaction Eng., 4, No. 4.


Kennedy, J. P., & Squires, R. G. (1967). Contributions to the Mechanism of Isobutene Polymerization I. Theory of Allylic Termination and Kinetic Considerations. J. Macromol. Sci., A1(5), 805-829.

Kirk-Othmer. (1991). Encyclopedia of Chemical Technology, 4th Ed. New York: Wiley Interscience.

Moore, J. G., West, M. R., & Brooks, J. R. (1979). The Anionic Solution Polymerization of Butadiene in a Stirred-Tank Reactor. ACS Symp. Ser., 104.

Muller, et. al. (1995). Kinetic-analysis of Living Polymerization Processes exhibiting slow equilibria. Application to group transfer and cationic polymerizations. 5th International Workshop on Polymer Reaction Engineering, 131, 9-11 October, Berlin: DECHEMA.

Odian, G. (1981). Principles of Polymerization, 3rd Ed. New York: Wiley Interscience.

Pepper, G. C. (1957). Cationic Polymerization. Proc. of the Intl. Symp. on Macromol. Chemistry. Prague.

Szwarc, M. (1996). Ionic Polymerization Fundamentals. New York: Hanser.

Treybig, M. N., & Anthony, R. G. (1979). Anionic Styrene Polymerization in a Continuous Stirred-Tank Reactor. ACS Symp. Ser., 104.

256 13 Segment-Based Reaction Model

13 Segment-Based Reaction Model

This section describes the segment-based power-law reaction model available in Aspen Polymers (formerly known as Aspen Polymers Plus).



• Segment-Based Model Allowed Reactions, 258



• Specifying , 276

Summary of Applications The segment-based power-law reaction model can be used to simulate polymerization reactions using a simple power-law type rate expression. This may be useful when simulating new processes that do not fit well into the other built-in models in Aspen Polymers, or when a very detailed mechanistic reaction model is not necessary.

The segment-based power-law model is the best choice for simulating step-growth addition processes—for example, the production of polyurethane.

This model may also be used to represent processes involving changes to polymer segments. The underlying kinetics are basic power law reactions in which segments and monomeric components may participate. Some examples of applicable polymers are:

• Polyvinyl alcohol (PVA) - Alcoholysis of polyvinylacetate

• Chlorinated polyethylene (CPE) - Chlorination of polyethylene

• Polymethylmethacrylate (PMMA) - Recovery of methylmethacrylate from PMMA

• Polyisobutylene - Chain scission of polyisobutylene

13 Segment-Based Reaction Model 257

Step-Growth Addition Processes Step-growth addition processes involve reactions between two functional groups to produce a new functional group without the loss of low molecular weight condensates. For example, in the production of polyurethane polymers a diol is reacted with a diisocyanate to produce an alternating copolymer with urethane linkages between the monomer units:

R OHHO X N=C=OO=C=N+ R OCNH

O

X NHCO

O

diol diisocyanate polyurethane

These reactions are usually irreversible. The individual reaction steps can be simulated using the segment-based power-law model.

Polymer Modification Processes The conventional route for synthesizing commercial polymers is through the polymerization of a monomeric compound. These polymerization reactions fall under different categories depending on the nature of the monomer and its growth mechanism.

However, once synthesized, polymers may undergo further reactions. In some instances, these reactions may be undesirable side reactions, in which case they may be considered as degradation reactions. In other cases, the only mechanism for producing certain polymers may be through the modification of a starting polymer. Typically, this situation occurs if a monomer is not readily available for that polymer. For example, polyvinyl alcohol is produced by alcoholysis of polyvinyl acetate.

Modification reactions are often used to improve polymer properties such as oil resistance (chlorosulfonation of polyethylene), heat resistance (chlorination of polyethylene), solubility ("-cellulose), and flammability (natural rubber). There are also a few cases where it is economically desirable to react scrap polymer for monomer recovery (methyl methacrylate from polymethyl methacrylate) (Rodriguez, 1989).

Reaction Categories

Regardless of the end effect of the polymer modification reaction, the events taking place fall into one of two categories based on the site where they occur on the polymer chain. The reactions may take place on:

• Side groups

• Polymer backbone: scission, depolymerization, cross-linking, or bond changes

There are some fundamental issues that distinguish reacting polymers from their low molecular weight counterparts. One obvious characteristic of reacting polymers is the potential for steric hindrance. A reacting side group may be too close to the polymer chain, for example. There may also be changes in solubility as reaction progresses.

Furthermore, crystallinity has an effect on the polymer reactivity; in general, for a semicrystalline polymer, only the amorphous region is able to react.


Finally, an important difference that characterizes polymers is the fact that a higher local concentration of reacting functional groups is observed than that indicated by the overall polymer concentration (Odian, 1991).

Segment-Based Model Allowed Reactions The reaction categories allowed in the segment-based reaction model, along with a brief summary of the conditions where each of these reactions may occur, is shown here:


Segment Based Model Reaction Categories

Conventional Species Reactions involving all non polymeric species fall under this category. Monomeric components may react among themselves to produce intermediate species. These reactions are represented as Category I in the Segment Based Model Reaction Categories figure on page 259.


Side Group or Backbone Modifications Polymer modification reactions aimed at altering end properties involve in most cases side group or backbone modifications. In such reactions, groups attached to the polymer chain are substituted. One example is that of the alcoholysis of polyvinyl acetate to produce polyvinyl alcohol:

+ CH3OH + CH3CO2CH3CH

CH3

CO

O

CH2 CH CH2

OH

Another example is the chlorination of polyethylene to produce chlorinated polyethylene (CPE):

CH2 + Cl2 CHCl + HCl

Side group and backbone reactions are illustrated as reaction Category II in the Segment Based Model Reaction Categories figure on page 259.

Chain Scission A common polymer degradation reaction is chain scission. In this case, bonds are broken along the polymer chain resulting in shorter polymer molecules with lower molecular weight. Chain scission may be induced by several factors. One example is the scission of polyisobutylene upon oxidation:

CH2 C CH2

CH3

CH2

CH2 CCH2

+ CH2

CH3

Some scission reactions may involve a monomeric component, such as an acid or base:

CH2 – CH2 + HCl CH2Cl + CH3

Chain scission reactions are represented as Category III reactions in the Segment Based Model Reaction Categories figure on page 259.

Depolymerization Depolymerization is the reverse of the propagation step of a polymerization reaction. In such reactions, monomer molecules are lost from the polymer chain. Depolymerization is often considered a degradation reaction. There are, however, cases where it is brought on by design to recover monomer from scrap polymer. An example depolymerization reaction is that of polymethyl methacrylate to regenerate methyl methacrylate:


CH2 C CH2 CCH3 CH3

C OOCH3

C OOCH3

CH2 C

CH3

OOC

CH3

+ CH2 CCH3

C OOCH3

Depolymerization is illustrated as Category IV in the Segment Based Model Reaction Categories figure on page 259.

Propagation Propagation reactions involve the addition of monomers to the end of a growing polymer chain. Propagation is illustrated as Category V in the Segment Based Model Reaction Categories figure on page 259.

Combination There are other mechanisms through which polymer segments react with each other. Some of these reactions, grouped as combination reactions, include kinetic events where two polymer molecules combine into one. These reactions are represented as Category VI in the Segment Based Model Reaction Categories figure on page 259.

Branch Formation Branch formation occurs when a polymer molecule attaches to another polymer chain, converting a repeat unit to a branch point. Monomers can also react with repeat units to initiate branch formation. Branch formation is illustrated as Category VII in the Segment Based Model Reaction Categories figure on page 259.

Cross Linking Cross linking occurs when a repeat unit in one chain reacts with a repeat unit in another chain, forming a cross link (branch 4) segment. Cross linking is illustrated as Category VIII in the Segment Based Model Reaction Categories figure on page 259.

Kinetic Rate Expression The segment-based reaction model uses a modified power-law rate expression where the rate of reaction is calculated as the product of the reacting species concentrations with a rate constant representing the specific reactivity of the reaction. The kinetic rate expression in the segment-based model is described below:


Equation

Tref specified ( )iref

bTTR

Ea

o iiinet flagUTTekCatalyst k

i

ref

i

i

⎟⎟⎠

⎞⎜⎜⎝

⎛=

⎟⎟⎠

⎞⎜⎜⎝

⎛−

− 11

, ][ α

Tref unspecified * ( )ibRT

Ea

o iiinet flagUTekCatalyst k i

ii

−

= α][,

Assign User Rate Constants is used: ∑∏ ⎟⎠⎞⎜

⎝⎛=

i inetj

ajmm kCactivity rate mj

,

Assign User Rate Constants is not used: mnetj

ajm kC rate mj

,⎟⎠⎞⎜

⎝⎛= ∏

Nomenclature Symbol Description

m User reaction number

i Rate constant set number

j Component number

Π Product operator

Cj Concentration* of component j, mol/L

iα Catalyst order term for catalyst i (default = 1)

mjα Power-law exponent for component j in reaction m

ko Pre-exponential factor in user-specified inverse-time and concentration units**

i,netk Net rate constant for set i assigned to reaction m

mnetk , Net rate constant for reaction m




T Temperature, K

Tref Optional reference temperature. Units may be specified, they are converted to K in the model. Defaults to global reference temperature (Global Tref) specified on the Specs sheet.


U User rate constant vector calculated by the optional user rate constant subroutine. The user flag indicates the element number in this array which is used in a given rate expression. When the user flag is not specified, or when the user rate constant routine is not present, this parameter is set to 1.0.

* The concentration basis may be changed to other units using the Concentration basis field on the

Specs sheet or using the optional concentration basis subroutine.

** The reference temperature may be specified globally on the Specs sheet or locally for each rate constant set on the Rate-Constants sheet. If global and local reference temperatures are both unspecified then this form of the equation is applied.


Customizing the Rate Expression; User Rate Constant Subroutine

You can modify the standard rate expression using the optional user rate constant feature. The rate constant form includes a parameter called the “user flag” that identifies an element in an array of user rate constants. This array is calculated by a user-written Fortran subroutine. The standard rate expression is multiplied by the user rate constants as shown above. See Program Files\Aspen Plus <version>\engine\user\USBRCN.f for a template for this routine.

Concentration Basis for Rate Calculations

Component concentrations depend on the calculation basis: molarity, mole fraction, mass fraction, mass concentration, etc. The polymer mole fraction is converted into its segment mole fractions according to the following equation:

Frac Frac SFRAC iMw

Mwsegs i pp

avg, * ( )*=

Where:

Fracs i, = Segment mole fraction

SFRAC i( ) = Polymer segment fraction (component attribute)

Mwp = Polymer molecular weight

Mwsegavg = Average segment molecular weight = SFRAC i Mw

Nseg

i( )*1∑

User Concentration Basis Subroutine

Alternately, a user basis subroutine can be used to calculate the component concentrations and the reacting-phase holdup basis used in the component and attribute conservation equations. Use this subroutine when rate constants are available in unusual concentration units not found in Aspen Polymers, or when the reacting phase volume or area calculated by the reactor model is not consistent with the real reactor (for example, in plug flow reactors with fixed liquid level). The segment-based model and step-growth model can use the same basis routine. See Program Files\Aspen Plus <version>\engine\user\USRMTS.f for a template for this routine.

Model Features and Assumptions The following assumptions are built into the segment-based reaction model:

• All reactions between two segments are intermolecular; ring formation reactions are specifically excluded unless the ring molecules are tracked as separate oligomer components


• Reactions may occur anywhere in the polymer chain

• Mass balance holds for components involved in the reactions on segment basis

• Moment of chain length distribution calculations cover up to the first moment (ZMOM, SFLOW, FMOM). Higher moments (SMOM, TMOM) are not predicted by the current version of the model

• Since higher moments not covered, segment-based model should be last in reaction block sequencing

Polymer Properties Calculated The segment-based reaction model calculates and returns the following information:

• Rate of change for all components involved in reaction scheme, and rate of change for all segments

• Polymer segment composition (SFLOW, SFRAC, EFRAC)

• Zeroth moment of chain length distribution (ZMOM)

• First moment of chain length distribution (FMOM)

• Number average degree of polymerization (DPN)

• Number average molecular weight (MWN)

• When the Reacting Site is specified on the Specifications form, the model will calculate rates for the zeroth moment, first moment, and segment flow rates at the specified site (attributes SZMOM, SFMOM, and SSFLOW for the specified site number). These attributes are used to calculate the composite attributes listed above.

This information is returned through the stream compositions for the component rate of change, and through the polymer component attributes for the segment rate of change and moment calculations.

The rate of change of polymer mass is calculated as follows:

RR Mw

Mwp

s i i

Nseg

p=∑ , *

1

This is the sum of the rates of change of segment masses.

Each segment type is assigned a value Ω, which indicates the number of “points of attachment” connecting the segment to other segments in the polymer chain:

Segment Type Ω

End 1

Repeat 2

Branch-3 3

Branch-4 4


The rate of change of the zeroth moment ( 0λ ) is calculated from the rate of change of the first moment ( 1λ ) and the segment type (Ω):

ttt ∂Ω∂

−∂∂

=∂∂

211 0 λλ

The factor of ½ accounts for the fact that each “connection” links two segments (without this correction the points of connection are counted twice). This method is best illustrated through these examples:

Valid Reaction Type† Stoichiometry† 1Δλ ½ΔΩ 0Δλ

Yes Initiation 2PMM →+ M + M → E + E +2 +1 +1

No Initiation 1PM → M → R +1 +1 0

Yes Propagation (addition) 1nn PMP +→+ E + M → R + E +1 +1 0

Yes Propagation (insertion)

*1n

*n PMP +→+ M → R +1 +1 0

Yes Combination mnmn PPP +→+ E + E → R + R 0 +1 -1

Yes Combination mnmn PPP +→+ E + E → R -1 +0 -1

Yes Branching 1nn PMP +→+ R + M → B3 + E +1 +1 0

Yes Branching mnmn PPP +→+ R + E → B3 + R 0 +1 -1

Yes Cross linking mnmn PPP +→+ R + R → B4 -1 +0 -1

† M = Monomer; E = End group segment; B3 = Branch-3 segment; B4 = Branch-4 segment

This method lets you specify most classes of reactions, however special care must be taken to ensure that the reaction is defined in a manner that is consistent with the previous equation. In particular, the segment-based model does not allow initiation reactions of the type 1PM → since the equation does not account for the initial formation of polymer molecules through this mechanism. Note, however, that this mechanism is valid since the same reaction can represent an insertion type propagation step in which the active polymer end group is conserved.

User Subroutines The segment-based power-law model can be customized by applying user-written subroutines. There are two types of subroutines available. The concentration and holdup basis for the model can be changed through a user basis subroutine. A user rate-constant subroutine can be used to extend the standard reaction rate expression. These routines can be used together in any combination.


User Basis Subroutine The user basis subroutine can be used to calculate the component concentrations and the reacting-phase holdup (typically volume in a CSTR or batch reactor or active area in a PFR). This routine can also be used to calculate rates of change of components and component attributes. Use this subroutine when rate constants are available in unusual concentration units not found in Aspen Polymers, or when the reacting phase volume or area calculated by the reactor model is not consistent with the real reactor (for example, in plug flow reactors with fixed liquid level).

This subroutine can be used in conjunction with Fortran blocks and user component attributes to calculate mass-transfer rates and to account for the influence of mass-transfer limitations on the component concentrations in the reacting phase.

The argument list for the user basis routine is provided here. This argument list is prepared in a Fortran template called USBBAS.F, which is delivered with Aspen Polymers.


SUBROUTINE USBBAS



3 NINTB, INTB, NREALB, REALB, NINTM,

4 INTM, NREALM, REALM, NIWORK, IWORK,


6 X1, X2, Y, DUM1, FLOWL,

7 FLOWL1, FLOWL2, FLOWV, FLOWS, VLQ,

8 VL1, VL2, VV, VSALT, VLIQRX,

9 VL1RX, VL2RX, VVAPRX, VSLTRX, RFLRTN,

* IFLRTN, CRATES, NTCAT, RATCAT, CSS,

1 VBASIS, IPOLY, NSEG, IDXSEG, AXPOS,

2 TIME )






1=MIXED

2=CISOLID

3=NC




IDSCC Input HOLLERITH 2,NCC Conventional component ID array


NBOPST Input INTEGER 6, NPO Property method array




NREALB Input INTEGER

User-specified length of REALB array


NINTM Input INTEGER User-specified length of INTM array

INTM Retention INTEGER NINTM User subroutine integer parameters (See Integer and Real Parameters, page 151)

NREALM Input INTEGER User-specified length of REALM array

REALM Retention REAL*8 NREALM User subroutine real parameters (See Integer and Real Parameters, page 151)












FLOWL Input REAL*8 Total liquid flow rate, kmol/sec

FLOWL1 Input REAL*8 First liquid flow rate, kmol/sec

FLOWL2 Input REAL*8 Second liquid flow rate, kmol/sec

FLOWV Input REAL*8 Vapor flow rate, kmol/sec

FLOWS Input REAL*8 Salt flow rate, kmol/sec



VL Input REAL*8 Total liquid molar volume, m3/ kmol

VL1 Input REAL*8 First liquid molar volume, m3/ kmol

VL2 Input REAL*8 Second liquid molar volume, m3/ kmol

VV Input REAL*8 Vapor molar volume, m3/ kmol

VSALT Input REAL*8 Salt molar volume, m3/ kmol






RFLRTN Retention REAL*8 (1) Real retention for FLASH

IFLRTN Retention INTEGER (1) Integer retention for FLASH

CRATES Output REAL*8 NCC Component rates of change, kmol/m3-sec

NTCAT Input INTEGER Number of component attributes

RATCAT Output REAL*8 NTCAT Component attribute rates of change, cat/m3-sec

CSS Output REAL*8 NCC Concentration vector for the active phase

VBASIS Output REAL*8 Holdup basis used to calculate reaction rates*




AXPOS Input REAL*8 RPlug only: axial position, m

TIME Input REAL*8 RBatch only: time, sec

* When using molar concentrations, this parameter is volume of the reacting phase in 3m

in RCSTR and RBatch or the cross-sectional area of the reacting phase in 2m in RPlug.

Note: The argument lists for the segment-based user basis routine and step-growth user basis routine are identical. Both types of models can reference the same basis routines.

Example 1 illustrates how to use the user basis routine to convert the concentration basis from the standard molar concentration basis (mol/L) to a mass concentration basis (mol/kg). (Note: the current version of Aspen Polymers supports several concentration basis through the BASIS keyword located on the Specs sheet. This example is a demonstration). Using these units, the reaction rates are calculated in units of mol/kg-sec. These rates are multiplied by the holdup basis (VBASIS) for the reactor in the segment-based power-law model. The holdup basis must be consistent with the concentration basis, e.g., in this case it must be in kg. The holdup basis pertains to the reacting phase, it does not include the phases that do not react.

Example 1: A User Basis Routine For the Mass-Concentration Basis


CX

Mii

Liquid=

Ci = Mass-concentration of component i

Xi = Mole fraction of component i

M Liquid = Average molecular weight of components in the liquid phase

CALL PPMON_VOLL( TEMP, PRES, X, NCPMX, IDXM, 1 NBOPST, GLOBAL_LDIAG, 1, VLQ, DVS, KER) C-unpack the mole fraction vector into the molar concentrations... CALL SHS_UNPACK ( X , NCPMX, IDXM, CSS ) C --------------------------------------------------------------- C C concentration (mole/kg)=(mole I / mole liquid )*( mole liquid/kg) C C --------------------------------------------------------------- DO 10 I = 1, NCOMP_NCC CSS(I) = CSS(I) * 1.D3 / STWORK_XMWL 10 CONTINUE C --------------------------------------------------------------- C C reacting phase basis must be consistent with concentration basis (kg) C liquid mass inventory = liquid volume * density C C --------------------------------------------------------------- VBASIS = VLIQRX * STWORK_XMWL * 1.D-3 / VLQ RETURN


The plug flow reactor model in Aspen Plus assumes that the vapor and liquid move at the same velocity through the reactor (e.g., no-slip conditions). This assumption is not consistent with the physical reality of polymer finishing reactors or wiped-film evaporators. The subroutine in Example 2 circumvents the no-slip assumption in RPlug, allowing you to specify the volume occupied by the liquid phase. In this example, you specifiy the first integer argument in the RPlug block as “1” and the first real argument as the volume fraction of the reactor occupied by the liquid phase.

Example 2: A User Basis Routine to Specify Liquid Volume in RPlug

UFRAC = 1.D0 IF ( REALB(1) .NE. RGLOB_RMISS ) UFRAC = REALB(1) IF ( INTB(1).EQ.1 ) THEN C - unpack the mole fraction vector into the molar concentrations... CALL SHS_UNPACK ( X , NCPMX, IDXM, CSS ) C - concentration = mole fraction divided by molar volume of phase DO 20 I = 1, NCOMP_NCC


CSS(I) = CSS(I) / VLQ 20 CONTINUE C - multiply total reactor volume by user-specified volume fraction - VBASIS = ( VLIQRX + VVAPRX ) * UFRAC C - this line makes RPlug calculate liquid residence time (not L+V) SOUT(NCOMP_NCC+8)=(SOUT(NCOMP_NCC+9)/ SOUT(NCOMP_NCC+6)) / VLQ RETURN END IF


User Rate-Constant Subroutine The user rate constant subroutine can be used to modify rate constant parameters for model-generated and user-specified reactions. Use this routine to modify the standard power-law rate expression for non-ideal reaction kinetics.

The user rate constant feature can be used to modify the standard power-law rate expression. This subroutine returns a list of real values, which are stored in an array “RCUSER”. The length of this array is defined by the keyword NURC (number of user rate constants) in the user rate constant subroutine form (USER-VECS secondary keyword). Each of the elements in the user rate constant array can store a different user rate constant. The USER-FLAG keyword in the Rate Constants form is used to specify which user rate constant is used with a particular set of rate constants.

Elements 1 through “NURC” of RCUSER are calculated by a user rate-constant subroutine. The standard rate expression is multiplied by the USER-FLAGth element of the user rate constant vector RCUSER. For example, if the USER-FLAG field contains the number “4”, the power-law rate term will be multiplied by the fourth element of array RCUSER. By default, the USER-FLAG keyword is set to zero. The zeroth element of the RCUSER array is set to a value of 1.0, so the rate expression remains unmodified unless the USER-FLAG keyword is specified.

The argument list for the subroutine is provided here. This argument list is prepared in a Fortran template called USBRCN.F, which is delivered with Aspen Polymers.



SUBROUTINE USBRCN



3 NINTB, INTB, NREALB, REALB, NINTR,

4 INTR, NREALR, REALR, NIWORK, IWORK,


6 X1, X2, Y, DUM1, VL,

7 VL1, VL2, VV, VSALT, IPOLY,

8 NSEG, IDXSEG, NCC, CSS, TEMP,

9 PRES, NURC, 1 RCUSER, CATWT )






1=MIXED

2=CISOLID

3=NC















NINTR Input INTEGER User-specified length of INTM array



INTR Retention INTEGER NINTR User subroutine integer parameters (See Integer and Real Parameters, page 151)

NREALR Input INTEGER User-specified length of REALM array

REALR Retention REAL*8 NREALR User subroutine real parameters (See Integer and Real Parameters, page 151)




















NCC Input INTEGER Number of components (unpacked)



PRES Input REAL*8 Pressure, Pa

NURC Input INTEGER Number of user rate constants (See User Rate-Constant Subroutine, page 140)




CATWT Input REAL*8 Catalyst weight, kg (in RPLUG, weight/length)

Example 3 illustrates how to use this subroutine to implement complex rate expressions in the segment-based power-law model.

Example 3: Implementing a Non-Ideal Rate Expression

Suppose a side reaction Q→Z is first order with respect to component Q and first order with respect to a catalyst C. The effectiveness of the catalyst is reduced by inhibitor I according to the following equation:

[ ] [ ][ ]C

Ca bT Ieff

actual=+ +1 ( )

Where:

[ ]Ceff = Effective catalyst concentration, mol/L

[ ]Cactual = Actual catalyst concentration, mol/L

[ ]I = Inhibitor concentration, mol/L

T = Temperature, K

a,b = Equation parameters

The net rate expression can thus be written as:

[ ][ ]rate Q

Ca bT I

k eactualo

ER T Tref=

+ +

−−

⎛

⎝⎜⎜

⎞

⎠⎟⎟

[ ]( )

*

1

1 1

Where:

ko = Pre-exponential factor, (L/mol)/sec

E* = Activation energy

R = Gas law constant

Tref = Reference temperature for ko


The standard rate expression for side reactions is:

rate k e C U jo

ER T T

ii

ref i=⎛⎝⎜

⎞⎠⎟

−−

⎛

⎝⎜⎜

⎞

⎠⎟⎟

∏*

* ( )1 1

α

Where:

∏ = Product operator

Ci = Concentration of component i


αi = Power-law exponent for component i

U = User rate constant

j = User rate-constant flag

Suppose the rate constant for the uninhibited reaction is 3 10 3× − (L/mol)/min at 150°C, with an activation energy of 20 kcal/mol, and the inhibition rate constants are A=0.20 L/mol, B=0.001 L/mol-K. The stoichiometric coefficients and power-law exponents are specified directly in the Stoic and PowLaw-Exp keywords. The Arrehnius rate parameters and reference temperature are also specified directly in the model.

The parameters for the user rate constant equation can be specified using the optional REALRC list. Including the parameters in the REALRC list allows the model user to adjust these parameters using the standard variable accessing tools, such as Sensitivity, Design-Specification, and Data-Regression.

The resulting model input is summarized below:

USER-VECS NREALRC=2 NUSERRC=1 REALRC VALUE-LIST=0.2D0 0.001D0 STOIC 1 Q -1.0 / Z 1.0 POWLAW-EXP 1 Q 1.0 / C 1.0 RATE-CON 1 3D-3<1/MIN> 20.000<kcal/mol> TREF=150.0<C> URATECON=1

The power-law term from this equation is:

[ ][ ]rate k e C Qo

ER T Tref=

−−

⎛

⎝⎜⎜

⎞

⎠⎟⎟

* 1 1

Where:


[C] = Catalyst concentration, mol/L

ko = Pre-exponential factor

Thus, the required user rate constant is:

U ja bT I

( )( ( )[ ]

= =+ +

11

1

Where:

[I] = Inhibitor concentration, mol/L

T = Temperature, K

a, b = Equation parameters

An excerpt from the user rate constant subroutine for this equation is shown below:

C - Component Name - INTEGER ID_IN(2) DATA ID_IN /'INHI','BITO'/ C ====================================================================== C EXECUTABLE CODE


C ====================================================================== C - find location of inhibitor in the list of components - DO 10 I = 1, NCOMP_NCC IF ( IDSCC(1,I).EQ.ID_IN(1).AND.IDSCC(2,I).EQ.ID_IN(2) ) I_IN=I 10 CONTINUE C - get the concentration of the inhibitor - C_IN = 0.0D0 IF ( I_IN .GT.0 ) C_IN = CSS( I_IN ) C ---------------------------------------------------------------------- C Parameters: each REALR element defaults to zero if not specified C ---------------------------------------------------------------------- A = 0.0D0 IF ( NREALR .GT. 0 ) A = REALR( 1 ) B = 0.0D0 IF ( NREALR .GT. 1 ) B = REALR( 2 ) C ---------------------------------------------------------------------- C User rate constant #1 U(1) = 1 / ( 1 + (A+BT)[I] ) C ---------------------------------------------------------------------- IF ( NURC.LT.1 ) GO TO 999 RCUSER(1) = 1.0D0 / ( 1.0D0 + ( A + B*TEMP ) * C_IN ) END IF 999 RETURN

Integer and Real Parameters Each user model has two sets of integer and real parameters. The first set comes from the subroutine form of the reactor block. The second set comes from the subroutine form of the step-growth reactions model. Each of these parameters are retained from one call to the next, thus these parameters can be used as model inputs, outputs, or retention.

The reactor block integer and real parameters can be used to specify data which are specific to a particular unit operation, such as reactor geometry, mass transfer coefficients, etc. The integer and real parameters in the subroutine forms can be used to specify global parameters, such as rate constants or physical property parameters.

Local Work Arrays You can use local work arrays by specifying the model workspace array length on the Subroutine forms. These work areas are not saved from one call to the next. Both user subroutines share a common work area. User subroutines are responsible for initializing the work space at the start of each subroutine.

Packed Vectors Aspen Plus frequently uses a technique called “packing” to minimize simulation time. The user models previously described use packed vectors to track the mole fractions of each phase (vectors X, X1, X2, and Y). These vectors contain NCPM elements (Number of Components Present in the Mixed substream). The component index associated with each element is listed in the vector “IDXM”. All other vectors used by the model, including the rates vectors and the component concentration vectors, are unpacked.


Calculating Unpacked Component Concentrations

Calculate unpacked component concentrations of the first liquid phase given the packed mole fractions of the first liquid phase and the molar volume of the first liquid phase.

IF ( VL1 .GT. 0.D0 .AND. FLOWL1.GT.0.D0 ) THEN DO 10 I = 1, NCPM CSS(I) = X1( IDXM( I ) ) / VL1 10 CONTINUE END IF

Note: NCPM steps were required to load the concentration vector. Since NCPM is always less than or equal to NCC (total number of conventional components), there is a reduction in the required number of steps to perform the operation. Using packed arrays for calculations reduces overhead by eliminating the need to check for zero values when carrying out mathematical operations.

Specifying Segment-Based Kinetics

Accessing the Segment-Based Model To access the Segment-based power-law kinetic model:






5 Select Segment-Bas as the reaction type and click OK.

Specifying the Segment-Based Model The Segment-Based model input forms are as listed below. Use these forms to specify reaction conditions and build a reaction scheme.

Use the Specifications forms to define reaction stoichiometry, enter reaction rate constant parameters, assign rate constants to reactions, and to specify the concentration, reacting phase, reacting site, and other model options.

Use this sheet To

Specs Define reacting phase, concentration basis, and reacting polymer

Reactions Define reaction stoichiomerty and enter reaction rate constant parameters


Use this sheet To

Rate Constants Specify reaction rate parameters and catalysts

Assign Rate Constants

Associate each reaction with one or more sets of rate constants

Use the User Subroutines forms to specify the names and parameters for optional user basis and rate constant subroutines. Use this sheet To

Rate Constants Specify the name of the user kinetics routine, the number of user rate constants calculated by the routine, and to give the integer and real arguments for the user arrays for this routine

Basis Specify the name of the user concentration and holdup basis routine and give the integer and real arguments for the user arrays for this routine

Specifying Reaction Settings Use the Specs sheet to define the reaction model settings:

1 In the Reacting polymer field, specify the reacting polymer.

2 In the Reference temperature field, specify the default global reference temperature for rate constant parameters.

3 In the Phase field, specify the phase in which reactions occur.

If the specified phase is Liquid phase 1 or Liquid phase 2 you may also choose to specify additional options (under the Options frame) to control how calculations are performed when the phases collapse into a single liquid phase. For details, see Selecting the Reacting Phase next.

4 In the Basis field, specify the basis for component concentrations in the reaction rate calculation.

Optionally, you can apply a user subroutine to calculate the concentration and holdup basis. For details, see User Basis Subroutine on page 266.

5 If desired, specify a site number in the Reacting Site field, and specify which method to use in the Segment concentration basis frame. For details, see Selecting the Reacting Site on page 278.

Selecting the Reacting Phase The Specs form lets you specify the phase in which the reactions occur.

Select the appropriate phase from the list in the Reacting Phase field. All of the reactions in the segment-based reaction object are assumed to take place in the same phase. You can use two (or more) segment-based models in the same reactor to account for simultaneous reactions in multiple phases.

Note: You must specify the Valid Phases keyword for each reactor model referencing the kinetics to ensure the specified reacting phase exists.

If the Reacting Phase option is set to Liquid phase 1 or Liquid phase 2 the model assumes two liquid phases exist. When the named phase is not present, the model prints a warning message and sets the reaction rates to zero. There are two options for handling phase collapse:




These options are especially convenient when modeling simultaneous reactions in two liquid phases using two step-growth models. In this situation, one would typically select the Use bulk liquid option for one phase and not the other (to avoid double-counting reactions when one phase collapses).

Selecting the Reacting Site The segment-based power-law reaction model can be used in conjunction with other Aspen Polymers reaction models to define side reactions. When combining the segment-based model with a Ziegler-Natta or ionic polymerization model, use the Reacting Site field on the Specs form to assign the reaction rates to a particular active site.

Note: The Segment Concentration Basis field lets you select the calculation method for the concentrations used within the reaction model.

• When you select Use composite segment concentration the segment mole fractions used to calculate the reaction rates are calculated from the following equation:

Frac Frac SFRAC iMw

Mwsegs i pp

avg, * ( )*=

• When you select Use segment concentration at specified site the

following equation is applied:

avg

ppis Mwseg

MwjiSSFRACFracFrac *),(*, =

Where j refers the specified reacting site number.

In both cases the attribute rates of change are mapped to the component attributes associated with the user-specified reacting site number (e.g., SSFLOW(i,j), SZMOM(i,j), etc.)

Building A Reaction Scheme You can build a list of reactions on the Reactions sheet. To do this you must specify a reaction stoichiometry. The Data Browser window can be resized to better view the reaction listing. Use the following options:

Click To



Rate Constants Specify reaction rate constant parameters for the


reactions



Click To

Hide/Reveal Activate or de-activate a set of reactions. Inactive reactions are highlighted with a gray background.


Adding or Editing Reactions To add a new reaction to the scheme or to edit an existing reaction, click New or Edit to open the Edit Stoichiometry subform:

Note that in the Reaction no. field, a unique number is assigned to the reaction being added.

1 Specify the Component ID and stoichiometric Coefficient for the reactants.

Reactants must have a negative coefficient.

2 Specify the Component ID and stoichiometric Coefficient for the products.

Products must have a positive coefficient.



Specifying Reaction Rate Constants The rate constants are summarized in a grid on the Rate Constants sheet:


Note: Reaction rates are defined on a molar basis (moles per volume per time). The time units for the pre-exponential factors are specified directly on the Rate Constant form. By default, the concentration units are assumed to be in SI units (kmole/m3 or mole/L). You can change the concentration basis to other units using the Concentration Basis field of the Specs sheet. Alternately, you may apply a user basis subroutine.


3 In the b field, enter the temperature exponent.

4 In the Tref field, enter the reference temperature. If this field is left blank the reference temperature will default to the user-specified global reference temperature on the Specs form.


5 If desired, specify a Catalyst Species and Catalyst Order.

6 If desired, specify a user rate constant element number on the User Flag field (For details, see the User Rate-Constant Subroutine on page 140).

Note: Use the Catalyst Species field to associate a rate constant with a particular catalyst. If you leave this field blank (empty) the model drops the catalyst concentration term from the rate expression. Use the Catalyst Order field to specify the reaction order with respect to the catalyst (the model assumes first order by default).

Assigning Rate Constants to Reactions There are two options for assigning rate constants to reactions. By default, the model assumes there is exactly one set of rate constants for each reaction (for example, rate constant set “i” is used for reaction “i”).

Alternately, you may use the Assign User Rate Constant sheet to assign one or more sets of rate constants to each reaction. This feature is convenient in two situations:

• Models with a large number of user side reactions when the rate constants of the various reactions are equal or are related to each other algebraically.

• Reactions catalyzed by several catalysts simultaneously.

The assignment option is recommended for two reasons:

• You can enter several sets of rate constants for each reaction without re-entering the reaction stoichiometry.

• You can assign a set of rate constants to multiple reactions, reducing the number of adjustable parameters in the model, which makes it easier to fit against data.

When several rate constants are assigned to a reaction the model calculates a net rate constant by summing all of the listed rate constants and multiplying the sum by a specified activity.

To assign rate constants to reactions:

1 On the Assign User Rate Constants form, use the Activity field to specify the activity factor (default value is unity).

2 In the Rate Constant Sets field, select from the list of pre-defined rate constant sets for each reaction. These numbers refer to the row numbers on the Rate Constants form.

Including a User Rate Constant Subroutine Use the User Subroutines Rate Constants form to specify parameters for user rate constants calculations:


2 Specify the size of vectors for Integer, Real and No. const. in Number of parameters.

3 Specify the size of vectors of Integer and Real in Length of work arrays.



Including a User Basis Subroutine Use the User Subroutines Basis form to specify parameters for basis calculations:


2 Specify the size of vectors for Integer and Real in the Number of parameters and Length of work arrays.


References Biesenberger, J. A., & Sebastian, D. H. (1983). Principles of Polymerization Engineering. New York: Wiley.

Kroschwitz, J. (Ed.). (1990). Concise Encyclopedia of Polymer Science and Engineering. New York: Wiley.

Odian, G. (1991). Principles of Polymerization, 3rd Ed. New York: Wiley.

Rodriguez, F. (1989). Principles of Polymer Systems. New York: Hemisphere.

Rudin, A. (1982). The Elements of Polymer Science and Engineering. New York: Academic Press Inc.

282 14 Steady-State Flowsheeting

14 Steady-State Flowsheeting

Aspen Polymers (formerly known as Aspen Polymers Plus) allows you to model polymerization processes in both steady-state and dynamic mode. In this chapter, flowsheeting capabilities for modeling processes in steady-state mode are described.


• Polymer Manufacturing Flowsheets, 282

• Modeling Polymer Process Flowsheets, 284

• Steady-State Modeling Features, 285

Following this introduction, Aspen Polymers flowsheeting capabilities for modeling steady state processes are discussed in several sections.

• 15 Steady-State Unit Operation Models, 286

• Plant Data Fitting, 331

• User Models, 351

• Application Tools, 366

Polymer Manufacturing Flowsheets Polymer production processes are usually divided into the following major steps:

• Monomer synthesis and purification

• Polymerization

• Recovery/separation

• Polymer processing

The modeling issues of interest in each of these steps were discussed in Chapter 1, and are summarized in the following figure. The focus here is on the various unit operations required in these processing steps.

14 Steady-State Flowsheeting 283

Monomer Synthesis During monomer synthesis and storage the engineer is concerned with purity since the presence of contaminants, such as water or dissolved gases, may

284 14 Steady-State Flowsheeting

adversely affect the subsequent polymerization stage by poisoning catalysts, depleting initiators, causing undesirable chain transfer or branching reactions which would cause less effective heat removal. Another concern is the prevention of monomer degradation through proper handling or the addition of stabilizers. Control of emissions, and waste disposal are also important factors.

Polymerization The polymerization step is the most important step in terms of capital and operating costs. The desired outcome for this step is a polymer product with specified properties (e.g. molecular weight distribution, melt index, viscosity, crystallinity) for given operating conditions. The obstacles that must be overcome to reach this goal depend on the type of polymerization process.

Polymerization processes may be batch, semi-batch, or continuous. In addition, they may be carried out in bulk, solution, suspension, or emulsion. Bulk continuous systems provide better temperature and molecular weight control at the expense of conversion; batch systems offer less control over molecular weight. In addition, they may result in a high viscosity product and require high temperatures and pressures. Solution systems also provide good temperature control but have associated with them the cost of solvent removal from the polymer.

In summary, for the polymerization step, the mechanisms that take place during the reaction introduce changes in the reaction media which in turn make kinetics and conversion, residence time, agitation, and heat transfer the most important issues for the majority of process types.

Recovery / Separations The recovery/separation step is the step where the desired polymer produced is further purified or isolated from by-products or residual reactants. In this step, monomers and solvents are separated and purified for recycle or resale. The important issues for this step are phase equilibrium, heat and mass transfer.

Polymer Processing The last step, polymer processing, can also be considered a recovery step. In this step, the polymer slurry is turned into solid pellets or chips. Heat of vaporization is an important issue in this step (Grulke, 1994).

Modeling Polymer Process Flowsheets The obvious requirement for the simulation of process flowsheets is the availability of unit operation models. Once these unit operation models are configured, they must be adjusted to match the actual process data. Finally,

14 Steady-State Flowsheeting 285

tools must be available to apply the fitted model to gain better process understanding and perform needed process studies. As a result of the application of the process models, engineers are able to achieve goals such as production rate optimization, waste minimization and compliance to environmental constraints. Yield increase and product purity are also important issues in the production of polymers.

Steady-State Modeling Features Aspen Polymers has tools available for addressing the three polymer process modeling aspects.

Unit Operations Modeling Features A comprehensive suite of unit operations for modeling polymer processes is available in Aspen Polymers. These include mixers, splitters, heaters, heat exchangers, single and multistage separation models, reactors, etc. For more information on available unit operation models, see 15 Steady-State Unit Operation Models on page 286.

Plant Data Fitting Features Several tools are available for fitting process models to actual plant data. Property parameters may be adjusted to accurately represent separation and phase equilibrium behavior. This can be done through the Data Regression System (DRS). See the Aspen Plus User Guide for information about DRS.

Another important aspect of fitting models to plant data has to do with the development of an accurate kinetic model within the polymerization reactors. The powerful plant data fitting feature (Data-Fit) can be used for fitting kinetic rate constant parameters. For more information, see Plant Data Fitting on page 331.

Process Model Application Tools The tools available for applying polymer process models include capabilities for performing sensitivity and case studies, for performing optimizations, and for applying design specifications. For more information, see Application Tools on page 366.

References Dotson, N. A, Galván, R., Laurence, R. L., & Tirrell, M. (1996). Polymerization Process Modeling. New York: VCH Publishers.


286 15 Steady-State Unit Operation Models

15 Steady-State Unit Operation Models

This section summarizes some typical usage of the Aspen Plus unit operation models to represent actual unit operations found in industrial polymerization processes.


• Summary of Aspen Plus Unit Operation Models, 286

• Distillation Models, 293

• Reactor Models, 294

• Mass-Balance Reactor Models, 294

• Equilibrium Reactor Models, 296

• Kinetic Reactor Models, 296

• Treatment of Component Attributes in Unit Operation Models, 328

Summary of Aspen Plus Unit Operation Models Aspen Plus includes a number of basic unit operation models that are typically used to represent one or more unit operations found in real processes. These models may be used alone to represent equipment such as pumps, heaters, valves, mixers, etc., or they may be used as generic “tools” to build models of more complex unit operations.

The following table summarizes the available unit operation models:

Basic Unit Operation Models and Stream Manipulators

Dupl Copies inlet stream to any number of outlet streams

Flash2 Performs two-phase (vapor-liquid) or three-phase (vapor-liquid-solid) phase equilibrium calculations

Flash3 Performs three-phase (vapor-liquid-liquid) phase equilibrium calculations

FSplit Splits inlet stream to any number of outlet streams

15 Steady-State Unit Operation Models 287


Heater Represents heaters, coolers, or mixers with known heat duty or specified temperature

Mixer Adiabatic mixing of any number of feed streams

Mult Multiplies stream flow rates by a constant

Pipe Calculates pressure drop through pipelines

Pump Represents pumps or liquid standpipes (pressure must be specified)

Distillation and Fractionation Models

Sep Mass-balance model for separation operations with any number of product streams

Sep2 Mass-balance model for separation operations with two product streams

RadFrac Predictive multistage distillation model

MultiFrac Predictive model for complex distillation operations with multiple columns



Reactor Models

RStoic Mass-balance model based on specified conversion for any number of stoichiometric reactions

RYield Mass-balance model based on specified product yield for any number of stoichiometric reactions

REquil Chemical equilibrium calculated from user-specified equilibrium constants

RGibbs Chemical equilibrium calculated by Gibbs free-energy minimization

RCSTR Predictive, reaction rate-based model to simulate continuous stirred tank reactors

RPlug Predictive, reaction rate-based model to simulate continuous plug-flow reactors

RBatch Predictive, reaction rate-based model to simulate batch and semi-batch stirred tank reactors

Dupl The Dupl block copies one inlet stream to two or more outlet streams. By design, the mass flow rate and attribute rates out of this block will be greater than the flow rates into the block, violating mass and attribute conservation principles.

Frequently, the Dupl block is used as a shortcut to reduce the simulation time required to model a process consisting of two or more parallel process lines. For example, consider the process shown here:

Operating Conditions

R1A R1B R2A R2B R3A R3B

Temperature, °C

250 250 260 260 270 265

Pressure, torr 760 760 1200 1200 1500 1700

Volume, liter 2000 2000 1500 1500 1000 1200


The second unit (“R2A” and “R2B”) in the “A” and “B” lines consist of identical unit operations operating at the same conditions. The third unit (“R3A” and “R3B”) operates differently in the two lines. Since the process lines are identical up to the third unit, there is no need to include both process lines in the model. Instead, we can consider one line, such as “A” and duplicate the outlet stream at the point where the process conditions diverge from each other.

Another application of the Dupl model is to carry out simple case studies. For example, assume there are two proposed scenarios for carrying out a given reaction. In the first scenario, the reaction is carried out at a high temperature in a small reactor with a short residence time. In the second scenario, the reaction is carried out at a low temperature in a large reactor


with high residence times. The two reactors can be placed in a single flow sheet model. The duplicator block is used to copy one feed stream to both reactors. The two “cases” can be compared by examining the stream summary.

Flash2 The Flash2 block carries out a phase-equilibrium calculation for a vapor-liquid split. The “chemistry” feature of this block can be used to extend the phase equilibrium to vapor-liquid-solid systems. The free-water option can be used to extend the phase equilibrium calculations to include a free water phase in addition to the organic liquid phase.

The Flash2 model can be used to simulate simple flash drums with any number of feed streams. The model is also a good tool for representing spray condensers, single-stage distillations, knock-back condensers, decanters, and other types of equipment which effectively operate as one ideal stage.

The Flash2 model assumes a perfect phase split, but an entrainment factor can be specified to account for liquid carryover in the vapor stream. The entrainment factor is specified by the user, it is not calculated by the model. If a correlation between the vapor flow rate and the entrainment rate is available, this correlation can be applied to the model using a Fortran block which reads the vapor flow rate calculated by the Flash block, calculates the entrainment rate, and writes the resulting prediction back to the Flash block. Note that this approach creates an information loop in the model which must be converged.

The Flash2 block does not fractionate the polymer molecular weight distribution. Instead, the molecular weight distribution of the polymer in each product stream is assumed to be the same as the feed stream.

Flash3 The Flash3 block carries out phase-equilibrium calculations for a vapor-liquid-liquid splits. The liquid phases may be organic-organic (including polymer-monomer) or aqueous-organic. For aqueous-organic systems, the Flash3 model is more rigorous than the Flash2/free water approach described above. The key difference is that the Flash3 model considers dissolved organic compounds in the aqueous phase while the free water approach assumes a pure water phase.

Generally, three-phase flashes are more difficult to converge than two-phase flashes. Three-phase flash failures may indicate bad binary interaction parameters between the components. The problem may also stem from bogus vapor pressures or heats of formation. In general, it is a good idea to study two-phase splits for the system in question before attempting to model a three-phase decanter or reactor.

As with the two-phase flash, the three-phase flash is more stable if temperature and pressure are specified. Other options, such as duty and vapor fraction, are more difficult to converge. Temperature estimates may aid convergence in duty-specified reactors.


The Flash3 block does not fractionate the polymer molecular weight distribution. Instead, the molecular weight distribution of the polymer in each product stream is assumed to be the same as the feed stream.

FSplit The flow splitter block, FSplit, is used to represent valves or tanks with several outlets. The outlet flow rates can be specified on a mass, mole, or volume basis, or they can be specified as a fraction of the feed stream. In general, the fraction specifications are best because they are independent of the feed stream flow rates. This makes the model more flexible and reliable when using tools like SENSITIVITY or DESIGN-SPEC which might directly or indirectly manipulate the stream which is being split. The FSplit block can also be used with reactor models to account for back-mixing.

The FSplit block assumes that the class 2 polymer attributes split according to mass mixing rules. For example, if the outlet stream is split 60:40, then the class 2 attributes, such as the segment flow rates, are also split 60:40. This approach is identical to assuming that the properties of the polymer in each outlet stream are the same as the properties of the polymer in the inlet stream.

Heater Heater can be used to represent heaters, coolers, mixers, valves, or tanks. The Heater block allows you to specify the temperature or heat duty of the unit, but does not carry out rigorous heat exchange equations. Any number of feed streams can be specified for the Heater block. This block follows the same mixing rules as the Mixer model.

Mixer The mixer block, Mixer, is used to mix two or more streams to form a single mixed outlet. The mixer block can be used to represent mixing tanks, static mixers, or simply the union of two pipes in a tee. The Mixer model assumes ideal, adiabatic mixing. The pressure of the mixer can be specified as an absolute value or as a drop relative to the lowest feed stream pressure.

The Mixer model is functionally equal to the Heater model, except it only allows adiabatic mixing. For this reason, the Heater model may be a better choice for modeling mixing tanks.

The Mixer block assumes that the class 2 polymer attributes are additive. For example if stream “A” and “B” are mixed to form stream “C”, and the zeroth moments of a polymer in stream “A” and “B” are 12 kmol/sec and 15 kmol/sec, then the polymer in the product stream has a zeroth moment of 12+15=27 kmol/sec.

Mult The Mult block is used to multiply the flow rate of a stream. A common application of this block is to collapse two parallel process line models into a


single line to avoid unnecessary duplicate calculations. For example, consider the process shown here:

In this process, the “A” and “B” lines consist of identical equipment with the same operating conditions. The Mult blocks “HALF” and “TWICE” are used to divide the feed stream flow rate by two after R1, representing the split between lines, and to double the product flow rate, representing the junction of the parallel lines into a single line at R3. This technique avoids the duplicate calculations for R2 “A” and “B” reactors, which should give the same results. This technique can save a great deal of simulation time.

Pump The Pump block changes the pressure of a stream. This block can be used to represent an actual pump, or it can be used to represent pressure increases due to liquid head in standpipes.

Pipe The Pipe model is used to calculate pressure drops in pipelines. The algorithms in this model are not designed for non-ideal fluids such as polymers, so the pipe model should be used with caution in polymer process models. A better option to calculate pressure drops in polymer pipelines is to use RPlug with a user-written pressure-drop subroutine.


Sep The Sep block is a generic separation model that allows component fractionation between two or more product streams. The products can be split according to flow rate or fractional specifications. The Sep block is commonly used to represent distillation columns or other separation equipment when the product stream purity is well known and the details of the separation process are not important.

The Sep block does not fractionate the polymer molecular weight distribution. Instead, the molecular weight distribution of the polymer in each product stream is assumed to be the same as the feed stream.

Sep2 The Sep2 block is a generic separation model that allows component fractionation between two product streams. The products can be split according to flow rate or fractional specifications. The Sep2 block is commonly used to represent distillation columns or other separation equipment when the product stream purity is well known and the details of the separation process are not important. Compared to the Sep block, the Sep2 block has more flexible input options, but it only allows two outlet streams.

The Sep2 block does not fractionate the polymer molecular weight distribution. Instead, the molecular weight distribution of the polymer in each product stream is assumed to be the same as the feed stream.

Distillation Models Aspen Plus includes several shortcut distillation models (DISTL, SFRAC, etc.) which can be used to represent distillation columns. These blocks do not fractionate the polymer molecular weight distribution. Instead, the molecular weight distribution of the polymer in each product stream is assumed to be the same as the feed stream. The class-2 component attributes in each product stream are set proportional to the mass flow rate of the attributed component in each product stream.

With the exception of the RadFrac model, the rigorous distillation models in Aspen Plus do not account for component attributes.

RadFrac The RadFrac block is a rigorous multistage distillation model for two- and three-phase systems. RadFrac allows polymer feed streams at any tray, but it does not account for polymerization reaction kinetics. The molecular weight distribution and other polymer properties are not fractionated between the phases. Instead, the class-2 component attributes of the polymer components are split at each stage in proportion to the polymer component mass fractions. For example, if 90% of the polymer fed to a given tray goes to the liquid phase leaving that tray, then 90% of the zeroth moment and other class-2 attributes are assigned to the liquid phase on that tray.


Reactor Models Aspen Plus includes three classes of reactor models which include various levels of rigor and predictive capability. These classes are: (1) mass-balance models; (2) equilibrium models; and (3) rigorous kinetic models.

The least predictive models, RStoic and RYield, calculate output flow rates based on user-specified input flow rates. If polymer components are involved in the reactions, then the component attributes associated with the polymer components must be specified for the product stream. These models calculate the mass and energy balances, but they do not perform rigorous kinetic calculations.

The RGibbs and REquil models assume chemical and phase equilibrium. When polymer components are involved in the reactions, then the specified stoichiometry must be consistent with the reference molecular weight of the polymer component. In addition, the component attribute values for the polymer product must be specified by the user. Since the solution algorithms for these models do not consider the influence of the segmental composition of polymer components, they cannot be applied to copolymers.

Rigorous kinetic models include RCSTR (continuous stirred tank reactor), RPlug (plug-flow reactor model), and RBatch (batch stirred tank reactor). Each of these models can consider one, two, or three reacting phases. These reactor models are with the reaction kinetic models to predict product stream composition and flow rates based on calculated reaction rates.

Mass-Balance Reactor Models

RStoic The RStoic reactor model is used to represent reaction equipment when reaction kinetics are unknown or are unimportant, for example when reactions are very fast and proceed until the limiting reagent is exhausted. RStoic requires knowledge of the net reaction stoichiometry, and the extent of reaction or conversion of a key component.

RStoic calculates the product stream flow rates based on user-specified reaction stoichiometries and extent of reaction or conversion of a key component. The reaction stoichiometry statements may include monomers, oligomers, or polymers, but may not include segments. Instead, the segment information (SFLOW or SFRAC) must be specified as component attributes in the COMP-ATTR sentence.

Reactions Involving Polymers If polymer components are involved in any of the reactions, use the COMP-ATTR form to specify molecular weight values (MWN, MWW or PDI) or degree of polymerization (DPN, DPW or PDI ) for the polymer products. Specify the SFRAC attribute for homopolymers or copolymers with a known product polymer composition. For copolymers with product compositions which


depend on the feed flow rates of monomers or polymer segments, specify dummy values for the SFLOW attribute and use a user-written Fortran block to predict product segment flow rates which are consistent with the calculated product flow rates. Write the calculated results into the product stream of the RStoic block.

When some of the specified reactions involve polymers, the reaction stoichiometry must be written in a manner consistent with the reference molecular weight of the polymer component. Otherwise, the mass and energy balance calculations will not be consistent.

Simulating Polymer Phase Change The RStoic model may be used with the substream feature to simulate phase changes in polymers. For example, the user may define a reaction to convert polymer from the liquid or amorphous state (in the MIXED substream) to crystalline polymer (in the CISOLID) substream. Conversely, melting can be simulated as a reaction that converts polymer in the CISOLID substream to polymer in the MIXED substream.

When RStoic is used in this manner, the model automatically fractionates the component attributes between the product substreams. If the user does not specify the product component attributes, the model sets the values of the class-2 attributes in each substream proportional to the flow rate of the attributed component in the substream. In effect, the model assumes that there is no selectivity of properties between the product phases. The polymer in each product phase will have the same characteristics (segment composition, mole weight, etc) as the polymer in the feed stream.

RYield The RYield reactor model is used to represent reaction equipment when reaction kinetics are unknown or are unimportant, and the reactions result in a product distribution with a known yield.

RYield calculates the product stream flow rates based on user-specified reaction stoichiometries and yield distributions. The reaction stoichiometry statements may include monomers, oligomers, or polymers, but may not include segments. Instead, the segment information (SFLOW or SFRAC) must be specified as component attributes in the COMP-ATTR sentence.

If polymer components are involved in any of the reactions, use the COMP-ATTR form to specify molecular weight values (MWN, MWW or PDI) or degree of polymerization (DPN, DPW or PDI ) for the polymer products. Specify the SFRAC attribute for homopolymers or copolymers with a known product polymer composition. For copolymers with product compositions which depend on the feed flow rates of monomers or polymer segments, specify dummy values for the SFLOW attribute and use a user-written Fortran block to predict product segment flow rates which are consistent with the calculated yield. Write the calculated results into the product stream of the RYield block.

When some of the specified reactions involve polymers, the reaction stoichiometry must be written in a manner consistent with the reference


molecular weight of the polymer component. Otherwise, the mass and energy balance calculations will not be consistent.

Equilibrium Reactor Models

REquil The REquil model calculates product stream flow rates using equilibrium constants determined from Gibbs free energy. The equilibrium constants are based on user-specified reaction stoichiometries and yield distributions. The reaction stoichiometry statements may include monomers or oligomers, but may not include polymers or segments. If the feed stream includes polymer components, the attributes of the polymer components will be copied to the outlet stream.

RGibbs The RGibbs model uses the Gibbs free energy minimization technique to determine the composition of each phase. This algorithm cannot predict the product of equilibrium polymerization reactions. Polymer phase equilibrium, however, can be predicted by the model. The RGibbs phase equilibrium algorithm assumes that the composition and molecular weight distribution of a polymer component is equal in each of the product phases. The class-2 component attributes of the polymer component are set in proportion to the mass flow of the polymer component in each of the product phases. The mass flow rates in the product phases are set by the Gibbs free energy minimization algorithm.

To properly split component attributes among the RGibbs solution phases, use the "Phase equilibrium only" option. With this the model can predict multiple liquid phases such as three liquid phases. Surface tension effects are not considered. If you are certain that there will be no vapor phase, uncheck the "Include vapor phase" box to speed up calculations. Use one outlet stream for each predicted phase, to separate out the component attributes of that phase.

Kinetic Reactor Models

RCSTR The RCSTR model represents a continuous stirred tank reactor with one or more phases.

The model assumes perfect mixing within and between the phases, phase equilibrium, and isothermal, isobaric operation. Non-ideal mixing can be represented using a network of RCSTR models.


Temperature The CSTR model allows you to specify duty or temperature. If duty is specified, it is a good idea to provide a temperature estimate, T-EST, to improve the convergence of the model. The maximum temperature step size, T-STEP, may also influence the CSTR convergence. This parameter defaults to 50°C, which results in substantial changes in reaction rates for reactions with typical activation energies. The temperature/duty iteration loop is referred to as the “Energy Balance” or “EB-LOOP” in the CSTR diagnostics.

Pressure Pressure can be specified as an absolute value or as a pressure drop relative to the feed stream with the lowest pressure. In Aspen Plus, pressure drops are expressed as non-positive pressure specifications given in absolute pressure units.

Residence Time The RCSTR model allows you to specify the effective hold-up in several different ways. For single-phase reactors, you can specify the total reactor volume or the total residence time. If the residence time is specified, then the estimated reactor volume should be specified to improve the residence-time/volume loop convergence (RT-LOOP).

When two or more condensed phases are present, the RCSTR model assumes that each condensed phase has the same residence time. This “no-slip” assumption implies that the volume ratios of the condensed phases in the reactor are equal to the volume flow ratios of the condensed phases exiting the reactor.

For multiphase reactors, specify the condensed phase volume or residence time in addition to the total reactor volume. Do not specify the total residence time, as this residence time is the average of the vapor and liquid phases. If the reacting phase residence time is specified, provide an estimate for the reacting phase volume. This will improve the reactor convergence. If residence time convergence is troublesome, try adjusting the volume step size.

Multiphase Reactors The RCSTR model can be used to simulate single- or multiple-phase reactors. The valid-phases keyword is used to define the number and type of fluid phases present in the reactor.

Amorphous solid polymers are treated as a “liquid” phase in Aspen Polymers (formerly known as Aspen Polymers Plus). Crystalline solids can be addressed by defining a “CISOLID” substream to track the flow rate of each inert crystalline solid.

Dissolving or crystallizing solids can be captured using the Chemistry feature to define chemical equilibrium reactions between the solid and fluid phases. Note, however, that the current version of RCSTR does not allow components to appear in both kinetic reactions and in chemistry equilibrium reactions.


The user may attach multiple outlet streams directly to the reactor model. The phase or phases flowing to these streams are identified on the streams form. When solids are present the solid phases will be added to the liquid outlet.

In older releases of Aspen Plus, the RCSTR model had one process fluid outlet stream containing all of the phases exiting the reactor. This option is still supported in the current release for upward compatibility. As shown in the following figure, a Flash2 or Flash3 block can be used to split the mixed outlet stream of the reactor:

Reactors with Non-Ideal Mixing Networks of RCSTR and RPlug blocks can be used to account for non-ideal mixing found in industrial reactors. For example, many industrial reactors are divided into zones by vertical or horizontal baffles. In addition, some reactors have poor mixing characteristics which result in dead zones. The figures that follow demonstrate ways to model some types of real reactors.

Since many of the “network” models involve recycle loops, they may require substantially more simulation time than a single RCSTR block. In addition, the recycle loop convergence may make the model more difficult to converge. For these reasons, the simplest model that agrees with process data is always the best choice.

This figure shows a two-phase CSTR with horizontal partitions:


This figure shows a two-phase CSTR with vertical partitions:

This figure shows a two-phase CSTR with an external heat exchanger:


This figure shows a two-phase CSTR with a dead-zone:

RCSTR Algorithm The RCSTR model uses a trial-and-error technique to solve the mass and energy balance equations. Trial-and-error solutions are difficult to reach when the reaction rates are high, the variables cover several orders of magnitude, when many equations must be solved simultaneously, and when the variables are strongly related to each other. All of these conditions are found in polymerization reaction kinetics, making reactor convergence especially challenging.

A good understanding of the design of the RCSTR model is required in order to troubleshoot convergence problems. Otherwise, it may be difficult to


understand how to apply the various convergence parameters to improve the reliability of the model.

The RCSTR algorithm consists of a series of nested loops, as shown in the following figure. The loops are solved from the inside to the outside using various trial-and-error solver algorithms. Some convergence parameters are associated with each of these loops.

The outer-most loop involves the volume and residence time of the CSTR. There are many options for specifying the characteristic volume of a multiphase CSTR. The following table shows the various calculations for volume and residence times in RCSTR:

Specifications: Total reactor volume (Vol)


θRR

j jj

VF v f

= ∑ Vf v

f vVj

j j

k kk

R= ∑ θ jj

j j

VFf v

=

Specifications: Total residence time (Res-time)

V F v fR R j jj

= ∑θ ** V

f vf v

Vjj j

k kk

R= ∑ θ jj

j j

VFf v

=

Specifications: Total reactor volume (Vol), key phase volume (Ph-vol)

θRR

j jj

VF v f

= ∑ V specifedj = * θ jj

j j

VFf v

=

Specifications: Total reactor volume (Vol), key phase volume fraction (Ph-vol-frac)

θRR

j jj

VF v f

= ∑ V r Vj j R= θ jj

j j

VFf v

=

Specifications: Total reactor volume (Vol), key phase residence time (Ph-res-time)

θRR

j jj

VF v f

= ∑ V Ff vj j j j= θ ** θ j specified=

Specifications: Total residence time (Res-Time), key phase volume fraction (Ph-vol-frac)

V F v fR R j jj

= ∑θ ** V r Vj j R= θ jj

j j

VFf v

=

RV = Total reactor volume;

jV = Volume of phase “j”; jv = Molar volume of

phase “j”

jr = Volume fraction of phase “j”; Rθ = Total residence time;

jθ = Residence

time of phase “j”

F = Total molar flow rate at reactor outlet; jf = Molar fraction of phase “j”

* If more than one condensed phase is present, and the key phase is liquid, then the specified volume applies to the sum of the condensed phase volumes.

** This equation is solved by trial-and-error technique.

When residence time is specified instead of volume, the RCSTR model adjusts the volume to satisfy the residence time specification.


Convergence problems in the residence time loop can be alleviated by providing initial volume estimates in the ESTIMATES form. If convergence problems persist, then the maximum volume step size (Max-Vstep) should be reduced. If the key phase residence time is specified, then the RCSTR model uses the specified reactor volume as an upper limit for the key phase volume.

EB LOOP

The second loop is the energy balance conservation equation (EB-LOOP). In this loop, the reactor temperature is adjusted to match the specified reactor duty. If the temperature is specified instead of the duty, this loop is by-passed.

Since the reaction rates are very sensitive to temperature, large changes in the reactor temperature between energy-balance iterations (EB-ITER) may cause the mass-balance loop (MB-LOOP) to diverge. This problem can be solved by providing a good temperature estimate (T-EST) in the ESTIMATES form. If the problem persists, the maximum temperature step size (Max-Tstep) should be reduced (the default, 50°C, is rather large).

MB-LOOP

The next loop is the mass-balance loop (MB-LOOP). This loop uses a multivariable solver to converge the conservation equations for component mole flow and for the class two component attributes.

Two solvers are available: Broyden and Newton. The Broyden algorithm tends to be relatively fast, but it may be unstable if the number of components and attributes is large and the reaction rates are high. The Newton algorithm tends to be slower, but more stable for many classes of problems. The Newton algorithm calculates the response of each variable to each other variable by perturbing the variables one at a time by a very small amount. These perturbation steps require lots of simulation time, which makes each iteration of the Newton algorithm slow.

The number of mass-balance iterations (MB-Maxit) is defined on the convergence form. By default, the model allows 50 mass-balance iterations. This default is sufficient for the Newton algorithm, but is usually too small for the Broyden algorithm. For polymer reaction kinetics, the number of required mass-balance iterations may be as high as 500.

Using a Damping Factor

The stability of the Broyden algorithm can be adjusted using a damping factor (DAMP-FAC) defined on the “Convergence” form. Decreasing the damping factor decreases the step-size, resulting in a larger number of smaller, more stable steps. Thus, the maximum number of iterations should be increased as the damping factor is decreased.

The damping factor is sensitive on a log scale. If the Broyden algorithm appears unstable, try setting the damping factor to 0.5, 0.3, 0.1, 0.05 etc. Optimum damping factors for polymerization kinetics typically fall between 0.1 and 0.001.

The conservation equations have the form:


accumulation input output Generation= − +

For the component mole balance equations: RS

FS

FS

G V

Si

i

iin

i

iout

i

i j jj

i= − +

∑ ,

For the class-2 component attributes equations: RS

AS

AS

G V

Si

i

iin

i

iout

i

i j jj

i= − +

∑ ' ,

Where:

Ri = Residual value for equation i, kmol/sec

Fiin = Molar flow rate of component i into the reactor, kmol/sec

Fiout = Molar flow rate of component i out of the reactor, kmol/sec

Gi j, = Molar generation rate of component i in phase j, kmol/m3 sec

Aiin = Flow rate of attribute i into the reactor, kmol/sec or

particle/sec

Aiout = Flow rate of attribute i out of the reactor, kmol/sec or

particle/sec

′Gi j, = Generation rate of attribute i in phase j, kmol/m3 sec or particle/m3 sec

Vj = Volume of phase j in the reactor

Si = Scaling factor for equation i

The mass-balance loop is converged when the maximum scaled residual of the conservation equations falls below the specified tolerance (MB-TOL):

Maximum error = MAX MB TOLiRS

i

i

⎛⎝⎜

⎞⎠⎟ < −

A secondary criteria is the root-mean-square scaled error, or RMS error:

RMS Error = 1

2

NRSi

i

ii

⎛⎝⎜

⎞⎠⎟∑

The CSTR mass-balance algorithm iterates until the maximum error falls below the specified mass-balance tolerance or the maximum number of mass-balance iterations is reached. If the maximum error criteria is reached, and the RMS error is decreasing by a factor of ten on each iteration, the CSTR model continues to iterate until the RMS error reaches the specified function tolerance (FUNC-TOL). This allows the model to reach very tight convergence tolerances when the convergence behavior is good.

Scaling Factors

The scaling factors play an important role in the convergence behavior of the model. If the scaling factors are large, and the variables are small, then the


model will be loosely converged. If the scaling factors are small, and the variables are large, the convergence criteria will be unacceptably tight, and the model will not converge. There are two scaling options in the RCSTR model, as shown here:

Variable Type Component Scaling Substream Scaling

Enthalpy Estimated outlet stream enthalpy 105

Component Mole Flows The larger of:

Estimated component mole flow in outlet stream (or retention value if available)

(Trace) x (Substream flow rate)

Total estimated outlet stream mole flow rate

Class 2 Attributes The larger of:

Estimated attribute value in outlet stream (or retention value if available)

(Attribute scaling factor from the TBS table) x (Estimated mole flow rate of the attributed component)

(Trace) x (Total estimated outlet mole flow rate) x (Attribute scaling factor from the TBS table)

1110−

Note: If the estimated component flow or attribute value is zero or missing, the default scaling factor is applied.

(Attribute scaling factor from the TBS table) x (Substream flow rate)

By default, the component scaling option is used. With this option, the minimum scaling factors depend on the value of the “TRACE” parameter. The trace scaling factor is effectively a minimum mole fraction. For components with concentrations below the trace level, the scaling factors are set to a minimum value.

The default scaling factors for component attributes are defined as constants in an Aspen Plus Table Building System (TBS) data file, “COMPATTR.DAT”. Although the default scaling factors are set to appropriate values for most classes of reaction kinetics, the optimal values for a particular type of kinetics may be different than the defaults. The default attribute scaling factors can be adjusted using the Components Attr-Scaling form.

The scaling factors should make the scaled values as close to unity as possible. For this reason, the scale factors are set to the predicted values from previously converged passes through the RCSTR block. On the first pass through the flowsheet, the scaling factors will be set to the estimated value for the variable. Thus, component flow and component attribute estimates can be used to set the initial scale factors.

The scaling factors for component attribute values are normalized with the total mole flow rate of the outlet stream. This keeps the scaling factors reasonable for models of any type of process, from bench scale to production scale units.

The inner-most loop is the phase equilibrium loop, or flash equations. For this reason, it is essential to have accurate physical properties over the entire range of temperatures and pressures found in the process.


The flash calculations start from retention values once the mass-balance error falls below the retention threshold (Ret-Thresh) specified in the convergence form. If the retention threshold is set very high, then the flash may fail, resulting in step-size cuts in the mass balance loop. If the retention threshold is reduced, the reactor calculations may require more time. For most

simulation problems, setting the retention threshold to 1 1010× results in fast flash convergence without errors. If errors occur, try using the default value, 1 105× . If errors persist, the most likely cause is a physical property problem.

Initialization Options

The convergence behavior of the RCSTR model depends on how the model is initialized. There are three initialization options for the RCSTR model.

• Solver Initialization—Do not use integration

By default, the solver algorithm initializes itself using previously saved simulation results (retention). This saves time if the RCSTR block is inside a flowsheet recycle loop, where the block will be run several times in succession. It also saves time if the block is inside a sensitivity, optimization, design-spec, or data-fit study.

Alternately, the user can force the model to restart from estimates every time by checking the restart flag on the block-options form.

When retention is not available, or when the restart option is active, the model uses user-specified estimates to initialize the solver algorithm. Estimates can be provided for the reactor volume, phase volume, reactor temperature, component flow rates, and component attribute values. The component attribute estimates can be specified using class-2 or class-0 attribute values.

If estimates are not provided, the model initializes the variables using the mixed feed stream (for example, the initial value of a component flow rate may be set to the total flow rate of that component in all feed streams to the reactor).

• Integration Initialization—Always use integration

In the integration algorithm, the RCSTR is treated as a dynamic stirred-tank reactor. The conservation equations are numerically integrated from an initial condition to the steady-state condition. The initial compositions in the reactor are set equal to those in the feed stream.

If temperature is specified in the reactor, then the temperature profile during initialization can be ramped from the feed stream temperature to the specified temperature over the interval of several residence times. If duty is specified, then the duty can be ramped from adiabatic conditions to the specified duty. Ramping allows the reactor to “cold-start” for improved integration performance.

The numerical integration carries forward until the residual terms (accumulation terms) drop below the specified mass-balance tolerance. At this point, the model enters the solver and continues until the model converges.

Note that initial guesses for component flow rates and component attributes should not be provided when using the integration initialization option unless the reactor exhibits multiple steady-state solutions. In this case, initial estimates may be used to force the reactor towards a particular solution.


• Hybrid Initialization—Initialize using integration

The hybrid option takes advantage of the robust integration algorithm to initialize the reactor during the first pass. On subsequent passes, when a previously converged solution is available, the solution algorithm bypasses integration and jumps directly into the trial-and-error solver. Since the solver algorithm is much faster than the integration algorithm, the hybrid option offers improved performance for most problems.

Note: By default, the RCSTR model does not use integration (e.g., the trial and error solution algorithm starts directly from the user-specified initial guesses or from retention values). Optionally, the RCSTR model can be initialized using an integration approach or a hybrid approach that uses integration only when retention values are not available.

Troubleshooting Convergence Problems To diagnose RCSTR convergence problems, set the terminal reporting level to “7” in the Block-Options form. This causes the RCSTR model to report the residence time iterations (RT-ITER), energy balance iterations (EB-ITER), and mass-balance iterations (MB-ITER) to the control panel. In addition, the model reports the maximum and root-mean-square errors for each loop.

The Simulation diagnostic reporting level controls the diagnostic messages written to the history file (.HIS file). The maximum mass-balance error is reported at level 5. At level 6, the model reports the value of each reacting component flow rate and each component attribute. At level 7, the model reports values and rates of change (reaction rates) for components and attributes. At level 8, the model reports the values, rates, and residuals (error) of each solved variable.

When troubleshooting convergence problems, simplify the problem by specifying temperature and volume instead of duty and residence time. If convergence problems persist, they must be related to the mass-balance loop, the reaction kinetic model or rate constants, or the underlying physical property calculations.

Numerical integration is much more reliable than trial-and-error solvers. If the RCSTR mass-balance fails to converge, try running the same kinetics in an RPlug model. If possible, set the phase criteria “liquid-only” to eliminate physical property problems from the list of possible sources of error. If the RPlug model cannot converge with the specified kinetics, then the problem is almost certainly related to reaction kinetics.

Possible sources of error in the reaction kinetics include:

• Errors in the molecular weight of a product or reactant

• Errors in the specified stoichiometry of a reaction (mass balance is violated)

• Unreasonable rate constants, especially activation energies (verify the units)

• Reactions with zeroth-order reactants which are not present

• Unreasonable concentrations of catalysts or inhibitors (put the feed stream in a flash block and verify that the concentrations in the reacting phase make sense).


• Errors in user-written Fortran subroutines.

If these sources of error are eliminated, and convergence problems persist, try simplifying the model by removing unnecessary side reactions or trace components from the model. Convergence is much easier if the number of equations is reduced, the speed of most convergence algorithms varies with the cube of the number of equations (the number of equations equals the number of reacting components plus the number of class-2 component attribute elements).

Common Problems

The following table summarizes solutions for some common problems encountered when using RCSTR:

Problem Solution

Initial flash failure This is usually a physical property problem.

Check the heat of formation (DHFORM) and ideal gas heat capacity parameters (CPIG) of the polymer and oligomer components.

If supercritical components are present, consider treating them as Henry’s law components

Verify that the property method you are using is appropriate for the specified temperature and pressure

Verify the specified phases are consistent with the specified temperature and pressure

Verify the specified local and global flash tolerance

Mass balance not converged in maximum number of iterations, but the error is decreasing from one iteration to the next.

Increase the maximum number of iterations. If more than 500 iterations are required for the Broyden algorithm, try adjusting the damping factor. Provide better initial guesses.

Mass balance not converged in maximum number of iterations, the maximum error is varying erratically between iterations, and the history file shows reasonable rates.

If using the Broyden algorithm, try decreasing the damping factor by logarithmic steps (0.5, 0.3, 0.1…0.0001) until the problem converges. If the problem persists, try using the Newton algorithm. Provide better initial guesses.

Mass balance is not converging, the maximum error appears to oscillate between values or gets “stuck” and does not change.

If using Newton algorithm, change the stabilization strategy from “dogleg” to “line search.” This works especially well for ionic and Ziegler-Natta kinetics.

Mass balance not converged in maximum number of iterations, the maximum error is varying erratically between iterations, and the history file shows some reaction rates or attribute rates are much larger than others (or are erratic between iterations).

Check the specified rate constants in the kinetic models, especially activation energies. Verify the units of the activation energies. Verify flow rates of catalysts and initiators in the feed streams to the reactor. If using user kinetics, check your subroutine for errors. Verify the reactor volume (residence time).

Mass balance not converged in maximum number of iterations. Reaction rates are very high, as expected.

Try using the Newton algorithm with good initial guesses. If this fails, delete the initial guesses and try using the integration initialization.


Problem Solution

Mass balance not converged in maximum number of iterations. Some reacting components (catalysts, initiators) are present in very small quantities.

Try adjusting the “trace” parameter in order-of-magnitude steps from the default (1 10 3× − ) down to the concentration of the trace components. If this fails, reset trace to the default value and try integration initialization.

Energy balance loop does not converge, or mass-balance loop does not converge after the second energy balance loop iteration, or temperature step-size cutting (T-CUT) iterations appear in the diagnostic messages

Verify that the reactor converges with the temperature specified. If not, see items listed above, otherwise,

provide a better temperature estimate (T-Est). If the problem persists, try adjusting the maximum temperature step-size (Max-Tstep) from 50°C to 10°C or even 5°C.

Residence time loop does not converge, or mass-balance loop does not converge after the second residence-time loop.

Verify that the reactor converges with the residence time specified. If not, see items listed above, otherwise, provide better volume estimates. If the problem persists, try adjusting the maximum volume step-size (Max-Vstep).

Verify that the correct residence time is specified (condensed-phase residence time for two-phase reactors).

Verify two phases exist if the reactor valid phases=vapor-liquid.

Flash failures appear during the mass-balance loop; the step-size cutting (X-CUT) diagnostic message appears.

This may be a physical property problem; it may reflect overly-tight flash tolerances; or the flash may be unstable when starting from retention values Loosen the local and global flash tolerance levels or increase the maximum number of flash iterations.

Reactor converges but an error message says that the mass-balance does not close

Check the molecular weights of each reactant and product. Verify that reaction stoichiometry is correct.

RPlug The RPlug model represents an ideal plug-flow reactor with one or more phases. The model assumes perfect radial mixing within and between the phases, phase equilibrium, and no-slip conditions between the phases (e.g., the phases all have the same residence time). Dead zones, back-mixing, and other types of non-ideal plug-flow behavior can be represented using RPlug in combination with other blocks. The RPlug model does not allow multiple feed streams. A mixer block must be used in conjunction with the RPlug block to account for multiple feed streams.

Temperature RPlug allows many options for specifying the reactor duty or temperature:

Type Specifications Calculations



ADIABATIC None Temperature is calculated at each axial position based on the enthalpy balance.

T-SPEC Process stream temperature as a function of axial position (linear interpolation between the points)

Duty is integrated along the length of the reactor. The model reports the net duty across the reactor

T-COOL-SPEC

Heat transfer routine optional

Heat media stream temperature (assumed constant along length of reactor). Overall heat-transfer coefficient. Area is determined from length, diameter , and number of tubes: A=NΒDL

Duty is integrated along the length of the reactor. The temperature of the process stream is determined from the energy balance. The model reports the net duty across the reactor

CO-COOL

Coolant stream required


Heat media (coolant) stream temperature, composition, and flow rate.

Overall heat-transfer coefficient. Area is determined from length, diameter, and number of tubes: A=NΒDL.

Duty is integrated along the length of the reactor and is reported as a net value. The temperature of the process and coolant streams are determined from the energy balance.

COUNTER-COOL

Coolant stream required


Heat media (coolant) composition, flow rate and effluent temperature. Overall heat-transfer coefficient. Area is determined from length, diameter, and number of tubes: A=NΒDL.

Duty is integrated along the length of the reactor and is reported as a net value. The temperature of the process and coolant streams are determined from the energy balance. A design specification may be used to fit coolant feed temperature by adjusting coolant outlet temperature.

RPlug allows one process stream and one heat media stream. Reactions can occur only in the process stream. Heat transfer calculations are carried out between the process stream and the heat media stream. The heat media stream represents a coolant stream or a heating stream and the heat media stream flows co- or counter-current to the process stream.

If a heat media stream is not specified, the model assumes a constant heat media temperature and solve for the process fluid temperature.

The heat transfer rate or heat transfer coefficient value is calculated as a function of axial position, stream conditions, etc., by a user-written Fortran subroutine. This feature is used to develop rigorous models non-reactive heat exchangers.

Pressure The pressure at the reactor entry can be specified as an absolute value or as a pressure drop relative to the feed stream. In Aspen Plus, pressure drops are expressed as non-positive pressure specifications given in absolute pressure units.


The pressure drop across the reactor can be specified as a constant or calculated in a user-written Fortran subroutine. If the pressure drop is specified, the model assumes it is linear along the length of the reactor.

Residence Time The RPlug model assumes a cylindrical geometry. The length, diameter, and number of tubes are specified. The process fluid is assumed to move through the tubes, and the coolant is assumed to flow on the outside of the tubes.

The total reactor volume cannot be specified, but the aspect ratio (length/diameter) has no influence on the model predictions. Thus, the diameter can be set to 1.12838 units, which corresponds to an area of 1.0000 units2 . With this area, the length in units and volume in units3 have the same numerical value, thus the specified length is equal to the volume.

The phase volumes cannot be specified independently. Instead, the RPlug model assumes that the phases move through the reactor without slipping past each other. This assumption is valid for situations where one phase is dispersed as droplets or bubbles in a second, continuous phase, such as dew in a vapor phase or small gas bubbles in a liquid phase. This assumption is not valid for multiphase plug flow reactors with controlled levels.

With this assumption in place, the reactor residence time is equal to the residence time of each phase present in the reactor. The residence time is calculated by numerical integration.

One work-around for the no-slip assumption is to write a user kinetic subroutine (or a step-growth mass-transfer routine) which calls the flash model directly. Then, specify the reactor as liquid-only and set the diameter to the hydraulic diameter of the reactor.

Calculating Residence Time

Equation to Calculate Residence Time in RPlug:

θπ

=∑∫

=

=D N dzF f vz j j z j zz

z L2

04 , ,

Where:

θ = Reactor residence time

D = Tube diameter

N = Number of tubes

Z = Axial position in reactor of length L

Fz = Total molar flow rate of process stream at axial location z

f j z, = Molar fraction of phase j at axial location z

v j z, = Molar volume of phase j at axial location z


Multiphase Reactors The RPlug models have one process fluid outlet stream that contains all of the phases exiting the reactor. As shown here, a flash block is used in conjunction with these blocks to split the liquid and vapor phases from the mixed outlet stream of the reactor:

In this application, it is good practice to specify PRES=0 (no pressure drop) and DUTY=0 in the flash block to ensure that the phase split occurs at conditions which are consistent with the reactor outlet. Another option is to specify temperature and to use a transfer block to copy the RPlug outlet stream temperature to the flash specifications.

Reactors with Non-Ideal Mixing Back-mixed plug flow reactors can be modeled using a recycle stream or by breaking the reactor down into a series of RCSTR blocks. For example:


The recycle-stream approach has the advantage of RPlug’s profile-based input and output plotting, but it requires a flowsheet convergence loop that may be difficult to converge, especially if the circulation ratio is large. The series-of-CSTRs approach does not require recycle loop convergence, but the results are not as easily interpreted as the RPlug model.

Reactors with dead zones can be represented using parallel plug-flow reactors, as shown here:


The dead zone is represented by a plug-flow reactor with a large residence time. The active zone is represented as a plug-flow reactor with a shorter residence time. The volumes of the two reactors sum to the total volume of the real reactor. This approach assumes the dead zone reaches steady state.

As always, the simplest model which agrees with process data is the best choice.

The following figure shows a reactor with injection ports:


Troubleshooting Convergence Problems To diagnose numerical problems in RPlug, set the terminal reporting level to “7” in the Block-Options form. With this setting, the RPlug block will report the normalized axial location, residence time (in seconds), pressure (in Pascal), temperature (in K), and vapor molar fraction at each converged step.

The Simulation diagnostic reporting level controls the diagnostic messages written to the history file (.HIS file). The maximum mass-balance error is reported at level 5. At level 6, the model reports reacting component flow rates and component attribute values. At level 7, the model also reports the rates of change of these variables. At level 8, the model also reports initial scale factors for all variables.

First, simplify the problem by specifying temperature instead of duty or heat-transfer parameters (coolant temperature, U, or coolant stream). Specify the reactor as “liquid-only”. This will eliminate many possible sources of error and help focus the problem on kinetics and integration parameters.

Scaling Factors

RPlug uses Gear’s variable-step-size algorithm to numerically integrate the mass, energy, and attribute conservation equations along the axial dimension of the reactor. At each axial step, the conservation equations are solved by a trial-and-error technique.

Like RCSTR, RPlug solves the conservation equations using scaling factors to normalize the variables. The values of these scaling factors can have a strong influence on the speed and reliability of the integration.

The Gear integrator in Aspen Plus offers three error scaling options (ERR-METHOD in RPlug):

• Static scaling

• Dynamic scaling

• Hybrid scaling

The RPlug static and dynamic scaling options are summarized in the following table:

Variable Type Static Scaling Dynamic Scaling

Enthalpy 105 (SI units) x total mass flow The larger of:

Enthalpy at 2

Cutoff

Component Mole Flows

The scaling factor at z = 0 to 1.0 is set to 0.1 x total mass flow

The scaling factor at z = z + Δz is set to the larger of:

Component mass flow at z

Cutoff

Scaling factors are updated at each step



Class 2 Attributes The scaling factor at z = 0 to 1.0 is set to the larger of:

Attribute value in inlet stream

(Attribute scaling factor from the TBS table) x (mole flow rate of the attributed component in the inlet)

(Cutoff) x (total mole flow rate at the inlet) x (Attribute scaling factor from the TBS table)

Scaling factors are held constant

The scaling factor at z = z + Δz is set to the larger of:

Attribute value at z

Cutoff


The static scaling method uses a constant set of scaling factors throughout the reactor. The dynamic scaling method updates the scaling factors based on the previously converged step. The scaling factors are never set lower than the specified minimum scale factor.

The static scaling method may result in faster integration for many types of problems, but there are potential numerical problems when using this method. Consider an irreversible reaction “A B” in a plug-flow reactor in which component “B” is not present in the feed. The scaling factor for component “A” will be set very large and the scaling factor for “B” will be set to the minimum scaling factor. This will result in relatively loose tolerance for the mass balance in “A” and tight tolerance for the mass balance in “B”. Further, as the reaction approaches completion the component “B” will have a large flow rate but a small scaling factor. This makes the conservation equation for “B” difficult to solve, which will result in small integration steps.

Consider the same situation with dynamic scaling. The initial scaling factors are the same as the static case. With each new step, however, the scaling factors are updated to the variable values from the previous step. This keeps the scaled variables close to one throughout the integration. For example:

One pitfall of dynamic scaling, however, occurs when a variable value decreases and approaches zero. As the value and the scaling factor get


progressively smaller, small absolute errors become large scaled errors. This also makes the solution difficult, and leads to small steps in the integrator. This problem can be controlled by setting the minimum scaling factor to a

reasonable value. The default value, 10-10 is much too small for most problems. A value of 10-5 is reasonable for most situations, and will result in better model performance.

The hybrid option uses static scaling for all variables except enthalpy, which is scaled dynamically. This option may be the best choice when the stream

enthalpy is far from the default scale factor, 510 .

In general, the dynamic scaling method results in tighter convergence, but it requires more simulation time than the static scaling method. This does not apply to every case, however, and it may also depend on the solver algorithm. It is a good idea to experiment with these parameters to find the most reliable convergence strategy for each reactor in each model. When component attributes are present, as in polymerization kinetics, dynamic scaling is used by default.

Solver Method

At each step during the integration, the energy, mass, and attribute conservation equations are solved by trial-and-error. One of the two “corrector” algorithms, direct substitution or Newton’s method, can be selected. The Newton algorithm perturbs each variable to determine the slope, resulting in a smaller number or larger steps compared to the Direct algorithm. Since the perturbation passes require some time, it is difficult to predict if the Newton’s method or the Direct method is best for a given problem. In general, the Newton’s method appears to give the best performance with polymerization kinetics, but it is a good idea to try using each algorithm with both dynamic and static scaling to determine the best combination of convergence parameters for a particular problem.

The corrector tolerance is set as a ratio from the integration tolerance (Corr-Tol-Ratio). By default, the corrector tolerance is ten times tighter than the integration tolerance (the corrector tolerance ratio is 0.1). For some problems, especially those involving reactors with heat transfer calculations, the optimal corrector tolerance ratio may be higher than 0.1, but this ratio should not be set larger than 1.0. The flash tolerance should be tighter than the corrector tolerance. Otherwise, round-off errors in the flash calculations make the corrector tolerance difficult to achieve. The model always uses the smaller of the specified RPlug flash tolerance (in the convergence form) or the global flash tolerance.

Other Integration Parameters

By default, the initial step size in RPlug is set to one percent of the reactor length (Hinit=0.01). If the solver cannot converge the equations with this step size, it will cut the step size by a factor of ten. This process will repeat up to six times. If the solver still cannot converge, the reactor calculation fails with an error message “solver cannot converge with minimum step size”.

Frequently, reaction rates or heat transfer rates are much faster near the entrance of the reactor than at the exit of a reactor due to step changes in temperature or pressure or due to the high concentrations of reactants at the inlet of the reactor. For these types of problems, the minimum step size may


need to be reduced. For step-growth kinetics, try using an initial step size of

1 10-4× . Smaller initial step-sizes may be required for addition kinetics, especially if quasi-steady-state approximations are not applied.

The maximum number of integration steps defaults to 1000. For very “stiff” kinetics, e.g., kinetics with fast reaction rates involving trace components, the maximum number of steps may need to be increased, especially if the corrector is using direct substitution. If more than 5000 steps are required, try changing the corrector method, scaling method, or increase the cutoff level.

RPlug stores many types of results at regular intervals (printing points). The number of intervals defaults to ten, but the number of print points can be increased to get smoother plots. Since the integration steps do not necessarily correspond to the print points, the model uses polynomial interpolation to determine the results for a print point based on the steps before and after this point. If the integration step sizes are very large, the interpolation algorithm may give strange results, such as sine waves. This problem can be fixed by reducing the maximum step size (Max-StepSize) to a value smaller than the increments between print points (this forces the model to use linear interpolation). By default, the maximum step size is much larger than the reactor length.

When hybrid scaling is used, the tolerance of the energy balance is controlled by the energy balance tolerance ratio.

Common Problems

The following table summarizes common problems encountered when using the RPlug unit operation block:

Problem Solution

Solver cannot converge for initial step

Try reducing the initial step size by orders of magnitude from the default (10-2 ) to 10-8 . If the problem persists, try increasing the cutoff parameter from 10-10 to 10-5 . If the problem still persists, verify the values and units of the rate constants in the kinetic model. Verify the heat-transfer coefficient if applicable. Verify the temperature, composition, and flow rates of the feed streams. Check the history file diagnostics for unusually high reaction rates.

Integration error: non-negativity violation.

This problem is usually related to infeasible reaction kinetics. If using a user kinetic routine, verify the code, otherwise, a zeroth-order reactant may be completely consumed. Check the history file diagnostics; look for the component flow rate or attribute element which has a value of zero and a negative rate of change.

Integration error: maximum number of steps is reached

Try increasing the cutoff parameter from 10-10 to 10-5 . If the problem persists, try different combinations of scaling method and corrector method. As a last resort, try increasing the number of steps to 5000. If the problem still continues, search for errors in the kinetics; check the diagnostics for unreasonable reaction rates.

Integration error: corrector tolerance cannot be achieved

Tighten the flash tolerance to a value below the corrector tolerance. Loosen the integration tolerance to 1 10-3× . Increase the corrector tolerance ratio to 0.2, 0.3, 0.5. If the problem continues, verify the kinetics and heat-transfer parameters. Check history diagnostics.

Flash failures appear during the integration

This may be a physical property problem; it may reflect overly-tight flash tolerances, loosen the local and/or global flash tolerance levels or increase the maximum number of flash iterations.



Check the molecular weights of each reactant and product. Verify that reaction stoichiometry is correct.

RBatch RBatch is a rigorous model for batch and semi-batch reactors. Any number of continuous feed streams can be specified in addition to a batch charge stream. Optionally, a vapor vent may be considered. The RBatch model does not have a vent condenser option; Aspen Custom Modeler is required to rigorously model batch polymerization reactors with vent condensers or overhead columns.

The RBatch model assumes feed and product accumulator holding tanks with continuous outlets. The accumulator concept provides a bridge between the continuous steady-state modeling environment in Aspen Plus and the inherently dynamic nature of batch reactors. The conversion between continuous streams and discreet charges and dynamic product accumulations is controlled by specified cycle times and continuous feed stream profiles specified in the reactor.

Temperature RBatch allows many options for specifying the reactor duty or temperature, as summarized here:


T-SPEC Reactor temperature The model reports the temperature profile, and the instantaneous and cumulative duty profiles.

T-PROFILE Reactor temperature as a function of time. Linear interpolation is used to determine temperatures between specified points.

The model reports the temperature profile, and the instantaneous and cumulative duty profiles.

T-COOL-SPEC Heat media stream temperature.

Overall heat-transfer coefficient.

Heat exchange surface area.

The temperature of the reactor is determined from the energy balance at each time step. The model reports the temperature profile, and the instantaneous and cumulative duty profiles.

DUTY-SPEC Instantaneous heat duty (assumed constant for entire cycle). Set the duty to zero to model an adiabatic reactor.

The temperature of the reactor is determined from the energy balance at each time step. The model reports the temperature profile.

DUTY-PROFILE Instantaneous heat duty as function of time. Linear interpolation is used to determine duty between specified points.

The temperature of the reactor is determined from the energy balance at each time step. The model reports the temperature profile, and the instantaneous and cumulative duty profiles.


USER-DUTY Heat transfer subroutine name The user routine returns the instantaneous heat duty at each time step. The temperature of the reactor is determined from the energy. The model reports the temperature profile, and the instantaneous and cumulative duty profiles.

The temperature or duty can be specified as a time-varying function. Heat transfer can be accounted for by assuming a constant coolant temperature, heat transfer area, and heat transfer coefficient, or by writing a Fortran routine that returns the instantaneous duty at each time step.

If the temperature or temperature profile is specified, RBatch assumes a temperature controller. If the reactor is single-phase, or if the reactor volume is specified, the model assumes perfect temperature control, otherwise, the model uses a proportional-integral-derivative (PID) controller equation to represent a temperature controller:

( ) ( ) ( )Q M K T T

KI

T T dt KDd T T

dtt treactor

t ts

t ts t t

st

= − + − +−⎡

⎣⎢⎢

⎤

⎦⎥⎥

∫0

Where:

Qt = Instantaneous heat duty (J/sec)

Mtreactor = Mass in reactor at time t (kg)

Tt = Temperature in reactor at time t (K)

Tts = Temperature setpoint at time t (K)

t = Time (sec)

K = Proportional gain (J/kg-K)

I = Integral time (sec)

D = Derivative time (sec)

By default, the proportional gain is 2500 J/kg-K, which results in very tight control at the expense of excessive simulation time. The speed of the model can be increased by reducing the gain (try a value of 25 J/kg-K).

Pressure If the reactor volume is not specified, the RBatch model assumes the reactor operates as a closed system with a variable volume. The pressure at the reactor is specified as constant value or as a time-varying profile.

If the reactor volume is specified, and there is a vent stream attached to the reactor, the flow rate of the vent stream is determined from the specified pressure or pressure profile. The vent flow is positive when the calculated reactor pressure exceeds the specified reactor pressure.


If the reactor volume is specified, there is no vent stream attached to the reactor, and the pressure profile is not specified, then the pressure is determined by the temperature and molar volume of the material inside the reactor.

If the reactor volume is controlled, a pressure controller model can be linked to a continuous feed stream. The flow rate of the feed stream is adjusted to maintain a constant pressure inside the vessel. The continuous feed stream flow rate can decrease to zero, but it cannot reverse direction if the pressure exceeds the specified setpoint. The model uses a proportional-integral-derivative (PID) controller equation to represent the pressure controller:

( ) ( ) ( )F K P P

KI

P P dt KDd P P

dtt t ts

t ts

tt t

s

= − + − +−⎡

⎣⎢⎢

⎤

⎦⎥⎥

∫0

Where:

Ft = Instantaneous flow rate (kmol/sec)

Pt = Pressure in reactor at time t (Pa)

Pts = Pressure setpoint at time t (Pa)

t = Time (sec)

K = Proportional gain (kmol/sec)/Pa

I = Integral time (sec)

D = Derivative time (sec)

Reactor Volume If the reactor pressure is not specified, then RBatch will predict the reactor pressure based on a specified reactor volume. The pressure will be manipulated by a trial-and-error algorithm to satisfy the specified volume.

If pressure and volume are both specified, you must either attach a vent stream to the reactor or attach a continuous make-up stream and pressure controller to the reactor.

Residence Time The residence time of the reactor is controlled by user-specified stop criteria. You can specify whether RBatch should halt the reaction when the stop criterion variable is approached from above or below. If several stop criteria are specified, RBatch stops at the first stop criteria it reaches.

In addition to stop criteria, you must specify a maximum time for the reactor. This prevents runaway calculations in the event that none of the stop criteria are feasible.

The stop criteria may include one or more of the following:

• A maximum reaction time

• A maximum or minimum component mole or mass fraction in the reactor


• The amount of material (mass, moles, or volume) in the reactor or vent accumulator

• A maximum vent flow rate

• A maximum or minimum reactor temperature, pressure, or vapor fraction

• The value of a Prop-Set property (includes user Prop-Set properties or system properties such as viscosity, etc.)

Batch Operations RBatch can represent batch or semi-batch reactors, depending on what streams are connected to it in the flowsheet. If a vent stream or time-varying continuous feed stream is connected to the RBatch block, then the model operates in semi-batch mode.

The batch reactor model is interfaced into the Aspen Plus continuous flow, steady-state modeling environment through the concept of holding tanks, as shown here:

The holding tanks convert the:

• Continuous batch charge stream to a discreet batch charge

• Final vent accumulator inventory to a continuous, time-averaged vent stream

• Final reactor inventory to a continuous, time-averaged reactor product stream

Four types of streams are associated with RBatch:

• Continuous Batch Charge

• Time-Varying Continuous Feed

• Time-averaged Continuous Reactor Product

• Time-averaged Continuous Vent Product

Continuous Batch Charge: The material transferred to the reactor at the start of the cycle. The mass of the batch charge equals the flow rate of the batch charge stream, multiplied by the batch cycle time. The mass of the


batch charge is equivalent to accumulating the batch charge stream in a holding tank during a reactor cycle. The contents of the batch charge holding tank are instantaneously transferred to the reactor at the start of each batch cycle.

Time-Varying Continuous Feed: Streams that are fed to the reactor over some discreet interval during the batch cycle. The composition, temperature, pressure, component attribute values, and time-averaged flow rate of the stream are specified in the flowsheet. The flow rate of the continuous feed streams can be specified as a constant value, a time-varying profile, or manipulated by the pressure controller model to meet a time-varying pressure setpoint.

Time-averaged Continuous Reactor Product: This stream is determined by dividing the final reactor inventory by the cycle time. This is analogous to instantaneously dumping the reactor contents to a large holding tank at the end of the cycle, and continuously draining the tank throughout each cycle.

Time-averaged Continuous Vent Product: This stream is determined by dividing the final vent accumulator inventory by the cycle time. During the batch cycle, the time-varying continuous vent stream is accumulated in the vent accumulator. The model assumes the vent accumulator contents are instantly drained to a large holding tank at the end of the cycle, and the holding tank contents are continuously removed throughout the cycle.

Cycle Time RBatch is a dynamic batch reactor model that is interfaced into the Aspen Plus continuous steady-state modeling environment. The interface requires converting batch charges and accumulator inventories into continuous stream flow rates. The cycle time is used to convert the batch charge flow rate into the initial reactor inventory. The cycle time is also used to convert the vent accumulator inventory and the reactor inventory into vent and reactor product streams.

For example, assuming a reactor has a cycle time of two hours and that no continuous feed streams are specified, then:

• If the batch charge stream is set to 50 kg/hour, the initial reactor inventory is 100 kg.

• If at the end of the reaction cycle, the vent accumulator contains 30 kg of material, the time-averaged continuous vent stream flow rate is 15 kg/hr. The composition of the time-averaged vent stream will be the same as the final composition in the vent accumulator.

• The final reactor inventory will be 70 kg, and the time-averaged reactor product flow rate will be 35 kg/hr.

RBatch allows you to specify a feed time and down time instead of the cycle time. In this case, the time-averaged batch charge stream is divided by the feed time to calculate the initial batch inventory. The time-averaged product flow rates are based on the cycle time, which is calculated from the sum of the feed time, the down time, and the reaction time. This option is not recommended unless it is used to correct the mass balance for the influence of time-varying continuous feed streams.


Troubleshooting Convergence Problems To diagnose numerical problems in RBatch, set the terminal reporting level to “7” in the Block-Options form. With this setting, RBatch reports the time (in seconds), pressure (in Pascal), temperature (in K), and vapor mole fraction at each converged integration step.

The Simulation diagnostic reporting level controls the diagnostic messages written to the history file (.HIS file). The maximum mass-balance error is reported at level 5. At level 6, the model reports reacting component flow rates and component attribute values. At level 7, the model also reports the rates of change of these variables. At level 8, the model reports initial scale factors for all integrated variables.

First, simplify the problem by specifying temperature instead of duty or heat-transfer parameters (coolant temperature, U, or heat transfer subroutine). Specify the reactor as “liquid-only”. Specify the reactor pressure, but not the reactor volume. This will eliminate many possible sources of error and help focus the problem on kinetics and integration parameters. Once the model works with these settings, then revert the settings to duty, volume, and so on, making sure the model converges with each new specification.

Scaling Factors

RBatch uses Gear’s variable-step-size algorithm to numerically integrate the mass, energy, and attribute conservation equations for the reactor and the mass-balance equations for the vent condenser (if applicable). At each time step, the conservation equations are solved by a trial-and-error technique.

RBatch solves the conservation equations using scaling factors to normalize the variables. The values of these scaling factors have a strong influence on the speed and reliability of the integration.

The Gear integrator in Aspen Plus offers three error scaling options (ERR-METHOD):

• Static scaling

• Dynamic scaling

• Hybrid scaling

The RBatch static and dynamic scaling factors are summarized here:


Enthalpy 105 (SI units) x mass holdup Enthalpy at previous time step

Component Mass Inventory In Reactor and Vent Accumulator

The scaling factor for each component inventory equation is set to:

0.1 * (mass of batch charge stream)


The scaling factor at t = t + Δt is set to the larger of:

Component mass flow at t

Cutoff


Class 2 Attribute Inventory in Reactor and Vent Accumulator

The scaling factor of each component attribute is set to:

(Attribute scaling factor from the TBS table) x (cycle time) (this is the attribute inventory at time = 0)


The scaling factor at t = t + Δt is set to the larger of:

Attribute inventory at time = t

Cutoff



The static scaling method uses a constant set of scaling factors throughout the reactor. The dynamic scaling method updates the scaling factors based on the previously converged step. The “cutoff” parameter is the minimum scaling factor used in dynamic scaling.

The static scaling method may result in faster integration for many types of problems, but there are potential numerical problems when using this method. Consider an irreversible reaction “A B” in a plug-flow reactor in which component “B” is not present in the feed. The scaling factor for component “A” will be set very large and the scaling factor for “B” will be set to the minimum scaling factor. This will result in relatively loose tolerance for the mass balance in “A” and tight tolerance for the mass balance in “B”. Further, as the reaction approaches completion the component “B” has a large flow rate but a small scaling factor. This makes the conservation equation for “B” difficult to solve, which will result in small integration steps.

The hybrid option uses static scaling for all variables except enthalpy, which is scaled dynamically. This option may be the best choice when the stream

enthalpy is far from the default scale factor, 510 .

Consider the same situation with dynamic scaling. The initial scaling factors are the same as the static case. With each new step, however, the scaling factors are updated to the variable values from the previous step. This keeps the scaled variables close to unity throughout the integration. For example:

One pitfall of dynamic scaling, however, occurs when a variable value decreases and approaches zero. As the value and the scaling factor get progressively smaller, small absolute errors become large scaled errors. This also makes the solution difficult, and leads to small steps in the integrator. This problem can be controlled by setting the minimum scaling factor (cutoff

in the convergence form) to a reasonable value. The default value, 10-10 is much too small for most problems. A value of 10-5 is reasonable for most situations, and results in better model performance.

In general, the dynamic scaling method results in tighter convergence, but it requires more simulation time than the static scaling method. This does not


apply to every case, however, and it may also depend on the solver algorithm. It is a good idea to experiment with these parameters to find the most reliable convergence strategy for each reactor in each model. When component attributes are present, as in polymerization kinetics, dynamic scaling is used by default.

Solver Method

At each step during the integration, the energy, mass, and attribute conservation equations are solved by trial-and-error. Two “corrector” algorithms, direct substitution and Newton’s method, can be selected. The Newton algorithm perturbs each variable to determine the slope, resulting in a smaller number or larger steps compared to the Direct algorithm. Since the perturbation passes require some time, it is difficult to predict if Newton’s method or the Direct method is best for a given problem. In general, Newton’s method appears to give the best performance with polymerization kinetics, but it is a good idea to try using each algorithm with both dynamic and static scaling to determine the best combination of convergence parameters for a particular problem.

The corrector tolerance is set as a ratio from the integration tolerance (Corr-Tol-Ratio). By default, the corrector tolerance is ten times tighter than the integration tolerance (the corrector tolerance ratio is 0.1). For some problems, especially those involving reactors with heat transfer calculations, the optimal corrector tolerance ratio may be higher than 0.1, but this ratio should not be set larger than 1.0. The flash tolerance should be tighter than the corrector tolerance. Otherwise, round-off errors in the flash calculations make the corrector tolerance difficult to achieve. The model always uses the smaller of the specified RPlug flash tolerance (in the convergence form) or the global flash tolerance.

Other Integration Parameters

By default, the initial step size in RBatch is set to one tenth of a second (Hinit=0.1). If the solver cannot converge the equations with this step size, it will cut the step size by a factor of ten. This process will repeat up to six times. If the solver still cannot converge, the reactor fails with an error message “solver cannot converge with minimum step size”.

Frequently, initial reaction rates or heat transfer rates are very fast, so the minimum step size may need to be reduced. For step-growth kinetics, the default value should be sufficient. Smaller initial step-sizes may be required for addition kinetics, especially if quasi-steady-state approximations are not applied.

The maximum number of integration steps defaults to 1000. For very “stiff” kinetics, e.g., kinetics with fast reaction rates involving trace components, the maximum number of steps may need to be increased, especially if the corrector is using direct substitution. If more than 5000 steps are required, try changing the corrector method, scaling method, or increase the cutoff level.

RBatch stores many types of results at regular intervals (printing points). The number of intervals depends on the reaction time. Since the integration steps do not necessarily correspond to the print points, the model uses polynomial interpolation to determine the results for a print point based on the steps before and after this point. If the integration step sizes are very large, the


interpolation algorithm may give strange results, such as sine waves. This problem can be fixed by reducing the maximum step size (Max-StepSize) to a value smaller than the increments between print points (this forces the model to use linear interpolation). By default, no maximum step size is enforced.

RBatch has the option to stop exactly at print points and vent accumulator points instead of interpolating these points. When the “exact” option is set to “yes”, the model adjusts the integration steps to exactly match these points. This requires extra steps in the integrator that may slow down the model, but it results in more accurate simulations.

When hybrid scaling is used, the tolerance of the energy balance is controlled by the energy balance tolerance ratio.

Common Problems

The following table summarizes common problems encountered when using RBatch:

Problem Solution

Solver cannot converge for initial step

Try reducing the initial step size by orders of magnitude from the default (10-1 ) to 10-8 . If the problem persists, try increasing the cutoff parameter from 10-10 to 10-5 . If the problem still persists, verify the values and units of the rate constants in the kinetic model. Verify the heat-transfer coefficient if applicable. Verify the temperature, composition, and flow rates of the feed streams. Check the history file diagnostics for unusually high reaction rates.

Integration error: non-negativity violation.

This problem is usually related to infeasible reaction kinetics. If using a user kinetic routine, verify the code, otherwise, a zeroth-order reactant may be completely consumed. Check the history file diagnostics; look for the component flow rate or attribute element that has a value of zero and a negative rate of change.

Integration error: maximum number of steps is reached

Try increasing the cutoff parameter from 10-10 to 10-5 . If the problem persists, try different combinations of scaling method and corrector method. As a last resort, try increasing the number of steps to 5000. If the problem still continues, search for errors in the kinetics; check the diagnostics for unreasonable reaction rates.

Integration error: corrector tolerance cannot be achieved

Tighten the flash tolerance to a value below the corrector tolerance. Loosen the integration tolerance to 1 10-3× . Increase the corrector tolerance ratio to 0.2, 0.3, 0.5. If the problem continues, verify the kinetics and heat-transfer parameters. Check history diagnostics.

Flash failures appear during the integration

This may be a physical property problem; it may reflect overly-tight flash tolerances, loosen the local and/or global flash tolerance levels or increase the maximum number of flash iterations.


Set the cycle time instead of the feed time.

Check the molecular weights of each reactant and product.

Verify that reaction stoichiometry is correct.


Treatment of Component Attributes in Unit Operation Models As described in previous chapters, Aspen Polymers includes two classes of component attributes. Class-2 attributes are “primary conserved quantities” and always have flow-type units (attribute value / unit time). These attributes include the zeroth moment of the polymer (polymer molecule flow rate), the segment flow rates, etc. Class-0 attributes are secondary quantities that can be derived from the primary quantities.

The class-2 attributes follow flow-based mixing rules. In other words, if two streams are mixed, the product stream class-2 attributes are equal to the sum of the feed stream class-2 attributes. These mixing rules apply to each unit operation that allows multiple feeds of the same type (for example, multiple process fluid feeds). In the distillation models, these mixing rules apply on a tray-by-tray basis (e.g., if two or more feed streams enter the same tray).

The blocks with more than one outlet (Flash2, Flash3, Sep, etc.) assume that the class 2 polymer attributes split according to mass mixing rules. For example, if 90% of the mass of the polymer flows to the liquid phase, then 90% of the polymer molecules also flow with the liquid phase. This approach is identical to assuming that the properties of the polymer, such as the molecular weight distribution, are not fractionated in any way; instead, the molecular weight distribution of each polymer component in each of the product phases is identical to that of the polymer in the feed stream.

The following table summarizes the attribute handling for the different models:

Block Component Attribute Handling

Basic Unit Operation Models

Dupl All attributes in feed stream are copied to each outlet stream.

FSplit

SSplit

Sep

Sep2

Class 2 attributes divide in proportion to flow rate of attributed component. Class 0 attributes are recalculated for each outlet stream.

Equation to calculate outlet stream attributes: AFF

Aoutout

inin=

F = Flow rate of attributed component (in = mixed feed, out = outlet)

A = Class-2 component attribute value (in = mixed feed, out = outlet)



Flash2

Flash3

Class 2 attributes divide in proportion to flow rate of attributed component. Class 0 attributes are recalculated for each outlet stream.

Polymer components are not fractionated by the phase equilibrium models used by these blocks.


Aoutout

inin=



When multiple substreams exist, the model distributes polymer attributes between substreams using the same rule.

Mult Class 2 attributes multiply in proportion to flow rate of attributed component. Class 0 attributes are recalculated for each outlet stream.


Aoutout

inin=



Mixer

Heater*

Class 2 attributes are summed across all feed streams. Class 0 attributes are recalculated for the outlet stream.

Equation to calculate outlet stream attributes: A Aout infeeds

= ∑


Distillation Models


RadFrac Component attribute conservation equations are included in this model at the tray-by-tray level. The class-2 attributes are calculated at each tray by the following equation:

AFF

Aoutout

inin=

F = Flow rate of attributed component (in = mixed feed to tray, out = outlet from tray)

A = Class-2 component attribute value (in = mixed feed to tray, out = outlet from tray)

The RadFrac model does not allow polymer reaction kinetics.

MultiFrac / BatchFrac

These unit operation blocks do not consider component attributes. Polymers must be converted to oligomer components if polymer fractionation is to be considered in these models.

Reactor Models

RStoic

RYield

If user specified attributes in the COMP-ATTR form, they are used for the product stream. Otherwise, class 2 attributes divide in proportion to the flow rate of the attributed component. Class 0 attributes are recalculated for each outlet stream.


Aoutout

inin=





RGibbs

REquil

Polymer and heterogeneous catalyst components may not participate in the reactions in these blocks. The class 2 attributes divide in proportion to the flow rate of the attributed component. Class 0 attributes are recalculated for each outlet stream.


Aoutout

inin=



RCSTR

RPlug

RBatch

When using Aspen Polymers reaction kinetics, these models calculate the class-2 component attributes using standard conservation equations. These models can be used with a user-written Fortran subroutine through the “USER” reaction option. If the user kinetics include component attributes, then the “COMP-ATTR” field in the user kinetics form of the reactor model must be set to “yes”. In RCSTR, initial guesses for the outlet attribute values can be specified in the COMP-ATTR form.

* This also applies to any block that allows multiple feed streams and uses an “implied” mixer to

calculate the net feed stream.

References Chan, W.-M., Gloor, P. E., & Hamielec, A. E. (1993). A Kinetic Model for Olefin Polymerization in High-Pressure Autoclave Reactors. AIChE J., 39, No. 1.

Chaudhari, R. V., & Shah, Y. T. (1986). Recent Advances in Slurry Reactors, Concepts and Design of Chemical Reactors. S.A. Whitaker & A. Cassano (Eds.). Switzerland: Gordon and Breach Science Publishers.

Henderson, J. N., & Bouton, T. C. (Eds.). (1979). Polymerization Reactors and Processes. ACS Symp. Ser.

Rodriguez, F. (1996). Principles of Polymer Systems. New York: Taylor & Francis.

Trambouze, P., van Landeghem, H., & Wauquier, J. P. (1988). Chemical Reactors: Design/Engineering/Operation. Paris: Editions Technips.

Walas, S. M. (1988). Chemical Process Equipment Selection and Design. Boston: Butterworths.

16 Plant Data Fitting 331

16 Plant Data Fitting

Aspen Polymers (formerly known as Aspen Polymers Plus) simulation models can be fit to plant or laboratory data using Data-Fit. One or more sets of measured data are provided which may include model inputs or results. Data-Fit adjusts or estimates input parameters to find the best match between the model predictions and data. Data-Fit can also reconcile measured data against the model.

Data-Fit minimizes the weighted sum of square errors, where each error is the difference between a reconciled input or calculated output and the data. In statistical terms, Data-Fit performs either ordinary least squares or maximum likelihood (errors-in-variables) estimation.


• Data Fitting Applications, 331

• Data Fitting For Polymer Models, 332

• Steps for Using the Data Regression Tool, 336 (including troubleshooting tips)

This section emphasizes using the Data-Fit tool to fit process reaction kinetic parameters. A more general description of this tool is available in the Aspen Plus User Guide.

Data Fitting Applications The data regression tool in Aspen Plus can be used to fit model parameters and reconcile process data. These applications may be carried out simultaneously.

Parameter regression usually involves adjusting model parameters to improve the agreement between model predictions and process data. For example, reaction rate constants may be manipulated to match the measured polymer molecular weight and monomer conversion. Manipulated parameters may include reaction rate or equilibrium constants, physical property constants, or equipment specifications. Fitted parameters may include model predictions such as reactant conversion, product yield, by-product content, polymer component attributes, stream compositions or flow rates, or equipment heat duty, temperature, pressure, or holdup.

332 16 Plant Data Fitting

Data reconciliation runs involve manipulating one or more sets of model inputs to match model predictions to process data. For example, the average feed rate of a makeup stream can be estimated based on the flow rate and composition of the feed and product streams. Manipulated data typically includes feed stream flow rates and compositions, equipment operating conditions, heat transfer coefficients, etc.

The Data-Fit model can be used to reconcile input data and fit model parameters simultaneously. Simultaneous regression and reconciliation is typically used to fine-tune models which already match process data and trends relatively well.

Data Fitting For Polymer Models Polymer process models frequently include non-ideal phase equilibrium, reaction kinetics, and complicated unit operations. Fitting these complex models against process and laboratory data is not a trivial task. A great deal of consideration must be given to the way this problem is approached.

A detailed example describing how to fit a free-radical reaction kinetics problem is included in the Aspen Polymers Examples & Applications Case Book.

A general procedure for fitting complex models is given below.

Step 1. Process Data Review

Collect data for the process. Sources of data include process information management system (PIMS), process design documents (PDDs), process flow diagrams (PFDs). Verify reproducibility / standard deviations of data by collecting multiple data sets for each case. Verify steady state by collecting data at regular intervals over several plant residence times. Verify data feasibility against mass and energy balance calculations.

Step 2. Literature Search

Collect information about the process. Sources of data include in-house lab data, databanks, trade journals, conference notes, polymer handbooks, on-line electronic databases, experimental designs, etc.

Step 3. Preliminary Model Fitting

Carry out physical property data regression, property constant parameter estimation runs. Test the parameters against all pertinent data from steps 1 and 2. To the extent possible, verify pure component physical properties and phase equilibrium predictions using Property Analysis tools.

Step 4. Preliminary Model Development

Develop a basic model of the process, ignoring details such as non-ideal mixing, heat transfer, etc. Specify temperature instead of duty, volume instead of residence time. Use parameters from steps 1-3.

Step 5. Trend Analysis


Use the sensitivity feature to evaluate trends between model outputs (conversion, polymer attributes, etc.) and model inputs (rate constants, operating conditions, etc.) Compare the predicted trends against available process or lab data. If the trends are not well matched, adjust specific model parameters to improve the predicted trend. Model fitting may be carried out using Sensitivity, Design-Specification, Data-Fit, or by trial and error.

Step 6. Model Refinement

Use the Data-Fit tool to carry out simultaneous parameter estimation and data reconciliation. Relax model assumptions, such as perfect mixing, as needed. Bring model up to the appropriate level of detail, fitting key parameters at each development step.

Data Collection and Verification The first step in fitting a model is to collect and review data. Sources of data may include process information management system (PIMS), process design documents (PDDs), and process flow diagrams (PFDs), shift log sheets, and laboratory analysis reports. It is important to verify the reproducibility of the data by collecting several duplicate sets of each datum. Duplicate data are especially important for analytical measurements such as melt flow index and intrinsic viscosity.

For continuous processes, it is a good idea to verify that the process operates under steady-state conditions by collecting data at regular intervals. The data should be collected at regular intervals over a period that exceeds the cumulative residence time of the key unit operations in the process.

Verify data feasibility against mass and energy balance calculations. It is impossible to force a rigorous model to match data that violates the fundamental conservation equations.

When possible, obtain calibration data for unit operating conditions, especially level calibration data for reactors and flow rate calibration data for flow meters. The method and assumptions used to calibrate these instruments must be taken into consideration for data reconciliation runs.

Literature Review Before you regress process data, it is a good idea to collect information about the process. Sources of data include in-house lab data, databanks, trade journals, conference notes, polymer handbooks, on-line electronic databases, experimental designs, and so on.

The open and in-house process literature may contain a wealth of information about key model parameters. Further, these sources may provide additional sources of fundamental data which can be used to independently evaluate model parameters.

Simulation studies described in trade journals are an excellent source of insight and know-how related to model development. These studies frequently point out which assumptions are valid and which parameters are important. In addition, these papers may elucidate reaction mechanisms or physical phenomena that should be considered in a rigorous process model.


The physical property and rate constant data reported in the open literature are never perfect, but they do serve as a good starting point for fitting the model.

Preliminary Parameter Fitting It is important to determine as many of the model parameters as possible early in the model development process. Try to decouple the parameters from each other whenever possible. For example, find ways to establish phase equilibrium parameters independently of reaction equilibrium constants. Make simplifying assumptions to reduce the number of unknown parameters.

Physical property parameters should be firmly established before fitting rate constants. When data are available, use the physical property data regression system (DRS) to fit the density, enthalpy, heat capacity, and vapor pressure of pure components. If phase equilibrium data are available, use DRS to regress phase equilibrium parameters.

When property data are unavailable for a component, the property constant estimation system (PCES) can be used to estimate property parameters from molecular structure. These estimations, however, should be checked against process data. If data are available for components with similar structures, they can be used to estimate the properties of components that are not found in the databank.

The following table lists some of the key physical property parameters in Aspen Polymers and describes how they influence polymerization kinetics:

Property Parameters Influence on Polymerization Reaction Kinetics

Density DNLRKT, DNLVK

Concentration is proportional to density. Reaction kinetics depend on component concentrations.

Vapor pressure

PLXANT, HENRY

The vapor pressure controls phase equilibrium of volatile components in vapor-liquid systems. The phase equilibrium strongly influences concentrations, which controls kinetics.

Enthalpy DHFORM, DHFVK, DHFVKM, DHSUB, DHCON, DHFMDP

The component enthalpies influence the predicted heat duties and temperatures in the model.

Heat capacity

CPIG, CPL, CPLVK, CPCVK

The heat capacity controls the influence of temperature on enthalpy.

Transition temperatures

TMVK, TGVK Phase transitions occur at the melting point and glass point. Predicted enthalpy, density, and heat capacity for polymer and oligomer components depend on the phase regime.

Phase equilibrium

In multiphase reactors the phase equilibrium determines the component concentrations in each phase, which influences the reaction rates.

Solubility (of a solid)

K-SALT The solubility parameter influences the concentration of partially soluble solids in the liquid phase. When catalysts, inhibitors, or monomers are fed as solids, this parameter


controls their concentration, which in turn controls their reaction rate.

If reaction kinetic parameters are unavailable from in-house or open literature, it may be necessary to carry out experiments to determine the magnitude of the rate constants. Carry out the reactions under controlled conditions to isolate the influence of reaction kinetics from phase equilibrium, mass transfer, heat transfer, etc. For example, carry out the experiments in sealed tubes so the liquid phase concentrations are unaffected by phase equilibrium.

Reaction experiments should be performed over a range of temperatures to allow determination of the activation energies.

Preliminary Model Development Once the preliminary parameter fitting is complete, these parameters can be used to develop a preliminary model. At this stage of the model development process, it may be best to use simplified models for some of the ancillary operations that are not directly involved in the polymerization reactors. For example, it may be more convenient to represent distillation columns using the non-predictive Sep or Sep2 models instead of the RadFrac or MultiFrac rigorous distillation models.

The most important rule for model development is to “keep it simple”. Model development must be carried out in several stages. Add detail to the model one step at a time. Each generation of the model can yield valuable insights into the process and can provide substantial benefit to the model developer. At each stage in the process, fit the appropriate model parameters and validate the model against all sources of available data. Verify the predicted trends against process data, operator experience, and engineering know-how. Over time, the level of detail and power of the model can be increased.

During the preliminary development, use the most basic specifications possible. For example, in the RCSTR model specify temperature and reacting phase volume instead of duty and residence time. This approach will make the model run faster and will help to isolate the influence of property parameters from reaction kinetic parameters.

Once the preliminary model is complete, it can be tested against process data. Major discrepancies between the data and the model predictions should be addressed during this step.

Trend Analysis Use the preliminary model to carry out trend evaluation studies. The sensitivity feature can be used to examine the influence of process variables on the model predictions. Compare these trends against process data. If the predicted trends are not consistent, adjust the appropriate model parameters to improve the match. For example, if the predicted slope of the monomer conversion versus temperature curve is less than the measured slope, the activation energy of the polymerization reaction may be too low.

Use the sensitivity tool to examine the influence of the model parameters on the model predictions and to determine which parameters are important in


the model. Parametric studies can be carried out by manipulating two or more variables in a sensitivity study.

It is good practice to include as many model predictions as possible in each sensitivity study. The simulation runs take the same amount of time regardless of the number of defined variables. It is much easier to understand the predicted trends when the sensitivity results are detailed.

Once you know which parameters are critical to the model predictions, the data regression tool can be used to adjust these parameters to match specific trends. Keep the number of manipulated parameters to a minimum until all of the key parameters are established independently.

Model Refinement The Data-Fit tool is the best choice for refining the fit between the model predictions and the process data, especially when several sets of data are available. Data-Fit can adjust several model parameters simultaneously, capturing subtle interactions among the parameters to get the best overall match between the process data and model predictions.

When the model predictions cannot match the process data, the assumptions in the model may be too broad. Perhaps the process is limited by heat- or mass-transfer, or a reactor is not ideally mixed. Maybe there are additional side reactions that should be considered in the model, or the rate expression needs to be modified to account for some unusual aspect of reaction kinetics. These issues can be addressed during the model refinement process by adding new layers of detail to the model. Avoid adding more detail than necessary, however, because model fitting is a process of diminishing returns.

Model refinement is an open-ended process. The model parameters can be tuned more accurately as more data become available from the process. Bad data points are easier to spot when there are more sets of data to compare.

It is impossible for a simulation model to match process data perfectly. There are several sources of error that lead to differences between the model results and process data, including:

• Variations in process operating conditions due to disturbances, excursions from steady state, control system actions, etc.

• Imperfect calibration of flow meters, level controllers, etc.

• Analytical error in lab measurements

• Simplifications and assumptions in the model, such as ideal mixing, isothermal and isobaric vessels, phase equilibrium, etc.

• Errors in the model parameters.

Steps for Using the Data Regression Tool There are three steps involved in using the data regression tool:

• Creating a base-case model


• Entering lab or process data and operating conditions into data sets

• Defining regression cases

Step 1. Creating a base-case model

If the regression tool is being used to fit reaction kinetic parameters from lab batch reactor data, use the RBatch model with an appropriate reaction kinetic model.

If the model parameters are being regressed from process data, develop a model of the process. Before setting up the data fit run, make sure the model predictions are reasonable and that the model is robust (converges without errors) over the ranges of each manipulated parameter. You can use sensitivity blocks to screen the model for accuracy and to test how robust the model is.

The rate constants and property parameters entered into the base case model become the initial estimates for the regression.

Step 2. Entering lab or process data and operating conditions into data sets

There are two types of data sets used with the regression tool, “Point-Data” and “Profile-Data”:

Use To specify

Point-Data Operating conditions for steady-state unit operation models.

Feed streams for continuous processes or batch charge streams.

Analytical data, measured flow rates, or composition data for product streams.

Polymer or catalyst component attribute data for product streams.

Profile-Data Operating profiles for batch reactors or plug-flow reactors, including temperature, pressure, and duty profiles, continuous feed stream profiles, etc.

Time-series measured data for a batch reactor or data along the axial profile of a plug-flow reactor.

Note: Component attribute profiles and user variable profiles are not available as profile data in this release of Aspen Polymers. To fit profile data for these types of variables, treat each data point in the profile as a point datum, and specify the coinciding stop-time (RBatch) or length (RPlug) of the reactor as another point datum in the same data set.

Step 3. Defining regression cases

For each case, specify the parameters to be adjusted and the data sets to be fitted. Several regression cases can be included in the same simulation run. The cases are run sequentially; a prompt will appear on the screen that lets you specify which cases to include in the run, and the sequence order of the cases. Each successive case uses the fitted parameters and reconciled data from the previous case. If the data regression is run again, the previously fit values are used as initial estimates unless the simulation is reinitialized.


Identifying Flowsheet Variables You must identify each measured and manipulated variable considered in the regression. Most types of variables, such as stream flow rates, equipment operating conditions, and component attribute values can be accessed directly using the variable accessing system.

In the data regression and data set forms, you cannot access vector data, such as the stream vector and component attribute vector. You must access each stream variable or component attribute element as a separate scalar variable.

When specifying feed stream data, avoid using mole, mass, or volume fractions as variables in the data set. If the composition of the feed stream changes from one validation case to another, specify the flow rates of the components in the stream. If the composition is constant but the flow rate changes, specify the composition and base-case flow rate in the model, and specify the total stream flow rate as a point-data variable. This avoids problems with normalizing fractions and reduces the number of variables handled by the data-fit algorithm.

Some unit operation models have both input and results variables for the same operating condition. For example, in the RCSTR model you can access the specified heat duty (DUTY), or the calculated reactor duty (QCALC). If a variable is an INPUT variable in the regression it must be specified in the unit operation model.

For example, if the reactor duty is a manipulated INPUT variable in the regression, it must be specified as an input variable (DUTY), and the reactor duty must be specified in the reactor model. If the reactor duty is a measured RESULTS variable, it must be specified as a results variable (QCALC), and is usually not specified in the model (the temperature is specified instead).

The following table provides a cross-reference of commonly-used INPUT and RESULTS variables for key specifications related to several unit operation models:

Model Operating Condition Input Variable Results Variable

RBatch Cumulative reactor duty DUTY QCALC

RCSTR with one phase

Duty

Pressure

Temperature

Reactor volume

Reactor residence time

DUTY

PRES*

TEMP

VOL

RES-TIME

QCALC

use outlet stream pressure

TCALC

VOL-CALC

RT-CALC

RCSTR with multiple phases

Reacting phase volume REACT-VOL VOLL-CALC for liquid volume

VOLV-CALC for vapor volume

VOLLS-CALC for total liquid+solid volume

Reacting phase residence time

PH-RES-TIME VOLL-CALC for liquid residence time

RTV-CALC for vapor residence time

RTLS-CALC for liquid or solid residence time


Model Operating Condition Input Variable Results Variable

RPlug Duty

Pressure (process fluid)

Temperature (process fluid)

Residence time (process fluid)

DUTY

PRES* (feed)

SPEC-TEMP**

RES-TIME

QCALC

REAC-PRES**

REAC-TEMP**

RT-CALC (entire reactor)

REAC-RESTIM** (residence time at a profile point)

Flash2 and Flash3

Duty

Pressure

Temperature

DUTY

PRES*

TEMP

QCALC

use outlet stream pressure

use outlet stream temperature

RadFrac and MultiFrac

Condenser duty

Reboiler duty

Reflux ratio

Boilup ratio

Stage temperature

Stage pressure

Design specification setpoint

Q1

QN

basis-RR***

basis-BR***

STAGE-TEMP

STAGE-PRES

VALUE

COND-DUTY

REB-DUTY

RR

BR

TEMP

PRES

various - it depends on the specification

* The pressure variable is treated as a pressure drop if the specified value is non-

positive.

** Specify location (RPlug) or stage number (RadFrac / MulitFrac)

*** Basis can be MOLE, MASS, or STDVOL - the variable specified in the data set must match the variable specified in the column .

Some measured data, such as polymer melt index and intrinsic viscosity, are not predicted by the standard property sets in Aspen Polymers. The best way to include these properties in a data regression is to write a user Prop-Set property subroutine. Each user property can be linked to a property set. Property sets can be accessed as stream-property variables.

Manipulating Variables Indirectly In-line Fortran blocks can be used to enforce assumptions in the model or to manipulate variables indirectly. Using these techniques to reduce the number of manipulated variables can greatly enhance the speed and reliability of the regression.

Example 1: Using Fortran Blocks to Enforce Modeling Assumptions

Suppose:

• Your process involves a catalyst and an initiator.

• The key variables involved in the regression cases are the process operating conditions and the monomer feed rate. The catalyst and initiator flow rates are always proportional to the monomer feed rate.

Create a Fortran block and define the monomer, catalyst, and initiator flow rates as flowsheet variables. Specify the monomer flow rate as a “read


variables” and the catalyst and initiator flow rates as “write variables” as shown below:

FORTRAN SETCAT DEFINE FLOMON MASS-FLOW STREAM=FEED COMPONENT=MONOMER DEFINE FLOINI MASS-FLOW STREAM=ADDITIVE COMPONENT=PEROXIDE DEFINE FLOCAT MASS-FLOW STREAM=CATALYST COMPONENT=METAL READ-VARS FLOMON WRITE-VARS FLOINI FLOCAT C Specify the base-case flow rates in kg/hr below F BCMON = 1200.0 F BCCAT = 20.0 F BCINI = 5.0 C Calculate the flow rates of initiator and catalyst F FLOINI = FLOMON * BCINI / BCMON F FLOCAT = FLOMON * BCCAT / BCMON

Define the monomer flow rate as a variable in a point-data set. During the data regression run, the regression model will write the monomer flow rate for each case. The Fortran block will be executed each time the regression block manipulates the monomer flow rate. The Fortran block will read the new monomer flow rate, calculate the initiator and catalyst flow rates, and write their values.

Using this technique to indirectly manipulate the additive flow rates reduces the number of variables in the regression, making the regression faster and more reliable. The cost of this approach is that the indirectly manipulated variables (catalyst and initiator flow rates) cannot be reconciled (the model has no information regarding the standard deviations of these variables).

Example 2: Using Parameters and Fortran Blocks to Indirectly Manipulate Process Variables

Suppose:

• Your polymerization process uses two monomers.

• The key variables involved in the regression cases are the monomer ratio and the polymer production rate. You want to vary these parameters in the data regression.

In the base-case model, define the monomer ratio and production rate as “parameter” variables in a Fortran block. Specify the base-case monomer ratio and production rate in the same Fortran block. Specify this block to sequence “first”, as shown below:

FORTRAN INITIAL DEFINE RATIO PARAMETER 1 DEFINE PRODRT PARAMETER 2 SEQUENCE FIRST C specify monomer mole ratio F RATIO = 1.05 C specify polymer production rate, kg/hr F PRODRT = 2000.0

Create a second Fortran block. Define the monomer flow rates as flowsheet variables. Access the monomer mole ratio and production rate parameters. Specify the parameter variables as “read variables” and the monomer flow rate variables as “write variables”. After solving the algebra, the Fortran block can be defined as shown below:


FORTRAN ADJUST DEFINE RATIO PARAMETER 1 DEFINE PRODRT PARAMETER 2 DEFINE FLOM1 MOLE-FLOW STREAM=FEED COMPONENT=MONO-1 DEFINE FLOM2 MOLE-FLOW STREAM=FEED COMPONENT=MONO-2 READ-VARS RATIO PRODRT WRITE-VARS RATEM1 RATEM2 C w = mole weight of each monomer F WM1 = 150.23 F WM2 = 230.30 C calculate average molecular weight of monomers F RATINV = 1.0 / RATIO F WMAVG = ( 1.0 + RATINV ) * ( WM1 + WM2*RATINV ) C calculate monomer flow rates in kmol/hr F FLONET = PRODRT / WMAVG F FLOM1 = FLONET / ( 1.0 + RATINV ) F FLOM2 = FLONET - RATEM1

The production rate and mole ratio parameters can be accessed as parameter variables in the data-set. The standard deviation for the production rate and mole ratio variables may be specified; the units of the standard deviations are the same as the units of the parameters.

Entering Point Data There are two types of point data: input variables and result variables. Input variables include feed stream flow rates, equipment operating conditions, and other parameters that are inputs to the simulation model. Result variables include product stream flow rates or composition, polymer or catalyst component attributes, stream properties, or any other simulation calculation that can be compared to measured process data.

If some results data are missing from one or more sets of data, they can be left blank on the input forms. The model will estimate the values of these results and tabulate them after the regression run.

Unknown input data may also be estimated. Leave the input field blank and specify large standard deviations (for example, 50%) for each missing datum. Supply a realistic initial guess and make sure the standard deviation results in reasonable bounds for each missing variable.

The upper and lower bounds for reconciled unknown input variables are determined from the specified standard deviation and the “bound factor”, which defaults to ten:

• Lower bound = Measured value - (Bound Factor)*(Standard Deviation)

• Upper bound = Measured value + (Bound Factor)*(Standard Deviation)

Make sure these limits are reasonable. In particular, the limits for a stream flow rate must not allow the stream flow rate to become zero or negative.


Entering Profile Data The plug-flow reactor model (RPlug) predicts results at various points along its length axis. The batch reactor model (RBatch) predicts results at various points in time during the batch cycle. You can define profile data sets to specify the operating profiles as input data, or to fit the model to measured results data.

To do this, specify the time and value for each datum in the profile. You can specify standard deviations for results variables. Data reconciliation is not allowed for input profile data.

The following table lists the profile data sets that are currently available for these reactor models. Other types of profiles, including component attribute, user variable, and user Prop-Set property profiles are planned for a future releases of Aspen Polymers.

Model Variable Type

Description Profile Name

RBatch, RPlug

Input Temperature of process fluid TEMPERATURE

Pressure of process fluid PRESSURE

Instantaneous reactor duty DUTY

Results Partial pressure of a component PARTIAL-PRES

Molar concentration of a component in the liquid phase

MOLECONC-L

Molar concentration of a component in the vapor phase

MOLECONC-V

Mole fraction of a component in the liquid phase MOLEFRAC-L

Molar fraction of a component in the vapor phase MOLEFRAC-V

Mass concentration of a component in the liquid phase

MASSCONC-L

Mass concentration of a component in a slurry phase MASSCONC-LS

Mass fraction of a component in the liquid phase MASSFRAC-L

Cumulative reactor heat duty CUM-DUTY

Instantaneous vent mole flow rate VENT-MOLFLOW

Instantaneous vent volume flow rate VENT-VOLFLOW

RBatch Input Feed stream component flow rates not applicable

If you are fitting component attribute or user Prop-Set property profiles, you must treat the measured variables as point data for the reactor outlet stream. Use the reactor length or stop-time as an additional point data. Each profile point must be treated as a separate data case in the data set.

If some results data are missing from one or more sets of profile data, they can be left blank on the input forms. The model will estimate the values of these results and tabulate them after the regression run.


Entering Standard Deviations Standard deviations may be specified for input and result variables. The standard deviation is the level of uncertainty in the measurement. You can enter the value as an absolute or percent error (append a percentage sign, %, to the value). Statistically determined standard deviations may be available from an on-line process information management system (PIMS), from lab databases, or from other information resources. When the standard deviations are not available, you can enter your best estimate of the expected error based on your experience or the specifications of the instrument.

The objective function of the data regression is to minimize the sum of weighted square errors. For results variables, each error is defined as the difference between the reconciled or specified datum and the value calculated by the model. Each error is scaled against the square of the standard deviation:

Objective function = Measurement Prediction

(Standard deviation)ii i

i2Σ −

If the specified standard deviation of a variable is too small, the model over-emphasizes the importance of the variable during the fitting process. This may cause the model to make unreasonable adjustments in some parameters to force good fits to variables with small standard deviations.

You must be careful to consider both the precision and accuracy of each variable. For example, a variable may have a low standard deviation because it is very precise (it reproduces well in successive trials), but the measurement may be inaccurate (it may not reflect the true value of the measured parameter). Consider the case where a level controller may show little deviation in the liquid volume in a reactor, but the calibration of the level transducer may not be accurate to within ten percent of the real liquid volume. In this case, the standard deviation of the specified liquid volume should be large enough to reflect the accuracy of the volume, not the deviation of the liquid level.

If standard deviations are specified for input variables, the model reconciles these variables. If you do not specify the standard deviation of an input variable, the model assumes the specified values are exact. Reconciling input variables accounts for measurement errors in the operating conditions and can lead to better models, but it can substantially increase how long the run takes to complete.

Standard deviations must be specified for each of the result variables. Specify reasonable standard deviations to keep the model from forcing a match by making wild adjustments to the parameters. The specified standard deviations are probably too small (or the data quality is poor) if several of the parameters reach their upper or lower bounds.

Defining Data Regression Cases You can fit any number of data sets in the same regression case. Point-Data and Profile-Data may both be included. Each regression case must involve at least one estimated parameter and at least one reconciled input variable.


There are no upper limits to the number of estimated parameters and reconciled inputs, however the required simulation time is very sensitive to the number of variables included in each regression case.

Each input variable with a non-zero standard deviation is reconciled (adjusted). The reconciled inputs are tabulated in the regression results.

Each estimated parameter must be defined in the base case, or have a default value (such as a physical property parameter). The specified values for the base case run are used as the initial guesses for the regression. If the base-case value lies outside the specified bounds, the boundary condition closest to the base case value is used.

Sequencing Data Regression Cases For data fit problems, Aspen Plus will:

• Run the base-case simulation

• Execute the data regression

• Replace the base-case parameter values with the estimated parameter values and rerun the base-case simulation

If Case-Study or Sensitivity blocks are present, Aspen Plus runs them after the regression is complete. The estimated parameter values are used to calculate the results for these blocks.

Flowsheet convergence loops and Design-Specification loops are used in the preliminary and final base-case simulations and they are sequenced inside the data regression loop. The sequencing of Fortran blocks and Transfer blocks depends on which variables are accessed.

If more than one regression is included in a simulation, the regressions can be affected sequentially. Each successive regression uses the estimated parameters from the previous regression.

Regression blocks can be manually sequenced if the automatic sequence does not meet the needs of a particular run, however automatic sequencing is usually the best choice.

Interpreting Data Regression Results The key results of the data regression tool are:

• The Chi-square statistic and critical Chi-square value for the fit.

• Estimates and standard deviations for each estimated parameter.

• A table of the measured values, estimated values, and normalized residuals for each data set.

The Chi-square value is an indicator of the quality of the fit. A model is considered well fit if the Chi-square value falls below the critical Chi-square value. The reliability of different fits or different modeling approaches can be tested by comparing the Chi-square values of the fits. For example, suppose a reactor is thought to have non-ideal mixing. This assumption can be evaluated by developing two models, one which assumes ideal mixing (one CSTR stage) and one which assumes non-ideal mixing (a series of CSTR stages). The two models can be fit against the same data using the same


parameters. The model with the lower Chi-square statistic represents the data more accurately, and can be considered the most realistic.

Ideally, the standard deviations of the estimated parameters are small, and the confidence interval of each parameter is narrow. In practice, however, the standard deviation of the parameters may be relatively large. This does not necessarily indicate a poor fit. For example, if the activation energy and pre-exponential factor for a reaction are both included as estimated parameters in the data regression, then the standard deviation of the estimated pre-exponential factor will be large. In this example, small differences in one parameter (the activation energy) requires large differences in another parameter (the pre-exponential factor) to keep the model predictions relatively constant.

The residual values are indicative of the difference between the measured data and model predictions. For fitted data, the residuals are defined as:

Residual = (Measured value - Predicted value ) (Standard deviationi i i2

i/ )

For reconciled data, the residuals are defined as:

Residual = (Measured value - Estimated value ) (Standard deviationi i i2

i/ )

Review the residual values to verify they are sensible. Large residual values may indicate a major problem with the model or data, or may reflect an unreasonably tight standard deviation. Never specify extremely tight standard deviations. This causes the data regression algorithm to waste time attempting to obtain tight fits on some variables. If some data are considered extremely accurate, they should be assigned standard deviations of zero.

The regression results may be plotted against the initial estimates and measured data. Plots of this type include a 45° dotted line that indicates a “perfect fit”, e.g., each prediction is exactly equal to the measured data. Points which fall far from this line are the least well fit. Verify these outliers to make sure the data is correctly entered into the model and that the units of measurement are consistent.

Troubleshooting Convergence Problems If the data regression tool fails to converge, check the objective function. A large objective function value indicates a poor fit between the model predictions and measured data. If the objective function is large, review the residual values for each type of measured data. Large residual values may indicate a very basic error in the data entry. For example, the data may be entered in the wrong units or there may be typing errors in the specified values. Always review the model thoroughly to eliminate these types of problems before adjusting convergence parameters or making other major changes to the regression.

Convergence errors can occur for a number of reasons. When a problem occurs, ask:

• Does the base case model converge well and give reasonable results?

• Is the base case model formulated to handle data that may be out of mass or energy balance?

• Are the initial estimates of the parameters good enough?


• Are the specified standard deviations reasonable?

• Do the model inputs completely determine the measured results?

• Do the specified bounds allow the regression to take the model into infeasible regions, causing the unit operation blocks or flowsheet convergence to fail?

• Are the assumptions and simplifications in the model reasonable?

Regression runs with many variables and runs for highly non-linear models may still be difficult to converge. In some cases, the convergence criteria may be unnecessarily tight.

The following table summarizes several convergence parameters that can be used to tune a regression run. It is not necessary to adjust the convergence parameters for most regressions.

Parameter Description

ALG-ITERATION Maximum number of algorithm iterations. The default value is sufficient for nearly all problems

MAX-PASSES Maximum number of flowsheet passes. This parameter may need to be increased for regressions involving a large number of variables.

SSQTOL Convergence tolerance for sum of weighted square errors (Absolute objective function tolerance)

This is the absolute tolerance for the objective function. The default tolerance is very tight, so regressions that converge to this tolerance should be reviewed thoroughly. Verify that the specified standard deviations are sensible. Change the default value of this parameter if you which to fit the model to achieve a particular objective function value.

RFCTOL Relative objective function tolerance. The problem is considered converged if the model predicts that the maximum possible objective function is less than the product of the relative function tolerance and the current value of the objective function. For example, if RFCTOL is 0.1, then the model is converged when the predicted change in the objective function is less than ten percent of the objective function value for the current iteration.

XCTOL Minimum variable step-size tolerance. The problem is converged if the relative step size in the variables falls below XCTOL and the objective function is decreasing slowly (less than 50% per iteration).

XFTOL Minimum objective step-size tolerance

INIT-STEP Factor used to determine initial step sizes. This factor can profoundly affect the performance of the algorithm. If the initial steps are too large or too small, the model must adjust the step size until appropriate step sizes are determined.

PERT-FACTOR During the regression, the model determines the response of each variable to each other variable by making small adjustments, or pertubations, to the variables. The size of these adjustments is determined by the algorithm, this parameter is used to determine the maximum pertubation step sizes for each variable. You may need to increase this value when the fitted data are not very sensitive to the manipulated parameters, or decrease this value when the sensitivity is very strong.

BOUND- Factor used to determine lower and upper bounds for reconciled


Parameter Description

FACTOR inputs. If the value is too large, the model may enter an infeasible region, for example a stream flow rate may go to zero. If the value is too small, the parameter ranges may be too narrow to fit the data.

INIT-METHOD Method used to initialize the regression. Specify BASE-CASE to use the base case values to initialize the reconciled input parameters. Specify MEASUREMENTS to use the measured data to initialize the reconciled inputs.

Ensuring Well-Formulated Regressions Poorly formulated regressions may result in large residual values and a large objective function. Before starting a regression run, use sensitivity studies to test the model. Verify that the manipulated parameters have a strong influence on the measured data. Don’t try to fit parameters which have only a weak impact on the model predictions.

Make sure the parameter ranges are sensible. It is a waste of time to fit a parameter within a narrow range (less than 5%). On the other hand, if the range is too large, the regression algorithm may push the model into an infeasible region. For example, if the distillate to feed ratio in a column is allowed to decrease to zero, the column model will fail.

The way the data regression is formulated has a major influence on how quickly and easily the problem converges. De-couple the manipulated variables as much as possible. For example, don’t fit the rate constants and phase equilibrium parameters at the same time if the two sets of parameters can be fit independently in two smaller data regression runs.

Use the weighing factors if some sets of data are more reliable than others. A larger weight may be assigned to a set of data that are based on long-term averages from the process information management system, lower weights might be assigned to data based on poorly kept records from the distant past.

Make sure the manipulated parameters can be determined from the available data. For example, the activation energy of a reaction cannot be determined from isothermal data.

The base-case file needs to be formulated in a robust manner. If the base case model does not converge reliably away from the base case condition, then it is likely that the regression run will fail. Use the sensitivity tool to verify that the model is stable over the entire range of each manipulated parameter and to verify that the model is sensitive to each parameter.

Where possible, use relative or normalized inputs instead of absolute inputs. For example, in column models use the distillate to feed ratio (D:F) instead of distillate flow rate. Use pressure drop specifications instead of pressure. These specifications make the model more reliable and help to avoid problems that occur if the measured data are inconsistent.


Fitting Activation Energy It is tempting to try to fit activation energies and pre-exponential factors in the same regression run. This can lead to significant headaches if the problem is not approached right. Consider, for example, the standard Arrehnius rate expression:

k knet o

ERT

act

=−

exp

Using this expression, the net rate constant, knet , is sensitive to the activation

energy, Eact . If the activation energy is adjusted a little bit, a large adjustment must be made to the pre-exponential factor to offset this difference. In other words, the activation energy controls the magnitude of the reaction rate as well as the temperature sensitivity of the reaction rate.

A better approach is to use the modified Arrehnius expression:

k knet o

ER T T

act

ref=−

−⎛

⎝⎜⎜

⎞

⎠⎟⎟

exp1 1

The parameter Tref is a reference temperature that typically represents the

middle of the temperature range used to estimate the activation energy. Using this formula, the net rate constant, knet , remains constant at the reference temperature regardless of the value of the activation energy. With this approach, the pre-exponential factor, ko , controls the magnitude of the

reaction rate at the reference temperature. The activation energy, Eact , controls the temperature sensitivity of the rate constant. This makes it much easier to fit the model.

Scaling the Fitted Parameters When several types of parameters are adjusted in the same run, the magnitude of the manipulated parameters may influence how well the data regression converges. Ideally, the manipulated parameters should be within several orders of magnitude of each other.

Suppose, for example, the manipulated parameters include rate constants for several different types of reactions. These expected values of the rate constants may differ by several orders of magnitude. In this situation, the regression procedure may over-emphasize the manipulated variables with the smallest magnitude.

You can get around this problem using two CALCULATOR blocks as shown in Example 3. Use one CALCULATOR block to define a PARAMETER variable for each manipulated variable in the regression. Initialize each parameter to one. Use a second CALCULATOR block to READ these parameter values, to multiply them by base case values, and then WRITE the results to the manipulated variables. In the data regression block, manipulate the PARAMETER variables.

This technique allows the data regression to operate on normalized variables instead of absolute variables which makes it much easier for the regression algorithm to choose appropriate step sizes and ensures that the variables are given equal weighting by the algorithm.


Example 3: Using Fortran Blocks to Scale Manipulated Parameters

Problem Description: Suppose two pre-exponential factors are adjusted to match conversion and intrinsic viscosity, which are defined as user Prop-Set properties. The pre-exponential factors have very different magnitudes, so scaling is required to get a good fit.

Instead of manipulating the rate constants directly, use PARAMETER variables to define and manipulate correction factors for the rate constants. Use a CALCULATOR block to initialize these correction factors to unity. Manipulate these PARAMETER variables in the regression. Use a second CALCULATOR block to adjust the pre-exponential factors using the correction factors manipulated by the data regression model.

USER-PROPERTY INT-VISC SUBROUTINE=USRPSP FLASH=YES USER-PROPERTY CONVERSN SUBROUTINE=USRPSP FLASH=YES PROP-SET INT-VISC INT-VISC PROP-SET CONVERSN CONVERSN DATA-SET DS-1 DEFINE CAT MASS-FLOW STREAM=CATALYST SUBSTREAM=MIXED COMPONENT=CAT DEFINE TEMP BLOCK-VAR BLOCK=CSTR1 SENTENCE=PARAM VARIABLE=TEMP DEFINE VISC STREAM-PROP STREAM=PRODUCT PROPERTY=INT-VISC DEFINE CONV STREAM-PROP STREAM=PRODUCT PROPERTY=CONVERSN USE STD-DEV 0.001 0.1 0.002 0.0050 / DATA 0.025 290.0 0.844 0.8550 / DATA 0.023 295.0 0.842 0.8700 / DATA 0.055 280.0 0.850 0.9050 / DATA 0.033 292.0 0.835 0.9000 STEP-GROWTH MYMODEL RATE-CON 1 PRE-EXP=9.67D14 ACT-ENERGY=41.0 RATE-CON 2 PRE-EXP=3.25D0 ACT-ENERGY=0.0 etc… CALCULATOR INITIAL DEFINE P1 PARAMETER 1 DEFINE P2 PARAMETER 2 P1 = 1.0D0 P2 = 1.0D0 EXECUTE FIRST CALCULATOR ADJUST DEFINE P1 PARAMETER 1 DEFINE P2 PARAMETER 2 DEFINE EXP1 REACT-VAR REACTION=MYMODEL VAR=PRE-EXP SENT=RATE-CON ID1=1 DEFINE EXP2 REACT-VAR REACTION=MYMODEL VAR=PRE-EXP SENT=RATE-CON ID2=2 C specify base case pre-exponential factors for side rxn 1 and 2 F BASE1 = 9.67D14 F BASE2 = 3.25D0 C calculate pre-exponential factors using correction factors C manipulated by the data regression block F EXP1 = BASE1 * P1 F EXP2 = BASE2 * P2 READ-VARS P1 P2 WRITE-VARS EXP1 EXP2


REGRESSION FIT-1 DATA DS-1 VARY PARAMETER 1 LABEL=”CORRECT” “FACTOR” “RXN #1” LIMITS 0.1 10.0 VARY PARAMETER 2 LABEL=”CORRECT” “FACTOR” “RXN #2” LIMITS 0.1 10.0

17 User Models 351

17 User Models

This section discusses the features available in Aspen Polymers (formerly known as Aspen Polymers Plus) for incorporating user modules into a simulation model.


• User Unit Operation Models, 351

• User Kinetic Models, 357

• User Physical Property Models, 361

Note: For more information on user models, see your Aspen Plus User Models documentation.

User Unit Operation Models There are cases where users may need to create special models to represent a process. Usually these models can be configured by combining several of the standard unit operation building blocks. For more complex reactor geometries or in order to represent highly non-ideal systems users may need to provide their own model as a Fortran subroutine.

There are two user unit operation blocks available: USER and USER2. The first allows a limited number of inlet and outlet streams. The second allows multiple inlet and outlet streams. Both unit operations take full advantage of the Aspen Plus flowsheeting capabilities. The required Fortran subroutine must process the feed streams and return the condition and composition of the outlet streams.

User Unit Operation Models Structure There are three stages to the execution of Aspen Plus unit operation models: input processing, simulation calculations, and report writing. Normally, the implementation of a new model requires that all three stages be accounted for. However, in the case of USER2 models, a generic framework handles the input setup and processing stage. A Fortran subroutine must be written to perform the simulation calculations and for writing the report. If no report

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writer is provided Aspen Plus automatically echoes the input data in the report.

The following figure summarizes the simulation sequence of a unit operation model:

User Unit Operation Model Calculations A user unit operation model can be programmed to represent any unit operation. Most applications would include combinations of the following: separations, reactions, heat transfer, mass transfer, mixing and splitting. There are some common steps that are found in the simulation calculations within unit operation models, including user models. These steps include:

• Feed processing

• Physical properties and phase equilibrium calculations

• Unit operation calculations (kinetics, heat transfer, mass transfer, etc)

• Results storage and outlet stream initialization

Utilities are available to facilitate each of these steps. The available Fortran utilities and monitors are:

Stream Handling

NPHASE Determines number of substreams

LPHASE Finds the location of a substream within a stream

SSCOPY Copies a substream from one stream to another

NSVAR Determines the size of the stream vector

Component Attribute Handling

GETDPN Find the number average degree of polymerization

GETMWN Find the number average molecular weight

17 User Models 353

GETPDI Find the polydispersity

GETSMF Find the segment mole fractions

GETSWF Find the segment weight fractions

CAUPT Load attributes into physical property system

LCATT Finds the location of a component attribute in the stream vector

Component Handling (See Appendix C)

CPACK Packs out trace components

ISPOLY Determines if a component is a polymer

ISSEG Determines if a component is a segment

ISOLIG Determines if a component is an oligomer

ISCAT Determines if a component is a catalyst

ISINI Determines if a component is an ionic initiator

KCCID Finds the component index (position in stream vector)

Property Monitors (See Aspen Plus User Models)

KVL Calculates vapor-liquid equilibrium ratio (K-value) KLL Calculates liquid-liquid equilibrium ratio

ENTHL Calculates liquid mixture enthalpy

VOLV Calculates liquid mixture molar volume

FUGLY Calculates liquid mixture fugacity coefficient

IDLGAS Performs ideal gas calculations

VISCL Calculates liquid mixture viscosity

Flash Routine (See Aspen Plus User Models)

FLASH Flash monitor

Error Handling (See Aspen Plus User Models)

IRRCHK Function to check diagnostic level

ERRPRT Error printing routine

WRTTRM Writer to terminal file or control panel

Report Writer (See Aspen Plus User Models)

RPTHDR Report pagination /header writer

Stream Processing In order to perform its calculations the user model must be able to read and process the Aspen Plus stream structure. The stream structure is documented in Aspen Plus User Models. Example 1 shows a USER2 model routine.

Note: The data in the streams coming in and out of the model are stored in SI units.

There are several utilities available for stream processing. These perform functions such as finding the number of stream variables, i.e. the size of the stream vector, copying one stream to another, finding the total number of substreams, and finding specific substreams within a stream. Several stream handling utilities are documented in Appendix C of this User Guide.

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In addition to the standard composition and state information found in the stream structure, there are also component attributes. If the user model processes polymers, then component attributes must be processed and their outlet stream values must be calculated and stored. The attributes available include polymer properties such as degree of polymerization, molecular weight, polydispersity, and copolymer composition. These are documented in the Polymer Structural Properties section of Chapter 2. In order to process attributes, there are Fortran utilities available that perform functions such as copying attributes from one stream to another, retrieving number average molecular weight and degree of polymerization, retrieving copolymer composition, locating specific component attributes within the stream vector, and determining the size of a vector component attribute. The component attribute handling utilities are documented in Appendix C.

There are also utilities for processing components: for excluding trace components, for determining component type (polymer, oligomer, segment, catalyst), etc. These can be found with the component attribute processing utilities.

Example 1: USER2 Model Routine

C---------------------------------------------------------------------- SUBROUTINE USRMOD (NMATI, SIN, NINFI, SINFI, NMATO, 2 SOUT, NINFO, SINFO, IDSMI, IDSII, 3 IDSMO, IDSIO, NTOT, NSUBS, IDXSUB, 4 ITYPE, NINT, INT, NREAL, REAL, 5 IDS, NPO, NBOPST, NIWORK, IWORK, 6 NWORK, WORK, NSIZE, SIZE, INTSIZ, LD) C---------------------------------------------------------------------- C IMPLICIT NONE C C DECLARE VARIABLES USED IN DIMENSIONING C INTEGER NMATI, NINFI, NMATO, NINFO, NTOT, + NSUBS, NINT, NPO, NIWORK,NWORK, + NSIZE C #include "ppexec_user.cmn" EQUIVALENCE (RMISS, USER_RUMISS) EQUIVALENCE (IMISS, USER_IUMISS) C #include "dms_plex.cmn" EQUIVALENCE (IB(1), B(1)) REAL*8 B(1) C #include "dms_rglob.cmn" C #include "dms_global.cmn" C #include "dms_ipoff1.cmn" C #include "dms_ncomp.cmn" C C DECLARE FUNCTIONS C INTEGER SHS_LCATT, DMS_KCCIDC

17 User Models 355

INTEGER XMW, LMW C C DECLARE ARGUMENTS C INTEGER IDSMI(2,NMATI), IDSII(2,NINFI), + IDSMO(2,NMATO), IDSIO(2,NINFO), + IDXSUB(NSUBS),ITYPE(NSUBS), INT(NINT), + IDS(2,3), NBOPST(6,NPO), + IWORK(NIWORK),INTSIZ(NSIZE),NREAL, LD, I INTEGER KH2O REAL*8 SIN(NTOT,NMATI), SINFI(NINFI), + SOUT(NTOT,NMATO), SINFO(NINFO), + WORK(NWORK), SIZE(NSIZE) C C DECLARE LOCAL VARIABLES C INTEGER IMISS REAL*8 REAL(NREAL), RMISS, WATER C INTEGER IDXP, LZMOM, LMWN, IMWN(2), IZMOM(2) REAL*8 AMWP, ZMOM C INITIALIZE ARRAY OF ATTRIBUTE NAMES DATA IZMOM / "ZMOM"," " / DATA IMWN / "MWN "," " / C C---------------------------------------------------------------------- C C BEGIN EXECUTABLE CODE C C---------------------------------------------------------------------- C OFFSETS TO COMPONENT MOLECULAR WEIGHTS XMW(I) = DMS_IFCMNC('MW') + I C C FIRST COPY FIRST INLET TO FIRST OUTLET C DO 100 I = 1, NTOT SOUT(I,1) = SIN(I,1) 100 CONTINUE C C INITIALIZE THE SECOND OUTLET C DO 200 I = 1, NCOMP_NCC+1 SOUT(I,2) = 0D0 200 CONTINUE C DO 300 I = NCOMP_NCC+2, NCOMP_NCC+9 SOUT(I,2) = RMISS 300 CONTINUE C C FIND LOCATION OF COMPONENT ATTRIBUTES C IDXP is position of polymer component in component list. C Can be obtained with ispoly function C find location of attributes in stream LZMOM = SHS_LCATT( 1, IDXP, IZMOM ) LMWN = SHS_LCATT( 1, IDXP, IMWN ) IF (LZMOM .NE. 0) ZMOM = SOUT(LZMOM+1,1) C

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C EXAMPLE OF FINDING A COMPONENT POSITION BY NAME C KH2O = DMS_KCCIDC ( 'H2O' ) C C CAN ALSO PASS POSITION AS PARAMETER IN INT VECTOR C E.G. KH2O = INT(2) IF ( KH2O .EQ. 0 ) GO TO 999 C C PUT COMPONENT (WATER) IN THE SECOND OUTLET C WATER = SIN(KH2O,1) SOUT(KH2O,1) = 0D0 SOUT(NCOMP_NCC+1,1) = SIN(NCOMP_NCC+1,1) - WATER SOUT(KH2O,2) = WATER SOUT(NCOMP_NCC+1,2) = WATER C 999 RETURN END

Physical Property Calculations Physical properties and phase equilibrium calculations can be performed within a user model. Property methods, models, and parameters specified in the input either through a built-in or a user-defined property method, can be used for the user model calculations. This can be done through property monitors. The user model requests the property of interest by calling a specific monitor, sets the state information and calculation codes in the call to the monitors, and in turn obtains thermodynamic properties such as fugacity coefficients, enthalpies, entropies, molar volumes, etc. A flash calculation routine is also available. See the table on page 352 for a listing of frequently used property monitors. The FLASH routine and the property monitors are documented in Aspen Plus User Models. See also User Physical Property Models on page 361.

Unit Operation Calculations The purpose of a user unit operation block is to allow the flexibility to program user correlations or algorithms to represent a process. Independently from the physical property calculations for which monitors are provided, users can take advantage of the Fortran subroutine structure to incorporate the calculations needed to represent their process. Aspen Plus System Management documents programming guidelines to be followed when defining the model calculations. The calculations performed within a user unit operator model for a polymer system are similar to those that could be performed within a kinetic model. See User Kinetic Models on page 357.

Diagnostics Throughout the simulation calculations, a user model may call the Aspen Plus error handler to issue diagnostic messages ranging from fatal errors to warnings and information. The error handler is documented in Aspen Plus

17 User Models 357

User Models. These diagnostics can be written to the terminal or the control panel. The USER labeled commons contains output file numbers through which the terminal, control panel and simulation files can be accessed. See Aspen Plus User Models for a description of the USER labeled common.

User Unit Operation Report Writing A report section can be included for a user model in the Aspen Plus simulation report. This requires a Fortran report writer subroutine. To write the report a report pagination utility is available. This utility is documented in Aspen Plus User Models. Note that in the user interface the integer and real arrays for the user model are displayed on the results screen of the user model.

User Kinetic Models User kinetic models are primarily intended for situations where the polymerization phenomena taking place are highly complex and cannot be represented by the built=in models. Users can write their own equations for the rate of change of components and the attributes of the polymer that they are intending to track. This is done through a USER reaction block. The USER block can be used in conjunction with built-in models. The user model gives the basic framework for specifying the reaction stoichiometry and the rate constant parameters. The user kinetic model requires a Fortran subroutine which performs all the computations that are required for computing the rates of change for components in the reactive phase and rates of change for polymer attributes. The structure of this subroutine is documented in Aspen Plus User Models. For polymerization kinetics user model, there are specific calculations that are typically performed. These include:

• Locating the polymer component attributes within the stream vector. This is done through the utility routine SHS_LCATT. Users need to determine and provide IDXP which is the component index for the polymer.

LDPN = SHS_LCATT( 1, IDXP, ICATYP( 1, IDPN ) ) LZMOM = SHS_LCATT( 1, IDXP,ICATYP( 1, IZMOM ) )

• Retrieving the polymer attribute values from the stream vector SOUT. The following code shows how to retrieve DPN from SOUT. Other attributes can be similarly obtained.

IF( LDPN .GT. 0 .AND. SOUT(LDPN+1) .GT. 0D0) DPN = SOUT(LDPN+1)

• Calculating the specific volume of the reacting phase from the stream vector SOUT. From the stream vector, calculate the total number of moles and volume of the reacting phase. This example assumes that the reacting phase is a single liquid phase.

CALL SHS_CPACK (SOUT, NCK, IDXX, XX, TOTFLO) CALL PPMON_VOLL ( + TEMP, PRES, XX, NCK, IDXX, NBOPST, 4, 1, + SVOL, DV, KER) VFLOW1 = SLIQRX VFLOW = SVOL * SOUT(NCK+1)

• Calculating molar concentration of each component and class 2 attributes in the reacting phase. This is obtained by dividing the mole fraction of the

358 17 User Models

component in the reacting phase by the molar volume of the reacting phase. It is also shown how to compute concentration of ZMOM, a class 2 attribute for the polymer.

DO 50 I = 1, NC CONC(I) = XX(I)/SVOL 50 CONTINUE IF(LZMOM .GT. 0 .AND. VFLOW .GT. RGLOM_RMIN) ZMOM=SOUT(LZMOM+1)/VFLOW

• Loading the rate constants for each reaction in the reacting phase. The vector REALR will hold the values of the kinetic constants.

DO 200 I = 1, NR AK(I) = REALR(I) 200 CONTINUE

• Calculating the rate of reaction for each component and returning that information to the reactor. The rate equations are user derived. For example assume that the following user reactions are to be included in the user kinetics:

A A A Waste kk1 2 3 1 11+ ⎯ →⎯ +

A Wastek3 22⎯ →⎯

The rate constants for user reactions are obtained as:

AK(1) = k1

AK(2) = k2

The reaction rate for the components ( 1=A1, 2=A2, 3=A3 ) are calculated as:

RATES(1) = -AK(1)*CONC(1)*CONC(2)*VFLOW RATES(2) = -AK(1)*CONC(1)*CONC(2)*VFLOW RATES(3) = (AK(1)*CONC(1)*CONC(2) - AK(2)*CONC(3))*VFLOW

• Calculating rate of change for Class 2 attributes for the polymer. The user is responsible for deriving the expression for the rate of change of attribute values.

DO 400 I = 1, NTCAT RATCAT(I) = 0D0 400 CONTINUE C

The following example code explains the above steps in greater detail.

Note: The data coming in and out of the model are stored in SI units.

Example 2: User Kinetic Subroutine

C------------------------------------------------------------------------ SUBROUTINE USRKIP (SOUT, NSUBS, IDXSUB, ITYPE, NINT, 2 INT, NREAL, REAL, IDS, NPO, 3 NBOPST, NIWORK, IWORK, NWORK, WORK, 4 NC, NR, STOIC, RATES, FLUXM, 5 FLUXS, XCURR, NTCAT, RATCAT, NTSSAT,

17 User Models 359

6 RATSSA, KCALL, KFAIL, KFLASH, NCOMP, 7 IDX, Y, X, X1, X2, 8 NRALL, RATALL, NUSERV, USERV, NINTR, 9 INTR, NREALR, REALR, NIWR, IWR, * NWR, WR, NRL, RATEL, NRV, 1 RATEV) C------------------------------------------------------------------------ IMPLICIT NONE C C DECLARE VARIABLES USED IN DIMENSIONING C INTEGER NSUBS, NINT, NPO, NIWORK,NWORK, + NC, NR, NTCAT, NTSSAT,NCOMP, + NRALL, NUSERV,NINTR, NREALR,NIWR, + NWR C #include "ppexec_user.cmn" EQUIVALENCE (RMISS, USER_RUMISS) EQUIVALENCE (IMISS, USER_IUMISS) C C C C.....RCSTR... #include "rcst_rcstri.cmn" #include "rxn_rcstrr.cmn" C C.....RPLUG... #include "rplg_rplugi.cmn" #include "rplg_rplugr.cmn" EQUIVALENCE (XLEN, RPLUGR_UXLONG) EQUIVALENCE (DIAM, RPLUGR_UDIAM) C C.....RBATCH... #include "rbtc_rbati.cmn" #include "rbtc_rbatr.cmn" C C.....PRES-RELIEF... #include "prsr_presri.cmn" #include "rbtc_presrr.cmn" C C.....REACTOR (OR PRES-RELIEF VESSEL OR STAGE) PROPERTIES... #include "rxn_rprops.cmn" EQUIVALENCE (TEMP, RPROPS_UTEMP) EQUIVALENCE (PRES, RPROPS_UPRES) EQUIVALENCE (VFRAC, RPROPS_UVFRAC) EQUIVALENCE (BETA, RPROPS_UBETA) EQUIVALENCE (VVAP, RPROPS_UVVAP) EQUIVALENCE (VLIQ, RPROPS_UVLIQ) EQUIVALENCE (VLIQS, RPROPS_UVLIQS) C C INITIALIZE RATES C C C DECLARE ARGUMENTS C INTEGER IDXSUB(NSUBS),ITYPE(NSUBS), INT(NINT), + IDS(2),NBOPST(6,NPO),IWORK(NIWORK),

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+ IDX(NCOMP), INTR(NINTR), IWR(NIWR), + NREAL, KCALL, KFAIL, KFLASH,NRL, + NRV, I REAL*8 SOUT(1), WORK(NWORK), + STOIC(NC,NSUBS,NR), RATES(1), + FLUXM(1), FLUXS(1), RATCAT(NTCAT), + RATSSA(NTSSAT), Y(NCOMP), + X(NCOMP), X1(NCOMP), X2(NCOMP) REAL*8 RATALL(NRALL),USERV(NUSERV), + REALR(NREALR),WR(NWR), RATEL(1), + RATEV(1), XCURR C C DECLARE LOCAL VARIABLES C INTEGER IMISS, IDPN(2), IZMOM(2), XMW REAL*8 REAL(NREAL), RMISS, XLEN, DIAM, TEMP, + PRES, VFRAC, BETA, VVAP, VLIQ, + VLIQS DATA IDPN / "DPN ", " " / DATA IZMOM / "ZMOM", " " / C BEGIN EXECUTABLE CODE C ASSUME WE ARE USING A BATCH REACTOR. FOR OTHER REACTORS THE C PROCEDURE IS SIMILAR C OFFSETS TO COMPONENT MOLECULAR WEIGHTS XMW(I)=DMS_IFCMNC('MW')+I C C FIND INDEX OF SPECIES BY NAME IDXP=DMS_KCCIDC('POLY') C C C DETERMINE POINTERS TO POLYMER ATTRIBUTES LDPN = SHS_LCATT( 1, IDXP, IDPN ) LZMOM = SHS_LCATT( 1, IDXP, IZMOM ) C C GET POLYMER ATTRIBUTES VALUES FROM SOUT C IF( LDPN .GT. 0 .AND. SOUT(LDPN+1) .GT. 0D0) DPN = SOUT(LDPN+1) C------------------------------------------------------------------ C GET REACTING PHASE SPECIFIC MOLAR VOLUME, SVOL ASSUMING IT IS C LIQUID C CALL SHS_CPACK (SOUT, NCK, IDX, X, TOTFLO) CALL PPMON_VOLL ( + TEMP, PRES, X, NCK, IDX, NBOPST, 4, 1, SVOL, DV, KER) VFLOW1 = SLIQRX C C C GET VOLUME OF REACTING PHASE, VFLOW C VFLOW = SVOL * SOUT(NCK+1) C C----------------------------------------------------------------- C

17 User Models 361

C.....CALCULATE MOLAR CONCENTRATIONS OF COMPONENTS AND CLASS 2 C ATTRIBUTES DO 50 I = 1, NC CONC(I) = XX(I)/SVOL 50 CONTINUE IF(LZMOM .GT. 0 .AND. VFLOW .GT. RGLOM_RMIN) ZMOM=SOUT(LZMOM+1)/VFLOW C------------------------------------------------------------------ C INITIALIZE THE RATES FOR COMPONENTS TO ZERO C DO 100 I = 1, NC RATES(I) = 0D0 100 CONTINUE C C------------------------------------------------------------------ C LOAD REACTION RATE CONSTANTS FROM THE REALR DO 200 I = 1, NR AK(I) = REALR(I) 200 CONTINUE C C------------------------------------------------------------------ C CALCULATE REACTION RATES FOR COMPONENTS C DO 300 I = 1, NC DO 310 J = 1, NC M = COMPUTE CORRECT INDEX RATES(I) = RATES(I) - AK(M) * CONC(I)*CONC(J)*VFLOW 300 CONTINUE C C C CALCULATE RATES FOR CLASS-2 ATTRIBUTE EXAMPLE C------------------------------------------------------------------ DO 400 I = 1, NTCAT RATCAT(I) = 0D0 400 CONTINUE C C INITIALIZE ATTRIBUTES OF INTEREST IN THIS WAY C FOR ARRAY ATTRIBUTES THIS GIVES FIRST LOCATION IN ARRAY C RACAT(LZMOM - (NC+9) + 1) = 0 RETURN END

User Physical Property Models There is often a need among industrial users to calculate one or more physical properties based on in-house or literature correlations and expressions that

362 17 User Models

are not available in Aspen Polymers. In such cases, users can take advantage of physical property user models.

A user subroutine needs to be supplied for each user model that will calculate the desired property. For each physical property, a fixed subroutine name and argument list exists; these can be found in Aspen Plus User Models. An example of a simple user subroutine that calculates and returns the liquid molar enthalpy of a mixture (HLMX) is provided below. For instructions on how to use user physical property models from the graphical user interface, see Volume 2 of this User Guide, Aspen Polymers Physical Property Methods and Models.

User model development in polymer simulation is very similar to that in the simulation of standard components. In case some polymer attributes are needed for the calculation of a user property, these can be retrieved by calling the appropriate utility routine (see the table on page 352 for a summary of the utilities available). The following can be helpful while developing a physical property user model in Aspen Polymers:

• The index vector, IDX, contains the indexes of the components present in the current calculation run. For example, if the first component present currently is listed third in the component list, then: IDX(1) = 3.

• Parameter values are retrieved using the utility DMS_IFCMNC. For example, suppose you want to pick up the molecular weight of a component. You need to define an integer array with elements the locations of the molecular weights of all the components in the component list on the plex vector, B:

XMW(I) = DMS_IFCMNC('MW') + I

Then, the molecular weight of the component listed third in the component list is B(XMW(3)).

• In polymer user models, it is often necessary to identify whether a particular component is polymer, oligomer, or segment. This is done by the utility logical functions SHS_ISPOLY, SHS_ISOLIG, and PPUTL_ISSEG. For instance, suppose you want to perform a certain manipulation on the polymer components present in your run:

IF (SHS_ISPOLY(I)) GO TO 10

Which will send the calculation to line number 10 if the component with index I is a polymer component.

• The mole fraction vector X (or Z) is based on the apparent molecular weight of the polymer components. If you need to perform calculations for a polymer run where the mole fractions are needed, then you must use the true mole fractions (which are based on the true molecular weight of the polymer) rather than the apparent mole fractions X. This is done by a conversion utility routine called POLY_XATOXT:

CALL POLY_XATOXT( N, IDX, XMW, X, XTRUE)

Where: XMW is the vector of the apparent molecular weights, IDX is the index vector, X is the stream apparent mole fraction vector, and XTRUE is the vector that contains the mole fractions based on the true molecular weight of the polymer.

• Polymer attributes needed for calculations in user physical property models are retrieved using utility subroutines. For a list of available utilities see the table on page 352. As an example, to get the number

17 User Models 363

average degree of polymerization, DPn, for a particular component you must give:

CALL POLY_GETDPN( 1, 1, I, DPN )

Where I is the component index. For a detailed description of all the polymer utilities available see Appendix C.

• Users can call several Aspen Plus subroutines to perform specific tasks. For example, routine IDLGAS will return the ideal-gas properties of the components and their mixture, while PL001 will return the vapor pressure of the desired components (see Aspen Plus User Models).

• After calculating a molar property, the appropriate conversion must be made so that the returned property is based on the apparent mole basis. For instance, after the calculation of the liquid enthalpy of a polymer component based on the true molecular weight, the following conversion should be made:

HL_app = HL_true * MW_app / MW_true

A sample user subroutine that calculates and returns the mixture liquid enthalpy is given in the Example 3.

Note: The data coming in and out of the model are stored in SI units.

Example 3: User subroutine for mixture liquid enthalpy calculation

C---------------------------------------------------------------------- SUBROUTINE HL2U (T ,P ,Z ,N ,IDX , 1 IRW ,IIW ,KCALC ,KOP ,NDS , 2 KDIAG ,QMX ,DQMX ,KER ) C C---------------------------------------------------------------------- C HV2U IS A USER MIXTURE ENTHALPY SUBROUTINE C C THIS USER SUBROUTINE CALCULATES THE LIQUID ENTHALPY OF A BINARY C MIXTURE CONTAINING ONE POLYMER AND ONE SOLVENT. C C C NAME OF MODULE: HL2U C C IMPLICIT NONE C DIMENSION Z(N), IDX(N), KOP(10) DIMENSION D(15) C... USER DIMENSION DIMENSION XTRUE(10) C C #include "dms_ncomp.cmn" #include "ppexec_user.cmn" #include "dms_plex.cmn" C EQUIVALENCE (IB(1), B(1))

364 17 User Models

INTEGER XMW, DHFORM, CPIG, II, DMS_IFCMNC INTEGER IMON, IPOL, IIMON, IIPOL, I, N, J, ISEG REAL*8 DELT1, DELT2, DELT3, DELT4, H_MON, H,POL, * HM_MIX, AVG_MW, T, TREF, QMX C C---------------------------------------------------------------------- C C STATEMENT FUNCTIONS FOLLOW C XMW(I) = DMS_IFCMNC('MW') + I DHFORM(I) = DMS_IFCMNC('DHFORM') + I CPIG(I,J) = DMS_IFCMNC('CPIG') + 11*(J - 1) + I C C *** NOTE ******************************************* C C PARAMETERS ARE LOCATED USING THE UTILITY DMS_IFCMNC C AND THE NAME OF THE PARAMETER. FOR EXAMPLE, C DMS_IFCMNC('MW') RETRIEVES THE LOCATIONS WHERE THE C COMPONENT MOLECULAR WEIGHTS ARE STORED. C C **************************************************** C DO 100 I=1,10 XSEG(I) = 0.D0 100 CONTINUE C TREF = 298.15 C C---------------------------------------------------------------------- C C *** NOTE ******************************************* C COMPONENT ID FOR MONOMER *HARD-WIRED* AT POSITION 2 C COMPONENT ID FOR POLYMER *HARD-WIRED* AT POSITION 3 C **************************************************** C IMON = 2 IPOL = 3 ISEG = 4 C C C## BOTH Z AND XSEG ARE PACKED: XSEG(IPOL) CONTAINS MOLE FRAC OF SEGMENT C CALL XATOXT(N, IDX, B(XMW(1)), Z, XTRUE) C C POLYMERIC SPECIES PROP-SET PROPERTIES C DELT1 = T - TREF DELT2 = (T**2 - TREF**2)/2.D0 DELT3 = (T**3 - TREF**3)/3.D0 DELT4 = (T**4 - TREF**4)/4.D0 H_MON = B(DHFORM(IMON)) + B(CPIG(1,IMON))*DELT1 + + B(CPIG(2,IMON))*DELT2 + B(CPIG(3,IMON))*DELT3 + B(CPIG(4,IMON)) +*DELT4 H_POL = B(DHFORM(IPOL)) + B(CPIG(1,IPOL))*DELT1 + + B(CPIG(2,IPOL))*DELT2 + B(CPIG(3,IPOL))*DELT3 + B(CPIG(4,IPOL)) +*DELT4 C

17 User Models 365

C *** NOTE ******************************************* C IN CASE A COMPONENT ATTRIBUTE WAS NEEDED FOR THE C CALCULATION OF THE POLYMER ENTHALPY, THE APPROPRIATE C UTILITY ROUTINE SHOULD BE CALLED. C C FOR EXAMPLE, SUPPOSE THE NUMBER-AVERAGE DEGREE OF C POLYMERIZATION (DPn) OF THE POLYMER WAS NECESSARY. C THE UTILITY ROUTINE GETDPN CAN BE USED TO RETURN C THE DESIRED ATTRIBUTE: C C CALL POLY_GETDPN (1, 1, IPOL, DPN) C C THE ARGUMENTS HAVE THE FOLLOWING MEANING: C C 1 = CONVENTIONAL SUBSTREAM C 1 = DPN FOR 1 COMPONENT IS REQUESTED (NCP=1) C IPOL = POLYMER COMPONENT INDEX C DPN = RETURNED VALUE OF THE NUMBER AVERAGE C DEGREE OF POLYMERIZATION C C **************************************************** C IIMON = 0 IIPOL = 0 DO 10 I=1,N II = IDX(I) IF (II.EQ.IMON) IIMON = I IF (II.EQ.IPOL) IIPOL = I 10 CONTINUE C HM_MIX = H_MON*XTRUE(IIMON) + H_POL*XTRUE(IIPOL) AVG_MW = B(XMW(IMON))*Z(IIMON) + B(XMW(IPOL))*Z(IIPOL) C C C CONVERT FROM TRUE TO APPARENT MOLE BASIS QMX = HM_MIX * AVG_MW / B(XMW(ISEG)) C C 999 CONTINUE RETURN END

References Aspen Plus User Models. Cambridge, MA: Aspen Technology, Inc.

Aspen Plus System Management. Cambridge, MA: Aspen Technology, Inc.

366 18 Application Tools

18 Application Tools

This section discusses the tools available for applying Aspen Polymers (formerly known as Aspen Polymers Plus) features to solve real-life problems.

The topics covered include:

• Example Applications for a Simulation Model, 366

• Application Tools Available in Aspen Polymers, 367

• Model Variable Accessing, 369

Example Applications for a Simulation Model The main purpose of a simulation model is to provide the engineer with a deeper understanding of the molecular and macroscopic processes which are vital to a polymer manufacturing process. This understanding will eventually lead to improvements in various aspects of the process related to safety, productivity, and polymer product quality. These are some typical scenarios in which a simulation model is used to meet this objective.

A model may be used to:

• Identify superior grade transition policies and better plant startup and shutdown procedures which minimize offspec polymer product

• Reduce the number of lengthy and costly experiments on bench, pilot, and plant scale for polymer product and polymerization process development

• Train process engineers, chemists, plant operators

• Identify sources of variance in polymer product quality

• Provide data for the design of rupture discs and vent lines

• Find optimal temperature profiles for a continuous reactor train which minimize reaction medium viscosity while meeting product specifications

• Investigate monomer feed policies for a semi-batch copolymerization process for keeping the chemical composition distribution narrow

• Design a free-radical initiator mix to maximize productivity under the constraints of safe reactor operations

18 Application Tools 367

Application Tools Available in Aspen Polymers Several analysis and flowsheeting tools are available in Aspen Polymers to configure a model for performing analyses and studies of a process. These include:

• CALCULATOR - used to incorporate Fortran or Microsoft Excel calculations in the simulation

• DESIGN-SPEC - used to apply specifications on process variables

• SENSITIVITY - used to examine the effect of varying one or more process variables

• CASE-STUDY - used to compare between different sets of operating conditions

• OPTIMIZATION - used to perform optimization calculations

For each of these tools, with the exception of CALCULATOR, Aspen Plus sets a loop around a model, flowsheet section, or entire flowsheet. Within this loop, selected operating variables are manipulated and key process variables are sampled.

The calculation procedure for analysis and flowsheeting tools is illustrated here:

The categories of accessible flowsheet variables are described in Model Variable Accessing on page 369.

Note that in most cases Aspen Plus automatically generates the calculation sequence. You can also specify a sequence manually. For details on how use these tools in your simulations, see the Aspen Plus User Guide. Example uses of these features are given in the Aspen Polymers Examples and Applications Case Book.

CALCULATOR Calculator blocks provide a mechanism for you to incorporate Fortran statements or Microsoft Excel spreadsheets into the flowsheet calculations. This can be used to calculate and set input variables based on special user


inputs. For this reason, calculator blocks can be used as feed-forward controllers. You can also use calculator blocks to calculate and write results to the Aspen Plus report, control panel, or external file.

Calculator blocks can be used to display charts, tables, or graphs through Excel.

To use this block you must specify which model variables to sample or manipulate, enter the Fortran statements or create the Excel sheet, and set the sequence in which the block must be executed during the flowsheet calculations.

An example use of a calculator block as a feed-forward controller would be to hold the flowrate of a catalyst proportional to a monomer flow for a situation where that monomer flow varies.

DESIGN-SPEC Design-Spec blocks allow you to set a process variable that is normally calculated during the simulation. For each specification, you must identify which process variable can be adjusted to meet that specification. For this reason, Design-Spec blocks can be used as feedback controllers.

To use this block you must specify which model variables must be fixed, what values they must be fixed at, and which model input variables can be manipulated. You can include Fortran statements in Design-Spec blocks.

An example use of a Design-Spec block would be to set a maximum amount for impurities in a product stream.

SENSITIVITY Sensitivity blocks provide a mechanism for you to analyze the effect of operating variables, which you select on the process. This block generates a matrix of manipulated variables versus sampled variables. If there is more than one manipulated variable, the sensitivity analysis is performed for each combination of manipulated variables. It is recommended that you use multiple Sensitivity blocks if you do not want to combine the manipulated variables.

To use this block you must specify which are the manipulated variables, which are the sampled variables, and how they must be tabulated. You can include Fortran statements in Sensitivity blocks.

An example use of a Sensitivity block would be to determine the effect of reactor temperature or pressure on the polymer product properties.

CASE-STUDY Case-Study blocks provide another mechanism for you to analyze the effect of operating conditions on process variables. They allow you to make several runs in series for the entire flowsheet. Since a report is generated for the whole flowsheet for each case, you do not need to specify output variables to be sampled.


To use this block you must identify the case study variables, assign values for these variables, and specify reporting options.

An example use of Case-Study would be to investigate the effect of changing feed conditions and composition on key process variables.

OPTIMIZATION Optimization blocks provide a mechanism for you to minimize or maximize an objective function calculated using key process variables. To define the objective function you would use Fortran statements.

To use this block you must define the objective function, specify manipulated variables, and define constraints, if any.

An example use of Optimization would be to find the optimal reactor temperature to meet polymer product property specifications while minimizing reaction medium viscosity.

Model Variable Accessing When using the various model analysis tools to perform sensitivity studies, optimization studies, case studies, or data fitting, or when applying design specifications, or adding calculator blocks to a simulation model, users must access many different flowsheet variables. These flowsheet variables are grouped by type:

• Unit operation block variable

• Stream variable (including polymer component attributes)

• Reaction variable

• Physical property variable

A partial list of accessible variables is given here:

Variable Type

Identifier Description

Block BLOCK-VAR Unit operation block variable

Unit operation block vector

Stream STREAM-VAR Non component dependent stream variable

MOLE-FLOW Component mole flow

MOLE-FRAC Component mole fraction

MASS-FLOW Component mass flow

MASS-FRAC Component mass fraction

STDVOL-FLOW Component standard volume flow

STDVOL-FRAC Component standard volume fraction

STREAM-PROP Stream Prop-Set property

STREAM-VEC Entire stream vector

SUBSTRM-VEC Entire substream vector

Stream COMPATTR-VAR Component attribute element (Notes 1-4)

COMPATTR-VEC Component attribute (Notes 1-4)


Variable Type

Identifier Description

SUBSATTR-VAR Substream attribute element

SUBSATTR-VEC Substream attribute

Reaction REACT-VAR Reaction variable (Note 5)

Physical UNARY-PARAM Unary physical property parameter

Properties BI-PARAM Binary physical property parameter

Notes:

1. Component attributes may be accessed in several ways. They may be accessed through STREAM-VEC or through SUBSTRM-VEC. In this case, users are responsible for locating the desired attribute and attribute element within the stream or substream vector. See the table that follows for the MIXED substream vector structure.

2. Component attributes may also be accessed with COMPATTR-VAR. With COMPATTR-VAR, users must provide the element number for attributes having more than one element. See the Polymer Structural Properties section of Chapter 2 to find out the dimensions of polymer component attributes. If the attribute is dimensioned by number of polymer segments, NSEGS, (e.g. SFLOW, or SFRAC polymer attributes), the ordering of elements follows the order in which the list of polymer segments was specified (See the Component Classification section of Chapter 2). For component attributes dimensioned by number of catalytic sites, each element represents a site number, i.e. site no. 1, no. 2, etc. For two-dimensional component attributes dimensioned by number of segments and number of catalytic sites (NSEGS*NSITES), the first dimension is NSEG, therefore, the ordering of elements is as follows: the list of specified segments is repeated for each site beginning with site no. 1.

3. Component attributes may also be accessed with COMPATTR-VEC. In this case, users are not required to provide an element number since the whole component attribute is returned as a vector having one or more elements. The ordering of elements within the attribute vector follows the description given in Note 2.

4. COMPATTR-VAR and COMPATTR-VEC are equivalent for component attributes having only one element.

5. REACT-VAR may be used to access kinetic constant parameters for reaction kinetic models, including free-radical, step-growth and Ziegler-Natta. The type of information required to access these parameters is model dependent. For free-radical, the reaction type (INIT-DEC, for example), and the reacting species are required, in addition to the name of the parameter to be accessed. The same is true for Ziegler-Natta which also requires a catalyst site type number. For step-growth, a reaction number is required. For the standard Aspen Plus reaction models, a reaction number, and/or substream identifier may be needed to locate the parameters.

The MIXED substream structure is summarized here:

Array Index Description


1, ..., NCC Component mole flows (kgmole/sec)

NCC + 1 Total mole flow (kgmole/sec)

NCC + 2 Temperature (K)

NCC + 3 Pressure (N/m2)

NCC + 4 Mass enthalpy (J/kg)

NCC + 5 Molar vapor fraction

NCC + 6 Molar liquid fraction

NCC + 7 Mass entropy (J/kg-K)

NCC + 8 Mass density (kg/m3)

NCC + 9 Molecular weight (kg/kgmole)

NCC + 10

⎪⎭

⎪⎬

⎫

ncat1

1

value

value

Values for component attribute 1 of component 1 (polymer or other attributed component)

⎪⎭

⎪⎬

⎫

ncat1

1

value

value


⎪⎭

⎪⎬

⎫

ncat1

1

value

value


Note: NCC is the number of conventional components (including polymers, segments and oligomers) entered on the Components Specifications Selection sheet. This parameter is stored as NCOMP_NCC in labeled common DMS_NCOMP (See Aspen Plus User Models, Appendix A).

References Aspen Plus User Guide. Cambridge, MA: Aspen Technology, Inc.

Convergence and Optimization in Aspen Plus, Course notes. Cambridge, MA: Aspen Technology, Inc.

372 19 Run-Time Environment

19 Run-Time Environment

This chapter discusses various topics related to working in the Aspen Polymers (formerly known as Aspen Polymers Plus) environment.

The topics covered include:

• Aspen Polymers Architecture, 372

• Installation Issues, 373

• Configuration Tips, 373

• User Fortran, 374

• Troubleshooting Guide, 374

Aspen Polymers Architecture Aspen Polymers is a layered product. In other words, this product works in conjunction with a main program. This main program is Aspen Plus for steady-state simulation and Aspen Dynamics or Aspen Custom Modeler for dynamic simulation. Aspen Polymers brings to these simulators the polymer process technology in the form of component characterization, physical property models and databanks, kinetic models, and the associated input forms.

As a result of this layered architecture the installation and configuration of Aspen Polymers is closely tied to that of Aspen Plus for steady-state simulation and that of Aspen Dynamics and Aspen Custom Modeler for dynamic simulation. In this chapter we will focus on topics related to the Aspen Plus environment.

The overall Aspen Polymers architecture is shown here:

19 Run-Time Environment 373

Installation Issues

Hardware Requirements Aspen Polymers is available on all the hardware platforms supported by Aspen Plus. For the user interface and engine, these are Windows 2000 with Service Pack 1 and Windows XP. Consult the Aspen Engineering Suite Installation Guide for the hardware requirements.

Installation Procedure Refer to the Aspen Engineering Suite Installation Guide, Aspen Polymers chapter for information on how to install Aspen Polymers on your system.

Configuration Tips

Startup Files The information needed to launch the main Aspen Plus application window is recorded in startup files. These files define the type of simulation, default settings for the user interface, hosts for the simulation engine, run settings, etc. One type of startup file is used to define defaults for the type of simulation. This is the simulation template.

Simulation Templates Simulation templates are available to help you get started setting up your model. These templates typically contain options such as unit sets, physical property method selection, and Table File Format (TFF) selection for stream result tables. Polymer simulation templates are available. You can create your own personal template to allow faster definition of a new simulation model.


To use a simulation template, after starting Aspen Plus, on the startup box select the template startup option. Then choose one of the polymer simulation templates. This will automatically setup a global unit set, an appropriate polymer property method, and a polymer TFF for the stream tables.

To learn more about TFF files see the Aspen Plus System Management.

User Fortran

User Fortran Templates There are several ways for you to customize your models by adding calculations in Fortran. The End-Use Properties section of Chapter 2 described how to setup a user Prop-Set for calculating end-use properties. Chapter 4 described how to setup user unit operation models, user kinetic models, and user property models. Templates are available for your use in creating the Fortran files used in these features. You will find these templates in the following location:

Version Location

Windows %asptop%\user

User Fortran Linking User Fortran calculations in the form of user routines are linked dynamically to Aspen Polymers during a simulation. Within user Fortran, you will often access utilities located within Aspen Polymers. In order to access these utilities, you will need to know the name of the object libraries where they are located. This applies to the utilities described in Appendix C. The name of the utility as shown in the example call sequence includes the name of the object library where it is located.

You can also create your own dynamic link libraries to hold your user Fortran files. The Aspen Plus System Management guide describes how to work with Fortran code modifications.

Troubleshooting Guide Following are tips to help you diagnose and resolve problems you may run into while setting up or running Aspen Polymers.

User Interface Problems A list of symptoms relating to problems you may encounter when using the user interface is provided below. Possible causes and solutions are given for each symptom.


Symptom Cause Solution

The polymer input forms cannot be found on the GUI.

The installation was not complete. You must locate your installation CD and do an incremental installation of Aspen Polymers. Select Aspen Polymers from the product list and chose the subcomponents button to select the Aspen Polymers steady state installation option.

Aspen Polymers is installed but not enabled.

Enable Aspen Polymers. From the Tools menu, select Options. On the Startup tab there is a box entitled Enable forms for layered products. Make sure you select Aspen Polymers

A file created without using polymer features appears incomplete in the components record.

You visited the polymer record while creating the file, then later switched off Aspen Polymers.

You must enable Aspen Polymers (From the Tools menu, Select Options, click on the Startup tab). In the Data Browser, select Polymers (Polymers will appear as incomplete), right mouse click, select Delete.

Windows crashes during input specifications.

An invalid operation was performed either by the Aspen Plus program or by another program running simultaneously.

Usually, when you crash, a backup file is created. Startup Aspen Plus again, then you should be able to recover your file. If the invalid operation was caused by Aspen Plus, repeat the input steps that lead to the crash, verify that it is reproducible, and submit the problem to Technical Support.

Windows crashes during simulation calculations.

The simulation engine encountered an error that could not be transferred to the GUI.

Export an input summary. Run the input summary alone, then examine the run history for simulation errors. Change the input specifications associated with the error and rerun.

Aspen Plus ran out of resources to create run files. This can happen especially for large simulations. You may see error messages referring to the amount of virtual memory available.

Free-up some disk space and run again. Also, consult the Aspen Plus System Management reference manual. An entire section is devoted to managing virtual memory on Win95/98 and WinNT.

Aspen Plus ran out of memory to load dynamic link libraries.

Make some disk space available or increase the amount of memory available to the application, then run again.

Windows crashes after simulation is complete.

Aspen Plus could not load the simulation results.

If you are running on a remote hosts, there may have been a communication failure at the end of the simulation calculations. You can submit the run again or you can manually load the results file (.SUM) from the remote host.

If you are running on a local PC host, Aspen Plus may have run out of memory to load the results. Make some disk space available or increase the amount of memory available to the application and run again.



If the load failure was not due to any of the above, there may be some information recorded in the results file (.SUM) that is causing the problem. Contact Technical Support and be prepared to supply the results file and/or your saved simulation file.

Simulation Engine Run-Time Problems A list of symptoms relating to problems you may encounter with the simulation engine at run-time are provided below. Possible causes and solutions are given for each symptom.


During simulation calculations an error message occurs for a license failure.

The application could not find a valid free license to complete the simulation.

If the license error message refers to "Feature 10". This means that you do not have a license for Aspen Plus itself. If you are using a licensed installation, then this could be a temporary license failure. This can happen for multi-user sites, or if you are using a license manager located on a network. In that case, you simply need to try again later.

If you are using an installation with a single activator, then your license key file may be corrupted, the port where the activator is plugged in could be damaged, or the activator could be damaged. To correct your license key files, perform a license key installation again. If the problem is your activator, contact Technical Support to have it replaced.

If the license error message refers to another feature number, you may still have run into a temporary license failure (see above). In that case, try again. If this was not a temporary license failure, then you created a simulation file which uses features for which you are not licensed. If the message refers to "Feature 15", then you are trying to use Aspen Polymers without a valid license. Other feature numbers refer to specific add-on products. You must contact AspenTech to obtain a valid Aspen Polymers license.

A message box comes up stating that an error occurred in the Aspen Plus engine.

See "Windows crashes during simulation calculations" under User Interface Problems. See also "After one run a subsequent run following an input change crashes" later in this section.

See "Windows crashes during simulation calculations" under User Interface Problems. See also "After one run a subsequent run following an input change crashes" later in this section.

A run history message appears referring to a dynamic load module error.

Aspen Plus ran out of resources to load dynamic link libraries.

See "Windows crashes during simulation calculations" under User Interface Problems.



You are referencing user Fortran and do not have the compiled object file in your working directory. The working directory is the location from which you opened an existing file. If you created a file from a template or opened an existing file from a floppy or a write protected area (e.g. \xmp or \app) the working directory is as specified in Tools Options Startup.

Compile the user Fortran and place it in your run directory.

A run history message appears which refers to "Virtual Memory Exhausted".

You ran out of virtual memory space to load the run files.

See the Aspen Plus System Management, which discusses virtual memory management.

After one run a subsequent run following an input change crashes.

The problem size has changed as a result of the input or for other reasons Aspen Plus unsuccessfully tried to reuse the previous run data space. Usually an error message appears which states that a "Fatal error has been encountered".

Usually after the crash you should be able to recover your file and run with the input change. To prevent this from happening for the same run, reinitialize the simulation before making repeated runs. This is still a problem that should be reported to Technical Support.

References Aspen Engineering Suite Installation Guide for Windows. Cambridge, MA: Aspen Technology, Inc.

Aspen Plus System Management. Cambridge, MA: Aspen Technology, Inc.


378 A Component Databanks

A Component Databanks

This appendix documents the Aspen Polymers (formerly known as Aspen Polymers Plus) component databanks. There are currently two databanks available:

• POLYMER Databank - containing polymer pure component parameters

• SEGMENT Databank - containing segment pure component parameters

In addition users may retrieve parameters from the Aspen Plus databanks.

Pure Component Databank The pure component databanks contain pure component data for over 1500 species. Typically components such as monomers, solvents, catalysts, initiators, etc. would be retrieved from the pure component databanks. The parameters in these databanks include those listed in POLYMER Property Parameters on page 378.

POLYMER Databank POLYMER contains property parameters for polymers.

Note that a generic polymer component is available in the databank for custom designed polymers.

POLYMER Property Parameters The following table shows the parameters stored in the POLYMER databank:

Parameter No. Element

Description

CPIG 11 Ideal gas heat capacity

DGFVK 1 Free energy of formation, ideal gas reference state

DHFVK 1 Heat of formation, ideal gas reference state

DHVLWT 5 Heat of vaporization

A Component Databanks 379

MW* 1 Polymer reference molecular weight

OMEGA 1 Acentric factor

PC 1 Critical pressure

PLXANT 9 Antoine coefficient

TC 1 Critical temperature

VC 1 Critical volume

VLTAIT 9 Tait molar volume model coefficients

ZC 1 Critical compressibility factor

* MW is a reference molecular weight calculated as the average

segment molecular weight using:

NSEGMWSEG

MW ∑=

For the generic polymer component MW is set to 1.

POLYMER Databank Components The following table shows the polymers contained in the POLYMER databank:

Alias Polymer Name

ABS Acrylonitrile-butadiene-styrene

BR-1 Poly(butadiene)

CA-1 Cellulose-acetate

Cellulose Cellulose

Chitosan Chitosan

CPE Chlorinated-Poly(ethylene)

CTA Cellulose-triacetate

Dextran Dextran

EVA Ethylene-vinyl-acetate

EEA Ethylene-ethyl-acrylate

EPR Ethylene-propylene

HDPE High-density-Poly(ethylene)

Heparin Heparin

Hyaluronic Hyaluronic-Acid

I-PB Isotactic-Poly(1-butene)

I-PMMA Isotactic-Poly(methyl-methacryl)

I-PP Isotactic-Poly(propylene)

Keratan Keratan-Sulfate

LDPE Low-density-poly(ethylene)

LLDPE Linear-low-density-poly(ethylene)

NBR Nitrile-butadiene-rubber

NYLON6 Nylon-6


Alias Polymer Name

NYLON66 Nylon-66

PAA Poly(acrylic-acid)

P(ACA&S) Poly(acrylamide-styrene)

PALA Poly(alanine)

PAMIDE Poly(amide)

PAMS Poly(alpha-methylstyrene)

P(AMS&AN) Poly(a-methylstyrene-AN)

PAN Poly(acrylonitrile)

PARA Poly(acrylamide)

PARG Poly(arginine)

PASN Poly(asparagine)

PASP Poly(aspartic-acid)

PB-1 Poly(1-butene)

PBA Poly(n-butyl-acrylate)

PBMA Poly(n-butyl-methacrylate)

P(BMA&S) Poly(n-butyl-methac-styrene)

PBS-1 Poly(butadiene-styrene)

PBT Poly(butylene-terephthalate)

PC-1 Poly(carbonate)

P(C&DMS) Poly(carbonate-dimet-siloxane)

PCHMA Poly(cyclohexyl-methacrylate)

PCYS Poly(cysteine)

PD-1 Poly(decene-1)

PDMA Poly(decyl-methacrylate)

PDMS Poly(dimethylsiloxane)

P(DMS&S) Poly(dimethylsiloxane-styrene)

PE Poly(ethylene)

PEA Poly(ethyl-acrylate)

PEEK Poly(ether-ether-ketone)

PEG Poly(ethylene-glycol)

P(EG&PG) Poly(eth-glycol-prop-glycol)

PEMA Poly(ethyl-methacrylate)

PEO Poly(ethylene-oxide)

P(EO&POX) Poly(eth-oxide-prop-oxide)

P(E&P) Poly(ethylene-propylene)

PET Poly(ethylene-terephthalate)

P(E&VAC) Poly(ethylene-vinyl-acetate)

PGLN Poly(glutamine)

PGLU Poly(glutamic-acid)

PGLY Poly(glycine)

PH Poly(heptene-1)

PHA Poly(n-hexyl-acrylate)

PHENOXY Phenoxy


Alias Polymer Name

PHIS Poly(histidine)

PHMA Poly(n-hexyl-methacrylate)

PI Poly(imide)

PIB Poly(isobutylene)

PIBMA Poly(isobutyl-methacrylate)

PILE Poly(isoleucine)

PIP-1 Poly(isoprene)

PLEU Poly(leucine)

PLYS Poly(lysine)

PMA Poly(methyl-acrylate)

P(MAA&MMA) Poly(methac-acid-met-methac)

P(MAA&S) Poly(methac-acid-styrene)

P(MAA&VAC) Poly(methac-acid-vin-acetate)

PMET Poly(methionine)

PMMA Poly(methyl-methacrylate)

PMMS Poly(m-methylstyrene)

PMP Poly(4-methyl-1-pentene)

PMVPD Poly(2-methyl-5-vinylpyridine)

PNA Poly(sodium-acrylate)

POCS Poly(o-chlorostyrene)

POE Poly(oxyethylene)

POLYMER Generic polymer component

POM Poly(oxymethylene)

POMS Poly(o-methylstyrene)

POP Poly(oxypropylene)

PP Poly(propylene)

PPA Poly(n-propyl-acrylate)

PPBRS Poly(p-bromostyrene)

PPEMA Poly(n-pentyl-methacrylate)

PPG Poly(propylene-glycol)

PPHE Poly(phenylalanine)

PPO Poly(phenylene-oxide)

PPMA Poly(n-propyl-methacrylate)

PPMOS Poly(p-methoxystyrene)

PPMS Poly(p-methylstyrene)

PPOX Poly(propylene-oxide)

PPRO Poly(proline)

PPS Poly(phenylene-sulfide)

PS-1 Poly(styrene)

PSBMA Poly(sec-butyl-methacrylate)

PSER Poly(serine)

PSF Poly(sulfone)

P(S&VP) Poly(sytrene-vinylpyrrolidone)


Alias Polymer Name

P(S&VPD) Poly(styrene-4-vinylpyridine)

PT-1 Poly(tetrahydrofuran)

PTFE Poly(tetrafluoroethylene)

PTHR Poly(threonine)

PTRP Poly(tryptophan)

PTYR Poly(tyrosine)

PU-1 Poly(urethane-fiber)

PVA Poly(vinyl-alcohol)

PVAC Poly(vinyl-acetate)

P(VAC&VAL) Poly(vin-acetate-vin-alcohol)

PVAL Poly(valine)

PVAM Poly(vinyl-amine)

PVC Poly(vinyl-chloride)

PVCAC Poly(vin-chloride-vin-acetate)

PVDC Poly(vinylidene-chloride)

PVDF Poly(vinylidene-fluoride)

PVF Poly(vinyl-fluoride)

PVI Poly(vinyl-isobutyl-ether)

PVME Poly(vinyl-methyl-ether)

PVO Poly(vinylpropionate)

PVP Poly(vinylpyrrolidone)

PVPD Poly(4-vinyl-pyridine)

SAN Styrene-acrylonitrile

SBR Styrene-butadiene-rubber

UF Urea-formaldehyde

SEGMENT Databank SEGMENT contains property parameters for polymer segments.

Note that a special nomenclature was devised to identify polymer segments. The segment name consists of the name of the monomer from which it originates, followed by a label to identify it as a repeat unit (-R) or an end group (-E). In cases where several molecular structures are possible, a numeric subscript is used to differentiate the isomers. A similar convention is used for assigning component aliases.

SEGMENT Property Parameters The following table shows the parameters stored in the SEGMENT databank:

Parameter No. Element

Description


ATOMNO 10 Vector of atomic number of chemical elements in segment (used with NOATOM)

CPCVK 6 Crystalline heat capacity

CPIG 11 Ideal gas heat capacity*

CPLVK 6 Liquid heat capacity

DGFVK 1 Free energy of formation, ideal gas reference state

DHCON 1 Enthalpy of condensation

DHFVK 1 Enthalpy of formation, ideal gas reference state

DHSUB 1 Enthalpy of sublimation

DNCVK 4 Crystalline density

DNGVK 5 Glass density

DNLVK 4 Liquid density

MW 1 Molecular weight

NOATOM 10 Vector of number of each type of chemical element in segment (used with ATOMNO)

TGVK 1 Glass transition temperature

TMVK 1 Melt transition temperature

VKGRP 24 Van Krevelen functional groups

VOLVW 1 Van der Waals volume

UFGRP 24 UNIFAC functional groups

* Estimated from Joback functional group.

SEGMENT Databank Components The following table shows the SEGMENT databank components:

Alias Segment Name Molecular Structure

CF2-R Methylene-fluoride-R CF2

CO-R Carbonyl-R CO

CHF2-E Methylene-fluoride-E CHF2

CH2O-R Oxymethylene-R OCH2

C2O2-R Oxalic-acid-R C C

O O

C2HO3-E Oxalic-acid-E C COH

O O



C2H2-R-1 cis-Vinylene-R

C2H2-R-2 trans-Vinylene-R

C2H2-R Vinylidene-R C CH2

C2H2CL-E Vinyl-chloride-E CH CHCl

C2H2F-E Vinyl-fluoride-E CH CHF

C2H2CL2-R Vinylidene-chloride-R CH2 CCl2

C2H2F2-R Vinylidene-fluoride-R CH2 CF2

C2H3-E Vinyl-E CH CH2

C2H3CL-R Vinyl-chloride-R CH2 CHCl

C2H3F-R Vinyl-fluoride-R CH2 CHF

C2H3NO-R Glycine-R CH2NHO

C

C2H3O-E Acetate-E ~COCH3

C2H3O-E-1 Oxyvinyl-E O CH2CH

C2H3O-E-2 Vinyl-alcohol-E CH CH

OH

C2H4-R Ethylene-R CH2 CH2

C2H4N-E Vinylamine-E-1 CH CH

NH2

C2H4NO-E Glycine-E-1 NH2 CH2 C

O

C2H4NO2-E Glycine-E-2 CH2 CO

NHOH

C2H4O-R-1 Ethylene-oxide-R CH2 CH2 O



C2H4O-R-2 Oxyethylene-R CH2 CH2O

C2H4O-R-3 Vinyl-alcohol-R CH2 CH

OH

C2H4O2-R Ethylene-glycol-R CH2 CH2O O

C2H5-E Ethylene-E CH2 CH3

C2H5N-R Vinylamine-R CH2 CH

NH2

C2H5O-E-1 Ethylene-oxide-E-1 CH2 CH2

OH

C2H5O-E-2 Ethylene-oxide-E-2 CH2CH3 O

C2H5O2-E Ethylene-glycol-E CH2O CH2 OH

C2H6N-E Ethyleneamine-E CH2 CH2

NH2

C2H6OSi-R Dimethyl siloxane-R

CH3

Si OCH3

C2H7OSi-E Dimethyl siloxane-E

CH3

Si OHCH3

C3H2O2-R Malonic -acid-R CCH2C

O O

C3H2O2Na-E Sodium acrylate-E-1

CH CHC

O ONa



C3H3N-R Acrylonitrile-R CHCH2

C N

C3H3NO-R Acrylamide-R-1

CH CHC

O NH

C3H3O2-E Acrylic acid-E-1

CH CHC

O OH

C3H3O2Na-R Sodium-acrylate-R CO

CHCH2

ONa

C3H303-E Malonic-acid-E CCH2COH

O O

C3H4NO-E Acrylamide-E-1 CO

CH CH

NH2

C3H4NO-B Acrylamide-B CO

CHCH2

NH

C3H4N2O-B Urea-formaldehyde-R CH2

N CO

N

CH2

C3H4O2-R Acrylic-acid-R

CH2

O

CHC

OH

C3H4O2Na-E Sodium-acrylate-E-2

CH2

OC

ONa

CH2



C3H5-E Propylene-E-1 CH CH

CH3

C3H5Cl-R 2-chloropropylene-R CH2 CHCl CH2

C3H5NO-R-1 Acrylamide-R-2

CH2

OCCH2

NH

C3H5NO-R-2 Acrylamide-R-3

CH2 CH

OC

NH2

C3H5NO-R-3 Alanine-R CHNH CO

CH3

C3H5NOS-R Cysteine-R CHNH C

O

CH2

SH

C3H5NO2-R Serine-R CHNH C

O

CH2

OH

C3H5O2-E Acrylic-acid-E-2 CO OH

CH2 CH2

C3H6-R Propylene-R CH2 CH

CH3

C3H6NO-E-1 Acrylamide-E-2

CH2 CH2

CO NH2



C3H6NO-E-2 Alanine-E-1 NH2 CH CO

CH3

C3H6NOS-E Cysteine-E-1 NH2 CH C

O

CH2

SH

C3H6NO2-E-1 Alanine-E-2

OCH CNH

OHCH3

C3H6NO2-E-2 Serine-E-1

OCH CNH2

CH2

OH

C3H6NO2S-E Cysteine-E-2

OCH CNHCH2

OH

SH

C3H6NO3-E Serine-E-2

OCH CNHCH2

OH

OH

C3H6O-R-1 Oxypropylene-R O CH2 CH

CH3

C3H6O-R-2 Propylene-oxide-R CH3

OCH2 CH



C3H6O-R-3 Vinyl-methyl-ether-R

CH3

OCH2 CH

C3H6O2-R Propylene-glycol-R CH3

OCH2 CHO

C3H6O2-R-1 1,3-Propanediol-R ~O(CH2)3O~

C3H6O2-R-2 1,2-Propanediol-R OCHCH2O

CH3

C3H7-E Propylene-E-2 CH3

CH2 CH2

C3H7O-E-1 Oxypropylene-E CH2 CH

CH3

HO

C3H7O-E-2 Propylene-oxide-E CH2 CH

CH3

OH

C3H7O-E-i i-Propanol-E ~OCH(CH3)2

C3H7O-E-n n-Propanol-E ~O(CH2)2CH3

C3H7O2-E Propylene-glycol-E CH2 CH

CH3

OHO

C3H7O2-E-1 1,3-Propanediol-E ~O(CH2)3OH

C3H7O2-E-P 1,2-Propanediol-E-P OCHCH2OH

CH3

C3H7O2-E-S 1,2-Propanediol-E-S OCH2CHCH3

OH

C4H2O2-R-cis Maleic-acid-R C

C

O

CH H

CO

C4H2O2-R-tra Fumaric-acid-R

CC

O

CH C

H

O



C4H3O3-E-cis Maleic-acid-E C

C

O

CH H

COHO

C4H3O3-E-tra Fumaric-acid-E

CC

O

CH COH

H

O

C4H4O2-R Succinic-acid-R C(CH2)2C

O O

C4H5-B Butadiene-B CH2 CH CH CH

C4H5-E-1 Butadiene-E-1 CH CH2CH CH

C4H5-E-2 Butadiene-E-2 CH2CH2 CH C

C4H5NO3-R Aspartic-acid-R

NH CH CO

CH2

CO OH

C4H5O2-E-1 Methyl-acrylate-E-1 CO OCH3

CH2C

C4H5O2-E-2 Methyl-acrylic-acid-E-1 C

O OH

CCH3

CH

C4H5O2-E-3 Vinyl-acetate-E-1 OCH3

CH CH

CO

C4H5O3-E Succinic-acid-E C(CH2)2COH

O O

C4H6-R-1 Butadiene-R-1 CH CHCH2 CH2



C4H6-R-2 Butadiene-R-2 CHCH2

CH CH2

C4H6NO3-E Aspartic-acid-E-1

CH

CH2

CO OH

CO

NH2

C4H6NO4-E Aspartic-acid-E-2

CH

CH2

CO OH

CO

NHOH

C4H6N2O2-R Asparagine-R

CH

CH2

CO

CO

NH

NH2

C4H6O2-R-1 Methyl-acrylate-R

CHC

O

CH2

O CH3

C4H6O2-R-2 Methyl acrylic-acid-R

O

CH2

CH3

CC

OH

C4H6O2-R-3 Vinyl-acetate-R

O

CH2 CHO

C CH3

C4H7-E-1 1-Butene-E CH CH

C2H5



C4H7-E-2 Isobutylene-E CH CCH3

CH3

C4H7-E-3 Butadiene-E-3 CH CH2CH2 CH2

C4H7-E-4 Butadiene-E-4 CHCH2 CH CH3

C4H7NO2-R Threonine-R

NH CH CO

CHOHCH3

C4H7N2O2-E Asparagine-E-1

NH2

CH2

CO

NH2 CH CO

C4H7N2O3-E Asparagine-E-2

NH2

CH2

CO

CO

CHNHOH

C4H7O2-E-1 Methyl-acrylate-E-2

CH2 CH2

CO O CH3

C4H7O2-E-2 Methyl-acrylic-acid-E-2

CH3

CHCH2

O OHC

C4H7O2-E-3 Methyl-acrylic-acid-E-3

CH3

O OH

C CH3

C



C4H7O2-E-4 Vinyl-acetate-E-2

CH2 CH2

CO O CH3

C4H8-R-1 1-Butene-R CH2 CH

C2H5

C4H8-R-2 Isobutylene-R CH2 CCH3

CH3

C4H8NO2-E Threonine-E-1

CHNH2 CO

CHOHCH3

C4H8NO3-E Threonine-E-2

CH C O

CHOHCH3

NHOH

C4H8O-R Tetrahydrofuran-R CH2 CH2 CH2 CH2 O

C4H8O2-R Butylene-glycol-R O C4H8 O

C4H8O3-R Diethylene-glycol-R O C2H4 O C2H4 O

C4H9O-E-1 Tetrahydrofuran-E-1 C4H8 OH

C4H9O-E-2 Tetrahydrofuran-E-2 C4H9 O

C4H9O2-E Butylene-glycol-E O C4H8 OH

C4H9O3-E Diethylene-glycol-E O C2H4 O C2H4 OH

C5H6O2-R Glutaric-acid-R C(CH2)3C

O O

C5H7NO-R Proline-R NCO



C5H7NO3-R Glutamic-acid-R

NH CH CO

C2H4

CO OH

C5H7O2-E-1 Methyl-methacrylate-E-1

CH3

CCHC

O O CH3

C5H7O2-E-2 Ethyl-acrylate-E-1

CH CHC

O O C2H5

C5H7O2-E-3 Vinyl-propionate-E-1

CH CHO

C C2H5O

C5H7O3-E Glutaric-acid-E C(CH2)3COH

O O

C5H8-R Isoprene-R CH2 C CH CH2

CH3

C5H8NO-E Proline-E-1 HNCO

C5H8NO2-E Proline-E-2

O

NC OH



C5H8NO3-E Glutamic-acid-E-1

NH2 CH CO

C2H4

CO OH

C5H8NO4-E Glutamic-acid-E-2

NHO

C2H4

CO OH

CH COH

C5H8N2O2-R-1 Glutamine-R

NHO

C2H4

CO

CH C

NH2

C5H8N2O2-R-2 Trimethylene-diisocyanate-R O

NH C3H6 NHC C

O

C5H8O2-R-1 Methyl-methacrylate-R CCH3

CH2

CO OCH3

C5H8O2-R-2 Ethyl-acrylate-R CO O C2H5

CHCH2

C5H8O2-R-3 Vinyl-propionate-R OC2H5

CHCH2

CO

C5H9-E 1-Pentene-E-1 CH CH

C3H7



C5H9NO-R Valine-R NH CH C

O

CH3 CH3

CH

C5H9NOS-R Methionine-R

NH CH CO

CH3

C2H4

S

C5H9N2O2-E Glutamine-E-1

O

C2H4

NH2 CCH

CO NH2

C5H9N2O3-E Glutamine-E-2


O CH3

CO

CH3

CH2 CH


O

CH3CC

CH3

OCH3

C5H9O2-E-3 Ethyl-acrylate-E-2

CH2 CH2

CO O C2H5



C5H9O2-E-4 Vinyl-propionate-E-2

CH2 CH2

O

OC2H5C

C5H10-R 1-Pentene-R CH2 CH

C3H7

C5H10NO-E Valine-E-1

C5H10NOS-E Methionine-E-1

O

CH3

CH CNH2

C2H4

S

C5H10NO2-E Valine-E-2 NH CH C

O

OHCH

CH3 CH3

C5H10NO2S-E Methionine-E-2

NH CH CO

OH

CH3

C2H4

S

C6H4S-R Phenylene-sulfide-R S

C6H5O-E Phenol-E O

C6H5S-E-1 Phenylene-sulfide-E-1 S

C6H5S-E-2 Phenylene-sulfide-E-2 SH



C6H6N2-R-M m-Phenylene-diamine-R

NH NH

C6H6N2-R-O o-Phenylene-diamine-R

NHNH

C6H6N2-R-P p-Phenylene-diamine-R NHNH

C6H7N2-E-M m-Phenylene-diamine-E

NH NH2

C6H7N2-E-O o-Phenylene-diamine-E

NH2NH

C6H7N2-E-P p-Phenylene-diamine-E NH2NH

C6H7N3O-R Histidine-R

C6H8NO-E Vinylpyrrolidnone-E-1 O

CNCHCH

C6H8N3O-E Histidine-E-1

C6H8N3O2-E Histidine-E-2



C6H8O2-R Adipic-acid-R CC (CH2)4

O O

C6H9NO-R Vinylpyrrolidnone-R

CH2 CHCN

O

C6H9O2-E-1 Ethyl-methacrylate-E-3

CH C CH3

CO C2H5O

C6H9O2-E-2 n-Propyl-acrylate-E-1

CH CHC

O C3H7O

C6H9O3-E Adipic-acid-E C OHC (CH2)4

O O

C6H10-R 1,4-Hexadiene-R

CH2 CH

CH2

CH3

CH

CH

C6H10NO-E Vinylpyrrolidnone-E-3

CH2 CH2

N CO

C6H10O2-R-1 Ethyl-methacrylate-R-1 CH2 C

CO C2H5O

CH3

C6H10O2-R-2 n-Propyl-acrylate-R

CH2 CHC

O C3H7O



C6H10O3-R Amylose-R OCH2OH

O

C6H10O5-R-1 Cellulose-R O

CH2OH

O

OH OH

C6H10O5-R-2 Dextran-R O

OH OH

HO

CH2O

C6H11-E-1 4-Methyl-1-pentene-E-1 CH CH

CH2 CHCH3

CH3

C6H11-E-2 1-Hexane-E-1 CH CH

C4H9

C6H11NO-R-1 Caprolactam-R NH (CH2)5 CO

C6H11NO-R-2 Isoleucine-R NH CH

CH C2H5

OC

CH3

C6H11NO-R-3 Leucine-R

OC

CH3

CHCH2

NH

CHCH3

C6H11O-E Vinyl-isobutyl-ether-E-1

CH3

CH CHO

CH2 CHCH3



C6H11O2-E-1 Ethyl-methacrylate-E-1 CH2 CH

CH3

CO O C2H5

C6H11O2-E-2 Ethyl-methacrylate-E-2

O O C2H5

C

CH3

CCH3

C6H11O2-E-3 n-Propyl-acrylate-E-2

O O C3H7

CCH2 CH2

C6H11O3-E Amylose-E C OCH2OH

HO

C6H11O5-E Cellulose-E-1 O

CH2OH

HO

OH OH

C6H11O6-E-1 Cellulose-E-2 O

CH2OH

OH

OH OH

O

C6H11O6-E-2 Dextran-E-2 O

OH

OH OH

CH2 O

HO

C6H12-R-1 1-Hexane-R CH2 CH

C4H9



C6H12-R-2 4-Methyl-1-pentene-R CH2 CH

CH2 CHCH3

CH3

C6H12NO-E-1 Caprolactam-E-1 NH2 (CH2)5 C

O

C6H12NO-E-2 Isoleucine-E-1 NH2 CH C

CH

O

CH3 C2H5

C6H12NO-E-3 Leucine-E-1 NH2 CH C

CH2 CH

O

CH3

CH3

C6H12NO2-E-1 Caprolactam-E-2 O

COH

(CH2)5NH

C6H12NO2-E-2 Isoleucine-E-2

OC

OHNH CH

CHC2H5CH3

C6H12NO2-E-3 Leucine-E-2

OC

OHNH CH

CH2

CH3CH CH3

C6H12N2O-R Lysine-R

OCNH CH

C4H8 NH2



C6H12N4O-R Arginine-R

NH CH CCH2

CH2

CH2

NHC NHNH2

O

C6H12O-R Vinyl-isobutyl-ether-R

CH2 CHO CH2 CH

CH3

CH3

C6H12O2-R Hexamethylene-diol-R O (CH2)6 O

C6H13-E-1 4-Methyl-1-pentene-E-2 CH2 CH2

CH2 CHCH3

CH3

C6H13-E-2 4-Methyl-1-pentene-E-3 CH3

CH3CH2 CHCHCH3

C6H13-E-3 1-Hexane-E-2 CH3 CH

C4H9

C6H13N2O-E Lysine-E-1 NH2 CH CO

NH2C4H8

C6H13N2O2-E Lysine-E-2

OCH CNH

OHNH2C4H8



C6H13N4O-E Arginine-E-1

OCH CCH2

CH2

CH2

NHC NHNH2

NH2

C6H13N4O2-E Arginine-E-2

CH CCH2

CH2

CH2

NHC NHNH2

NHO

OH

C6H13O-E Vinyl-isobutyl-ether-E-2

CH2 CH2

OCH2 CH

CH3

CH3

C6H13O2-E Hexamethylene-diol-E O (CH2)6 OH

C6H14N2-R Hexamethylene-diamine-R (CH2)6 NHNH

C6H15N2-E Hexamethylene-diamine-E (CH2)6NH NH2

C7H5O-E Benzoic-acid-E C

O

C7H5O2-E Phenylcarbonate-E CO

O

C7H6N-E 4-Vinyl-pyridine-E-1

CH CH

N



C7H7N-R 4-Vinyl-pyridine-R

N

CHCH2

C7H8N-E 4-Vinyl-pyridine-E-2

N

CH2 CH2

C7H10O2-R Pimelic-acid-R C(CH2)5C

O O

C7H11O2-E-1 n-Butyl-acrylate-E-1

CH CHC

O O C4H9

C7H11O2-E-2 n-Propyl-methacrylate-E-1 CH C

CO O C3H7

CH3

C7H11O3-E Pimelic-acid-E C(CH2)5COH

O O

C7H12O2-R-1 n-Butyl-acrylate-R

CH

O O C4H9

CCH2

C7H12O2-R-2 n-Propyl-methacrylate-R

O O C3H7

CH2 CC

CH3

C7H13-E 1-Heptene-E-1 CH CH

C5H11

C7H13O2-E-1 n-Butyl-acrylate-E-2

O O C4H9

CH2 CH2

C



C7H13O2-E-2 n-Propyl-methacrylate-E-2

O O C3H7

CH2 CHC

CH3

C7H13O2-E-3 n-Propyl-methacrylate-E-3

O O C3H7

CH3

CCH3 C

C7H14-R 1-Heptene-R CH2 CH

C5H11

C7H15-E-1 1-Heptene-E-2 CH2 CH2

C5H11

C7H15-E-2 1-Heptene-E-3 C5H11

CH3 CH

C8H4O2-R Terephthalate-R C CO O

C8H4O2-R-1 Phthalate-R C

C

O

O

C8H4O2-R-2 Isophthalate-R C

COO

C8H5O3-E Terephthalic-acid-E C CO O

OH

C8H5O3-E-1 Phthalic-acid-E C

C OH

O

O



C8H5O3-E-2 Isophthalic acid-E C

COO

OH

C8H6Br-E p-Bromostyrene-E-1

Br

CHCH

C8H6Cl-E-1 o-Chlorostyrene-E-1

CHCHCl

C8H6Cl-E-2 p-Chlorostyrene-E-1

CHCH

Cl

C8H7-E Styrene-E-1

CHCH

C8H7Br-R p-Bromostyrene-R

CH

Br

CH2

C8H7Cl-R-1 o-Chlorostyrene-R

CHCl

CH2

C8H7Cl-R-2 p-Chlorostyrene-R

CH

Cl

CH2

C8H8-R Styrene-R

CHCH2



C8H8Br-E p-Bromostyrene-E-2

CH2 CH2

Br

C8H8Cl-E-1 o-Chlorostyrene-E-2

CH2 CH2Cl

C8H8Cl-E-2 p-Chlorostyrene-E-2

CH2 CH2

Cl

C8H8N-E 2-Methyl-5-vinylpyridine-E-1

CH CH

NCH3

C8H8O-R Phenylene-oxide-R

CH3

CH3

O

C8H9-E Styrene-E-2

CH2 CH2

C8H9N-R 2-Methyl-5-vinylpyridine-R

NCH3

CHCH2

C8H10N-E 2-Methyl-5-vinylpyridine-E-2

CH2 CH2

CH3N



C8H12O2-R Suberic-acid-R C(CH2)6C

O O

C8H12O6-R Cellulose-acetate-R O

OH OH

O

CH2 O C CH3

O

C8H13O2-E-1 n-Butyl-methacrylate-E-1 CH C

CH3

CO O C4H9

C8H13O2-E-2 Isobutyl-methacrylate-E-1 CH C

CH3

CO O CH2 CH CH3

CH3

C8H13O2-E-3 sec-Butyl-methacrylate-E-1 CH C

CH3

CO O CH

CH3

C2H5

C8H13O3-E Suberic-acid-E C(CH2)6COH

O O

C8H13O6-E Cellulose-acetate-E O

OH OH

CH2 O C CH3

O

OH

C8H14N2O2-R Hexamethylene-diisocyanate-R C NH (CH2)6 NH CO O

C8H14O2-R-1 n-Butyl-methacrylate-R CH2 C

CH3

CO O C4H9



C8H14O2-R-2 Isobutyl-methacrylate-R CH2 C

CH3

CO O CH2 CH CH3

CH3

C8H14O2-R-3 sec-Butyl-methacrylate-R CH2 C

CH3

CO O CH

CH3

C2H5

C8H15-E 1-Octene-E-1 CH CH

C6H13

C8H15O2-E-1 n-Butyl-methacrylate-E-2 CH2 CH

CO O C4H9

CH3

C8H15O2-E-2 n-Butyl-methacrylate-E-3

O O C4H9CCCH3

CH3

C8H15O2-E-3 Isobutyl-methacrylate-E-2

O O CH2 CHC

CH3CH2 CHCH3

CH3

C8H15O2-E-4 Isobutyl-methacrylate-E-3

O O CH2 CHC

CH3

CH3

CH3

CH3 C

C8H15O2-E-5 sec-Butyl-methacrylate-E-2

O O CH C2H5C

CH3

CH3CH2 CH



C8H15O2-E-6 sec-Butyl-methacrylate-E-3

O O CHC

CH3

CH3CH3 C

C2H5

C8H16-R 1-Octene-R CH2 CH

C6H13

C8H17-E-1 1-Octene-E-2 CH2 CH2

C6H13

C8H17-E-2 1-Octene-E-3 C6H13

CH3 CH

C9H7O3-E Dimethyl-terephthalate-E C CO O

CH3O

C9H9-E-1 Alpha-Methylstyrene-E-1 CCHCH3

C9H9-E-2 m-Methylstyrene-E-1

CH3

CHCH

C9H9-E-3 o-Methylstyrene-E-1

CHCHCH3

C9H9-E-4 p-Methylstyrene-E-1

CHCH

CH3



C9H9NO-R Phenylalanine-R CH2

CH CNHO

C9H9NO2-R Tyrosine-R CH2

CH C

OH

NHO

C9H9O-E p-Methoxystyrene-E-1

OCH3

CHCH

C9H10-R-1 alpha-Methylstyrene-R CCH2

CH3

C9H10-R-2 m-Methylstyrene-R

CH3

CHCH2

C9H10-R-3 o-Methylstyrene-R

CHCH3

CH2

C9H10-R-4 p-Methylstyrene-R

CH

CH3

CH2



C9H10NO-E Phenylalanine-E-1 CH2

CH CNH2

O

C9H10NO2-E-1 Phenylalanine-E-2 CH2

CH CNHO

OH

C9H10NO2-E-2 Tyrosine-E-1 CH2

CH CNH2

OH

O

C9H10NO3-E Tyrosine-E-2 CH2

CH C

OH

NHO

OH

C9H10O-R p-Methoxystyrene-R

CH

OCH3

CH2

C9H11-E-1 alpha-Methylstyrene-E-2 CHCH3

CH2



C9H11-E-2 alpha-Methylstyrene-E-3

CH3

CH3 C

C9H11-E-3 m-Methylstyrene-E-2

CH3

CH2 CH2

C9H11-E-4 o-Methylstyrene-E-2 CH3

CH2 CH2

C9H11-E-5 p-Methylstyrene-E-2

CH3

CH2 CH2

C9H11O-E p-Methoxystyrene-E-2

OCH3

CH2 CH2

C9H12-R Ethylidene-norbornene-R CH2

CH

CH2CH3

CH

CH

CH

C

CH

C9H14O2-R Azelaic-acid-R C(CH2)7C

O O

C9H15O2-E-1 n-Hexyl-acrylate-E-1

CH CHC

O O C6H13



C9H15O2-E-2 n-Pentyl-methacrylate-E-1 CH C

C

CH3

O O C5H11

C9H15O3-E Azelaic-acid-E C(CH2)7COH

O O

C9H16O2-R-1 n-Hexyl-acrylate-R

O O C6H13

CHC

CH2

C9H16O2-R-2 n-Pentyl-methacrylate-R

C9H17-E 1-Nonene-E-1 CH CH

C7H15

C9H17O2-E-1 n-Hexyl-acrylate-E-2 O O C6H13

CH2 CH2

C

C9H17O2-E-2 n-Pentyl-methacrylate-E-2

O O C5H11

CH3

CHCH2C

C9H17O2-E-3 n-Pentyl-methacrylate-E-3

O O C5H11

C

CH3

CCH3

C9H18-R 1-Nonene-R CH2 CH

C7H15

C9H19-E-1 1-Nonene-E-2 CH2 CH2

C7H15

C9H19-E-2 1-Nonene-E-3 CHC7H15

CH3



C10H12-R Dicyclopentadiene-R

CH2

CH

CH2

CH

CH

CH

CH

CH

CH

CH

C10H15O2-E Cyclohexyl-methacrylate-E-1

O OC

CH3

CCH

C10H16O2-R Cyclohexyl-methacrylate-R

O OC

CH3

CCH2

C10H16O2-R-1 Sebacic-acid-R C(CH2)8C

O O

C10H17O2-E-1 Cyclohexyl-methacrylate-E-2

O OC

CH3

CHCH2

C10H17O2-E-2 Cyclohexyl-methacrylate-E-3

O OC

CH3CCH3

C10H17O2-E-3 n-Hexyl-methacrylate-E-1

O OC

C6H13

CH3CCH

C10H17O3-E Sebacic-acid-E C(CH2)8COH

O O



C10H18O2-R n-Hexyl-methacrylate-R

O OC

C6H13

CH3CCH2

C10H19-E 1-Decene-E-1 CH CH

C8H17


O OC

C6H13

CH3CHCH2


O OC

C6H13

CH3CCH3

C10H20-R 1-Decene-R CHC8H17

CH2

C10H21-E-1 1-Decene-E-2 CH2 CH2

C8H17

C10H21-E-2 1-Decene-E-3 CH3 CH

C8H17

C11H10N2O-R Tryptophan-R

NH CH CCH2

N

O

C11H11N2O-E Tryptophan-E-1 CH2

N

CH CNH2

O



C11H11N2O2-E Tryptophan-E-2

NH CH CCH2

N

O

OH

C11H21-E 1-Undecene-E-1 CH CH

C9H19

C11H22-R 1-Undecene-R CHC9H19

CH2

C11H23-E-1 1-Undecene-E-2 CH2 CH2

C9H19

C11H23-E-2 1-Undecene-E-3 CH3 CH

C9H19

C12H6O2-R 2,6-Napthalene-diacid-R

C12H7O3-E 2,6-Napthalene-diacid-E

C12H16O8-R Cellulose-triacetate-R O

O O

O

CCCH3 CH3

CH2

OO

O C CH3

O

C12H17O8-E Cellulose-triacetate-E O

O O CCCH3 CH3

CH2

HOOO

O C CH3

O



C12H22N2O8-R Chitosan-R O

O

OH NH2

CH2OH

OCH2OH

O

NH2OH

C12H23-E 1-Dodecene-E-1 CH CH

C10H21

C12H23N2O8-E Chitosan-E-1 O

O

OH NH2

CH2OH

OCH2OH

NH2OH

OH

C12H23N2O9-E Chitosan-E-2 O

O

OH NH2

CH2OH

HOO

CH2OH

NH2OH

O

C12H24-R 1-Dodecene-R CH2 CH

C10H21

C12H25-E-1 1-Dodecene-E-2 CH2 CH2

C10H21

C12H25-E-2 1-Dodecene-E-3 C10H21

CH3 CH

C13H9O3-E 2,6-Napthalene-dimethylester-E

C14H23NO10-R Heparin-R O

O

O OH

CH2OH

HOO

OH NH C CH3

CH2OH

O



C14H24NO10-E Heparin-E-1 O

O

OH

CH2OH

HO

OH

O

OH NH C CH3

CH2OH

O

C14H24NO11-E Heparin-E-2

OO

OH

CH2OH

HO

O

O

OH NH

OH

CH2OH

C CH3

O

C14H25O2-E Decyl-methacrylate-E-1 CH C

CH3

CO C10H21

O

C14H26O2-R Decyl-methacrylate-R

O C10H21O

CCH3

CCH2

C14H27O2-E-1 Decyl-methacrylate-E-2 CHCH3

O C10H21

CCH2

O

C14H27O2-E-2 Decylmethacrylate-E-3

O C10H21

C

CH3

CH3 C

O

C15H14O2-R Bisphenol-A-R O CCH3

CH3

O

C15H15O2-E Bisphenol-A-E O CCH3

CH3

OH

B Kinetic Rate Constant Parameters 421

B Kinetic Rate Constant Parameters

This appendix provides decomposition rate parameters for commonly used initiators. Within each group the initiators are arranged by increasing total number of carbon atoms.

The parameters are grouped as follows:

• Water Soluble Azo-nitriles

• Solvent Soluble Azo-Nitriles

• Diacyl Peroxides

• Peroxycarbonates

• Alkyl Peroxides

• Hydroperoxides

• Peroxyesters

• C-C Initiators

• Sulfonyl Peroxides

Initiator Decomposition Rate Parameters The table at the end of this section shows the decomposition rate parameters for monofunctional free-radical initiators. These parameters assume first-order decomposition kinetics. These data are all included in the INITIATOR database in Aspen Polymers (formerly known as Aspen Polymers Plus).

Initiator decomposition rates depend on several factors including temperature, pressure, solvent type, and initiator concentration.

Solvent Dependency Decomposition rates are lowest in solvents that act as radical scavengers, such as poly chlorinated organic compounds (e.g., TCE). Initiators used for bulk-phase vinyl chloride polymerizations are typically in these types of

422 B Kinetic Rate Constant Parameters

compounds since they closely mimic the solvent environment during polymerization. Decomposition rates may be increased by a factor of 2-3 in polar solvents such as chlorobenzene compared to reactions in non-polar solvents such as benzene. Decomposition rates of water-soluble initiators are typically measured in water. The table that follows lists the solvents in which the rate parameters are measured. The user may wish to apply correction factors to the rate parameters when the polymerization solvent environment is different than the measurement basis.

Concentration Dependency At high initiator concentrations there is an induced initiation effect. Primary radicals attack and split un-decomposed initiator molecules. This reduces the measured half-life time and efficiency of the initiator. All of the data reported in the following table are based on measurements at relatively low initiator concentrations (0.2 molar or less). Although the standard decomposition rate expressions do not account for induced initiator, the user may modify the rate expression using a gel effect term.

Temperature Dependency Initiator decomposition rates are reported in several formats including rate constants, half-life times at specified temperatures, and half-life temperatures at specified times. These data are all related to each other through the following equations:

⎟⎟⎠

⎞⎜⎜⎝

⎛ −×=

refT RT

EAkref

exp ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−

−×=

refTT TTR

Ekkref

11exp

TT t

k,2

1

)5.0ln(−=

⎟⎠⎞

⎜⎝⎛ −−

=

AR

ET

3600)5.0ln(ln

60

Where:

A = Pre-exponential factor (1/sec)

refTk = Decomposition rate at reference temperature (1/sec)

Tk = Decomposition rate at temperature T, K

E = Activation energy (J/kmol-K)


refTf

= Reference temperature, K

T = Temperature, K

Tt ,21 = Half life at temperature T, sec

These equations were applied to the published raw data to allow the rate constants to be published in a concise format here.

B Kinetic Rate Constant Parameters 423

Pressure Dependency Most sources do not publish activation volume, which describe the pressure dependency of the reaction rates. Initiator decomposition reactions are known to exhibit pressure dependence over very wide ranges of pressure. For example, the half-life of organic peroxides double with a 3000 bar pressure increase (Degussa, 2004), which implies an activation volume of 1.9x10-5

kmolm /3 . This term can be ignored for processes that operate at reasonably low pressures.

The following table shows the decomposition rate parameters for monofunctional free-radical initiators at a reference temperature of 60°C (Tref(K)=333.15). These data are all included in the INITIATOR database in Aspen Polymers.

42

4

B

Kin

eti

c R

ate

Co

nst

an

t P

ara

mete

rs

D

eco

mp

osi

tio

n R

ate

P

ara

mete

rs

Deco

mp

osi

tio

n

Act

ivati

on

En

erg

y

Half

Lif

e

Tem

pera

ture

, °C

ID

Lo

ng

Nam

e

Tra

de N

am

e(s

) Fo

rmu

la /

Mo

lecu

lar

Str

uct

ure

M

W

CA

S N

o

kre

f (1

/s)

A

(1

/se

c)

kca

l/m

ol

GJ/

km

ol

1 m

in

1 h

r 1

0 h

r S

olv

en

t S

ou

rce

Wate

r S

olu

ble

Azo

-Nit

rile

s

ABAH

2,2

’-az

o-b

is(2

-am

idin

opro

pan

e)

dih

ydro

chlo

ride

Vaz

o 5

6 (

DuPo

nt)

V-5

0 (

Wako

Chem

) C8H

20N

6Cl2

NN

HN

H2N

NH

2

NH

HC

lH

Cl

271.1

9264

2997-9

2-4

3.3

436E-0

5

6.4

4E+

14

29.4

0.1

2300

110.5

73.7

55.9

W

ate

r D

uPo

nt

VAZO

68

4,4

’-az

o-b

is

(4-c

yanova

leric

acid

) Vaz

o 6

8 (

DuPo

nt)

C12H

22N

2O

4

NN

CO

OH

HO

OC

258.3

1776

2638-9

4-0

7.3

642E-0

6

5.1

2E+

12

27.2

0.1

1380

132.7

88.7

68.0

W

ate

r D

uPo

nt

VA61

2,2

’-az

o-b

is[2

-(2-

imid

azolin

-2-y

l)pro

pan

e]

VA-0

61 (

Wako

Chem

) C12H

22N

6

NN

N N HH

NN

250.3

4712

20858-1

2-2

1.3

404E-0

3

1.0

0E+

15

27.2

0.1

1400

78.4

45.0

28.9

Aci

dic

wate

r W

ako

VA86

2,2

’-Azo

bis

[2-m

ethyl

-N-(

2-

hyd

roxy

ethyl

)pro

pio

nam

ide]

VA-0

86

C12H

24N

4O

4

NN

HN

CH

2CH

2OH

HO

H2C

H2C

NH

OO

288.3

4712

61551-6

9-7

6.7

869E-0

6

7.9

5E+

14

30.6

0.1

2800

123.9

86.0

67.7

W

ate

r W

ako

VAZO

44

2,2

’-az

o-b

is(N

,N’-

dim

ethyl

ene

isobuty

ram

idin

e)

dih

ydro

chlo

ride

Vaz

o 4

4 (

DuPo

nt)

VA-4

4 (

Wak

oChem

) C12H

24Cl2

N6 N

NN N H

HNN

2HC

l

323.2

6840

27776-2

1-2

1.3

564E-0

4

8.1

0E+

12

25.6

0.1

0700

103.3

63.0

44.0

W

ate

r D

uPo

nt

VA46B

2,2

’-az

o-b

is[2

-(2-

imid

azolin

-2-y

l)pro

pan

e dis

ulfat

e dih

ydra

te

VA-0

46B (

Wako

Chem

) C12H

30N

6O

10S2

NN

N N HH

NNH

2SO

4H

2O

482.5

3664

20858-1

2-2

1.4

388E-0

3

1.1

8E+

17

30.4

0.1

2700

75.9

46.0

31.4

W

ate

r W

ako

VA41

2,2

’-az

o-b

is[2

-(5-m

ethyl

- 2-i

mid

azolin

-2-y

l)pro

pan

e]

dih

ydro

chlo

ride

VA-0

41 (

Wako

Chem

) C14H

26Cl2

N6

NN

N N HN HN H

Cl

HC

l

349.3

0628

n/a

2.7

035E-0

4

2.5

3E+

15

28.9

0.1

2100

91.3

57.4

41.0

W

ate

r W

ako

VA58

2,2

’-az

obis

[2-(

3,4

,5,6

-te

trah

ydro

pyr

imid

in-2

-yl

)pro

pan

e] d

ihyd

roch

loride

VA-0

58 (

Wako

Chem

) C14H

28Cl2

N6 N

N2H

Cl

HNN

N NH

351.3

2216

102834-3

9-0

2.5

342E-0

5

1.4

4E+

15

30.1

0.1

2600

111.8

75.5

58.0

W

ate

r W

ako

VA57

2,2

’-az

obis

[N-(

2-

carb

oxy

ethyl

)-2-

met

hyl

pro

pio

nam

idin

e]

tetr

ahyd

rate

VA-0

57 (

Wako

Chem

) C14H

34N

6O

8

NN

HN

HN

NH

NH

CO

OH

HO

OC

4 H

2O

414.4

5960

n/a

2.8

824E-0

5

5.5

6E+

14

29.4

0.1

2300

112.0

74.9

57.0

W

ate

r W

ako

B

Kin

eti

c R

ate

Co

nst

an

t P

ara

mete

rs

42

5

Deco

mp

osi

tio

n R

ate

P

ara

mete

rs

Deco

mp

osi

tio

n

Act

ivati

on

En

erg

y

Half

Lif

e

Tem

pera

ture

, °C

ID

Lo

ng

Nam

e

Tra

de N

am

e(s

) Fo

rmu

la /

Mo

lecu

lar

Str

uct

ure

M

W

CA

S N

o

kre

f (1

/s)

A

(1

/se

c)

kca

l/m

ol

GJ/

km

ol

1 m

in

1 h

r 1

0 h

r S

olv

en

t S

ou

rce

VA85

2,2

’-Azo

bis

{2-m

ethyl

-N-[

2-

(1-h

ydro

xybuth

yl)]

pro

pio

nam

ide}

VA-0

85 (

Wako

Chem

) C16H

32N

4O

4

NN

HN

NH

OO

CH

2CH

3

CH

2OH

HO

H2C

H3C

H2C

344.4

5464

n/a

7.8

450E-0

7

6.4

1E+

13

30.4

0.1

2700

148.2

105.4

85.0

W

ate

r W

ako

VA60

2,2

’-az

o-b

is{2-[

1-(

2-

hyd

roxy

ethyl

)-2-i

mid

azolin

-2-y

l]pro

pan

e}

dih

ydro

chlo

ride

VA-0

60 (

Wako

Chem

) C16H

32Cl2

N6O

2

NN

N NNN

2HC

l

CH

2CH

2OH

CH

2CH

2OH

411.3

7472

11858-1

3-0

1.9

254E-0

5

9.5

6E+

15

31.5

0.1

3200

111.7

76.9

60.0

W

ate

r W

ako

So

lven

t S

olu

ble

Azo

-Nit

rile

s

V30

1-c

yano-1

-met

hyl

-et

hyl

azofo

mam

ide

V-3

0 (

Wako

Chem

) C5H

8N

4O

NN

CONH

2

CN

140.1

4488

10288-2

8-5

4.4

161E-0

8

1.8

6E+

15

34.5

0.1

4430

164.9

123.9

104.0

Tolu

ene

Wako

AIB

N

2,2

'-az

o-b

is-i

sobuty

ronitrile

Vaz

o 6

4 (

DuPo

nt)

Pe

rkad

ox

AIB

N

(Akz

oN

obel

)

C8H

12N

4

NC

NN

CN

164.2

1024

78-6

7-1

1.0

464E-0

5

2.7

4E+

15

31.1

0.1

3023

118.3

82.0

64.4

Chlo

roben

zene

Akz

oN

obel

AM

BN

2,2

'-az

o-b

is(2

-m

ethyl

buty

ronitrile

) Vaz

o 6

7 (

DuPo

nt)

Pe

rkad

ox

AM

BN

(A

kzoN

obel

)

V-5

9 (

Wako

Chem

)

C10H

16N

4

C2H

5

CN

NN

CN

C2H

5

192.2

6400

13472-0

8-7

8.4

357E-0

6

1.3

8E+

15

30.8

0.1

2893

121.2

84.0

66.0

Chlo

roben

zene

Akz

oN

obel

V601

dim

ethyl

2,2

'-az

obis

(2-

met

hyl

pro

pio

nat

e)

V-6

01 (

Wako

Chem

) C10H

18N

2O

4

NN

OO

OC

H3

H3C

O

230.2

6400

2589-5

7-3

8.5

556E-0

6

6.9

9E+

14

30.4

0.1

2700

122.1

84.3

66.0

Tolu

ene

Wako

ACCN

1,1

-azo

-di-

(hex

a

hyd

roben

zenen

onitrile

) Vaz

o 8

8 (

DuPo

nt)

Pe

rkad

ox

ACCN

(A

kzoN

obel

)

V-4

0 (

Wako

Chem

)

C14H

20N

4 N

NCNNC

244.3

3976

2094-9

8-6

5.4

449E-0

7

1.0

7E+

16

34.0

0.1

4219

140.2

103.0

84.9

Chlo

roben

zene

Akz

oN

obel

AM

VN

2,2

'-az

o-b

is(2

,4-d

imet

hyl

va

lero

nitrile

) Vaz

o 5

2 (

DuPo

nt)

V-6

5 (

Wako

Chem

) C14H

24N

4

248.3

7152

4419-1

1-8

1.0

349E-0

4

1.7

8E+

14

27.8

0.1

1630

102.1

65.0

47.2

Tolu

ene

DuPo

nt

VF0

96

2,2

'-az

o-b

is[N

-(2-

pro

pen

yl)-

2-

met

hyl

pro

pio

nam

ide]

VF-

096 (

Wako

Chem

) C14H

24N

4O

2

NN

OO

HN

NH

280.3

7032

129136-9

2-1

1.5

480E-0

7

4.6

7E+

14

32.7

0.1

3700

157.8

116.1

96.0

Tolu

ene

Wako

42

6

B

Kin

eti

c R

ate

Co

nst

an

t P

ara

mete

rs

Deco

mp

osi

tio

n R

ate

P

ara

mete

rs

Deco

mp

osi

tio

n

Act

ivati

on

En

erg

y

Half

Lif

e

Tem

pera

ture

, °C

ID

Lo

ng

Nam

e

Tra

de N

am

e(s

) Fo

rmu

la /

Mo

lecu

lar

Str

uct

ure

M

W

CA

S N

o

kre

f (1

/s)

A

(1

/se

c)

kca

l/m

ol

GJ/

km

ol

1 m

in

1 h

r 1

0 h

r S

olv

en

t S

ou

rce

AM

OM

VN

2,2

'-az

o-b

is(4

-met

hoxy

-2,4

-dim

ethyl

vale

ronitri

le)

V-7

0 (

Wako

Chem

) C16H

28N

4O

2

H2C

CN

NN

CN

CH

2O

CH

3H

3CO

308.4

2408

15545-9

7-8

1.1

718E-0

3

1.2

6E+

15

27.5

0.1

1500

79.4

46.1

30.0

Tolu

ene

Wako

VAM

110

2,2

'-az

o-b

is(N

-buty

l-2-

met

hyl

pro

pio

nam

ide)

Vam

-100 (

Wako

Chem

) C16H

32N

4O

2

NN

HN

C4H

9C

4H9

NH

OO

312.4

5584

n/a

2.3

941E-0

8

4.4

0E+

14

33.9

0.1

4200

174.2

130.9

110.0

Tolu

ene

Wako

VAM

111

2,2

'-az

o-b

is(N

-cyc

lohex

yl-

2-m

ethyl

pro

pio

nam

ide)

Vam

-110 (

Wako

Chem

) C20H

36N

4O

2

NN

HN

NH

OO

364.5

3160

n/a

3.4

427E-0

8

1.7

1E+

13

31.5

0.1

3200

181.3

133.7

111.0

Tolu

ene

Wako

Dia

cyl P

ero

xid

es

PP

dip

ropio

nyl

per

oxi

de

C6H

10O

4 O

OO

O

146.1

4300

3248-2

8-0

4.3

006E-0

5

1.1

4E+

15

30.5

0.1

2760

119.1

81.9

63.9

Ben

zene

Poly

mer

H

andbook

SAP

succ

inic

aci

d p

eroxi

de

Luper

ox

SAP

(Ato

fina)

SU

CP-

70-W

(D

eguss

a)

C8H

10O

8

O

OO

OO

HH

OO

O

234.1

6260

123-2

3-9

8.7

924E-0

6

4.8

9E+

10

24.0

0.1

0043

142.3

91.0

67.4

Ace

tone

Ato

fina

IBP

diis

obuty

ryl per

oxi

de

Trigonox

187-C

30

(Akz

oN

obel

) C8H

14O

2

O

OO

O

142.1

9796

3437-8

4-1

2.7

220E-0

3

3.4

2E+

14

26.1

0.1

0906

72.7

39.0

22.8

Chlo

roben

zene

Akz

oN

obel

BP

dib

enzo

yl p

eroxi

de

Luper

ox

AFR

40 (

Ato

fina)

C14H

10O

4

OO

OO

242.2

3100

94-3

6-0

3.8

607E-0

6

3.4

0E+

14

30.4

0.1

2721

130.3

91.0

72.1

Ben

zene

Ato

fina

DCLB

P bis

(2,4

-dic

hlo

roben

zoyl

) per

oxi

de

DCLB

P (D

eguss

a)

C16H

6Cl2

O4

OO

OO

Cl

Cl

Cl

Cl

333.1

2664

133-1

4-2

4.2

163E-0

5

3.9

5E+

14

28.9

0.1

2100

109.1

72.0

54.1

Ben

zene

Deg

uss

a

B

Kin

eti

c R

ate

Co

nst

an

t P

ara

mete

rs

42

7

Deco

mp

osi

tio

n R

ate

P

ara

mete

rs

Deco

mp

osi

tio

n

Act

ivati

on

En

erg

y

Half

Lif

e

Tem

pera

ture

, °C

ID

Lo

ng

Nam

e

Tra

de N

am

e(s

) Fo

rmu

la /

Mo

lecu

lar

Str

uct

ure

M

W

CA

S N

o

kre

f (1

/s)

A

(1

/se

c)

kca

l/m

ol

GJ/

km

ol

1 m

in

1 h

r 1

0 h

r S

olv

en

t S

ou

rce

OM

BP

bis

(ort

ho-m

ethyl

ben

zoyl

) per

oxi

de

Perk

adox

20 (

Akz

o

Nobel

)

OM

BP

(Deg

uss

a)

C16H

14O

4

OO

OO

270.2

8476

3034-7

9-5

1.5

072E-0

5

6.8

5E+

13

28.4

0.1

1900

120.9

81.0

61.9

Ben

zene

Deg

uss

a

PMBP

bis

(par

a-m

ethyl

ben

zoyl

) per

oxi

de

PMBP

(Deg

uss

a)

C16H

14O

4

OO

OO

270.2

8476

895-9

5-2

5.1

895E-0

6

2.0

6E+

14

29.9

0.1

2500

128.6

89.0

70.0

Ben

zene

Deg

uss

a

OP

dio

ctan

oyl

per

oxi

de

Trigonox

SE-8

(A

kzoN

obel

) C16H

30O

4

H3C

(CH

2)6

O

OO

(CH

2)6C

H3

O 2

86.4

1180

762-1

6-3

1.3

761E-0

5

2.3

6E+

15

30.8

0.1

2905

116.3

80.0

62.4

Chlo

roben

zene

Akz

oN

obel

INP

bis

(3,5

,5-

trim

ethyl

hex

anoyl

) per

oxi

de

Trigonox

36

(Akz

oN

obel

)

Luper

ox

219 (

Ato

Fina)

C18H

34O

4

OO

OO

314.4

6556

3851-8

7-4

2.0

300E-0

5

2.7

0E+

15

30.7

0.1

2835

112.8

77.0

59.6

Chlo

roben

zene

Akz

oN

obel

DP

did

ecan

oyl

per

oxi

de

Luper

ox

DEC (

Ato

fina)

Pe

rkadox

SE-1

0

(Akz

oN

obel

)

C20H

38O

4

OO

O

OC

9H19

C9H

19

342.5

1932

762-1

2-9

1.4

646E-0

5

8.3

4E+

14

30.1

0.1

2600

117.2

80.0

62.0

Ben

zene

Deg

uss

a

LP

dila

uro

yl p

eroxi

de

Luper

ox

LP (

Ato

fina)

Lauro

x (A

kzoN

obel

) C24H

46O

4

OO

O

OC

11H

23C

11H

23

398.6

2684

105-7

4-8

1.7

414E-0

5

3.8

4E+

14

29.5

0.1

2337

116.9

79.0

60.8

Chlo

roben

zene

Akz

oN

obel

Pero

xyca

rbo

nate

s

BPI

C

tert

-buty

lper

oxy

iso

pro

pyl

ca

rbonat

e Trigonox

BPI

C

C8H

16O

4

OO

OO

176.2

1264

2372-2

1-6

7.0

005E-0

8

2.4

4E+

16

35.9

0.1

5015

154.9

117.0

98.5

Chlo

roben

zene

Akz

oN

obel

42

8

B

Kin

eti

c R

ate

Co

nst

an

t P

ara

mete

rs

Deco

mp

osi

tio

n R

ate

P

ara

mete

rs

Deco

mp

osi

tio

n

Act

ivati

on

En

erg

y

Half

Lif

e

Tem

pera

ture

, °C

ID

Lo

ng

Nam

e

Tra

de N

am

e(s

) Fo

rmu

la /

Mo

lecu

lar

Str

uct

ure

M

W

CA

S N

o

kre

f (1

/s)

A

(1

/se

c)

kca

l/m

ol

GJ/

km

ol

1 m

in

1 h

r 1

0 h

r S

olv

en

t S

ou

rce

IPPC

diis

opro

pyl

per

oxy

dic

arbonat

e IP

PC (

Deg

uss

a)

C8H

16O

6

OO

O

OO

O

208.2

1144

105-6

4-6

1.6

931E-0

4

7.7

0E+

14

28.4

0.1

1900

96.3

61.0

44.0

Ben

zene

Deg

uss

a

NPP

C

di-

n-p

ropyl

per

oxy

dic

arbonat

e Lu

per

ox

221 (

Ato

Fina)

Trigonox

NPP

-CK85

(Akz

oN

obel

)

C8H

16O

6

OO

O

OO

O

208.2

1144

16066-3

8-9

1.4

752E-0

4

3.5

6E+

15

29.5

0.1

2362

96.1

62.0

45.5

Chlo

roben

zene

Akz

oN

obel

SBPC

di-

secb

uty

l per

oxy

dic

arbonat

e Lu

per

ox

225 (

Ato

Fina)

Trigonox

SBP

(Akz

oN

obel

)

C10H

16O

6

OO

O

OO

O

232.2

3344

19910-6

5-7

1.2

919E-0

4

3.3

8E+

15

29.6

0.1

2385

97.2

63.0

46.4

Chlo

roben

zene

Akz

oN

obel

TBPI

C

tert

-buty

lper

oxy

-is

opro

pyl

carb

onat

e Trigonox

BPI

C (

Akz

o)

Luper

ox

TBIC

(Ato

Fina)

TBPI

C (

Deg

uss

a)

C11H

20O

6

OO

O O

248.2

7620

2372-2

1-6

7.0

005E-0

8

2.4

4E+

16

35.9

0.1

5015

154.9

117.0

98.5

Chlo

roben

zene

Akz

oN

obel

TBPE

HC

tert

-buty

lper

oxy

2-

ethyl

hex

yl c

arbonate

Trigonox

117

(Akz

oN

obel

)

Luper

ox

TBEC (

Ato

Fina)

C13H

26O

4 O

OO

OC

4H9 C2H

5

246.3

4704

12/4

/3443

6.4

441E-0

8

3.9

5E+

16

36.3

0.1

5172

154.4

117.0

98.7

Chlo

roben

zene

Akz

oN

obel

CH

PC

dic

yclo

hex

yl

per

oxy

dic

arbonat

e CH

PC (

Deg

uss

a)

C14H

22O

6

OO

O

OO

O

286.3

2508

1561-4

9-5

1.9

626E-0

4

3.3

0E+

16

30.8

0.1

2900

91.9

59.9

44.2

Chlo

roben

zene

Akz

oN

obel

(P

oly

mer

H

andbook)

TAPE

HC

tert

-am

ylper

oxy

2-

ethyl

hex

yl c

arbonate

Trigonox

131

(Akz

oN

obel

)

Luper

ox

TAEC (

Ato

Fina)

C14H

28O

4

OO

OC

2H5

O

C2H

5

C4H

9

260.3

7392

70833-4

0-8

1.2

326E-0

7

2.2

9E+

16

35.5

0.1

4841

150.5

113.0

94.7

Chlo

roben

zene

Akz

oN

obel

EH

PC

di(

2-e

thyl

hex

yl)

per

oxy

dic

arbonat

e Lu

per

ox

223 (

Ato

Fina)

Trigonox

EH

P (A

kzoN

obel

)

C18H

34O

6

OO

O

OO

O

346.4

6436

16111-6

2-9

1.1

396E-0

4

1.8

0E+

15

29.3

0.1

2245

98.9

64.0

47.1

Chlo

roben

zene

Akz

oN

obel

B

Kin

eti

c R

ate

Co

nst

an

t P

ara

mete

rs

42

9

Deco

mp

osi

tio

n R

ate

P

ara

mete

rs

Deco

mp

osi

tio

n

Act

ivati

on

En

erg

y

Half

Lif

e

Tem

pera

ture

, °C

ID

Lo

ng

Nam

e

Tra

de N

am

e(s

) Fo

rmu

la /

Mo

lecu

lar

Str

uct

ure

M

W

CA

S N

o

kre

f (1

/s)

A

(1

/se

c)

kca

l/m

ol

GJ/

km

ol

1 m

in

1 h

r 1

0 h

r S

olv

en

t S

ou

rce

BCH

PC

Di(

4-t

ert-

buty

lcyc

lohex

yl)

per

oxy

dic

arbonat

e Pe

rkadox

16

(Akz

oN

obel

) C22H

38O

6

OO

OO

O

O 3

98.5

4012

15520-1

1-3

1.1

205E-0

4

7.3

4E+

15

30.2

0.1

2639

97.7

64.0

47.6

Chlo

roben

zene

Akz

oN

obel

MYPC

D

imyr

isty

l per

oxy

dic

arbonat

e Pe

rkadox

26

(Akz

oN

obel

) C30H

58O

6

OO

O

OO

OC

14H

29C

14H

29

514.7

8692

53220-2

2-7

9.9

164E-0

5

3.0

6E+

15

29.7

0.1

2430

99.5

65.0

48.3

Chlo

roben

zene

Akz

oN

obel

CEPC

dic

etyl

per

oxy

dic

arbonat

e Pe

rkad

ox

24

(Akz

oN

obel

) C34H

66O

6

OO

O

OO

OC

16H

33C

16H

33

570.8

9444

26322-1

4-5

9.9

270E-0

5

2.8

5E+

15

29.7

0.1

2410

99.6

65.0

48.2

Chlo

roben

zene

Akz

oN

obel

Alk

yl P

ero

xid

es

DTBP

di-

tert

-buty

l per

oxi

de

Trigonox

B (

Akz

oN

obel

) Lu

per

ox

DI

(Ato

Fina)

C8H

18O

2 O

O

146.2

2972

110-0

5-4

3.7

905E-0

9

4.3

6E+

15

36.7

0.1

5346

182.9

141.0

120.7

Chlo

roben

zene

Akz

oN

obel

DTAP

di-

tert

-am

yl p

eroxi

de

Trigonox

201

(Akz

oN

obel

)

Luper

ox

DTA (

Ato

Fina)

C10H

22O

2 O

O

174.2

8348

10508-0

9-5

2.1

965E-0

8

3.9

9E+

15

35.5

0.1

4835

168.7

128.0

108.3

Chlo

roben

zene

Akz

oN

obel

BCU

P te

rt-b

uty

lcum

yl p

eroxi

de

Trigonox

T (

Akz

oN

obel

) BCU

P (D

eguss

a)

C13H

20O

2

OO

208.3

0060

3457-6

1-2

1.0

091E-0

8

1.1

2E+

15

35.1

0.1

4698

178.8

136.0

115.3

Chlo

roben

zene

Akz

oN

obel

DCU

P dic

um

yl p

eroxi

de

Perk

adox

BC

(Akz

oN

obel

)

Luper

ox

500 (

Ato

Fina)

C18H

22O

2

OO

270.3

7148

80-4

3-3

1.0

731E-0

8

9.2

8E+

15

36.5

0.1

5267

172.2

132.0

112.4

Chlo

roben

zene

Akz

oN

obel

DTBCP

di-

tert

-buty

l cu

myl

per

oxi

de

C26H

38O

2

382.5

8652

OO

3.6

200E-0

9

3.0

5E+

15

36.5

0.1

5260

184.4

142.0

121.4

Tolu

ene

Wars

on

(1980)

Hyd

rop

ero

xid

es

43

0

B

Kin

eti

c R

ate

Co

nst

an

t P

ara

mete

rs

Deco

mp

osi

tio

n R

ate

P

ara

mete

rs

Deco

mp

osi

tio

n

Act

ivati

on

En

erg

y

Half

Lif

e

Tem

pera

ture

, °C

ID

Lo

ng

Nam

e

Tra

de N

am

e(s

) Fo

rmu

la /

Mo

lecu

lar

Str

uct

ure

M

W

CA

S N

o

kre

f (1

/s)

A

(1

/se

c)

kca

l/m

ol

GJ/

km

ol

1 m

in

1 h

r 1

0 h

r S

olv

en

t S

ou

rce

TBH

P te

rt-b

uty

l hyd

roper

oxi

de

Trigonox

A (

Akz

oN

obel

) Lu

per

ox

TBH

(Ato

Fina)

TBH

P (D

eguss

a)

C4H

10O

2 O

OH

90.1

2220

75-9

1-2

2.1

276E-1

2

3.0

9E+

17

44.5

0.1

8600

226.9

185.0

164.4

Chlo

roben

zene

Akz

oN

obel

TAH

P te

rt-a

myl

hyd

roper

oxi

de

Trigonox

TAH

P (A

kzo)

TAH

P (A

toFi

na)

C5H

12O

2

C2H

5O

OH

104.1

4908

3425-6

1-4

6.2

470E-0

9

6.1

4E+

07

24.4

0.1

0200

234.1

190.0

153.0

Chlo

roben

zene

Akz

oN

obel

TM

BH

P 1,1

,3,3

-tet

ram

ethyl

buty

l hyd

roper

oxi

de

Trigonox

TM

BH

(A

kzoN

obel

) C8H

18O

2

OO

H

146.2

2972

5809-0

8-5

9.0

052E-1

1

9.1

3E+

18

44.2

0.1

8500

172.7

153.0

135.0

Chlo

roben

zene

Akz

oN

obel

CU

HP

cum

ene

hyd

roper

oxi

de

Trigonox

K (

Akz

oN

obel

) Lu

per

ox

CU

(Ato

Fina)

CU

HP

(Deg

uss

a)

C9H

12O

2

OO

H

152.1

9308

80-1

5-9

1.8

527E-0

9

1.1

3E+

12

31.7

0.1

3256

221.8

166.0

139.8

Chlo

roben

zene

Akz

oN

obel

IPCH

P is

opro

pyl

cum

yl

hyd

roper

oxi

de

Trigonox

M (

Akz

oN

obel

) C12H

18O

2

OO

H

194.2

7372

26762-9

3-6

5.6

157E-0

9

2.2

8E+

12

31.4

0.1

3144

207.1

154.0

129.0

Chlo

roben

zene

Akz

oN

obel

Pero

xyest

ers

TBPA

te

rt-b

uty

l per

oxy

acet

ate

Trigonox

F (A

kzoN

obel

) Lu

per

ox

7 (

Ato

Fina)

C6H

12O

3

OO

O

132.1

5948

107-7

1-1

5.7

708E-0

8

1.5

1E+

16

35.7

0.1

4936

157.5

119.0

100.2

Chlo

roben

zene

Akz

oN

obel

TAPA

te

rt-a

myl

per

oxy

acet

ate

Trigonox

133

(Akz

oN

obel

)

Luper

ox

555 (

Ato

Fina)

C7H

14O

3

OO

C2H

5

O

146.1

8636

690-8

3-5

2.5

042E-0

7

1.5

3E+

17

36.3

0.1

5171

141.3

106.0

88.7

Chlo

roben

zene

Akz

oN

obel

TBPI

B

tert

-buty

l per

oxy

isobuty

rate

Trigonox

41

(Akz

oN

obel

) C8H

16O

3

OO

O

160.2

1324

109-1

3-7

1.3

027E-0

6

2.0

2E+

15

32.3

0.1

3516

136.3

98.0

79.5

Chlo

roben

zene

Akz

oN

obel

B

Kin

eti

c R

ate

Co

nst

an

t P

ara

mete

rs

43

1

Deco

mp

osi

tio

n R

ate

P

ara

mete

rs

Deco

mp

osi

tio

n

Act

ivati

on

En

erg

y

Half

Lif

e

Tem

pera

ture

, °C

ID

Lo

ng

Nam

e

Tra

de N

am

e(s

) Fo

rmu

la /

Mo

lecu

lar

Str

uct

ure

M

W

CA

S N

o

kre

f (1

/s)

A

(1

/se

c)

kca

l/m

ol

GJ/

km

ol

1 m

in

1 h

r 1

0 h

r S

olv

en

t S

ou

rce

TBPP

I te

rt-b

uty

l per

oxy

piv

alat

e Trigonox

25

(Akz

oN

obel

)

Luper

ox

11 (

Ato

Fina)

TBPP

I (D

eguss

a)

C9H

18O

3 O

OO

174.2

4012

927-0

7-1

2.8

161E-0

5

6.7

2E+

14

29.5

0.1

2359

111.9

75.0

57.2

Chlo

roben

zene

Akz

oN

obel

TBPE

A

tert

-buty

l per

oxy

die

thyl

acet

ate

Trigonox

27

(Akz

oN

obel

) C10H

20O

3

OO

O

188.2

6700

2550-3

3-6

2.4

603E-0

6

2.5

2E+

15

32.0

0.1

3400

130.6

93.0

74.8

Chlo

roben

zene

Akz

oN

obel

TAPP

I te

rt-a

myl

per

oxy

piv

ala

te

Trigonox

125

(Akz

oN

obel

)

Luper

ox

554 (

Ato

Fina)

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on

(1980)

434 B Kinetic Rate Constant Parameters

References Note: Anonymous data sources from the internet are documented by the vendor name and the year in which the data were collected.

AkzoNobel (2004). Initiators for Polymer Production, Product Catalog.

AtoFina (2004). Organic Peroxides, General Catalog.

AtoFina (2004). Organic Peroxides, Product Bulletin, Diacyl Peroxides.

AtoFina (2004). Organic Peroxides, Product Bulletin, Dialkyl Peroxides.

AtoFina (2004). Organic Peroxides, Product Bulletin, Peroxydicarbonates.

AtoFina (2004). Organic Peroxides, Product Bulletin, Tertiary Alkyl Hydroperoxides.

AtoFina (2004). Fine Chemicals Technical Data.

Degussa (2004). Technical Information. Half-Life Times of Organic Peroxides.

Dupont (2004). Vazo Free radical initiators. (http://www.dupont.com/vazo/grades.html)

Masson, J.C. (1989). Decomposition Rates of Organic Free Radical Initiators. Polymer Handbook, 3rd Edition. New York.

Wako Chemical (2004). Water Soluble Azo-Initiator. (http://www.wako-chem.co.jp/specialty/waterazo/main.htm)

Wako Chemical (2004). Solvent Soluble Azo-Initiator. (http://www.wako-chem.co.jp/specialty/oilazo/main.htm)

Warson, H. (1980). Per-Compounds and Per-Salts in Polymer Processes. England: Solihull Chemical Services, 5-17.

http://www.dupont.com/vazo/grades.html

http://www.wako-chem.co.jp/specialty/waterazo/main.htm

http://www.wako-chem.co.jp/specialty/oilazo/main.htm

C Fortran Utilities 435

C Fortran Utilities

This appendix describes the input and output arguments for various Fortran utilities useful for writing user kinetic subroutines. For each utility a list of variables in the argument list is given along with their I/O status, their type, and a brief description. These utilities are available to you in addition to those documented in the Aspen Plus User Models reference manual.

The utilities documented in this appendix are:

Component Attribute Handling Utilities

CAELID

CAID

CAMIX

CASPLT

CASPSS

CAUPDT

COPYCA

GETCRY

GETDPN

GETMWN

GETMWW

GETPDI

GETSMF

GETSWF

LCAOFF

LCATT

NCAVAR

Component Handling Utilities

CPACK

IFCMNC

ISCAT

ISINI

ISOLIG

ISPOLY

ISSEG

SCPACK

XATOWT

XATOXT

General Stream Handling Utilities

IPTYPE

LOCATS

LPHASE

NPHASE

NSVAR

SSCOPY

Other Utilities

VOLL

436 C Fortran Utilities

Component Attribute Handling Utilities

CAELID

Utility Description This utility finds a component attribute element ID given the attribute ID and the element number.

Argument List SUBROUTINE SHS_CAELID ( IDCAT, IELEM, IDCAEL )

Variable I/O Type Dimension Description

IDCAT I INTEGER 2 Comp attr. ID in two integer words

IELEM I INTEGER --- Comp attr. element no.

IDCAEL O INTEGER 2 Comp attr. element ID in two integer words

Calling Sequence in User Routine INTEGER IDCAT(2), IELEM, IDCAEL(2) DATA IDCAT / 'DPN ',' ' / IELEM=1 . . . CALL SHS_CAELID ( IDCAT, IELEM, IDCAEL )

CAID

Utility Description This utility finds a component attribute ID given the component sequence number, the attribute type number, and the substream structure.

Argument List SUBROUTINE SHS_CAID ( ISSCNC, NCSEQ, J, IDCAT )



ISSCNC I INTEGER --- Flag:

1 = conventional substream

2 = nonconventional substream

NCSEQ I INTEGER --- Attributed component sequence number

J I INTEGER --- Comp attr. type no.

IDCAT O INTEGER 2 Comp attr. ID in two integer words

Calling Sequence in User Routine INTEGER ISSCNC, NCSEQ, J, IDCAT(2) ISSCNC=1 !'Conventional substream' J=1 . . . CALL SHS_CAID ( ISSCNC, NCSEQ, J, IDCAT )

CAMIX

Utility Description This is the component attribute mixing utility. It mixes the attributes from two inlet streams into an outlet stream.

Argument List SUBROUTINE SHS_CAMIX ( IP, SS1, SS2, SSO )


IP I I --- Substream type

1 or 2 = conventional

3 = nonconventional

SS1 I R 1 1st input substream

SS2 I R 1 2nd input substream

SSO O R 1 Output substream

Calling Sequence in User Routine INTEGER IP REAL*8 SS1(1), SS2(1), SS0(1) IP=1 !'Conventional substream' .


.

. CALL SHS_CAMIX ( IP, SS1, SS2, SSO )

CASPLT

Utility Description This is the component attribute splitting utility. It calculates the attribute values in a product stream for a given feed stream.

Argument List SUBROUTINE SHS_CASPLT ( FEED, PROD, NSUBS, IDXSUB, ITYPE )

Variable I/O Type Dimension

Description

FEED I DBL (1) Combined feed stream

PROD O DBL (1) Given outlet stream

NSUBS I INT --- Number of substreams

ITYPE I INT NSUB Substream type vector

IDXSUB I INT NSUB Substream index vector

Calling Sequence in User Routine INTEGER NSUBS, ITYPE(1), IDXSUB(1) REAL*8 FEED(1), PROD(1) IDXSUB(1)=1 !'First substream' ITYPE(1)=1 !'Conventional' . . . CALL SHS_CASPLT ( FEED, PROD, NSUBS, IDXSUB, ITYPE )

CASPSS

Utility Description This is the component attribute splitting utility for substreams. It calculates the attribute values in a product substream for a given feed substream.

Argument List SUBROUTINE SHS_CASPSS ( FEED, PROD, ITYPE )



FEED I DBL (1) Feed substream

PROD O DBL (1) Outlet substream

ITYPE I INT NSUB Substream type

Calling Sequence in User Routine INTEGER ITYPE(1) REAL*8 FEED(1), PROD(1) ITYPE(1)=1 !'Conventional' . . . CALL SHS_CASPSS ( FEED, PROD, ITYPE )

CAUPDT

Utility Description This utility calculates class zero component attribute values in a product stream based on class 2 component attributes.

Argument List SUBROUTINE SHS_CAUPDT ( STREAM, NSUBS, IDXSUB, IPHASE )


STREAM R*8 I (1) Stream vector

NSUBS I I --- Number of substreams

IDXSUB I I NSUBS Substream index vector

IPHASE I I NSUBS Substream type vector

1= MIXED

2= CISOLID

3= NCSOLID

Calling Sequence in User Routine INTEGER NSUBS, IDXSUB(1), IPHASE(1) REAL*8 STREAM(1) IPHASE(1)=1 !'First phase' .


.

. CALL SHS_CAUPDT ( STREAM, NSUBS, IDXSUB, IPHASE )

COPYCA

Utility Description This utility copies all attribute values from one stream into another stream of the same type.

Argument List SUBROUTINE SHS_COPYCA( LDIN, LD, LVRIN, LVR, IPHIN, IPH )


LDIN I I --- Location of the descriptor bead for the input stream

LD I I --- Location of the descriptor bead for the output stream

LVRIN I I --- Location of the real stream variable data for the input stream

LVR I I --- Location of the real stream variable

IPHIN I I --- Phase no. in the input stream

IPH I I --- Phase no. in the output stream data for the output stream

Calling Sequence in User Routine INTEGER IPHIN, IPH INTEGE LDIN, LD, LVRIN, LVR !'Use LOCATS utility model to obtain these values' IPHIN=1 IPH=1 . . . CALL SHS_COPYCA( LDIN, LD, LVRIN, LVR, IPHIN, IPH )

GETCRY

Utility Description This utility returns the crystallinity of a list of components.


Argument List SUBROUTINE POLY_GETCRY ( NCNC, NCP, IDX, CRY )


NCNC I I --- 1 = conventional substream

2 = non-conventional substream

NCP I I --- Number of components

IDX I I NCP Component index vector

CRY O I NCP Crystalline fraction

Calling Sequence in User Routine INTEGER NCNC, NCP, IDXP, CRY(1) NCNC=1 !'Conventional substream' NCP=1 IDXP=2 !'Polymer is 2nd component' . . . CALL POLY_GETCRY( NCNC, NCP, IDX, CRY )

GETDPN

Utility Description This utility returns the number average degree of polymerization.

Argument List SUBROUTINE POLY_GETDPN ( NCNC, NCP, IDX, DPN )


NCNC I I --- 1 = conventional substream


NCP I I --- Number of components

IDX I I NCP Component index vector

DPN O R NCP Degree of polymerization


Calling Sequence in User Routine INTEGER NCNC, NCP, IDXP REAL*8 DPN NCNC=1 !'Conventional substream' NCP=1 IDXP=2 !'Polymer is 2nd component' . . . CALL POLY_GETDPN( NCNC, NCP, IDX, DPN )

GETMWN

Utility Description This utility calculates the true molecular weight of a polymer, from the degree of polymerization and the average segment molecular weight.

Argument List SUBROUTINE POLY_GETMWN ( NCNC, NCP, IDX, XMWTRU )


NCNC I INT --- 1 = conventional substream


NCP I INT --- Number of components

IDX I INT NCP Component index vector

XMWTRU O DBL NCP True number average molecular weight

Calling Sequence in User Routine INTEGER NCNC, NCP, IDXP REAL*8 XMWTRU(1) NCNC=1 !'Conventional substream' NCP=1 IDXP=2 !'Polymer is 2nd component' . . . CALL POLY_GETMWN( NCNC, NCP, IDX, XMWTRU )


GETMWW

Utility Description This utility returns the weight-average molecular weight vector for all of the polymer components present. For standard components, the component molecular weight is returned.

Argument List SUBROUTINE POLY_GETMWW ( NCNC, NCP, IDX, MWW )


NCNC I INTEGER --- 1 = conventional substream


NCP I INTEGER --- Number of components present

IDX I INTEGER NCP Component index vector

MWW O DBL NCP Weight-average molecular weight

Calling Sequence in User Routine REAL*8 MWW INTEGER NCNC, NCP, IDXI NCNC=1 !'Conventional substream' NCP=1 !'Only one component (polymer)' IDXI=2 !'Polymer is 2nd component' . . . CALL POLY_GETMWW( NCNC, NCP, IDXI, MWW )

GETPDI

Utility Description This utility returns the polydispersity index for all components listed in the IDX array. For standard components, the PDI is set equal to the value of the POLPDI parameter.

Argument List SUBROUTINE POLY_GETPDI ( NCNC, NCP, IDX, MWW )







PDI O DBL NCP Polydispersity index

Calling Sequence in User Routine INTEGER NCNC, NCP, IDXI REAL*8 PDI NCNC=1 !'Conventional substream' NCP=1 !'Only one component (polymer)' IDXI=2 !'Polymer is 2nd component' . . . CALL POLY_GETPDI( NCNC, NCP, IDXI, PDI )

GETSMF

Utility Description This utility returns the segment mole fractions for the specified polymer or oligomer component.

Argument List SUBROUTINE POLY_GETSMF ( NCNC, IDX, SMFRAC )




IDX I INTEGER --- Component index

SMFRAC O DBL NCOMP_NSEG Segment mole fractions

The number of segments is retrieved from common NCOMP. The SMFRAC variable must be dimensioned to NCOMP_NSEG or larger.

Calling Sequence in User Routine INTEGER NCNC, NCP, IDXI


REAL*8 SMFRAC(10) ! dimension must be > Nseg NCNC=1 !'Conventional substream' IDXI=2 !'Polymer is 2nd component' . . . CALL POLY_GETSMF( NCNC, IDXI, SMFRAC)

GETSWF

Utility Description This utility returns the segment weight (mass) fractions for the specified polymer or oligomer component.

Argument List SUBROUTINE POLY_GETSWF ( NCNC, IDX, SMFRAC )




IDX I INTEGER --- Component index

SWFRAC O DBL NCOMP_NSEG Segment mole fractions

The number of segments is retrieved from common NCOMP. The SWFRAC variable must be dimensioned to NCOMP_NSEG or larger.

Calling Sequence in User Routine INTEGER NCNC, NCP, IDXI REAL*8 SWFRAC(10) ! dimension must be > Nseg NCNC=1 !'Conventional substream' IDXI=2 !'Polymer is 2nd component' . . . CALL POLY_GETSWF( NCNC, IDXI, SWFRAC)


LCAOFF

Utility Description This utility finds the offset of a component attribute from the beginning of the substream given the structure of the substream, the component sequence number and the attribute type number.

Argument List FUNCTION SHS_LCAOFF (ISSCNC, NCSEQ, J)



1 = Conventional substream

2 = non conventional substream


J I INTEGER --- Comp. attribute type no.

LCAOFF O INTEGER --- Attribute offset from substream

Calling Sequence in User Routine INTEGER ISSCNC, NCSEQ, J, SHS_LCAOFF ISSCNC=1 !'Conventional substream' NCSEQ=2 !'Second attributed component' J=1 !'First component attribute in the list for this component' . . . N = SHS_LCAOFF (ISSCNC, NCSEQ, J)

LCATT

Utility Description This utility finds the offset of a component attribute from the substream given the structure of the substream, attributed component sequence number and the attribute ID.

Argument List


FUNCTION SHS_LCATT (ISSCNC, NCSEQ, IDCATT)






IDCATT I INTEGER 2 Component attribute ID in two integer words

LCATT O INTEGER --- Attribute offset

Calling Sequence in User Routine INTEGER ISSCNC, NCSEQ, IAID(2), SHS_LCATT DATA IAD / 'DPN ', / ' ' / ISSCNC=1 NCSEQ=1 . . . N = SHS_LCATT (ISSCNC, NCSEQ, IAID)

NCAVAR

Utility Description This utility finds the number of elements in a component attribute given the attribute type index, the component index, and the substream type.

Argument List FUNCTION SHS_NCAVAR (ISSCNC, NCSEQ, J)






J I INTEGER --- Comp attribute type no.

NCAVAR O INTEGER --- Attribute length


Calling Sequence in User Routine INTEGER ISSCNC, NCSEQ, J, SHS_NCAVAR ISSCNC=1 !'Conventional substream' NCSEQ=1 J=1 . . . N = SHS_NCAVAR (ISSCNC, NCSEQ, J)

Component Handling Utilities

CPACK

Utility Description This utility packs a list of conventional components into an output vector that contains components whose mole fraction is greater than a minimum value XMIN.

Argument List SUBROUTINE SHS_CPACK (PHASE, NCP, IDX, X, FLOW)


PHASE I REAL NVCP Vector of component flows

NCP O INTEGER --- Number of components actually present

IDX O INTEGER NCC Index vector of components actually present

X O REAL NCC Mole fraction vector of components actually present

FLOW O REAL --- Total molar flow of the phase

Calling Sequence in User Routine INTEGER NCP, IDX(1) REAL*8 X(1), FLOW, PHASE(1) . . . CALL SHS_CPACK (PHASE, NCP, IDX, X, FLOW)


IFCMNC

Utility Description This utility is used to retrieve parameter values from the plex.

Argument List FUNCTION DMS_IFCMNC ( NAME )


NAME I CHARACTER*8 --- Parameter name as a character string

Calling Sequence in User Routine C INTEGER TC, I . . . TC(I)=DMS_IFCMNC('TC')+I

ISCAT

Utility Description This utility determines whether a component is a catalyst.

Argument List FUNCTION PPUTL_ISCAT ( ICOMP )


ICOMP I I --- Component index

ISCAT O L --- True for catalysts

Calling Sequence in User Routine INTEGER ICOMP LOGICAL PPUTL_ISCAT


ICOMP=2 ! . . . If ( PPUTL_ISCAT( ICOMP ) ) then...

ISINI

Utility Description This utility determines whether a component is an ionic initiator.

Argument List FUNCTION PPUTL_ISINI ( ICOMP )



ISINI O L --- True for initiators

Calling Sequence in User Routine INTEGER ICOMP LOGICAL PPUTL_ISINI ICOMP=2 ! . . . If ( PPUTL_ISINI( ICOMP ) ) then...

ISOLIG

Utility Description This utility determines whether a component is an oligomer.

Argument List FUNCTION SHS_ISOLIG ( ICOMP )



ISOLIG O L --- True for oligomers


Calling Sequence in User Routine INTEGER ICOMP LOGICAL SHS_ISOLIG ICOMP=3 ! . . . If ( SHS_ISOLIG( ICOMP ) ) then...

ISPOLY

Utility Description This utility determines whether a component is a polymer.

Argument List FUNCTION SHS_ISPOLY ( ICOMP )



ISPOLY O L --- True for polymers

Calling Sequence in User Routine INTEGER ICOMP LOGICAL SHS_ISPOLY ICOMP=2 ! . .. If ( ISPOLY( ICOMP ) ) then...

ISSEG

Utility Description This utility determines whether a component is a segment.

Argument List FUNCTION PPUTL_ISSEG ( ICOMP )




ISSEG O L --- True for segments

Calling Sequence in User Routine INTEGER ICOMP LOGICAL PPUTL_ISSEG ICOMP=5 ! . . . If ( PPUTL_ISSEG( ICOMP ) ) then...

SCPACK

Utility Description This utility packs lists of conventional component flow rates from several phases into an output array which contains mole fractions of components that are present in at least one of the phases.

Argument List SUBROUTINE SHS_SCPACK (NPHASE, LPHASE, NCP, IDX, X, FLOW)


NPHASE I INTEGER --- Number of phases to be packed

LPHASE I INTEGER NPHASE Vector of phase plex addresses

NCP O INTEGER --- Number of components actually present

IDX O INTEGER NCC Index vector of components actually present

X O REAL NCC, NPHASE

Mole fraction array of components actually present

FLOW O REAL NPHASE Vector of phase flow rates

Calling Sequence in User Routine INTEGER NPHASE, LPHASE(1), NCP, IDX(1) REAL*8 X(2), FLOW(2) . . .


CALL SHS_SCPACK (NPHASE, LPHASE, NCP, IDX, X, FLOW)

XATOWT

Utility Description This utility returns the true weight fractions for all of the components present.

Argument List SUBROUTINE POLY_XATOWT ( X, NCP, IDX, WT )


X I DBL NCP Apparent mole fraction vector



WT O DBL NCP True weight fraction vector

Calling Sequence in User Routine C Dimension of WT can be set high enough C to avoid overwriting; C Alternatively, the proper work space can C be assigned to the C array WT (preferred method) C REAL*8 WT(10) . . . CALL POLY_XATOWT (X, NCP, IDX, WT)

XATOXT

Utility Description This utility returns the true mole fractions for all of the components present.

Argument List SUBROUTINE POLY_XATOXT ( NCP, IDX, XMW, X, XTRUE )





XMW I DBL NCC Molecular weight vector

NCC I INTEGER --- Number of components listed

X I IDNL NCP Apparent mole fraction vector

XTRUE O DBL NCP True mole fraction vector

Calling Sequence in User Routine C Dimension of XTRUE can be set high C enough to avoid overwriting; C Alternatively, the proper work space C can be assigned to the C array XTRUE (preferred method) C REAL*8 XTRUE(10) . . . CALL POLY_XATOXT (NCP, IDX, XMW, X, XTRUE)

General Stream Handling Utilities

IPTYPE

Utility Description This utility returns the substream type number from the stream class descriptor bead.

Argument List FUNCTION SHS_IPTYPE (LD, I)


LD I INTEGER --- Address of stream class descriptor bead

I I INTEGER --- Substream number


Calling Sequence in User Routine INTEGER I, SHS_IPTYPE INTEGR LD !'Use LOCATS utility model to obtain LD' I=1 !'Substream 1' . . . N = SHS_IPTYPE (LD, I)

LOCATS

Utility Description This utility finds the integer and real plex addresses of a stream, the stream class bead location and bead number, given the stream bead number.

Argument List SUBROUTINE SHS_LOCATS (NB, LVI, LVR, LD, NBD)


NB I INTEGER --- Stream bead number

LVI O INTEGER --- Integer plex location of the stream bead

LVR O INTEGER --- Real plex location of the real portion of the bead

LD O INTEGER --- Integer plex location of the descriptor bead

NBD O INTEGER --- Descriptor bead number

LOFFDB --- INTEGER --- Offset to the descriptor bead number in the stream bead

Calling Sequence in User Routine INTEGER LVI, LVR, LD, NBD, LOFFDB INTEGER NB !'NB is obtained from the argument list' . . . CALL SHS_LOCATS (NB, LVI, LVR, LD, NBD)


LPHASE

Utility Description This utility finds the offset of a substream from the beginning of a stream structure.

Argument List FUNCTION SHS_LPHASE (LD, I)


LD I INTEGER --- Address of stream class descriptor bead

LPHASE O INTEGER --- Offset of substream I in the stream structure

I I INTEGER --- Substream number

Calling Sequence in User Routine INTEGER I, SHS_LPHASE INTEGER LD !'Use LOCATS utility to obtain LD' I=1 . . . N = SHS_LPHASE (LD, I)

NPHASE

Utility Description This utility finds the number of substreams from the stream class descriptor bead.

Argument List FUNCTION SHS_NPHASE (LD)


LD I INTEGER --- Address of stream

NPHASE O INTEGER --- No. of substreams


Calling Sequence in User Routine INTEGER SHS_NPHASE INTEGER !'Use LOCATS utility model to obtain LD' . . . N = SHS_NPHASE (LD)

NSVAR

Utility Description This utility returns the number of stream variables.

Argument List FUNCTION SHS_NSVAR (LD)


LD I INTEGER

--- Address of stream class descriptor bead

NSVAR O INTEGER

--- Length of stream variable

Calling Sequence in User Routine INTEGER SHS_NSVAR INTEGER LD !'Use LOCATS utility model to obtain LD' . . . N = SHS_NSVAR (LD)

SSCOPY

Utility Description This utility copies substream information from one stream to another.

Argument List SUBROUTINE SHS_SSCOPY( LD, S1, S2, IDX, I)



LD I I --- Locator of descriptor bead

S1 I R (1) Stream vector to copy from

S2 O R (1) Stream vector to copy into

IDX I I --- Location of substream within stream vector

I I I --- Substream number

Calling Sequence in User Routine INTEGER LD !'Use LOCATS utility model to obtain LD' INTEGER IDX(1), I REAL*8 S(1), S2(1) I=1 !'Substream 1' . . . CALL SHS_SSCOPY( LD, S1, S2, IDX, I)

Other Utilities

VOLL

Utility Description This utility calculates the mixture molar volume of liquid.

Argument List SUBROUTINE PPMON_VOLL ( T, P, X, N, IDX, NBOPST, KDIAG, KKV, V, DV, KER )


T I REAL*8 --- Temperature (K)

P I REAL*8 --- Pressure )(N/m2

N I INTEGER --- Number of components present

IDX I INTEGER N Component index vector

X I REAL*8 N Liquid mole fraction vector

NBOPST I INTEGER 6 Physical property method vector

KDIAG I INTEGER --- Diagnostic level code

KKV I INTEGER --- Mole volume calculation code

V O REAL*8 --- Mixture molar volume /kgmole)(m3


DV O REAL*8 --- Partial derivatives of mixture molar volume with respect to temperature K)-/kgmole(m3

KER O INTEGER --- Error return code (=0 if an error or warning condition occurred in any physical property model; =0 otherwise)

Calling Sequence in User Routine INTEGER N, IDX(N), NBOPST(6) !'These variables are obtained from the argument list' INTEGER KDIAG, KKV REAL*8 T, P, X(N) !'X is obtained from the argument list' KDIAG=4 KKV=1 . . . CALL PPMON_VOLL (T, P, X, N, IDX, NBOPST, KDIAG, KKV, V, DV, KER)

460 D Input Language Reference

D Input Language Reference

This section describes the input language for:

• Specifying Components, 460

• Specifying Component Attributes, 464

• Specifying Attribute Scaling Factors, 466

• Requesting Distribution Calculations, 467

• Calculating End Use Properties, 468

• Specifying Physical Property Inputs, 470

• Specifying Step-Growth Polymerization Kinetics, 474

• Specifying Free-Radical Polymerization Kinetics, 482

• Specifying Emulsion Polymerization Kinetics, 493

• Specifying Ziegler-Natta Polymerization Kinetics, 499

• Specifying Ionic Polymerization Kinetics, 510

• Specifying Segment-Based Polymer Modification Reactions, 517

Specifying Components This section describes the input language for specifying components.

Naming Components Following is the input language used to name components.

Input Language for Components

COMPONENTS cid [cname] [outid] / ...

Input Language Description for Components

COMPONENTS cid Component ID. Used to refer to the component in all subsequent input and is also used to identify the component in the simulation report. Aspen Plus input language conventions and naming guidelines apply to this keyword.

D Input Language Reference 461

cname The databank name or alias used for that component. Refer to the documentation for the desired databank to find out the correct databank name or alias for the desired component. Place an asterisk (*) in the cname position if you do not wish to retrieve the component from the databank. Note that in this case you are required to provide all necessary physical property parameters.

outid Eight-character name used for the component in reports. (Default=cid)

Input Language Example for Components

DATABANKS PURE13 / POLYMER / SEGMENT / INITIATOR

COMPONENTS

INI1 LP INIT / ; INITIATOR

STY STYRENE STYRENE / ; MONOMER

CAN ACRYLONITRILE CAN / ; MONOMER

XYLENE P-XYLENE XYLENE / ; SOLVENT

STYSEG STYRENE-R STY-SEG / ; STYRENE SEGMENT

ACNSEG ACRYLONITRILE-R ACN-SEG / ; ACN SEGMENT

SAN SAN SAN ; COPOLYMER

Specifying Component Characterization Inputs A POLYMERS paragraph is used to define polymers, their segments, oligomers, and heterogeneous catalysts, if any, involved in the polymerization. This paragraph is also used to define the polymer and catalyst component attributes desired in the simulation. Only the names of the attributes need to be specified in the POLYMERS paragraph. Initial values for the component attributes may be entered for the polymer and catalyst components in each stream via the STREAM paragraph. Following is the input language for the POLYMERS paragraph.

Input Language for Polymers, Oligomers, and Catalysts


POLYMERS PARAM kwd=value SEGMENTS seg-id seg-type / … OLIGOMERS olig-id seg-id number / … POLYMERS poly-id / … CATALYSTS cat-id mol-site / … INITIATORS ini-id/ … ATTRIBUTES comp-id attr-list / … DISTRIBUTION polyid disttype NPOINTS=value FUNCLOG=YES/NO UPPER=value

Input Language Description for Polymers, Oligomers, and Catalysts

PARAM Used to enter special parameters. Keywords are as follows.

NSITE Number of catalyst site types

N-BIFUN-INIT

Number of bifunctional initiators

SEGMENTS Used to specify all the segments used in the simulation. The information entered through this keyword is used by the system to pass segment property information.

seg-id Name of the segment (must be a valid component ID)

seg-type Segment type. This information is used to differentiate segment types. The options are END, REPEAT, BRANCH3, or BRANCH4. The default value is REPEAT

POLYMERS Used to identify all polymers present in the simulation.

poly-id Name of the polymer (must be a valid component ID)

OLIGOMERS Used to specify the structure of oligomers present in the simulation.

olig-id Oligomer component ID

seg-id ID for segment contained in that oligomer. All the segment names must be valid component IDs (Optional)

number Number of this segment in the oligomer (Default=1)

POLYMERS Used to identify all polymers present in the simulation.

poly-id Name of the polymer (must be a valid component ID)


CATALYSTS Used to identify all the heterogeneous polymerization catalysts present in the simulation and to specify the moles of catalytic sites per mole of catalyst.

cat-id Catalyst component ID

mol-site Moles of catalytic sites per unit mass of that catalyst

INITIATORS Used to identify all the ionic polymerization initiators present in the simulation.

ini-id Initiator component ID

ATTRIBUTES Used to specify all the polymer/catalyst component attributes desired for each polymer/catalyst in the simulation. Only the attribute names need to be specified here. Values for the component attributes are entered in the COMP-ATTR sentence of the STREAM paragraph.

comp-id Polymer or catalyst component ID

attr-list List of component attributes. The component attributes specific to polymers are listed in Polymer Component Attributes in Chapter 2, while those for catalysts are listed in Site-Based Species Attributes in Chapter 2.

DISTRIBUTION Used to request polymer property distribution plots.

polyid Polymer ID

disttype Distribution type

NPOINTS Number of points

FUNCLOG Calculate distribution as rW(r) vs. r on a log scale. Default is NO

upper Upper limit

Since component attributes represent a significant feature in Aspen Polymers (formerly known as Aspen Polymers Plus), a complete subsection has been devoted to their use in the simulator. For more detailed information regarding component attributes, see the Polymer Structural Properties section of Chapter 2.

Input Language Example for Polymers, Oligomers and Catalysts


POLYMERS

POLYMERS SAN ; DEFINE SEGMENTS IN POLYSTYRENE

SEGMENTS STYSEG REPEAT/

ACNSEG REPEAT ; DEFINE TYPE OF SEGMENTS PRESENT

; DEFINE ATTRIBUTES FOR POLYMERS

ATTRIBUTES SAN DPN DPW PDI MWN MWW ZMOM FMOM SMOM SFLOW SFRAC &

LDPN LZMOM LFMOM LSFLOW LSFRAC LEFLOW LEFRAC LPFRAC

DISTRIBUTION PS CHAIN-SIZE NPOINTS=100 UPPER=9999

Specifying Component Attributes This section describes the input language for specifying component attributes..

Specifying Characterization Attributes See Specifying Component Characterization Inputs on page 461.

Specifying Conventional Component Attributes To assign user component attributes to a conventional component use the ATTR-COMPS paragraph as follows:

Input Language for Catalyst Component Attributes

ATTR-COMPS comp-id attr-list CLASS=CV / ...

Input Language Description for Catalyst Component Attributes

comp-id Standard component ID.


attr-list List of attributes. Valid attributes were given in User Attributes in Chapter 2.

Initializing Attributes in Streams Following is the input language used to enter attribute values in streams.

Input Language for Material Streams

STREAM sid SUBSTREAM ssid keyword=value basis-FLOW cid flow / . . . basis-FRAC cid frac / . . . COMP-ATTR cname cattrname (value-list) / . . .

Keywords: TEMP PRES basis-FLOW

Optional Keywords: NPHASE PHASE

Input Language Description for Material Streams

SUBSTREAM Used to enter state and flash specifications for substreams.

Ssid Substream ID

TEMP Temperature

PRES Pressure

basis-FLOW

Flow rate on a MOLE, MASS, or VOLUME basis

NPHASE Number of phases

PHASE Used to specify the phase when NPHASE=1 PHASE=V (vapor), L (liquid), or S (solid)

basis-FLOW Used to enter component flows.

cid Component ID

flow Component mole or mass flow

basis-FRAC Used to enter component fractions.

cid Component ID

frac Component mole or mass fraction

COMP-ATTR Used to enter component attribute values.

Cname Component name


cattrname Component attribute name. For polymer attributes, values must be entered for at least SFRAC or SFLOW, and DPN or both ZMOM and FMOM

value-list List of values for each element in the attribute. Use “*” to skip entries

Input Language Example for Material Streams

STREAM FEED

SUBSTREAM MIXED TEMP=70 PRES=1

MASS-FLOW STY 13.5 /ACN 7.27 /XYLENE 79 /SAN 0.1E-5/INI1 0.23

COMP-ATTR SAN DPN (3000) /

DPW (6000) /

PDI (2) /

MWN (312450) /

MWW (624900) /

ZMOM (0.39E-10) /

FMOM (1.17E-7) /

SMOM (7.02E-4) /

SFLOW (0.55E-7 0.55E-7) /

SFRAC (0.5 0.5) /

LSFLOW (0. 0.) /

LEFLOW (0. 0.)

Specifying Attribute Scaling Factors This section describes the input language used to change the default scaling factors for component attributes.

Specifying Component Attribute Scale Factors The ATTR-SCALING paragraph is used to override the default scaling factors and upper bounds for component attributes. The standard values for these


parameters are defined in the Aspen Plus system definition file through the TBS data table PPCMATTR.DAT.

The component attribute scaling factors are used in flowsheet tear-stream convergence and in reactor model convergence as described in Component Attribute Scale Factors in Chapter 2.

The model uses one set of scaling parameters for all elements of each component attribute. If one component attribute is used by more than one component, different scaling factors can be applied for each instance of the attribute.

Input Language for Attribute Scaling Factors

ATTR-SCALING SCALING COMP=comp-id ATTR=attr-id

SCALE-FACTOR=scale UPPER-BOUND=upper

Input Language Description for Attribute Scaling Factors

SCALING Used to enter special parameters. Keywords are as follows.

comp-id Attributed component ID

attr-id Attribute ID

scale Number of catalyst site types

upper Upper limit

Input Language Example for Component Attribute Scaling

ATTR-SCALING

SCALING PP LSEFLOW SCALE=1E-008 UPPER=1.E35

SCALING PP LZMOM SCALE=1E-008 UPPER=1.E35

SCALING PP LSZMOM SCALE=1E-008 UPPER=1.E35

SCALING TICL4 CVSFLOW SCALE=1E-008 UPPER=1.E35

SCALING TICL4 CPSFLOW SCALE=1E-008 UPPER=1.E35

Requesting Distribution Calculations See Specifying Component Characterization Inputs on page 461.


Calculating End Use Properties This section describes the input language for calculating end use properties.

Input Language for Prop-Set

PROP-SET propsetid propname-list keyword=value

Optional Keywords:

COMPS PHASE UNITS TEMP PRES

Input Language Description for Prop-Set

Use the Prop-Set paragraph to define a property set. A property set is a collection of thermodynamic, transport, and other properties. Each property set you define is identified by an ID you supply.

Propsetid Property set ID.

Propname-list List of property names. (See Aspen Physical Property System Physical Property Data documentation.)

COMPS List of component Ids (applies to all properties listed in Aspen Physical Property System Physical Property Data documentation). (Default=all components actually present when the property is calculated.)

PHASE PHASE=V Vapor

PHASE=L Total liquid

PHASE=L1 First-liquid

PHASE=L2 Second-liquid

PHASE=T Total mixture

PHASE=S Solid

Phase compositions are determined at stream conditions. (Default=T, if listed as a valid phase for the property in Aspen Physical Property System Physical Property Data documentation; otherwise no default.)

UNITS Units options selected for the units keywords that are listed for the property in Aspen Physical Property System Physical Property Data documentation. (Default=IN-UNITS if Prop-Set is specified for design specifications, Fortran blocks, optimization paragraphs and constraint paragraphs. Default=OUT-UNITS if Prop-Set is specified for reports. If a property has mole, mass, or flow units, the default will be mole units.)


TEMP Temperatures for property calculations. (Default=stream temperature. For VVSTD and VVSTDMX, Default=25°C.)

PRES Pressures for property calculations. (Default=stream pressure. For VVSTD and VVSTDMX, Default=1 atm.)

Input Language for USER-PROPERTY

USER-PROPERTY userpropid propname-list keyword=value

Keyword: SUBROUTINE

Optional Keywords: FLASH UNIT-TYPE UNIT-LABEL COMP-DEP LVPCT-DEP CURVE-PROP DEFAULT-PROP BLEND-METHOD BLEND-OPT EXTRAPOLATE

Input Language Description for USER-PROPERTY

Use the USER-PROPERTY paragraph to define the property. This property can be referenced in the Prop-Set paragraph in the same way as built-in properties. You must supply a Fortran subroutine to calculate the value of the user Prop-Set properties.

userpropid User property set ID. This property must be different from built-in properties. (See Aspen Physical Property System Physical Property Data documentation.)

SUBROUTINE Name of user-supplied subroutine for calculating the property. For details on writing the user-supplied subroutine, see Aspen Plus User Models reference manual.

FLASH FLASH=NO Does not flash the stream before the user-supplied subroutine is called (Default)

FLASH= NOCOMPOSITE

Does not flash the stream for total stream properties (When PHASE=T in the Prop-Set paragraph), but flashes for any other phase specification

FLASH=YES Always flashes stream before the user-supplied subroutine is called

UNIT-TYPE Units keyword for the property. If not entered, unit conversion is not performed on property values returned from the user-supplied subroutine.


UNIT-LABEL Unit label for the property printed in the report. A unit label is used only when unit conversion is performed by the user-supplied subroutine (that is, when UNIT-TYPE is not given).

COMP-DEP COMP-DEP=YES Property is component property

COMP-DEP=NO Property is a mixture property (Default)

Specifying Physical Property Inputs This section describes the input language for specifying physical property inputs. More information on physical property methods and models is given in Volume 2 of this User Guide.

Specifying Property Methods Following is the input language used to specify property methods.

Input Language for Property Methods

PROPERTIES opsetname keyword=value / opsetname [sectionid-list] keyword=value /...

Optional keywords: FREE-WATER SOLU-WATER HENRY-COMPS

HENRY-COMPS henryid cid-list

Input Language Description for Property Methods

The PROPERTIES paragraph is used to specify the property method(s) to be used in your simulation. In this paragraph properties may be specified for the entire flowsheet, for a flowsheet section, or for an individual unit operation block. Depending on the component system used, additional information may be required such as Henry's law information, water solubility correlation, free-water phase properties. The input language for specifying property methods is as follows.

opsetname Primary property method name (See the Aspen Polymers User Guide, Volume 2).

sectionid-list List of flowsheet section IDs.

FREE-WATER Free water phase property method name (Default=STEAM-TA).

SOLU-WATER Method for calculating the K-value of water in the organic phase.


SOLU-WATER=0 Water solubility correlation is used, vapor phase fugacity for water calculated by free water phase property method

SOLU-WATER=1 Water solubility correlation is used, vapor phase fugacity for water calculated by primary property method

SOLU-WATER=2 Water solubility correlation is used with a correction for unsaturated systems, vapor phase fugacity for water calculated by primary property method

SOLU-WATER=3 Primary property method is used. This method is not recommended for water-hydrocarbon systems unless water-hydrocarbon interaction parameters are available. (Default)

HENRY-COMPS Henry's constant component list ID.

The HENRY-COMPS paragraph identifies lists of components for which Henry's law and infinite dilution normalization are used. There may be any number of HENRY-COMPS paragraphs since different lists may apply to different blocks or sections of the flowsheet.

henryid Henry's constant component list ID

cid-list List of component IDs

Input Language Example for Property Methods

HENRY-COMPS HC INI1

PROPERTIES POLYNRTL HENRY-COMPS=HC

Specifying Property Data Following is the input language used to specify property data.

Input Language for Property Data


PROP-DATA PROP-LIST paramname [setno] / . . . PVAL cid value-list / value-list / . . . PROP-LIST paramname [setno] / . . . BPVAL cid1 cid2 value-list / value-list / . . . COMP-LIST cid-list CVAL paramname setno 1 value-list COMP-LIST cid2-list BCVAL paramname setno 1 cid1 value-list / 1 cid1 value-list / . . .

Physical property models require data in order to calculate property values. Once you have selected the property method(s) to be used in your simulation, you must determine the parameter requirements for the models contained in the property method(s), and ensure that they are available in the databanks. If the model parameters are not available from the databanks, you may estimate them using the Property Constant Estimation System, or enter them using the PROP-DATA or TAB-POLY paragraphs. The input language for the PROP-DATA paragraphs is as follows. Note that only the general structure is given, for information on the format for the input parameters required by polymer specific models see the relevant chapter in Volume 2 of this User Guide.

Input Language Description for Property Data

PROP-LIST Used to enter parameter names and data set numbers.

PVAL Used to enter the PROP-LIST parameter values.

BPVAL Used to enter the PROP-LIST binary parameter values.

COMP-LIST Used to enter component IDs.

CVAL Used to enter the COMP-LIST parameter values.

BCVAL Used to enter the COMP-LIST binary parameter values.

paramname Parameter name

setno Data set number. For CVAL and BCVAL the data set number must be entered. For setno > 1, the data set number must also be specified in a new property method defined using the PROP-REPLACE paragraph. (For PROP-LIST, Default=1)

cid Component ID

cid1 Component ID of first component of binary pair

cid2 Component ID of second component of binary pair

value-list List of parameter values. For PROP-LIST, enter one value for each element of the property;


for COMP-LIST, enter one value for each component in the cid-list.

cid-list List of component ID

Input Language Example for Property Data

PROP-DATA

IN-UNITS SI

PROP-LIST PLXANT / TB

PVAL HOPOLY -40.0 0 0 0 0 0 0 0 1D3 / 2000.0

PVAL COPOLY -40.0 0 0 0 0 0 0 0 1D3 / 2000.0

PROP-DATA

IN-UNITS SI

PROP-LIST MW

PVAL HOPOLY 1.0

PVAL COPOLY 1.0

PVAL ABSEG 192.17

PVAL ASEG 76.09

PVAL BSEG 116.08

PROP-DATA

IN-UNITS SI

PROP-LIST DHCONM / DHSUB / TMVK / TGVK

PVAL HOPOLY -3.64261D4 / 8.84633D4 / 1.0 / 0.0

PVAL COPOLY -3.64261D4 / 8.84633D4 / 1.0 / 0.0

PROP-DATA

IN-UNITS SI

PROP-LIST GMRENB / GMRENC

BPVAL MCH ASEG -92.0 / 0.2

BPVAL ASEG MCH 430.0 / 0.2

Estimating Property Parameters Following is the input language used to estimate property parameters.


Input Language for Property Parameter Estimation

ESTIMATE [option]

STRUCTURES method SEG-id groupno nooccur / groupno nooccur /...

Input Language Description for Property Parameter Estimation

The main keywords for specifying property parameter estimation inputs are the ESTIMATE and the STRUCTURES paragraphs. A brief description of the input language for these paragraphs follows. For more detailed information please refer to the Aspen Physical Property System Physical Property Data documentation.

option Option=ALL Estimate all missing parameters (default)

method Polymer property estimation method name

SEG-id Segment ID defined in the component list

groupno Functional group number (group IDs listed in Appendix B of Volume 2 of this User Guide)

nooccur Number of occurrences of the group

Input Language Example for Property Parameter Estimation

ESTIMATE ALL

STRUCTURES

VANKREV ABSEG 115 1 ;-(C6H4)-

VANKREV BSEG 151 2 / 100 2 ; -COO-CH2-CH2-COO-

VANKREV ABSEG 115 1 / 151 2 / 100 2 ;-(C6H4)-COO-CH2-CH2-COO-

Specifying Step-Growth Polymerization Kinetics Following is the input language for the STEP-GROWTH REACTIONS paragraph.

Input Language for Step-Growth Polymerization

REACTIONS rxnid STEP-GROWTH DESCRIPTION '...'


REPORT REPORT=yes/no RXN-SUMMARY=yes/no RXN-DETAILS=yes/noI STOIC reactionno compid coeff / ... RATE-CON setno pre-exp act-energy [T-exp] [T-ref] [USER-RC=number] [CATALYST=compid] [CAT-ORDER=value] POWLAW-EXP reactionno compid exponent / [ASSIGN reactionno [ACTIVITY=value] RC-SETS=setno-list]

SPECIES POLYMER=polymerid OLIGOMER=oligomer-list REAC-GRP groupid type /… SPEC-GROUP compid groupid number / groupid number / ... RXN-SET rxn-setno [A-NUCL-SPEC=compid] [A-ELEC-GRP=groupid] & [V-ELEC-SPEC=compid] [V-NUCL-GRP=groupid] & [V-NUCL-SPEC=compid] [V-ELEC-GRP=groupid] & RC-SETS=rc-setno-list SG-RATE-CON rc-setno [CAT-SPEC=compid] [CAT-GRP=groupid] & sgpre-exp [sgact-energy] [sgt-exp] [sgt-ref] [USER-RC=number] SUBROUTINE KINETICS=kinname RATECON=rcname MASSTRANS=mtname USER-VECS NINTK=nintk NREALK=nrealk NINTRC=nintrc & NREALRC=nrealc NINTMT=nintmt NREALMT=nrealmt & NIWORK=niwork NWORK=nwork NURC=nurc INTK value-list REALK value-list INTRC value-list REALRC value-list INTMT value-list REALMT value-list INCL-COMPS compid-list REAC-TYPE FOR-CON=yes/no REV-CON=yes/no REARRANGE=yes/no EXCHANGE=yes/no

CONVERGENCE SOLVE-ZMOM=yes/no OLIG-TOL=tolerance

OPTIONS REAC-PHASE=phaseid CONC-BASIS=basis SUPPRESS-WARN=yes/no USE-BULK=yes/no

The keywords for specifying rate constant parameters for the built-in reactions, and for specifying user reactions are described here.

Input Language Description for Step-Growth Polymerization

rxnid Unique paragraph ID.

DESCRIPTION Up to 64 characters between double quotes.

REPORT Reaction report options- controls writing of reaction report in .REP file.

REPORT=YES Print reaction report

REPORT=NO Do not print reaction report

RXN-SUMMARY=YES

Print stoichiometry for each model-generated and user-specified reaction. (Default).


RXN- SUMMARY=NO

Do not print this summary.

RXN-DETAILS=YES Print stoichiometry, rate constants, and probability factors for each model-generated and user-specified reaction.

RXN-DETAILS=NO Do not print this detailed summary.

STOIC Used to specify stoichiometry for user reactions.

Reactionno Reaction number

compid Component ID

coeff Stoichiometric coefficient (positive for products, negative for reactants)

RATE-CON Used to specify rate constants for user reactions.

SetNo Rate constant set number

pre-exp Pre-exponential factor in inverse-time units

act-energy Activation energy in mole enthalpy units

T-exp Temperature exponent

T-ref Reference temperature

number User rate constant flag

CATALYST= compid

Optional catalyst component ID

CAT-ORDER=value Optional reaction order for catalyst (default=1)

POWLAW-EXP Used to specify power-law exponents for user reactions.

reactionno Reaction number

compid Component ID

exponent Power law exponent

ASSIGN Used to assign rate constant(s) to user reactions.


ACTIVITY= value

Multiplying factor used to calculate net rate constant

RC-SETS = setno-list

List of rate constants (from RATE-CON) which apply to this user reaction

SPECIES Used to specify key components involved in the reactions.

polymerid Component ID for polymer product

oligomer-list List of oligomers to be tracked

REAC-GRP Used to identify the names and types of reacting functional groups participating in the reaction network.


groupid Functional group ID

type Functional group type

EE-GRP Electrophilic repeat unit

NN-GRP Nucleophilic repeat unit

EN-GRP Mixed electrophilic/nucleophilic repeat unit

E-GRP Electrophilic leaving group

N-GRP Nucleophilic leaving group

EX-GRP Electrophilic modifier (end cap)

NX-GRP Nucleophilic modifier (end cap)

SPEC-GROUP Used to characterize the reacting functional group composition of the components (segments and monomers) participating in the step-growth reaction network.

compid Component ID

groupid Reactive functional group ID

number Number of occurrences of group in species

SG-RATE-CON Used to specify rate constants for model-generated step-growth reactions and to specify which catalyst they apply to (if any).

setno Rate constant set number

CAT-SPEC= compid

Component ID of catalyst species

CAT-GRP= groupid

Group ID of catalyst group

USER-RC= number

User rate expression flag

sgpre-exp Pre-exponential factor in inverse-time units

sgact-energy Activation energy in mole-enthalpy units

sgt-exp Temperature exponent

sgt-ref Reference temperature in temperature units

RXN-SET Used to assign sets of rate constants to model-generated reactions.

A-NUCL-SPEC= compid

Component ID of reactant which acts as the attacking nucleophile

A-ELEC-GRP= groupid

Group ID of electrophilic leaving group in attacking nucleophilic reactant

V-ELEC-SPEC= compid

Component ID of reactant which acts as the nucleophile. When reactions occur inside polymer molecules, this may be a segment.


V-ELEC-GRP= groupid

Group ID of electrophilic group in victim species (attached to V-NUCL-GRP)

V-NUCL-SPEC= compid

Component ID of nucleophilic reactant attached to the victim electrophilic reactant at the reacting site

V-NUCL-GRP= groupid

Group ID of nucleophilic group in victim species (attached to V-ELEC-GRP)

RC-SETS = rcsetno-list

List of rate constants (from SG-RATE-CON) which apply to the set of reactions identified by the previous keywords

SUBROUTINE Used to provide the names of user-supplied Fortran subroutines. The subroutine argument lists are documented in the User Subroutines section of Chapter 3.

KINETICS= kinname

User kinetic subroutine name

RATECON= rcname

User rate constant subroutine name

MASSTRAN= mtname

User concentration basis / mass-transfer subroutine name

USER-VECS Used to specify the size of vectors for user subroutines.

NINTK=nintk Length of integer array for kinetics

NREALK=nrealk Length of real array for kinetics

NINTRC=nintrc Length of integer array for rate constants

NREALRC= nrealrc

Length of real array for rate constants

NINTMT=nintmt Length of integer array for user basis routine

NREALMT= nrealmt

Length of real array for user basis routine

NIWORK= niwork

Total length of integer workspace

NWORK=nwork Total length of real workspace

NURC=nurc Number of rate constants calculated by user subroutine

INTK Used to enter integer parameter for kinetics.

REALK Used to enter real parameters for kinetics.

INTRC Used to enter integer parameters for rate constants.

REALRC Used to enter real parameters for rate constants.

INTMT Used to enter integer parameters for mass transfer.

REALMT Used to enter real parameters for mass transfer.


INCL-COMPS Used to list components which participate in reactions in the user kinetics model, but which do not appear in model-generated or user-specified reactions.

Compid-list List of additional components to include in the mass-balance calculations

REAC-TYPE Used to specify which classes of reactions will be generated by the step-growth model (default is “YES” for all types of reactions.

FOR-CON= yes/no

Generate forward condensation reactions

REV-CON= yes/no

Generate reverse condensation reactions

REARRANGE= yes/no

Generate re-arrangement reactions

EXCHANGE= yes/no

Generate end-group exchange reactions

CONVERGENCE Used to specify convergence parameters.

SOLVE-ZMOM= yes/no

Explicitly solve zeroth moment (default = no)

OLIG-TOL= tolerance

Specify tolerance for oligomer fractionation calculations (default is 1x10-4)

OPTIONS Used to specify reaction model options.

REAC-PHASE= phaseID

Specify the reacting phase as L, L1, L2, or V (default is L)

CONC-BASIS= basis

Specify concentration units for rate constants as MOL/L (default), MMOL/L, MOL/KG, or MMOL/KG

SUPRESS-WARN= yes/no

YES: do not print warnings when the specified phase is not present

NO: always print warnings when the specified phase is not present (default)

USE-BULK= yes/no

YES: force the model to apply the specified reaction kinetics to the bulk phase when the specified phase is not present (default)

NO: rates are set to zero when the specified phase is not present

Input Language Example for Step-Growth Polymerization



REACTIONS NYLON STEP-GROWTH

DESCRIPTION “NYLON-6 KINETICS: SIMPLE MODEL WITHOUT CYCLICS”

REPORT RXN-DETAILS=YES

SPECIES POLYMER=NYLON6

REAC-GROUP TNH2 E-GRP / TCOOH N-GRP / BCAP EN-GRP

SPECIES-GRP T-NH2 TNH2 1 / T-NH2 BCAP 1 / T-COOH TCOOH 1 / &

T-COOH BCAP 1 / ACA TNH2 1 / ACA TCOOH 1 / &

ACA BCAP 1 / B-ACA BCAP 1 / H2O TNH2 1 / H2O TCOOH 1

SG-RATE-CON 1 TREF=260 PRE-EXP= 5.461 ACT-ENERGY=23.271

SG-RATE-CON 2 CAT-SPEC=ACA TREF=260 PRE-EXP=40.678 ACT-ENERGY=20.670

SG-RATE-CON 3 CAT-SPEC=T-COOH TREF=260 PRE-EXP=40.678 ACT-ENERGY=20.670

SG-RATE-CON 4 TREF=260 PRE-EXP=0.0124 ACT-ENERGY=29.217

SG-RATE-CON 5 CAT-SPEC=ACA TREF=260 PRE-EXP=0.0924 ACT-ENERGY=26.616

SG-RATE-CON 6 CAT-SPEC=T-COOH TREF=260 PRE-EXP=0.0924 ACT-ENERGY=26.616

RXN-SET 1 ELECTRO-GRP=TNH2 NUCLEO-GRP=TCOOH RC-SETS= 1 2 3

RXN-SET 2 NUCLEOPHILE=H2O RC-SETS= 4 5 6

STOIC 1 CL -1.0 / H2O -1.0 / ACA 1.0

STOIC 2 CL -1.0 / H2O -1.0 / ACA 1.0

STOIC 3 CL -1.0 / H2O -1.0 / ACA 1.0

STOIC 4 ACA -1.0 / CL 1.0 / H2O 1.0

STOIC 5 ACA -1.0 / CL 1.0 / H2O 1.0

STOIC 6 ACA -1.0 / CL 1.0 / H2O 1.0

STOIC 7 CL -1.0 / B-ACA 1.0



STOIC 10 B-ACA -1.0 / CL 1.0

STOIC 11 B-ACA -1.0 / CL 1.0

STOIC 12 B-ACA -1.0 / CL 1.0

STOIC 13 CL -1.0 / ACA -1.0 / T-NH2 1.0 / T-COOH 1.0



STOIC 16 T-NH2 -1.0 / T-COOH -1.0 / ACA 1.0 / CL 1.0





STOIC 19 CL -1.0 / B-ACA 1.0

STOIC 20 CL -1.0 / B-ACA 1.0

STOIC 21 CL -1.0 / B-ACA 1.0

RATE-CON 1 PRE-EXP=0.00424 ACT-ENERGY=19.880 TREF=260





















POWLAW-EXP 1 CL 1.0 / H2O 1.0

POWLAW-EXP 2 CL 1.0 / H2O 1.0 / T-COOH 1.0

POWLAW-EXP 3 CL 1.0 / H2O 1.0 / ACA 1.0

POWLAW-EXP 4 ACA 1.0

POWLAW-EXP 5 ACA 1.0 / T-COOH 1.0


POWLAW-EXP 7 CL 1.0 / T-NH2 1.0

POWLAW-EXP 8 CL 1.0 / T-NH2 1.0 / T-COOH 1.0



POWLAW-EXP 9 CL 1.0 / T-NH2 1.0 / ACA 1.0

POWLAW-EXP 10 T-NH2 1.0

POWLAW-EXP 11 T-NH2 1.0 / T-COOH 1.0

POWLAW-EXP 12 T-NH2 1.0 / ACA 1.0

POWLAW-EXP 13 CL 1.0 / ACA 1.0

POWLAW-EXP 14 CL 1.0 / ACA 1.0 / T-COOH 1.0

POWLAW-EXP 15 CL 1.0 / ACA 2.0


POWLAW-EXP 17 T-COOH 1.0 / ACA 1.0



POWLAW-EXP 20 ACA 1.0 / T-COOH 1.0

POWLAW-EXP 21 ACA 2.0 CONVERGENCE SOLVE-ZMOM=YES

OPTIONS REAC-PHASE=L CONC-BASIS=’MOL/KG’

Specifying Free-Radical Polymerization Kinetics Following is the input language for the FREE-RAD REACTIONS paragraph. The reaction keywords and rate coefficient parameters for free-radical polymerization are given. Users may select a subset of the built-in reactions for a given simulation.


Input Language for Free-Radical Polymerization

REACTIONS reacid FREE-RAD PARAM QSSA=yes/no QSSAZ=yes/no QSSAF=yes/no RAD-INTENS=value SPECIES POLYMER=cid INITIATOR=cid-list MONOMER=cid-list INHIBITOR=cid-list & SOLVENT=cid-list BI-INITIATOR=cid-list COINITIATOR=cid-list CHAINTAG=cid-list & CATALYST=cid-list INIT-DEC cid idpre-exp idact-energy idact-volume ideffic & idnrad ref-temp [GEL-EFFECT=gelid] [EFF-GEFF=gelid] [COEF1=value BYPROD1=cid] & [COEF2=value BYPROD2=cid] INIT-CAT cid1 cid2 icpre-exp icact-energy icact-volume iceffic icnrad ref-temp [GEL-EFFECT=gelid] [EFF-GEFF=gelid] &

[COEF1=value BYPROD1=cid] [COEF2=value BYPROD2=cid] INIT-SP cid1 cid2 ispre-exp isact-energy isact-volume ref-temp &

[GEL-EFFECT=gelid] [COEF1=value BYPROD1=cid] [COEF2=value BYPROD2=cid] INIT-SP-EFF cid coeffa coeffb coeffc BI-INIT-DEC cid bdpre-exp bdact-energy bdact-volume bdeffic ref-temp [GEL-EFFECT=gelid] [EFF-GEFF=gelid] &

[COEF1=value BYPROD1=cid] [COEF2=value BYPROD2=cid] SEC-INIT-DEC cid sdpre-exp sdact-energy sdact-volume sdeffic ref-temp [GEL-EFFECT=gelid] [EFF-GEFF=gelid] &

[COEF1=value BYPROD1=cid] [COEF2=value BYPROD2=cid] CHAIN-INI cid cipre-exp ciact-energy ciact-volume ref-temp [GEL-EFFECT=gelid] PROPAGATION cid1 cid2 prpre-exp pract-energy pract-volume ref-temp [GEL-EFFECT=gelid] CHAT-MON cid1 cid2 cmpre-exp cmact-energy cmact-volume ref-temp [GEL-EFFECT=gelid] CHAT-POL cid1 cid2 cppre-exp cpact-energy cpact-volume ref-temp [GEL-EFFECT=gelid] CHAT-AGENT cid1 cid2 capre-exp caact-energy caact-volume ref-temp [GEL-EFFECT=gelid] CHAT-SOL cid1 cid2 cspre-exp csact-energy csact-volume ref-temp [GEL-EFFECT=gelid] B-SCISSION cid bspre-exp bsact-energy bsact-volume ref-temp [GEL-EFFECT=gelid] TERM-DIS cid1 cid2 tdpre-exp tdact-energy tdact-volume ref-temp [GEL-EFFECT=gelid] TERM-COMB cid1 cid2 tcpre-exp tcact-energy tcact-volume ref-temp [GEL-EFFECT=gelid] INHIBITION cid1 cid2 inpre-exp inact-energy inact-volume ref-temp [GEL-EFFECT=gelid] SC-BRANCH cid1 cid2 scpre-exp scact-energy scact-volume ref-temp [GEL-EFFECT=gelid] HTH-PROP cid1 cid2 hppre-exp hpact-energy hpact-volume ref-temp [GEL-EFFECT=gelid] CIS-PROP cid1 cid2 pcpre-exp pcact-energy pcact-volume ref-temp [GEL-EFFECT=gelid]

TRANS-PROP cid1 cid2 ptpre-exp ptact-energy pcact-volume ref-temp [GEL-EFFECT=gelid]

TDB-POLY cid1 cid2 tdpre-exp tdact-energy tdact-volume ref-temp [GEL-EFFECT=gelid]

PDB-POLY cid1 cid2 pbpre-exp pbact-energy pbact-volume ref-temp [GEL-EFFECT=gelid]

GEL-EFFECT gelid CORR-NO=corrno & MAX-PARAMS=maxparams GE-PARAMS=paramlist / ... SUBROUTINE GEL-EFFECT=subname OPTIONS REAC-PHASE=phaseid SUPRESS-WARN=yes/no USE-BULK=yes/no

Input Language Description for Free-Radical Polymerization

reacid Paragraph ID.

PARAM Used to specify polymerization mechanism, radiation intensity, and request the Quasi-Steady-State Approximation (QSSA).

RAD-INTENS= value

Used to specify a value for the radiation intensity to be used for the induced initiation reaction (default is 1.0)

QSSA= YES/NO

Used to request QSSA for all moments (default is NO)


QSSAZ= YES/NO

Used to request QSSA for the zeroth moment only (default is NO)

QSSAF= YES/NO

Used to request QSSA for the first moment only (default is NO)

QSSAS= YES/NO

Used to request QSSA for the second moment only (default is NO)

SPECIES Reacting species identification. This sentence is used to associate components in the simulation with reactive species in the built-in free-radical kinetic scheme. The following species keywords are currently valid

INITIATOR List of standard initiators

BI-INITIATOR List of bifunctional initiators

CATALYST List of catalysts

COINITIATOR List of coinitiators

MONOMER List of monomers

POLYMER Reacting polymer ID

CHAINTAG Chain transfer agends

SOLVENT List of solvents which act as chain transfer agents

INHIBITOR List of inhibitors

MON-RSEG Specifies the pairing between monomers and their corresponding repeat segments in a polymer.

monomer Monomer ID

r-seg Corresponding repeat segment ID

INIT-DEC Identifier for initiator decomposition reaction.

cid1 Initiator ID

idpre-exp Preexponential factor

idact-energy Activation energy

idact-volume Activation volume (default is 0.0)

ideffic Initiator efficiency (default is 1.0)

idnrad Number of radicals from one initiator molecule (default is 2.0)

ref-temp Reference temperature

GEL-EFF=gelid Gel effect sentence ID

EFF-GEFF=gelid

Efficiency factor gel effect sentence ID

COEF1=value Stoichiometric coefficient of first by-product (default=1.0)


BYPROD1=cid Byproduct 1 component ID

COEF2=value Stoichiometric coefficient of 2nd by-product (default=1.0)


INIT-CAT Identifier for catalyzed initiator decomposition reaction.

cid1 Initiator ID

cid2 Catalyst ID

icpre-exp Preexponential factor

icact-energy Activation energy

icact-volume Activation volume (default=0.0)

iceffic Initiator efficiency (default=1.0)

icnrad Number of radicals from one initiator molecule (default=2.0)



EFF-GEFF=gelid






INIT-SP Identifier for thermal and radiation induced initiation reaction.

cid1 Monomer ID

cid2 Co-initiator ID

ispre-exp Preexponential factor

isact-energy Activation energy

isact-volume Activation volume (default is 0.0)


INIT-SP-EFF Parameters for thermal and radiation induced initiation reaction.

cid Monomer ID

coeffa Exponent for coinitiator concentration (default is 0.0)


coeffb Exponent for monomer concentration (default is 0.0)

coeffc Exponent for radiation intensity (default is 0.0)


BI-INIT-DEC Bifunctional initiator primary decomposition

cid1 Bi-initiator ID

bdpre-exp Preexponential factor

bdact-energy Activation energy

bdact-volume Activation volume (default is 0.0)

bdeffic Initiator efficiency (default is 1.0)



EFF-GEFF=gelid






SEC-INIT-DEC Bifunctional initiator secondary decomposition

cid1 Bi-initiator ID

sdpre-exp Preexponential factor

sdact-energy Activation energy

sdact-volume Activation volume (default is 0.0)

sdeffic Initiator efficiency (default is 1.0)



EFF-GEFF=gelid







CHAIN-INI Identifier for chain initiation reaction.

cid1 Monomer ID

cipre-exp Preexponential factor

ciact-energy Activation energy

ciact-volume Activation volume (default is 0.0)



PROPAGATION Identifier for chain propagation reaction.

cid1 Active segment ID

cid2 Monomer ID

prpre-exp Preexponential factor

pract-energy Activation energy

pract-volume Activation volume (default is 0.0)



CHAT-MON Identifier for chain transfer to monomer reaction.

cid1 Monomer corresponding to polymer active segment ID

cid2 Monomer ID

cmpre-exp Preexponential factor

cmact-energy Activation energy

cmact-volume Activation volume (default is 0.0)



CHAT-POL Identifier for chain transfer to polymer reaction.


cid2 Segment ID on dead chain

cppre-exp Preexponential factor

cpact-energy Activation energy

cpact-volume Activation volume (default is 0.0)



CHAT-AGENT Identifier for chain transfer to transfer agent reaction.


cid2 Transfer agent ID


capre-exp Preexponential factor

caact-energy Activation energy

caact-volume Activation volume (default is 0.0)



CHAT-SOL Identifier for chain transfer to solvent reaction.


cid2 Solvent ID

cspre-exp Preexponential factor

csact-energy Activation energy

csact-volume Activation volume (default is 0.0)



B-SCISSION Identifier for beta-scission reaction.


bspre-exp Preexponential factor

bsact-energy Activation energy

bsact-volume Activation volume (default is 0.0)



TERM-DIS Identifier for chain termination by disproportionation reaction.

cid1 First polymer active segment ID

cid2 Second polymer active segment ID

tdpre-exp Preexponential factor

tdact-energy Activation energy

tdact-volume Activation volume (default is 0.0)



TERM-COMB Identifier for chain termination by combination reaction.

cid1 Monomer corresponding to first polymer active segment ID

cid2 Monomer corresponding to second polymer active segment ID

tcpre-exp Preexponential factor


tcact-energy Activation energy

tcact-volume Activation volume (default is 0.0)



INHIBITION Identifier for chain inhibition reaction.

cid1 Polymer active segment ID

cid2 Inhibitor ID

inpre-exp Preexponential factor

inact-energy Activation energy

inact-volume Activation volume (default is 0.0)



SC-BRANCH Identifier for short chain branching reaction.

cid1 Reactant polymer active segment ID

cid2 Product active segment ID

scpre-exp Preexponential factor

scact-energy Activation energy

scact-volume Activation volume (default is 0.0)



HTH-PROP Head-to-head propagation reaction


cid2 Monomer ID

hppre-exp Preexponential factor

hpact-energy Activation energy

hpact-volume Activation volume (default is 0.0)



CIS-PROP Cis-propagation for diene monomers


cid2 Diene monomer ID

pcpre-exp Preexponential factor

pcact-energy Activation energy

pcact-volume Activation volume (default is 0.0)




TRANS-PROP Trans-propagation for diene monomers


cid2 Diene monomer ID



pract-volume Activation volume (default is 0.0)



TDB-POLY Terminal double bond polymerization


cid2 Terminal double bond segment ID

tbpre-exp Preexponential factor

tbact-energy Activation energy

tbact-volume Activation volume (default is 0.0)



PDB-POLY Pendent double bond polymerization


cid2 Pendent double bond segment ID

pbpre-exp Preexponential factor

pbact-energy Activation energy

pbact-volume Activation volume (default is 0.0)



GEL-EFFECT Gel effect switch and correlation selection. This sentence is used to:

Modify the reaction rate expression or initiator efficiency factor, typically to account for the gel effect at high conversion.

Select a gel effect correlation from a list of built-in and user specified gel effect correlations

Specify the maximum number of parameters

Specify the parameter values for the selected correlation

The default action is to not include a gel effect.


gelid Gel effect sentence ID

GETYPE= reactiontype

Used to identify the type of reaction to apply gel effect to. A list of valid reaction types follows

CORR-NO= corrno

Used to select a correlation number. If a correlation number greater than the number of built-in correlations (currently 2) is specified then the user should supply a Fortran subroutine containing the user gel effect correlation.

MAX-PARAMS= maxparams

Used to enter the maximum number of gel effect parameters for the correlation selected.

GE-PARAMS= paramlist

Used to enter a list of parameters for the correlation selected.

SUBROUTINE User subroutines sentence.

GEL-EFFECT= subname

Used to specify the name of the subroutine containing user gel effect correlations. The user gel-effect subroutine argument list was shown in the Gel Effect section in Chapter 3. A Fortran template called USRGEL.F is available for your use.


REAC-PHASE= phaseID





USE-BULK= yes/no



Input Language Example for Free-Radical Polymerization

REACTIONS SBD FREE-RAD

DESCRIPTION "test file"

PARAM QSSA=yes


SPECIES INITIATOR=APS MONOMER=STY BD &

SOLVENT=EB POLYMER=SBD CHAINTAG=DDM COINITIATOR=CINI

INIT-DEC APS 1.6220E+11 1.1530E+08 0.0 EFFIC=.80 NRADS=2 &

BYPROD1=CO2 COEF1=0.1 BYPROD2=CO COEF2=0.2

INIT-SP STY CINI 438000.0 1.1480E+08 0.0

CHAIN-INI STY 2.2E7 3.2E7

CHAIN-INI BD 1.2E8 3.88E7

PROPAGATION STY STY 2.2E7 3.2E7

PROPAGATION STY BD 4.4E7 3.2E7

PROPAGATION BD BD 1.2E8 3.88E7

PROPAGATION BD STY 8.5E7 3.88E7

HTH-PROP STY STY 2.2E5 3.2E7

HTH-PROP BD BD 1.2E6 3.88E7

CIS-PROP BD BD 1.2E6 3.88E7

CIS-PROP STY BD 4.4E5 3.2E7

TRANS-PROP BD BD 1.2E6 3.88E7

TRANS-PROP STY BD 4.4E5 3.2E7

CHAT-MON STY STY 2200. 3.2E7

CHAT-MON STY BD 4400. 3.2E7

CHAT-MON BD BD 12000. 3.88E7

CHAT-MON BD STY 8500. 3.88E7

CHAT-AGENT STY DDM 1051.0 2.9590E+07 0.0

CHAT-AGENT BD DDM 900.0 2.9590E+07 0.0

CHAT-SOL STY EB 1051.0 2.9590E+07 0.0

CHAT-SOL BD EB 900.0 2.9590E+07 0.0

B-SCISSION STY 1.00E6 4.5E7 TDB-FRAC=1

B-SCISSION BD 1.00E6 4.5E7 TDB-FRAC=1

TERM-COMB STY STY 1.30E7 9.90E6 GEL-EFFECT=1

TERM-COMB STY BD 1.30E7 9.90E6 GEL-EFFECT=1

TERM-COMB BD BD 1.30E7 9.90E6 GEL-EFFECT=1

TERM-COMB BD STY 1.30E7 9.90E6 GEL-EFFECT=1

TERM-DIS STY STY 1.30E6 9.90E6 GEL-EFFECT=1

TERM-DIS STY BD 1.30E6 9.90E6 GEL-EFFECT=1

TERM-DIS BD BD 1.30E6 9.90E6 GEL-EFFECT=1

TERM-DIS BD STY 1.30E6 9.90E6 GEL-EFFECT=1

TDB-POLY STY STY 2.2E5 3.2E7

TDB-POLY STY BD 4.4E5 3.2E7


TDB-POLY BD BD 1.2E6 3.88E7

TDB-POLY BD STY 8.5E5 3.88E7

PDB-POLY STY BD 4.4E3 3.2E7

PDB-POLY BD BD 1.2E2 3.88E7

INIT-SP-EFF STY COEFFA=0.0 COEFFB=3.0 COEFFC=0.0

GEL-EFFECT 1 CORR-NO=2 MAX-PARAMS=10 &

GE-PARAMS=1 0 2.57 -5.05E-3 9.56 -1.76E-2 -3.03 7.85E-3 0.0 2

Specifying Emulsion Polymerization Kinetics Following is the input language for the EMULSION REACTIONS paragraph. Users are able to select the phases in which the reactions are occurring and also define the kinetics of particle absorption, desorption, and termination.

Input Language for Emulsion Polymerization

REACTIONS reacid EMULSION PARAM KBASIS=monomer/aqueous SPLIT-PM spm-cid kll SPECIES INITIATOR=cid MONOMER=cid INHIBITOR=cid & DISPERSANT=cid . . . INIT-DEC phasid cid idpre-exp idact-energy [idact-volume] ideffic & idnrad ref-temp INIT-CAT phased cid1 cid2 icpre-exp icact-energy [icact-volume] iceffic & icnrad ref-temp INIT-ACT phasid cid1 cid2 iapre-exp iaact-energy [iaact-volume] iaeffic & ianrad ref-temp PROPAGATION phasid cid1 cid2 prpre-exp pract-energy [pract-volume] ref-temp CHAT-MON phasid cid1 cid2 cmpre-exp cmact-energy [cmact-volume] ref-temp CHAT-POL phasid cid1 cid2 cppre-exp cpact-energy [cpact-volume] ref-temp CHAT-AGENT phasid cid1 cid2 capre-exp caact-energy [caact-volume] ref-temp TERM-DIS phasid cid1 cid2 tdpre-exp tdact-energy [tdact-volume] ref-temp TERM-COMB phasid cid1 cid2 tcpre-exp tcact-energy [tcact-volume] ref-temp INHIBITION phasid cid1 cid2 inpre-exp inact-energy [inact-volume] ref-temp REDUCTION phasid cid1 cid2 rdpre-exp rdact-energy [rdact-volume] rdeffic & rdnrad ref-temp OXIDATION phasid cid1 cid2 oxpre-exp oxact-energy [oxact-volume] ref-temp GEL-EFFECT GETYPE=reactiontype CORR-NO=corrno & MAX-PARAMS=maxparams GE-PARAMS=paramlist / ... SUBROUTINE GEL-EFFECT=subname ABS-MIC ampre-exp amact-energy ABS-PART appre-exp apact-energy DES-PART dppre-exp dpact-energy EMUL-PARAMS emulid cmc-conc area

Input Language Description for Emulsion Polymerization

reacid Paragraph ID.

PARAM Use to enter basis parameters.


KBASIS= monomer/ aqueous

Basis for phase split ratios

SPLIT-PM Used to enter homosaturation solubility of species in the polymer phase.

spm-cid Component ID of the species partitioning into the polymer phase

kll Ratio of mass fraction of species in polymer phase to mass fraction in reference phase. KBASIS determines whether the reference phase is the monomer of aqueous phase

SPECIES Reacting species identification. This sentence is used to associate components in the simulation with species in the built-in free-radical kinetic scheme. The following species keywords are currently valid

INITIATOR CATALYST MONOMER CHAINTAG DISPERSANT INHIBITOR POLYMER EMULSIFIER ACTIVATOR REDOX-AGENT REDUCTANT

INIT-DEC Identifier for initiator decomposition reaction.

phasid Reaction phase (DISPERSANT)

cid Initiator ID

idpre-exp Preexponential factor

idact-energy Activation energy

idact-volume Activation volume (optional)

ideffic Initiator efficiency

idnrad Number of radicals from one initiator molecule


INIT-CAT Identifier for catalyzed initiator decomposition reaction.


cid1 Initiator ID

cid2 Catalyst ID

icpre-exp Preexponential factor

icact-energy Activation energy

icact-volume Activation volume (optional)

iceffic Initiator efficiency

icnrad Number of radicals from one initiator molecule



INIT-ACT Identifier for initiation by activator and initiator.


cid1 Initiator ID

cid2 Activator ID

iapre-exp Preexponential factor

iaact-energy Activation energy

iaact-volume Activation volume (optional)

iaeffic Initiator activation efficiency

ianrad Initiator activation number of radicals


PROPAGATION Identifier for chain propagation reaction.

phasid Reaction phase (POLYMER or DISPERSANT)

cid1 Monomer corresponding to active polymer segment ID

cid2 Monomer ID



pract-volume Activation volume (optional)


CHAT-MON Identifier for chain transfer to monomer reaction.

phasid Reaction phase (POLYMER)


cid2 Monomer ID

cmpre-exp Preexponential factor

cmact-energy Activation energy

cmact-volume Activation volume (optional)


CHAT-POL Identifier for chain transfer to polymer reaction.



cid2 Monomer corresponding to reacting polymer segment ID or dead chain


cppre-exp Preexponential factor

cpact-energy Activation energy

cpact-volume Activation volume (optional)


CHAT-AGENT Identifier for chain transfer to transfer agent reaction.



cid2 Transfer agent ID

capre-exp Preexponential factor

caact-energy Activation energy

caact-volume Activation volume (optional)


TERM-DIS Identifier for chain termination by disproportionation reaction.


cid1 First active polymer segment ID

cid2 Second active polymer segment ID

tdpre-exp Preexponential factor

tdact-energy Activation energy

tdact-volume Activation volume (optional)


TERM-COMB Identifier for chain termination by combination reaction.


cid1 First active polymer segment ID

cid2 Second active polymer segment ID



tcact-volume Activation volume (optional)


INHIBITION Identifier for chain inhibition reaction.


cid1 Active polymer segment ID

cid2 Inhibitor ID


inpre-exp Preexponential factor

inact-energy Activation energy

inact-volume Activation volume (optional)


REDUCTION Identifier for reduction step of redox initiation.


cid1 Reductant ID

cid2 Redox agent (catalyst) ID

rdpre-exp Preexponential factor

rdact-energy Activation energy

rdact-volume Activation volume (optional)

rdeffic Reduction activation efficiency

rdnrad Reduction activation number of radicals


OXIDATION Identifier for oxidation step of redox initiation.


cid1 Initiator ID

cid2 Redox agent (catalyst) ID

oxpre-exp Preexponential factor

oxact-energy Activation energy

oxact-volume Activation volume (optional)


GEL-EFFECT Gel effect switch and correlation selection. This sentence is used to

Include a gel effect for any reactions in the built-in kinetic scheme and for the initiator efficiency

Select a gel effect correlation from a list of built-in and user specified gel effect correlations

Specify the maximum number of parameters

Specify the parameter values for the selected correlation

The default action is to not include a gel effect.

GETYPE= reactiontype

Used to identify the type of reaction to apply gel effect to. A list of valid reaction types follows

INITIATION Initiator decomposition

INIT-EFF Initiator efficiency


PROPAGATION Propagation, chain initiation and induced initiation reactions

CHAT-MON Chain transfer to monomer

CHAT-POL Chain transfer to polymer

CHAT-AGENT Chain transfer to agent

TERMINATION Termination

CORR-NO= corrno

Used to select a correlation number. If a correlation number greater than the number of built-in correlations (currently 2) is specified then the user should supply a Fortran subroutine containing the user gel effect correlation.

MAX-PARAMS= maxparams

Used to enter the maximum number of gel effect parameters for the correlation selected.

GE-PARAMS= paramlist

Used to enter a list of parameters for the correlation selected.

SUBROUTINE User subroutines sentence.

GEL-EFFECT= subname

Used to specify the name of the subroutine containing user gel effect correlations. The user gel-effect subroutine argument list was shown in the Gel Effect section in Chapter 3. A Fortran template called USRGEL.F is available for your use.

ABS-MIC Used to specify rate of radical absorption by micelles.

ampre-exp Preexponential factor

amact-energy Activation energy

ABS-PART Used to specify rate of radical absorption by particles.

appre-exp Preexponential factor

apact-energy Activation energy

DES-PART Identifier for radical desorption.

dppre-exp Preexponential factor

dpact-energy Activation energy

EMUL-PARAMS Used to specify emulsion parameters for micellar nucleation.

emulid Emulsifier ID

cmc-conc Critical micelle concentration

area Surface coverage or area per unit mole of emulsifier


Input Language Example for Emulsion Polymerization

REACTIONS EMLRXN EMULSION

DESCRIPTION "EXAMPLE EMULSION INPUT"

PARAM KBASIS=MONOMER

SPECIES INITIATOR=APS MONOMER=STY NBA EMULSIFIER=EMUL &

DISPERSANT=H2O POLYMER=POLYMER

INIT-DEC DISPERSANT APS 1.0000E+16 1.4020E+08 & 0.0 EFFIC=.80 NRADS=2

PROPAGATION POLYMER STY STY 2341450.0 2.6000E+07

PROPAGATION POLYMER STY NBA 3265600.0 2.6000E+07

PROPAGATION POLYMER NBA NBA 1909530.0 2.2400E+07

PROPAGATION POLYMER NBA STY 1.4918E+07 2.2400E+07

CHAT-MON POLYMER STY STY 3310000.0 5.3020E+07

CHAT-MON POLYMER STY NBA 3310000.0 5.3020E+07

CHAT-MON POLYMER NBA NBA 438.90 2.7600E+07

CHAT-MON POLYMER NBA STY 438.90 2.7600E+07

TERM-COMB POLYMER STY STY 1.6125E+09 7000000.0

TERM-COMB POLYMER STY NBA 7.3204E+09 1.4600E+07

TERM-COMB POLYMER NBA NBA 3.3217E+10 2.2200E+07

TERM-COMB POLYMER NBA STY 7.3204E+09 1.4600E+07

ABS-MIC 1.0000E-07 0.0

ABS-PART 1.0000E-07 0.0

DES-PART 0.0 0.0

EMUL-PARAMS EMUL 0.0 5.0000E+08

SPLIT-PM STY .40

SPLIT-PM NBA .40

Specifying Ziegler-Natta Polymerization Kinetics Following is the input language for the part of the polymerization REACTIONS paragraph specific to Ziegler-Natta kinetics. Ziegler-Natta inputs may be used to define the reaction kinetics for a wide variety of homo- and co-polymers produced by catalyzed polymerization, including HDPE. A subset of the built-in kinetics can be defined for a simulation by including the reaction keywords for the desired reactions and specifying the rate coefficient parameters for these


reactions. The reaction keywords and rate coefficient parameters for Ziegler-Natta polymerization are also provided. Currently for two phase systems the polymerization reactions are applied to the liquid phase in the reactor. For gas phase polymerization systems the solid polymer, or the amorphous part of the polymer, is modeled as a liquid.

Input Language for Ziegler-Natta Polymerization

REACTIONS reacid ZIEGLER-NAT SPECIES PRECAT=cid CATALYST=cid COCATALYST=cid MONOMER=cid CHAINTAG=cid & SOLVENT=cid POISON=cid BYPRODUCT=cid HYDROGEN=cid POLYMER=cid & ELECDONOR=cid TDBSEGMENT=cid ACT-SPON site-id cid1 aspre-exp asact-energy asorder ref-temp ACT-COCAT site-id cid1 cid2 acpre-exp acact-energy acorder ref-temp ACT-EDONOR site-id cid1 cid2 aepre-exp aeact-energy aeorder ref-temp ACT-H2 site-id cid1 cid2 ahpre-exp ahact-energy ahorder ref-temp ACT-MON site-id cid1 cid2 ampre-exp amact-energy amorder ref-temp CHAIN-INI site-id cid1 cipre-exp ciact-energy ciorder ref-temp PROPAGATION site-id cid1 cid2 prpre-exp pract-energy prorder ref-temp CHAT-MON site-id cid1 cid2 cmpre-exp cmact-energy cmorder cmtdb-frac ref-temp CHAT-AGENT site-id cid1 cid2 capre-exp caact-energy caorder catdb-frac ref-temp CHAT-SOL site-id cid1 cid2 cspre-exp csact-energy csorder cstdb-frac ref-temp CHAT-COCAT site-id cid1 cid2 ccpre-exp ccact-energy ccorder cctdb-frac ref-temp CHAT-H2 site-id cid1 cid2 chpre-exp chact-energy chorder chtdb-frac ref-temp CHAT-EDONOR site-id cid1 cid2 cepre-exp ceact-energy ceorder cetdb-frac ref-temp CHAT-SPON site-id cid1 cid2 cnpre-exp cnact-energy cnorder cntdb-frac ref-temp DEACT-POISON site-id cid1 dppre-exp dpact-energy dporder ref-temp DEACT-COCAT site-id cid1 dcpre-exp dcact-energy dcorder ref-temp DEACT-MON site-id cid1 dmpre-exp dmact-energy dmorder ref-temp DEACT-EDONOR site-id cid1 depre-exp deact-energy deorder ref-temp DEACT-H2 site-id cid1 dhpre-exp dhact-energy dhorder ref-temp DEACT-SPON site-id dspre-exp dsact-energy dsorder ref-temp COCAT-POISON cid1 cid2 copre-exp coact-energy coorder ref-temp FSINH-H2 site-id cid1 fhpre-exp fhact-energy fhorder ref-temp RSINH-H2 site-id cid1 rhpre-exp rhact-energy rhorder ref-temp FSINH-POISON site-id cid1 fppre-exp fpact-energy fporder ref-temp RSINH-POISON site-id cid1 rppre-exp rpact-energy rporder ref-temp TDB-POLY site-id cid1 cid2 tdpre-exp tdact-energy tdorder ref-temp ATACT-PROP site-id cid1 cid2 atpre-exp atact-energy atorder ref-temp CAT-ACTIVATE cid1 cid2 avpre-exp avact-energy avorder ref-temp OPTIONS REAC-PHASE=phaseid SUPPRESS-WARN=yes/no USE-BULK=yes/no

Input Language Description for Ziegler-Natta Polymerization

reacid Reaction paragraph ID.

SPECIES Reacting species identification. This sentence is used to associate components in the simulation with the reactive species in the built-in kinetic scheme. The following species keywords are currently valid

PRECAT CATALYST COCATALYST MONOMER CHAINTAG SOLVENT POISON BYPRODUCT HYDROGEN POLYMER ELECDONOR TDBSEGMENT

MON-RSEG Specifies the pairing between monomers and their corresponding repeat segments in a polymer.

monomer Monomer ID

r-seg Corresponding repeat segment ID


ACT-SPON Reaction identifier for spontaneous site activation of a catalyst potential site to a vacant active site of type k.

site-id Site type identifier for active site formed

(k = 1, 2, ... , NSITE)

cid1 Component ID of catalyst

aspre-exp Preexponential factor (default is 0.0)

asact-energy Activation energy (default is 0.0)

asorder Reaction order for potential site concentration (default is 0.0)


ACT-COCAT Reaction identifier for site activation by cocatalyst of a catalyst potential site to a vacant active site of type k.

site-id Site type identifier for active site

(k = 1, 2, ... , NSITE)


cid2 Component ID of cocatalyst

acpre-exp Preexponential factor (default is 0.0)

acact-energy Activation energy (default is 0.0)

acorder Reaction order for cocatalyst concentration (default is 0.0)


ACT-EDONOR Reaction identifier for site activation by electron donor of a catalyst potential site to a vacant active site of type k.


(k = 1, 2, ... , NSITE)


cid2 Component ID of electron donor

aepre-exp Preexponential factor (default is 0.0)

aeact-energy Activation energy (default is 0.0)

aeorder Reaction order for electron donor concentration (default is 0.0)


ACT-H2 Reaction identifier for site activation by hydrogen of a catalyst potential site to a vacant active site of type k.


(k = 1, 2, ... , NSITE)



cid2 Component ID of hydrogen

ahpre-exp Preexponential factor (default is 0.0)

ahact-energy Activation energy (default is 0.0)

ahorder Reaction order for hydrogen concentration (default is 0.0)


ACT-MON Reaction identifier for site activation by monomer of a catalyst potential site to a vacant active site of type k.


(k = 1, 2, ... , NSITE)


cid2 Component ID of monomer

ampre-exp Preexponential factor (default is 0.0)

amact-energy Activation energy (default is 0.0)

amorder Reaction order for monomer concentration (default is 0.0)


CHAIN-INI Reaction identifier for polymer chain initiation on a vacant active site of type k. The vacant site becomes a propagation site of type k.

site-id Site type identifier (k = 1, 2, ... , NSITE)


cipre-exp Preexponential factor (default is 0.0)

ciact-energy Activation energy (default is 0.0)

ciorder Reaction order for monomer concentration (default is 0.0)


PROPAGATION Reaction identifier for polymer chain propagation on an active site of type k.


cid1 Component ID of active segment (specified in terms of the corresponding monomer ID)


prpre-exp Preexponential factor (default is 0.0)

pract-energy Activation energy (default is 0.0)

prorder Reaction order for monomer concentration (default is 0.0)



CHAT-MON Reaction identifier for chain transfer to monomer on active site of type k.




cmpre-exp Preexponential factor (default is 0.0)

cmact- energy

Activation energy (default is 0.0)

cmorder Reaction order for monomer concentration (default is 0.0)

cmtdb-frac Fraction of generated dead polymer chains with terminal double bonds (default is 0.0)


CHAT-AGENT Reaction identifier for chain transfer to agent on active site of type k.



cid2 Component ID of chain transfer agent

capre-exp Preexponential factor (default is 0.0)

caact-energy Activation energy (default is 0.0)

caorder Reaction order for agent concentration (default is 0.0)

catdb-frac Fraction of generated dead polymer chains with terminal double bonds (default is 0.0)


CHAT-SOL Reaction identifier for chain transfer to solvent on active site of type k.



cid2 Component ID of solvent

cspre-exp Preexponential factor (default is 0.0)

csact-energy Activation energy (default is 0.0)

csorder Reaction order for solvent concentration (default is 0.0)


cstdb-frac Fraction of generated dead polymer chains with terminal double bonds (default is 0.0)


CHAT-COCAT Reaction identifier for chain transfer to cocatalyst on active site of type k.




ccpre-exp Preexponential factor (default is 0.0)

ccact-energy Activation energy (default is 0.0)

ccorder Reaction order for cocatalyst concentration (default is 0.0)

cctdb-frac Fraction of generated dead polymer chains with terminal double bonds (default is 0.0)


CHAT-H2 Reaction identifier for chain transfer to hydrogen on active site of type k.




chpre-exp Preexponential factor (default is 0.0)

chact-energy Activation energy (default is 0.0)

chorder Reaction order for hydrogen concentration (default is 0.0)

chtdb-frac Fraction of generated dead polymer chains with terminal double bonds (default is 0.0)


CHAT-EDONOR Reaction identifier for chain transfer to electron donor on active site of type k.




cepre-exp Preexponential factor (default is 0.0)

ceact-energy Activation energy (default is 0.0)


ceorder Reaction order for electron donor concentration (default is 0.0)

cetdb-frac Fraction of generated dead polymer chains with terminal double bonds (default is 0.0)


CHAT-SPON Reaction identifier for spontaneous chain transfer on active site of type k.



cnpre-exp Preexponential factor (default is 0.0)

cnact-energy Activation energy (default is 0.0)

cnorder Reaction order (not used)

cntdb-frac Fraction of generated dead polymer chains with terminal double bonds (default is 0.0)


DEACT-POISON Reaction identifier for site deactivation by poison of a catalyst active site of type k to a dead site.


cid1 Component ID of poison

dppre-exp Preexponential factor (default is 0.0)

dpact-energy Activation energy (default is 0.0)

dporder Reaction order for poison concentration (default is 0.0)


DEACT-COCAT Reaction identifier for site deactivation by cocatalyst of a catalyst active site of type k to a dead site.



dcpre-exp Preexponential factor (default is 0.0)

dcact-energy Activation energy (default is 0.0)

dcorder Reaction order for cocatalyst concentration (default is 0.0)


DEACT-MON Reaction identifier for site deactivation by monomer of a catalyst active site of type k to a dead site.




dmpre-exp Preexponential factor (default is 0.0)

dmact-energy Activation energy (default is 0.0)

dmorder Reaction order for monomer concentration (default is 0.0)


DEACT- EDONOR Reaction identifier for site deactivation by electron donor of a catalyst active site of type k to a dead site.



depre-exp Preexponential factor (default is 0.0)

deact-energy Activation energy (default is 0.0)

deorder Reaction order for electron donor concentration (default is 0.0)


DEACT-H2 Reaction identifier for site deactivation by hydrogen of a catalyst active site of type k to a dead site.



dhpre-exp Preexponential factor (default is 0.0)

dhact-energy Activation energy (default is 0.0)

dhorder Reaction order for hydrogen concentration (default is 0.0)


DEACT-SPON Reaction identifier for spontaneous site deactivation of a catalyst active site of type k to a dead site.


dspre-exp Preexponential factor (default is 0.0)

dsact-energy Activation energy (default is 0.0)

dsorder Reaction order (not used)


COCAT- POISON

Reaction identifier for cocatalyst poisoning reaction.



copre-exp Preexponential factor (default is 0.0)

coact-energy Activation energy (default is 0.0)

coorder Reaction order (not used)



FSINH-H2 Reaction identifier for site inhibition by hydrogen-forward reaction.



fhpre-exp Preexponential factor (default is 0.0)

fhact-energy Activation energy (default is 0.0)

fhorder Reaction order for hydrogen concentration (default is 0.0)


RSINH-H2 Reaction identifier for site inhibition by hydrogen-reverse reaction.



rhpre-exp Preexponential factor (default is 0.0)

rhact-energy Activation energy (default is 0.0)

rhorder Reaction order for inhibited site concentration (default is 0.0)


FSINH-POISON Reaction identifier for site inhibition by poison-forward reaction.



fppre-exp Preexponential factor (default is 0.0)

fpact-energy Activation energy (default is 0.0)

fporder Reaction order for poison concentration (default is 0.0)


RSINH-POISON Reaction identifier for site inhibition by poison-reverse reaction.



rppre-exp Preexponential factor (default is 0.0)

rpact-energy Activation energy (default is 0.0)

rporder Reaction order for inhibited site concentration (default is 0.0)



TDB-POLY Reaction identifier for terminal double bond propagation reaction.


cid1 Component ID of active segment (specified in terms of the corresponding monomer)

cid2 Component ID of TDB segment

tdpre-exp Preexponential factor (default is 0.0)

tdact-energy Activation energy (default is 0.0)

tdorder Reaction order (not used)


ATACT-PROP Reaction identifier for atactic propagation reaction.


cid1 Component ID of active segment (specified in terms of the corresponding monomer)


atpre-exp Preexponential factor (default is 0.0)

atact-energy Activation energy (default is 0.0)

atorder Reaction order for monomer concentration (default is 0.0)


CAT-ACTIVATE Reaction identifier for catalyst activation reaction.

cid1 Component ID for pre-catalyst


avpre-exp Preexponential factor (default is 0.0)

avact-energy Activation energy (default is 0.0)

avorder Reaction order for catalyst



REAC-PHASE= phaseID






USE-BULK= yes/no



Input Language Example for Zielger-Natta Polymerization

REACTIONS ZN-R2 ZIEGLER-NAT

DESCRIPTION "ZIEGLER-NATTA KINETIC SCHEME"

SPECIES CATALYST=CAT COCATALYST=CCAT MONOMER=E2 &

SOLVENT=HEXANE HYDROGEN=H2 POLYMER=HDPE

ACT-SPON 1 CAT .080 0.0 1.0

ACT-SPON 2 CAT .080 0.0 1.0

ACT-SPON 3 CAT .080 0.0 1.0

ACT-SPON 4 CAT .080 0.0 1.0

ACT-COCAT 1 CAT CCAT .150 0.0 1.0




CHAIN-INI 1 E2 255.0 0.0 1.0

CHAIN-INI 2 E2 90.0 0.0 1.0

CHAIN-INI 3 E2 255.0 0.0 1.0

CHAIN-INI 4 E2 90.0 0.0 1.0

PROPAGATION 1 E2 E2 255.0 0.0 1.0

PROPAGATION 2 E2 E2 90.0 0.0 1.0

PROPAGATION 3 E2 E2 255.0 0.0 1.0

PROPAGATION 4 E2 E2 90.0 0.0 1.0

CHAT-MON 1 E2 E2 .090 0.0 1.0

CHAT-MON 2 E2 E2 .240 0.0 1.0

CHAT-MON 3 E2 E2 .090 0.0 1.0

CHAT-MON 4 E2 E2 .240 0.0 1.0

CHAT-H2 1 E2 H2 5.550 0.0 1.0

CHAT-H2 2 E2 H2 18.50 0.0 1.0

CHAT-H2 3 E2 H2 5.550 0.0 1.0

CHAT-H2 4 E2 H2 18.50 0.0 1.0

CHAT-SPON 1 E2 .0040 0.0 1.0


CHAT-SPON 2 E2 .0120 0.0 1.0

CHAT-SPON 3 E2 .0040 0.0 1.0

CHAT-SPON 4 E2 .0120 0.0 1.0

DEACT-SPON 1 .00010 0.0 1.0

DEACT-SPON 2 .00060 0.0 1.0

DEACT-SPON 3 .00010 0.0 1.0

DEACT-SPON 4 .00060 0.0 1.0 OPTIONS REAC-PHASE=L

Specifying Ionic Polymerization Kinetics Following is the input language for the IONIC REACTIONS paragraph.

Input Language for Ionic Polymerization

REACTIONS reacid IONIC SPECIES ASSO-INI=cid INIT=cid CATALYST=cid & EX-AGENT=cid CT-AGENT=cid TM-AGENT=cid & POLYMERS MON-RSEG cid segid / cid segid / … INIT-DISSOC cid1 cid2 idpre-exp-f idact-ener-f idpre-exp-r idact-ener-r idasso-no & idref-temp ACT-CATALYST site-id cid1 cid2 acpre-exp-f acact-ener-f acpre-exp-r acact-ener-r & accoefb accoefd acref-temp CHAIN-INI-1 site-id cid i1pre-exp-f i1act-ener-f i1ref-temp CHAIN-INI-2 site-id cid1 cid2 i2pre-exp-f i2act-ener-f i2coefd CHAIN-INI-T site-id cid itpre-exp-f itact-ener-f itref-temp PROPAGATION site-id cid1 cid2 prpre-exp-f pract-ener-f prref-temp ASSOCIATION site-id cid aspre-exp-f asact-ener-f aspre-exp-r asact-ener-r EXCH-GENERAL rxn id site-id1 cid1 site-id2 cid2 egpre-exp-f egact-ener-f egref-temp EXCH-AGENT rxn id site-id1 cid1 site-id2 cid2 eapre-exp-f eaact-ener-f & eapre-expr eaact-ener-r eacoefd earef-temp EQUILIB-CION site-id1 cid1 site-id2 eqpre-exp-f eqact-ener-f eqpre-exp-r & eqexp-ener-r eqcoefd eqref-temp CHAT-SPON site-id cid cspre-exp-f csact-ener-f csref-temp CHAT-MONOMER site-id cid1 cid2 cmpre-exp-f cmact-ener-f cmref-temp CHAT-DORM-P rxn id site-id1 cid1 site-id2 cid2 cdpre-exp-f cdact-ener-f cdref-temp CHAT-AGENT site-id cid1 cid2 capre-exp-f caact-ener-f caorder caref-temp TERM-C-ION site-id cid tcpre-exp tcact-energy tccoefb tcref-temp TERM-AGENT site-id cid1 cid2 tapre-exp-f taact-ener-f taorder taref-temp COUPLING site-id1 site-id2 site-id3 copre-exp-f coact-ener-f copre-exp-r & coact-eng-r coref-temp OPTIONS REAC-PHASE=phaseid SUPPRESS-WARN=yes/no USE-BULK=yes/no

Input Language Description for Ionic Polymerization

reacid Reaction paragraph ID.


SPECIES Reacting species identification. This sentence is used to associate components in the simulation with the reactive species in the built-in kinetic scheme. The following species keywords are currently valid:

ASSOC-INIT INITIATOR CATALYST EXCH-AGENT CHAT-AGENT TERM-AGENT POLYMER

MON-RSEG Identifying the reacting monomer and the corresponding repeat segment associated with it.


cid2 Component ID of corresponding repeat segment

INIT-DISSOC Reaction identifier for initiator dissociation reaction. Associated initiator of type m dissociates into type p initiator.

cid1 Component ID of associated initiator


idpre-exp-f Preexponential factor for forward reaction

idact-ener-f Activation energy for forward reaction

idpre-exp-r Preexponential factor for reverse reaction

idact-ener-r Activation energy for reverse reaction

idasso-no Initiator Association number

idref-temp Reference temperature

ACT-CATALYST Reaction identifier for active species activation by catalyst of type n of an initiator of type m to form active species and/or counter-ion of type i.

site-id Site type identifier for active species formed

(i = 1, 2, ..., NSITE)

cid1 Component ID of initiator


acpre-exp-f Preexponential factor for forward reaction

acact-ener-f Activation energy for forward reaction

acpre-exp-r Preexponential factor for reverse reaction

acact-ener-r Activation energy for reverse reaction

accoefb 0 if cid2 does not participate in the reaction. 1 if cid2 participates in the reaction

accoefd 0 if counter-ion is absent. 1 if counter-ion is present

acref-temp Reference temperature


CHAIN-INI-1 Reaction identifier for chain initiation of active species of type i by monomer of type j.


(i = 1, 2, ..., NSITE)

cid Component ID of monomer

i1pre-exp-f Preexponential factor

i1act-ener-f Activation energy

i1ref-temp Reference temperature

CHAIN-INI-2 Reaction identifier for chain initiation of active species of type i by monomer of type j reacting with initiator of type m.


(i = 1, 2, ..., NSITE)

cid1 Component ID of initiator


i2pre-exp-f Preexponential factor

i2act-ener-f Activation energy

i2coefd 1 if counter-ion is formed. 0 otherwise

tref Reference temperature

CHAIN-INI-T Reaction identifier for chain initiation of transfer active species of type i by monomer of type j.


(i = 1, 2, ..., NSITE)

cid Component ID of monomer

itpre-exp-f Preexponential factor

itact-ener-f Activation energy

itref-temp Reference temperature

PROPAGATION Reaction identifier for polymer chain propagation on an active species of type i.


(i = 1, 2, ..., NSITE)

cid1 Component ID of active segment


prpre-exp-f Preexponential factor

pract-ener-f Activation energy

prref-temp Reference temperature


ASSOCIATION Reaction identifier for polymer association with active species of type i.

site-id Site type identifier for active species formed (i = 1, 2, ..., NSITE)

cid Component ID of active segment

aspre-exp-f Preexponential factor for forward reaction (forming aggregate polymer)

asact-ener-f Activation energy for forward reaction

aspre-exp-r Preexponential factor for reverse reaction

asact-ener-r Activation energy for reverse reaction

asasso-no Polymer association

asref-temp Reference temperature

EXCH-GENERAL Reaction identifier for general exchange reaction between two growing polymer chains with unique active species and end segments attached to them.

rxn id Reaction ID for a unique rate constant

site-id1 Site type identifier for first active species

(i = 1, 2, ... , NSITE)

cid1 Component ID of active segment on siteid1

site-id2 Site type identifier for second active species (i = 1, 2, ... , NSITE)


egpre-exp-f Preexponential factor

egact-ener-f Activation energy

egref-temp Reference temperature

EXCH-AGENT Reaction identifier for exchange between growing i polymer species with k segment attached to it and an exchange-agent of type m.



(i = 1, 2, ... , NSITE)


site-id2 Site type identifier for second active species

(i = 1, 2, ... , NSITE) formed

cid2 Component ID of exchange agent

eapre-exp-f Preexponential factor for forward reaction

eaact-ener-f Activation energy for forward reaction


eapre-exp-r Preexponential factor for reverse reaction

eaact-ener-r Activation energy for reverse reaction

eacoefd 0 if Po is absent. 1 if Po is present

earef-temp Reference temperature

EQUILIB-CION Reaction identifier for equilibrium with counter-ion between i and j active species with kth segment attached to it.


(i = 1, 2, ... , NSITE)


site-id2 Site type identifier for second active species

(j = 1, 2, ... , NSITE)

eqpre-exp-f Preexponential factor for forward reaction

eqact-ener-f Activation energy for forward reaction

eqpre-exp-r Preexponential factor for reverse reaction

eqact-ener-r Activation energy for reverse reaction

eqcoefd 0 if counter-ion is absent. 1 if counter-ion is present

eqref-temp Reference temperature

CHAT-SPON Reaction identifier for spontaneous chain transfer on active species of type i.

site-id Site type identifier for active species

(i=1, 2, ... , NSITE)


cspre-exp-f Preexponential factor

csact-ener-f Activation energy

csref-temp Reference temperature

CHAT-MONOMER Reaction identifier for chain transfer to monomer of type j on active species of type i.


(i=1, 2, ... , NSITE)



cmpre-exp-f Preexponential factor

cmact-ener-f Activation energy

cmref-temp Reference temperature


CHAT-DORM-P Reaction identifier for chain transfer on active species of type i to form dormant polymer of type j.


site-id1 Site type identifier for growing active species (i = 1, 2, ... , NSITE)


site-id2 Site type identifier for product active species (j = 1, 2, ... , NSITE) formed


cdpre-exp-f Preexponential factor

cdact-ener-f Activation energy

cdref-temp Reference temperature

CHAT-AGENT Reaction identifier for chain transfer to chain transfer agent on active species of type i.


(i=1, 2, ... , NSITE)


cid2 Component ID of chain transfer agent

capre-exp-f Preexponential factor

caact-ener-f Activation energy

caorder Reaction order for chain transfer agent concentration

caref-temp Reference temperature

TERM-C-ION Reaction identifier for chain termination with counter-ion.


(i=1, 2, ... , NSITE)




tcoefb 0 if counter-ion does not participate in the reaction. 1 if it does

tcref-temp Reference temperature

TERM-AGENT Reaction identifier for termination with terminating agent.

site-id Site type identifier (i = 1, 2, ... , NSITE)

cid1 Component ID of active agent

cid2 Component ID of terminating agent


tapre-exp-f Preexponential factor

taact-ener-f Activation energy

taorder Reaction order for terminating agent concentration

taref-temp Reference temperature

COUPLING Reaction identifier for coupling reaction between active species of type i and type j to form active species of type k.

site-id1 Site identifier for active species of type i participating in the reaction

site-id2 Site identifier for active species of type j participating in the reaction

site-id3 Site identifier for active species of type k formed by coupling reaction

copre-exp-f Preexponential factor

coact-ener-f Activation energy

copre-exp-r Preexponential factor

coact-ener-r Activation energy

coref-temp Reference temperature

OPTIONS Specify reaction model options.

REAC-PHASE= phaseid





USE-BULK= yes/no



Input Language Example for Ionic Polymerization


REACTIONS rxnid SEGMENT-BAS DESCRIPTION '...' PARAM TREF=value PHASE=V/L/L1/L2 SOLVE-ZMOM=YES/NO &

[SUPRESS-WARN=yes/no] [USE-BULK=yes/no] CBASIS=basis &

[REAC-SITE=siteno S-BASIS=basis]

SPECIES POLYMER=polymerid STOIC reactionno compid coef / ... RATE-CON reactionno pre-exp act-energy [t-exp] [TREF=ref-temp] & [CATALYST=cid CAT-ORDER=value] [USER-RC=userid] / ... POWLAW-EXP reactionno compid exponent /

[ASSIGN reactionno [ACTIVITY=value] RC-SETS=setno-list]

SUBROUTINE RATECON=rcname MASSTRANS=mtname

USER-VECS NINTRC=nintrc NREALRC=nrealc NINTMT=nintmt NREALMT=nrealmt & NIWORKRC=niwork NWORKRC=nwork NIWORKMT=niwork NWORKMT=nwork &

NURC=nurc INTRC value-list REALRC value-list INTMT value-list REALMT value-list

Specifying Segment-Based Polymer Modification Reactions The input language for the SEGMENT-BAS REACTIONS paragraph is described here.

Input Language for Segment-Based Polymer Modification Reactions

REACTIONS rxnid SEGMENT-BAS DESCRIPTION '...' PARAM T-REFERENCE=value PHASE=V/L/L1/L2 CBASIS=basis &

SOLVE-ZMOM=YES/NO SPECIES POLYMER=polymerid STOIC reactionno compid coef / ... RATE-CON reactionno pre-exp act-energy [t-exp] / ... POWLAW-EXP reactionno compid exponent /

The keywords for specifying rate constant parameters, reaction stoichiometry, and reacting polymer are described here.

Input Language Description for Segment-Based Polymer Modification Reactions

reacid Unique paragraph ID.

DESCRIPTION Up to 64 characters between double quotes.

PARAM Used to enter reaction specifications.


T-REF= value

Reference temperature. If no reference temperature is given, the term 1/Tref is dropped from the rate expression:

( )rate C k ej j oi

EaR T Tij

i

ref= ∏−

−⎛

⎝⎜⎜

⎞

⎠⎟⎟α

1 1

For more information, see the Segment-Based Reaction Model section in Chapter 3.

PHASE=V/L/L1/L2

Reacting phase

CBASIS Basis for power law rate expression. Choices are:

MOLARITY MOLALITY MOLEFRAC MASSFRAC MASSCONC




USE-BULK= yes/no



SOLVE-ZMOM= YES/NO

Option to explicitly solve for zeroth moment based on segment types (default=no)

REAC-SITE=siteno

Site number associated with all reactions in this model

S-BASIS=basis

For multi-site kinetics there are two options for calculating the segment concentrations used by the reactor model:

COMPOSITE: use the composite segment concentrations (from SFLOW)

SITE: use the site-based segment concentrations (from SSFLOW)

SPECIES Used to specify reacting polymer.

POLYMER= polymerid

Polymer component ID (for reacting polymer)

STOIC Used to specify stoichiometry for user reactions.



compid Component ID

coef Stoichiometric coefficient (negative for reactants and positive for products)

POWLAW-EXP Used to specify power-law exponents.


compid Component ID

exponent Power law exponent

ASSIGN Used to assign rate constant(s) to user reactions.


ACTIVITY= value

Multiplying factor used to calculate net rate constant

RC-SETS = setno-list

List of rate constants (from RATE-CON) which apply to this user reaction

RATE-CON Used to specify rate constant parameters.

SetNo Rate constant set number

pre-exp Pre-exponential factor in inverse time units

act-energy Activation energy in mole enthalpy units

t-exp Temperature exponent

T-ref Reference temperature (default is global reference temperature in PARAM sentence)

USER-RC=number

Used to specify an element number in the user rate constant array (default=do not apply user rate constant)

CATALYST= compid

Optional catalyst ID

CAT-ORDER=value

Optional reaction order for catalyst (default=1)

SUBROUTINE Used to provide the names of user-supplied Fortran subroutines. The subroutine argument lists are documented in the User Subroutines section of Chapter 3.

RATECON= rcname

User rate constant subroutine name

BASIS= mtname User concentration basis / mass-transfer subroutine name

USER-VECS Used to specify the size of vectors for user subroutines.

NINTRC=nintrc Length of integer array rate constant routine

NREALRC= nrealrc

Length of real array for rate constant routine


NINTMT=nintmt Length of integer array for basis subroutine

NREALMT= nrealmt

Length of real array for basis subroutine

NIWORKRC= niwork

Length of integer workspace for rate constant subroutine

NWORKRC=nwork Length of real workspace for rate constant subroutine

NIWORKMT= niwork

Length of integer workspace for basis routine

NWORKRC=nwork Total length of real workspace for basis subroutine

NURC Number of rate constants returned by user rate constant routine

INTRC Used to enter integer parameters for user rate constant subroutine

REALRC Used to enter real parameters for user rate constant subroutine

INTMT Used to enter integer parameters for user basis subroutine

REALMT Used to enter real parameters for user basis subroutine

Input Language Example for Segment-Based Polymer Modification Reactions

REACTIONS R-1 SEGMENT-BAS

SPECIES POLYMER=PU

STOIC 1 DEG -1. / MDI -1. / DEG-E 1. / MDI-E 1. / &

URETHANE 1.

STOIC 2 DEG -1. / MDI-E -1. / DEG-E 1. / MDI-R 1. / &

URETHANE 1.

STOIC 3 DEG-E -1. / MDI -1. / DEG-R 1. / MDI-E 1. / &

URETHANE 1.

STOIC 4 DEG-E -1. / MDI-E -1. / DEG-R 1. / MDI-R 1. / &

URETHANE 1.

STOIC 5 MDI-E -1. / H2O -1. / MDA-E 1. / CO2 1.

STOIC 6 MDA-E -1. / MDI -1. / MDI-R 1. / MDI-E 1. / &

UREA-R 1.

STOIC 7 MDA-E -1. / MDI-E -1. / MDI-R 2. / UREA-R 1.

STOIC 8 MDI -1. / URETHANE -1. / MDI-E 1. / ALLOPHAN 1.


STOIC 9 MDI-E -1. / URETHANE -1. / MDI-R 1. / ALLOPHAN 1.

STOIC 10 MDI -1. / UREA-R -1. / MDI-E 1. / BIURET 1.

STOIC 11 MDI-E -1. / UREA-R -1. / MDI-R 1. / BIURET 1

RATE-CON 1 2500. <1/sec> 10.

RATE-CON 2 1000. <1/sec> 10.

RATE-CON 3 5000. <1/sec> 10.

RATE-CON 4 10. <1/sec> 10.

RATE-CON 5 100. <1/sec> 10.

ASSIGN-URC 1 ACTIVITY=4. RC-SETS=1



ASSIGN-URC 4 RC-SETS=1








POWLAW-EXP 1 DEG 1. / MDI 1.

POWLAW-EXP 2 DEG 1. / MDI-E 1.

POWLAW-EXP 3 DEG-E 1. / MDI 1.

POWLAW-EXP 4 DEG-E 1. / MDI-E 1.

POWLAW-EXP 5 MDI-E 1. / H2O 1.

POWLAW-EXP 6 MDA-E 1. / MDI 1.

POWLAW-EXP 7 MDA-E 1. / MDI-E 1.

POWLAW-EXP 8 MDI 1. / URETHANE 1.

POWLAW-EXP 9 MDI-E 1. / URETHANE 1.

POWLAW-EXP 10 MDI 1. / UREA-R 1.

POWLAW-EXP 11 MDI-E 1. / UREA-R 1.

References Aspen Physical Property System Physical Property Data. Cambridge, MA: Aspen Technology, Inc.

Aspen Plus User Models. Cambridge, MA: Aspen Technology, Inc.

522 Index

Index

A

Absorption 209 Acrylic acid 195 Activated initiation 207 Activation energy

fitting 348 Active species formation 246 Adding

emulsion reactions 217 free-radical reactions 191 gel-effect 192, 218 ionic reactions 253 segment-based reactions 279 user basis subroutine 157, 281 user kinetic subroutine 157 user rate constant subroutine

157, 280 user step-growth reactions 155 Ziegler-Natta reactions 238

Addition polymerization about 78 ionic process differences 242 step-growth processes 257

Addition polymers 55 Addition reactions 99 Aggregate polymer 33, 34 Aggregation reactions 248 Aliphatic polycarbonates 85 Amorphous polymers 16 Analysis tools

available 11, 366–71 calculation procedure 367 case studies 368 optimization 369 sensitivity 368

Application tools 285 Applications

data fitting 331 example uses 366 tools 366–71

Architecture

Aspen Polymers 372 Aromatic polycarbonates 85 Aspen Plus

distillation models 287, 293 Dupl 288–90 equilibrium reactor models 296 Flash2 290 Flash3 290 fractionation models 287 FSplit 291 Heater 291 kinetic reactor models 296–327 mass-balance reactor models

294–96 Mixer 291 Mult 291 Pipe 292 Pump 292 RadFrac 293 RBatch 319–27 RCSTR 296–309 reaction models 83 reactor models 288, 294 REquil 296 RGibbs 296 RPlug 309–19 RStoic 294 RYield 295 Sep 293 Sep2 293 stream manipulators 286 unit operation models 351–57

Aspen Polymers application tools 285, 366–71 architecture 372 built-in models 82 component attribute treatment in

unit operations 328–30 component databanks 378–420 configuring 372–73 data fitting 285, 331–32 decomposition rate parameters

421–23

Index 523

emulsion model 195–219 end-use properties 72 features 5, 9–13 files 373 flowsheets 284 fortran utilities 435–59 free-radical polymerization

model 159–94 input language 460–520 installation 373 ionic model 241–55 key parameters 334 kinetic rate constant parameters

421–34 model definition 12 polyester technology package 91 property approach 56 reaction models 82 segment approach 27 segment-based reaction model

256–81 steady-state features 285 steady-state modeling 282–85 step-growth polymerization

model 85–158 templates 373 troubleshooting 374–77 unit operation models 286–330 unit operations 285 user models 83, 351–65 user subroutines 136–51, 265–

76 Ziegler-Natta model 220–40

Aspen PolyQuest 92 AspenTech support 3 AspenTech Support Center 3 Association reactions 248 Attributes See also Component

attributes aggregate polymers 39, 48 bulk polymers 46 calculation methods 46 catalyst 44 fortran utilities 436–48 handling in unit operations 328 initialization scheme 46–50 initializing in streams 465 input language 436–48 live polymers 38, 48 polymers 35–36 required 43, 46 scale factors 50 scaling 466

site-based aggregate polymers 42, 49

site-based bulk polymers 48 site-based live polymers 41, 49 site-based polymers 39 specifying conventional

component 464 user 45 variables for data regression 338 Ziegler-Natta 44

Average properties 56–57

B

Backbone modifications 260 Batch reactors 322 BatchFrac

attribute handling 329 Beta-scission 179 Bifunctional initiator decomposition

167 Bifunctional initiators 170, 171 Bimodal distributions 54 Bivariate distributions 53 Block length 34 Branch formation 261 Branching

degree of 32 free-radical polymerization 188 frequency 34 number of chains 34 reactions 235

Broyden solver 303 Bulk

free-radical polymerization 159–94

polymer chain 165 polymer chain length moment

equation 183 polymerization 160

Bulk polymerization 82 Butadiene 195 Butyl acrylate 195 Butyl methacrylate 195

C

CAELID 436 CAID 436 Calculator block 367 CAMIX 437 Case study block 368 CASPLT 438

524 Index

CASPSS 438 Catalyst sites

inhibited 226 propagation 226 types 226 vacant 226

Catalysts poisoning 235 preactivation 232 site activation 232 types 221–24 Ziegler-Natta 24, 221 Ziegler-Natta reactions 225

Catalyzed initiation reaction 169 Categorizing polymers 19 CAUPDT 439 Chain

initiation for ionic 247 initiation for Ziegler-Natta 232 scission 260 termination 249

Chain length average properties 57 distribution 20, 34, 57–58, 62 first moment 46 instantaneous weight distribution

60 instanteous number-average 61 weight-average 61 zeroth moment 46

Chain size 53 Chain transfer

dormant polymer formation 249 ionic reactions 249 spontaneous 234, 249 to agent 233, 249 to cocatalysts 234 to electron donor 234 to hydrogen 234 to monomer 175, 234, 249 to polymer 177 to small molecules 174, 233 to solvent 174, 233 to transfer agent 174

Chain-growth polymerization bulk 82 commercial polymers 81 comparison to step-growth 79 emulsion 82 overview 80

precipitation 82 solution 82 suspension 82

Characterizing approach 19 components 10, 12, 27

Chlorinated polyethylene 256 Chloroprene 195 Class 0 component attributes 33,

45, 328 Class 1 component attributes 33 Class 2 component attributes 33,

45–46, 305, 328 CMC See Critical micelle

concentration Cocatalysts

poisoning 235 Combination reactions 100, 261 Component attributes

about 19 aggregate polymer 33 available 35–44 calculation methods 46 categories 34 class 0 33, 45 class 0 treatment in unit

operations 328 class 1 33 class 2 33, 45–46, 305 class 2 treatment in unit

operations 328 classes 33 composite 34 copolymer composition 32 degree of branching 32 degree of cross-linking 32 degree of polymerization 23, 32 emulsion polymerization 214 for aggregate polymers 39, 48 for blocks 51 for bulk polymers 46 for catalysts 33, 44 for composite aggregate

polymers 35 for composite live polymers 34 for composite polymers 34 for ionic initiators 32, 44 for live polymers 38, 48 for polymer properties 32 for polymers 34–35, 35–36

Index 525

for site-based aggregate polymers 35, 42, 49

for site-based bulk polymers 48 for site-based live polymers 35,

41, 49 for site-based polymers 35, 39–

43 for site-based species 44 for streams 51 for structural properties 32 for Ziegler-Natta catalysts 32 free-radical polymerization 187 initialization 46, 51 initialization scheme 46 input language 436–48 ionic polymerization 252 live polymer 33 molecular architecture 32 molecular weight 32 required 43, 46 scale factors 50 segment composition 32 segment-based reaction model

264 sequence length 32 specifying 51–52 specifying conventional 51 specifying conventional

attributes 464 specifying scale factors 52 specifying scaling factors 466 step-growth polymerization 120 structural properties tracked 23 types 34 unit operation model treatment

328–30 user-specified 45 Ziegler-Natta 44 Ziegler-Natta polymerization 236

Component databanks about 25 for initiators 26 for PC-SAFT 26 for polymers 11, 26 for POLYPCSF 26 for pure components 25 for segments 11, 26 selecting 28

Components adding reacting 150 catalysts 24 categories 21–25 characterizing 12

conventional 22 databanks 378–420 defining 12 defining types 28 fortran utilities 352, 436–48,

448–54 input language 460–64 ionic initiators 24 naming 28, 460 oligomers 23 POLYMER databank 378–82,

379–82 polymers 22 pure component databank 378 segment approach 27 SEGMENT databank 383–420 segments 24 site-based 24 specifying 27 specifying catalysts 461–64 specifying oligomers 461–64 specifying polymers 461–64 specifying step-growth 153

Composition 8 Condensation polymerization 78,

122 Condensation reactions 99 Configuring

Aspen Polymers 372–73 Consumption of radicals 59–60 Continuous polymerization 88 Conventional components 22 Conventional species 259 Convergence

for RCSTR 300 improving 50 initialization options (RCSTR)

306 parameter tuning 346 RBatch troubleshooting 324–27 RCSTR troubleshooting 307–9 RPlug troubleshooting 315–19 scaling factors (RBatch) 324 scaling factors (RCSTR) 304 scaling factors (RPlug) 315 solver method (RBatch) 326 solver method (RPlug) 317 step size (RBatch) 326 step size (RPlug) 317 troubleshooting data regression

345–47 Conversion

energy balance 303

526 Index

Copolymer density 75

Copolymerization 61 free-radical 159–94 ionic 241–55 ionic propagation 248 user input for ionic model 246 user input for Ziegler-Natta

model 231 Ziegler-Natta 220–40

Copolymers 16 COPYCA 440 Coupling reactions 250 CPACK 448 CPE See Chlorinated polyethylene Critical micelle concentration 197 Cross linking 261 Cross-link formation 181 Cross-linking 32, 34 Crystalline polymers 16 Crystallinity 8 Custom

prop-sets 73 Custom models See User models,

See User models customer support 3 Cycle time 323 Cyclodepolymerization reactions

100

D

DAMP-FAC 303 Damping factor 303 Data

collection 333 defining regression cases 343 fitting 331–32 interpreting regression results

344 literature search 332, 333 point 337 profile 337 regression 331–32 review 332 sequencing regression cases 344 trend analysis 333, 335 verification 333

Data fitting See also Data regression

applications 331 data collection 333 data review 332 data verification 333 features 285 literature search 332, 333 model development 332, 335 model refinement 333, 336 parameters 334–35 preliminary fit 332, 334–35 procedure 332–36 trend analysis 333, 335

Data regression See also Data fitting

activation energy 348 base-case model 337 choosing parameters 347 convergence problems 345–47 data sets 337 defining cases 337, 343 entering data 337 entering operating conditions

337 flowsheet variables 369–71 fortran blocks 339 interpreting results 344–45 manipulating variables 339 point data 341 procedure 332–36, 336–50,

336–50 profile data 342 Prop-Sets 339 scaling fitted parameters 348 sensitivity studies 347 sequencing cases 344 standard deviation 343 troubleshooting 345–47 tuning 346

Databanks component 25, 378–420 functional group 11 INITIATOR 26 PC-SAFT 26 polymer 11 POLYMER 26, 378–82 POLYPCSF 26 pure component 25, 378 segment 11 SEGMENT 26, 382–420 selecting 28

Index 527

Dead polymer 34 Dead polymer chain 165 Dead sites 44 Dead zones 300, 313 Defining

additional simulation options 13 components 12 feed streams 13 flowsheet options 12 global simulation options 12 polymerization kinetics 13 property models 13 regression cases 343 UOS model operating conditions

13 Degree of

branching 32, 53 cross-linking 32 polymerization 32, 55

Density as polymer property 8 function 56–57 of copolymer 75

Depolymerization 260 Design-spec block 368 Desorption 209 Developing

models 12 Direct esterification 86 Displaying

distribution data for reactors 67 distribution data for streams 67 distribution data tables 67

Disproportionation 176 Distillation models

about 293 available 287 RadFrac 293

Distribution average properties and moments

56–57 calcuations 467 chain length 62 copolymerization 61 displaying data table 67 displaying for reactors 67 displaying for streams 67 functions 54, 56 GPC 64, 65 in process models 56 kinetic reactors 62 method of instantaneous

properties 58–61

moment equation 183–84 moments 56–57 particle size 212–14 plotting data 67, 68 plug flow reactors 63 polymer 62 procedure 65 specifying calculations 66–68 specifying characteristics 66 streams 64 structural property 53–69 tracking 62 verification 65

Distribution calculations specifying input language 467

Dupl about 288–90 attribute handling 328

Duty in RBatch 319 in RCSTR 297 in RPlug 309

Dyads 34 free-radical rate equation 184

Dynamic models 10, 13

E

EB-LOOP 303 e-bulletins 3 Editing

emulsion reactions 217 free-radical reactions 191 ionic reactions 253 segment-based reactions 279 user step-growth reactions 155 Ziegler-Natta reactions 239

Elastomers 16 Electrophilic reactions 97 Emulsion polymerization

absorption 209 accessing model 215 activated initiation 207 adding reactions 217 applications 195 aqueous phase 204 assigning rate constants 217 attributes 214 built-in reaction listing 216 chain growth 82 desorption 209 editing reactions 217

528 Index

homogeneous nucleation 200–202

industrial processes 196 input language 493–99 kinetics 196–211, 207 kinetics scheme (figure) 200 latex 198 latex reactions 203 micellar nucleation 197–200 model 195–219 model assumptions 211 model features 211–14 monomer partitioning 211–12 nomenclature 204 nucleation time 199 particle growth 197, 202 particle number 199 particle phase 206 particle size distribution 212–14 population balance equation 213 products produced 196 properties calculated 214 radical balance 203–7 rate constant 210 rate of particle formation 202 reactions 200 redox initiation 208 seed process 202 Smith-Ewart theory 207 specifying calculation options

218 specifying gel-effect 218 specifying model 215 specifying particle growth

parameters 219 specifying phase partitioning 218 specifying reacting species 216 stage I (seed) 198 stage II (growth) 198, 202 stage III (finishing) 198 user profiles 214

End group reformation reactions 100

End-use properties about 70–76 adding a Prop-Set 76 calculating 73, 76 density of copolymer 75 input language 468–70 intrinsic viscosity 74

melt index 75 melt index ratio 76 relationship to structure 72 selecting 76 zero-shear viscosity 74

Energy balance conversion 303 Entering

point data 341 profile data 342 standard deviations 343

Equilibrium for ionic polymerization 250 for Ziegler-Natta polymerization

235 phase 184 reactions with counter-ion 248 reactor models 296

Equilibrium models RGibbs 296 RYield 296

Esterification batch process 90 direct 86 operating conditions 89 results 88 secondary 87

Estimating property parameters 473

Ethylene process types 222

Ethylene-propylene 221, 224 Exchange reactions 248

F

Features 5, 9–13 Feed streams

defining 13 with polymers 23, 46

Files startup 373

Fitting activation energy 348 choosing parameters 347

Flash2 about 290 attribute handling 329 input variables 339 results variables 339

Flash3

Index 529

about 290 attribute handling 329 input variables 339 results variables 339

Flowsheeting options 11 Flowsheets

basic unit operation models 286 calculation procedure 367 calculator block 367 case studies 368 design-spec block 368 distillation models 287, 293 Dupl block 288–90 equilibrium reactor models 296 Flash2 block 290 Flash3 block 290 fractionation models 287 FSplit block 291 Heater block 291 incorporating spreadsheets 367 kinetic reactor models 296–327 mass-balance reactor models

294–96 Mixer block 291 model configuration tools 367–

69 Mult block 291 optimization 369 Pipe block 292 polymer process 284 process studies 367–69 Pump block 292 RadFrac block 293 RBatch block 319–27 RCSTR block 296–309 reactor models 288, 294 REquil block 296 RGibbs block 296 RPlug block 309–19 RStoic block 294 RYield block 295 sensitivity study 368 Sep block 293 Sep2 block 293 setting fixed variables 368 steady-state 282–85 stream manipulators 286 unit operation models 286–330 variables 369–71 variables for data regression

369–71 Fortran

arguments 435–59

linking 374 monitors 352 templates 374 utilities 352, 435–59

Fortran blocks in data regression 339 to enforce assumptions 339 to manipulate process variables

340 to scale paramters 349

Fortran utilities CAELID 436 CAID 436 CAMIX 437 CASPLT 438 CASPSS 438 CAUPDT 439 component handling 352 COPYCA 440 CPACK 448 for component attributes 436–48 for components 448–54 for mixture molar volume 458 for streams 454–59 GETCRY 440 GETDPI 443 GETDPN 441 GETMWN 442 GETMWW 443 GETSMF 444 GETSWF 445 IFCMNC 449 IPTYPE 454 ISCAT 449 ISINI 450 ISOLIG 450 ISPOLY 451 ISSEG 451 LCAOFF 446 LCATT 446 LOCATS 455 LPHASE 456 NCAVAR 447 NPHASE 456 NSVAR 457 SCPACK 452 SSCOPY 457 stream handling 352 VOLL 458 XATOWT 453 XATOXT 453

Fractionation models 287 Free-radical iniators

530 Index

decomposition rate parameters 421–23

Free-radical polymerization accessing model 189 adding reactions 191 applications 159 beta-scission reactions 179 bifunctonal initiator

decomposition reaction 170, 171

branching 188 built-in reaction listing 190 bulk 160 bulk polymer chain length

moment equation 183 calculation method 182 catalyzed initiation reaction 169 chain transfer reactions 174 dyads 184 editing reactions 191 gel effect 166 gel effect 184–86 induced initiation reaction 169 industrial processes 160 initiation reactions 167 initiator decomposition reaction

168 input language 482–93 kinetics 161–79 kinetics nomenclature 162 kinetics scheme (figure) 161 live polymer chain length

moment equation 183 model 159–94 model assumptions 182–87 model features 182–87 modifying the rate expression

166 moment-property relationship

equation 187 parameters 187–89 pendent double bond

polymerization 181 phase equilibrium 184 propagation reactions 172 properties calculated 187–89 quasi-steady-state

approximation 184 rate constant 166 reactions 161

solution 160 specifying calculation options

192 specifying gel-effect 192 specifying model 190 specifying reacting species 190 specifying reactions 191 specifying user profiles 193 structural properties 188 termination reactions 174–75 user profile properties 188

Frequency function 56–57 FSplit

about 291 attribute handling 328

Functional group databank 11

G

Gas-phase process 222 Gear integrator 315, 324 Gel effect

built-in correlations 185 free-radical 166 free-radical polymerization 184–

86 specifying 192, 218 user specified correlations 186 user subroutine arguments 186

Gel effect subroutine free-radical 166

Gel permeation chromatography 64 Generation of radicals 59 GETCRY 440 GETDPI 443 GETDPN 441 GETMWN 442 GETMWW 443 GETSMF 444 GETSWF 445 Glycol recovery 87 GPC 64

H

HDPE See High density polyethylene

Heat exchangers 299 Heater


Index 531

help desk 3 Heterogeneous catalysts 221 High density polyethylene

about 220 processes 222

High impact polypropylene 224 HIPP See High impact

polypropylene Hold-up

in RCSTR 297 Homogeneous catalysts 221 Homogeneous nucleation

particle formation 197 process 200–202 rate of particle formation 202

Homopolymers 15

I

IFCMNC 449 INCL-COMPS 150 Induced initiation reaction 169 Industrial applications

polymer production steps 282–84

polymer production steps (figure) 282

Industrial processes emulsion polymerization 196 free-radical polymerization 160 ionic polymerization 242 model uses 366 segment-based reaction model

257 step-growth polymerization 86 Ziegler-Natta polymerization 221

Inhibited sites 226 Inhibition

catalyst sites 44, 234 Initators

for ionic polymerization 246 Initialization

hybrid option 307 integration option 306 options for RCSTR 306 solver option 306

Initiation activated 207 catalyzed 167 decomposition rate 167 free-radical 168, 170, 171 free-radical polymerization 167 induced 167

ionic 44, 243 reaction for catalyzed 169 reaction for decomposition 168 reaction for induced 169 redox 208

INITIATOR databank about 26

Initiators databank 26 free-radical 421–23 ionic 24

Injection ports 314 Input language

attribute scaling factors 466 catalysts 461–64 component attributes 436–48 components 460–64 conventional component

attributes 464 distribution calculations 467 emulsion 493–99 end-use properties 468–70 for Aspen Polymers 460–520 free-radical 482–93 ionic 510–17 oligomers 461–64 physical properties 470–74 polymers 461–64 property data 471 property methods 470 property parameter estimation

473 prop-set 468–70 segment-based reactions 517–21 step-growth 474–82 streams 465 Ziegler-Natta 499–509

Input variables Flash2 339 Flash3 339 MultiFrac 339 RadFrac 339 RBatch 338 RCSTR 338 RPlug 339 standard deviations 343

Installing Aspen Polymers 373

Instantaneous number-average 61 properties 56, 58–61, 62 weight chain length 60–61

Interfacial processes 82

532 Index

Intermolecular reactions 99 Intramolecular reactions 99 Intrinsic viscosity 74 Ionic initiator 24 Ionic initiators

component attributes 32 properties tracked 44

Ionic polymerization accessing model 252 active species formation 246 adding reactions 253 aggregation 248 applications 241 assigning rate constants 254 association 248 built-in reaction listing 253 chain initiation 247 chain termination 249 chain transfer 249 comparison to other addition

processes 242 copolymerization steps 246, 248 coupling 250 editing reactions 253 equilibrium with counter-ion 248 exchange 248 industrial processes 242 initiator attributes 243 initiator types 246 input language 510–17 kinetics scheme 242–50 kinetics scheme (figure) 244 model 241–55 model assumptions 250–51 model features 250–51 nomenclature 245 phase equilibria 250 polymers tracked 243 propagation 247 properties calculated 251–52 rate calculations 250 rate constants 246 reactions 244 specifying model 252 specifying reacting species 252

IPTYPE 454 ISCAT 449 ISINI 450 ISOLIG 450 ISPOLY 451

ISSEG 451

K

Kinetic models RBatch 319–27 RCSTR 296–309 RPlug 309–19

Kinetics data fitting 331–32 decomposition rate parameters

421–23 defining polymerization 13 emulsion (input language) 493–

99 emulsion polymerization 196–

211, 207 free-radical (input language)

482–93 free-radical polymerization 161–

79 ionic (input language) 510–17 ionic polymerization 242–50 mechanisms 10 melt polycarbonate 118–20 multi-site 63 nylon reactions 107–18 parameter influence on 334 polyester reactions 101–7 polymerization 78 rate constant parameters 421–

34 reactor models 296–327 segment-based reaction model

261 single-site 63 specifying emulsion 215–19 specifying free-radical 189–93 specifying ionic 252–54 specifying step-growth 51–52 specifying step-growth (input

language) 474–82 specifying Ziegler-Natta 237–39 step-growth polymerization 97–

120 user fortran arguments 435–59 user models 357–61 user subroutine (example) 358 user subroutines 145

Index 533

Ziegler-Natta (input language) 499–509

Ziegler-Natta polymerization 225–35

L

Latex definition 198 number of particles per liter 199 reactions 203

LCAOFF 446 LCATT 446 Linear condensation polymers 55 Linear low density polyethylene

about 220 processes 222, 223

Linking fortran 374

Liquid enthalpy user subroutine (example) 363

Liquid process 223 Live

polymer chain 165 polymer chain length moment

equation 183 Live polymer 33, 34 LLDPE See Linear low density

polyethylene Local work arrays 151, 275 LOCATS 455 Low density polyethylene 160 Low molecular weight polymer 55 LPHASE 456

M

Mass balance 303 Mass-balance models

RStoic 294 RYield 295

Material streams 46 MB-LOOP 303 Melt index 8, 75 Melt index ratio 76 Melt polycarbonate

rate constants 119 reaction components 118 reaction kinetics 118–20 step-growth reactions 119

Melt-phase nylon-6,6 processes 118 polymerization 96

processes 81 Metallocene catalysts 221 Method of instantaneous properties

56, 58–61, 62 Method of moments 56, 182 Methylmethacrylate 195 Micellar nucleation 197–200 MIXED

substream variables 370 Mixer


Mixing non-ideal in RCSTR 298 non-ideal in RPlug 312

Modeling applications 85, 159, 195, 220,

241, 256 data fitting 285, 331–32 enforcing assumptions 339 features 285 nylon 92–96 nylon-6,6 112 polycarbonates 96–97 polyesters 86–92 polymer phase change 295 polymer processes 284 steady-state 282–85 tools 285 unit operations 285, 286–330

Models accessing variables 369–71 analysis tools 367–69 application tools 366–71 base case 337 calculations for user models

352–57 defining 12 developing 332, 335 parameter fitting 334–35 possible uses 366 process studies 367–69 refining 333, 336 structure for user models 351 trend analysis 333, 335 unit operation 11 user 351–65 USER2 routine 354

Molar volume fortran utilities 458

Molecular structure SEGMENT databank 383–420

Molecular weight

534 Index

as component attribute 32 distribution 8, 56 number-average 75 weight-average 34, 75

Moment equations bulk polymer 183 general 182 live polymer 183 relationship to properties 187

Moments of chain length distribution

first 38, 46 Monomers

corresponding segment formulas 123

definition 15 functional groups 125 partitioning 211–12 purification 283 synthesis 283–84, 283

Most-probable distribution 55, 110, 116, 127

Mult about 291 attribute handling 329

MultiFrac attribute handling 329 input variables 339 results variables 339

Multimodal distributions 54

N

NCAVAR 447 Newton solver 303 Nomenclature

for emulsion model 204 for free-radical model 162 for ionic model 245 for segment-based reaction

model 262 for step-growth model 99 for Ziegler-Natta model 229 POLYMER databank 379–82 SEGMENT databank 382

NPHASE 456 NSVAR 457 Nucleation

homogeneous 197, 200–202 micellar 197–200

period 198 time 198 time (equation) 199

Nucleophilic reactions about 97 nomenclature 99

Number average chain length distribution 61 degree of polymerization 55

Number-average degree of polymerization 34

Nylon aqueous salt solutions 94 melt-phase polymerization 96 production process 92–96 salt preparation 94

Nylon-6 production process 92 rate constants 109 reaction components 108 reaction kinetics 107 step-growth reactions 108 user-specified reactions 109

Nylon-6,6 melt-phase polymerization 118 modeling approaches 112 production process 94 rate constants 114, 115 reaction components 112 reaction kinetics 111 step-growth reactions 113 user-specified reactions 116

O

Occupied sites 44 Oligomers

as components 23 definition 15 fractionation 126 segments 24 specifying 30

Optimization 369 Orienticity 34

P

Packed vectors 151, 275 Parameters

data fitting 331–32 decomposition rate 421–23

Index 535

estimating property 473 fitting 332, 334–35 for free-radical polymerization

187–89 influence of kinetics 334 integer 151, 275 kinetic rate constant 421–34 POLYMER property 378 real 151, 275 scaling 348 SEGMENT property 382 to manipulate process variables

340 tuning for data regression 346

Particle growth in emulsion polymerization 202 specifying parameters 219

PBT See Polybutylene terephthalate

PC-SAFT databank 26

PC-SAFT databank about 26

PEN See Polyethylene naphthalate Pendent double bond

polymerization 181 PET See Polyethylene terephthalate Phase equilibria

ionic polymerization 250 step-growth polymerization 122 Ziegler-Natta polymerization 235

Phase equilibrium free-radical polymerization 184

Phase partitioning specifying 218

Physical properties calculations in user models 356 fitting parameters 334–35 input language 470–74 user models 361–65 user subroutine (example) 363

Pipe 292 Plant data fitting 331–32 Plot

distribution data 67, 68 PMMA See Polymethyl

methacrylate Point data

about 337 entering 341

Polyamides 86 Polybutadiene 241 Polybutene 241

Polybutylene terephthalate 91 Polycarbonates

aliphatic 85 aromatic 85 production process 96–97 reaction kinetics 118–20

Polydispersity index 61

Polyesters assigning rate constants 104 polyester technology package 91 production process 85, 86–92 reaction components 102 reaction kinetics 101–7 side reactions 105 step-growth reactions 103 user-specified reactions 106

Polyethylene chlorinated 256 low density 160

Polyethylene naphthalate 91 Polyethylene terephthalate

batch processes 89–91 continuous step-growth

polymerization 86–89 solid-state models 92

Polyisobutylene 241, 256 Polymer chain

bulk 165 dead 165 definition 165 live 165

POLYMER databank about 11, 26, 378 components 379–82 nomenclature 379–82

Polymerization addition 78 bulk 82 chain-growth 79, 80 condensation 78 condensation polymerization 122 continuous 88 degree of 32 emulsion 82, 195–219 free-radical 159–94 interfacial 82 ionic 241–55 kinetics 10, 13, 78 manufacturing step 284 melt phase 81 precipitation 82 process overview 6–7

536 Index

process types 81 reaction types 78 reactions 78 solid-state 81 solution 82 step-growth 79, 80, 85–158 suspension 82 Ziegler-Natta 220–40

Polymers acrylic acid 195 addition 55 aggregate 33, 34 aliphatic polycarbonates 85 amorphous 16 aromatic polycarbonates 85 as components 23 average properties and moments

56–57 branched 16 bulk polymer chain length

moment equation 183 butadiene 195 butyl acrylate 195 butyl methacrylate 195 by chemical structure 18 by physical structure 16 by property 17 chain-growth 81 characterizing 19 chlorinated polyethylene 256 chloroprene 195 component attribute sets 34–35 component attributes 32, 34 component characterization 10 crystalline 16 data fitting procedure 332–36 data regression procedure 336–

50 dead 34 definition 6 elastomers 16 emulsion properties calculated

214 end-use properties 70–76 ethylene-propylene 221 free-radical properties calculated

187–89 high density polyethylene 220 high-impact polystyrene 159

ionic properties calculated 251–52

ladder 16 linear 16 linear condensation 55 linear low density polyethylene

220 live 33, 34 live polymer chain length

moment equation 183 low density polyethylene 160 low molecular weight 55 mass 120, 264 method of instantaneous

properties 56, 58, 62 method of moments 56 methylmethacrylate 195 mole fraction 263 monomer purification 283 monomer synthesis 283–84, 283 network 16 nomenclature 379–82 phase change 295 polyamides 86 polybutadiene 241 polybutene 241 polyesters 85 polyisobutylene 241, 256 polymerization step 284 polymethyl methacrylate 160,

256 polyoxides 241 polypropylene 221 polystyrene 159, 160, 241 polyurethanes 86 polyvinyl acetate 159 polyvinyl alcohol 160, 256 polyvinyl chloride 159 processing 6–7 processing step 284 production rate 60 production steps 282–84 properties 19 properties tracked 34 property distributions 53–69 property parameters 378 prop-sets 71 purification 283–84 reacting 257 recovery 9, 284

Index 537

segment-based properties calculated 264

segments 24, 382 separation 9, 284 specifying 29 star 16 step-growth 80 structural properties 23 structure 15 structure of 15–19 styrene 195 synthesis 284 tetrafluroethylene 195 thermoplastics 16 thermosets 16 tracking structural properties 32 vinyl chloride 195 vinylacetate 195 Ziegler-Natta properties

calculated 236 Polymethyl methacrylate 160, 256 Polyoxides 241 POLYPCSF

databank 26 POLYPCSF databank

about 26 Polypropylene

about 221 process types 223

Polypropylene terephthalate 91 Polystyrene 159, 160, 241 Polyurethanes 86 Polyvinyl acetate 159 Polyvinyl alcohol 160, 256 Polyvinyl chloride 159 Population balance

equation for emulsion polymerization 213

equation for free-radical polymerization 182

Potential sites 44 Power-law reaction model See

Segment-based reaction model:about

PPT See Polyproylene terephthalate Precipitation polymerization 82 Pressure

drop 297, 310 in RBatch 320 in RCSTR 297 in RPlug 310

Process modeling data fitting 285

dynamic 10, 13 features 285 flowsheets for polymer processes

284 issues for polymers 7–9 steady-state 10, 13, 282–85 tools 285 unit operations 285

Processing polymers 284

Profile data about 337 data sets 342 entering 342 RBatch 342 RPlug 342

Propagation depolymerization 260 free-radical polymerization 172 ionic polymerization 247 segment-based reaction model

261 sites 226 Ziegler-Natta polymerization 233

Properties average polymer 56–57 branching 23 chain size 53 composition 8 copolymer composition 23, 53 copolymerization 61 crystallinity/density 8 degree of branching 53 degree of polymerization 23 density of copolymer 75 end-use 70–76 estimating parameters 473 for polymers 56 input language 470–74 intrinsic viscosity 74 melt index 8, 75 melt index ratio 76 method of instantaneous 58 molecular structure 23 molecular weight 23 molecular weight 8 moments of molecular weight

distribution 23 particle size 53 polymer structural 32, 53 prop-set 71 segment composition 23 specifying data 471

538 Index

viscosity 8 zero-shear viscosity 74

Property distributions bimodal 54 bivariate 53 most-probable 55 multimodal 54 Schulz-Flory 54 Stockmayer bivariate 56 structural 53–69 types 53 unimodal 54

Property methods input language 470

Property parameter databanks 11 Property set See also Prop-Sets Prop-Sets

adding 76 custom 73 defining 71 for data regression 339 for polymers 71 properties 71 uses 71

Propylene processes 223, 224

Pseudocondensation reactions 99 Pump 292 Pure components

databank 25, 378 Purification

monomer 283 process step 283–84

PVA See Polyvinyl alcohol

Q

QSSA See Quasi-steady-state approximation

Quasi-steady-state approximation 184

R

RadFrac about 293 attribute handling 329 input variables 339 results variables 339

Radiation initiation reaction 169 Radicals

absorption 206 balance 203–7 consumption of 59–60 depletion 204 desorption 206 generation 204 generation of 59 rate of production 204 termination 206

Random scission 100 Rate constant parameters

data-fitting 285 Rate constants

assigning to emulsion reactions 217

assigning to ionic reactions 254 assigning to step-growth

reactions 154, 156 assigning to Ziegler-Natta

reactions 239 data fitting 331 emulsion 210 for melt polycarbonate 119 for model generated reactions

131 for nylon-6 109 for nylon-6,6 114, 115 for polyesters 104 for user-specified reactions 135,

280 free-radical 166 ionic 246 kinetic parameters 421–34 segment-based 261 specifying for segment-based

power-law reactions 279 specifying for step-growth user

reactions 155 step-growth 149 user subroutines 140, 270 Ziegler-Natta 231

Rate expression step-growth 129, 134

RBatch about 319–27 attribute handling 330 batch reactors 322 common problems 327 cycle time 323 duty 319

Index 539

dynamic scaling 324 hybrid scaling options 325 input variables 338 pressure 320 profile data 342 residence time 321 results variables 338 scaling options 324 semi-batch reactors 322 solver method 326 specifying user profiles 193 static scaling options 324 step size 326 streams 322 temperature 319 troubleshooting convergence

324–27 volume 321

RCSTR about 296–309 algorithm 300 attribute handling 330 calculation loops 301 calculation table 301 common problems 308 component scaling 305 condensed phases 297 convergence 300 duty 297 effective hold-up 297 external heat exchanger 299 horizontal partition 298 hybrid initialization 307 initialization options 306 input variables 338 integration initialization 306 multiphase 297 non-ideal mixing 298 pressure 297 residence time 297 results variables 338 scaling options 304 single-phases 297 solver initialization 306 substream scaling 305 temperature 297 troubleshooting convergence

307–9 vertical partition 299 with dead zone 300

Reacting phase specifying for segment-based

power-law model 277

specifying for step-growth 156 Reacting polymers 257 Reaction models

Aspen Plus 83, 351–57 available 351–57 basic unit operation 286 built-in 82 custom 83 distillation 287, 293 Dupl 288–90 equilibrium 296 Flash2 290 Flash3 290 fractionation 287 FSplit 291 generic 83 Heater 291 kinetic 296–327 mass-balance 294–96 Mixer 291 Mult 291 Pipe 292 Pump 292 RadFrac 293 RBatch 319–27 RCSTR 296–309 reactor 288, 294 REquil 296 RGibbs 296 RPlug 309–19 RStoic 294 RYield 295 Sep 293 Sep2 293 stream manipulators 286 treatment of component

attributes 328–30 Reactions

active species 246 adding emulsion 217 adding free-radical 191 adding ionic 253 adding segment-based 279 adding user 155 adding Ziegler-Natta 238 addition 99 aggregation 248 assigning emulsion rate

constants 217 assigning ionic rate constants

254 assigning step-growth rate

constants 154

540 Index

assigning user rate constants 156

assigning Ziegler-Natta rate constants 239

association 248 backbone 260 beta-scission 179 bifunctional initiator

decomposition 170, 171 branching (segment-based) 261 branching (Ziegler-Natta) 235 catalyst preactivation 232 catalyst site activation 232 catalyzed initiation 167, 169 chain initiation (free-radical 167 chain initiation (ionic) 247 chain initiation (Ziegler-Natta)

232 chain scission 260 chain termination (free-radical)

174–75 chain termination (ionic) 249 chain transfer (free-radical) 174 chain transfer (ionic) 249 chain transfer (Ziegler-Natta)

233 chain-growth 80 classifying 78 cocatalyst poisoning 235 combination 100, 261 condensation 99 conventional species 259 coupling 250 cross linking 261 cyclodepolymerization 100 depolymerization 260 editing emulsion 217 editing free-radical 191 editing ionic 253 editing segment-based 279 editing user 155 editing Ziegler-Natta 239 electrophilic 97 emulsion polymerization 200 end group reformation 100 equilibrium with counter-ion 248 exchange 248 for step-growth polymerization

122 free-radical polymerization 161

homogeneous nucleation 200 including user 154 induced initiation 167, 169 Inhibition 177 initiator decomposition 167, 168 intermolecular 99 intramolecular 99 ionic polymerization 244 latex 203 melt polycarbonate kinetics 118–

20 micellar nucleation 197 micellar nucleation (figure) 198 modification See Segment-based

reaction model nucleophilic 97 nylon-6 kinetics 107 nylon-6,6 kinetics 111 particle growth 202 polyester kinetics 101–7 polymerization 78 propagation (free-radical) 172 propagation (ionic) 247 propagation (segment-based)

261 propagation (Ziegler-Natta) 233 pseudocondensation 99 radiation initiation 169 radical balance 203 rearrangement 100 reverse condensation 99 ring addition 100 ring closing 100 ring opening 100 side group 260 site deactivation 234 site inhibition 234 specifying segment-based 276–

80 specifying user rate constants

155 spontaneous initiation 169 step-growth 80 step-growth functional groups

124 step-growth polymerization 100 step-growth rate constants 154 supplied by emulsion model 211–

14

Index 541

supplied by free-radical model 182–87

supplied by ionic model 250 supplied by segment-based

model 264 supplied by step-growth model

129–34 supplied by Ziegler-Natta model

236 terminal double bond 235 termination (free-radical) 174–

75 termination (ionic) 249 thermal initiation 169 types affecting catalyst states

225 user-specified step-growth 134–

36 viewing emulsion 216 viewing free-radical 190 viewing ionic 253 viewing segment-based 278 viewing step-growth 153 viewing Ziegler-Natta 238 Ziegler-Natta polymerization 227

Reactor models about 294 available 288 data sets 342 equilibrium 296 input variables 338 kinetic 296–327 mass-balance 294–96 results variables 338

Reactors condensed phase RCSTR 297 convergence problems for

RBatch 324–27 convergence problems for RCSTR

307–9 convergence problems for RPlug

315–19 displaying distribution data 67 distribution 62 horizontal partition 298 multiphase RCSTR 297 multiphase RPlug 312 RCSTR algorithm 300 single-phase RCSTR 297 vertical partition 299 with dead zones 300, 313 with external heat exchanger

299

with injection ports 314 Rearrangement reactions 100 Recovery/separation 9, 284 Redox initiation 208 Regression See Data regression Reports

for user models 357 step-growth options 156

REquil about 296 attribute handling 330

Residence time RBatch 321 RCSTR 297 RPlug 311

Results variables Flash2 339 Flash3 339 MultiFrac 339 RadFrac 339 RBatch 338 RCSTR 338 RPlug 339 standard deviations 343

Reverse condensation reactions 99 Rgibbs

about 296 RGibbs

attribute handling 330 Ring addition reactions 100 Ring closing reactions 100 Ring opening reactions 100 Routines

USER2 354 RPlug

about 309–19 attribute handling 330 common problems 318 duty 309 dynamic scaling 315 hybrid scaling 317 input variables 339 multiphase 312 non-ideal mixing 312 pressure 310 profile data 342 residence time 311 results variables 339 scaling options 315 solver method 317 specifying user profiles 193 static scaling options 315 step size 317

542 Index

temperature 309 troubleshooting convergence

315–19 with dead zone 313 with injection ports 314

Rstoic about 294

RStoic attribute handling 329

Ryield about 295

RYield attribute handling 329

S

Salt aqueous solutions 94 preparation 94

Scale factors about 50 specifying 52

Scaling factors 466

Scaling factors component (RCSTR) 305 dynamic (RBatch) 324 dynamic (RPlug) 315 hybrid (RBatch) 325 hybrid (RPlug) 317 RBatch 324 RCSTR 304 RPlug 315 static (RBatch) 324 static (RPlug) 315 substream (RCSTR) 305

Schulz-Flory distribution 54 Scission 100, 260 SCPACK 452 Secondary esterification 87 Seed process 202 Segment approach 27 SEGMENT databank

about 11, 26, 382 components 383–420 nomenclature 382

Segment flow 34 Segment fraction 34 Segment-based model

assigning rate constants 280

including user rate constant subroutine 280

Segment-based power-law model specifying reacting phase 277 user subroutines 265–76

Segment-based reaction model about 256–81 accessing 276 adding reaction schemes 278 adding reactions 279 applications 256 assumptions 263 backbone modifications 260 branch formation 261 chain scission 260 combination 261 conventional species 259 cross linking 261 depolymerization 260 editing reactions 279 features 263 including user basis subroutine

281 industrial processes 257 input language 517–21 kinetics 261 mole fraction conversion 263 nomenclature 262 propagation 261 properties calculated 264 rate calculations 264 rate constants 261 reaction categories 258–63 reactions allowed 258–63 side group modifications 260 specifying model 276 specifying pre-exponential units

279 specifying rate constants 279 specifying reaction settings 277

Segments composition 15, 32 copolymers 16 definition 24 homopolymers 15 methodology in Aspen Polymers

27 mole fraction 263 molecular structure 383–420 nomenclature 382

Index 543

property parameters 382 sequence 15 specifying 29 structure 15 types 24

Semi-batch reactors 322 Semi-crystalline copolymer density

75 Sensitivity blocks 368 Sep


Sep2 about 293 attribute handling 328

Separation/recovery 9, 284 Side group modifications 260 Simulations

dynamic 10 templates 373

Site activation 232 Site deactivation 234 Site inhibition 234 Site-based components

about 24 attributes 44 specifying 30

Slurry process 222, 223 Smith-Ewart theory 207 Solid-state models 92 Solid-state processes 81 Solution polymerization 82, 160 Solution process 222 Solution processes 82 Solver methods

RBatch 326 RPlug 317

Specifying additional simulation options 13 Aspen Polymers options 372–73 attribute scaling factors (input

language) 466 catalysts 461–64 component attributes 51–52 component attributes (input

language) 436–48 component attributes in blocks

51 component attributes in streams

51 component names 460 components 12, 27

components (input language) 460–64

conventional component attributes 51, 464

data fit 332–36 data regression 336–50 databanks 28 distribution calculations 66–68 distribution calculations (input

language) 467 distribution characteristics 66 emulsion calculation options 218 emulsion kinetics 215–19 emulsion kinetics (input

language) 493–99 emulsion model 215 emulsion rate constants 217 emulsion reacting species 216 end-use properties 76 end-use properties (input

language) 468–70 feed streams 13 fixed process variables 368 flowsheet options 12 free-radical calculation options

192 free-radical kinetics 189–93 free-radical kinetics (input

language) 482–93 free-radical model 190 free-radical reacting species 190 gel-effect 192, 218 global simulation options 12 ionic kinetics 252–54 ionic kinetics (input language)

510–17 ionic model 252 ionic rate constants 254 ionic reacting species 252 oligomers 30, 461–64 particle growth parameters 219 phase partitioning 218 physical properties (input

language) 470–74 point data 341 polymerization kinetics 13 polymers 29, 461–64 pre-exponential units 157, 279 profile data 342 property data 471 property models 13 reacting phase 277 regression cases 343

544 Index

scale factors 52 segment-based reaction model

276 segment-based reaction rate

constants 279 segment-based reaction scheme

278 segment-based reaction settings

277 segment-based reactions 276–80 segment-based reactions (input

language) 517–21 segments 29 site-based components 30 standard deviations 343 step-growth components 153 step-growth kinetics 51–52 step-growth kinetics (input

language) 474–82 step-growth model 152 step-growth rate constants 154,

155, 156 step-growth reacting phase 156 step-growth report options 156 stream attributes 465 UOS model operating conditions

13 user models 351–65 user profiles 193 user step-growth reactions 154 Ziegler-Natta kinetics 237–39 Ziegler-Natta kinetics (input

language) 499–509 Ziegler-Natta model 237 Ziegler-Natta rate constants 239 Ziegler-Natta reacting species

237 Spontaneous initiation reaction 169 Spreadsheets

incorporating in flowsheets 367 SSCOPY 457 SSplit

attribute handling 328 Standard deviations 343 Starting

Aspen Polymers 372–73 Startup files 373 Steady-state models

data fitting 285 features 285

flowsheeting 282–85 tools 285 unit operation 286–330 unit operations 285

Step-growth polymerization accessing model 152 adding user reactions 155 addition processes 257 applications 85 Aspen PolyQuest 92 assigning rate constants 131,

135, 154, 156 batch PET 89–91 built-in reaction listing 153 commercial polymers 80 comparison to chain-growth 79 continuous PET 86–89 editing user reactions 155 electrophilic reactions 97 functional groups 124, 125 including user basis subroutine

157 including user kinetic subroutine

157 including user rate constant

subroutine 157 including user reactions 154 industrial processes 86 input language 474–82 interfacial 82 kinetics 97–120 melt phase 81 melt polycarbonate reaction

kinetics 118–20 model 85–158 model features 120–23 model predictions 120 model structure 123–51 model-generated reactions 129–

34 nomenclature 99 nucleophilic reactions 97 nylon 92–96 nylon-6 reaction kinetics 107 nylon-6,6 reaction kinetics 111 oligomer fractionation 126 overview 80 PBT 91 PEN 91 phase equilibria 122

Index 545

polycarbonates 96–97 polyester reaction kinetics 101–7 polyester technology package 91 polyesters 86–92 PPT 91 rate constants 118, 129, 149 rate constants example 149 rate expression 129, 134 reacting groups 123 reacting species 123, 126 reaction mechanism 122 reaction stoichiometry 128 reactions 100 solid-state 81 solid-state models 92 solution 82 specifying components 153 specifying model 152 specifying pre-exponential units

157 specifying rate constants 154,

155 specifying reacting phase 156 specifying report options 156 specifying subroutines 157 user reactions 134 user subroutines 136–51

Stockmayer bivariate distribution 56

Stoichiometry step-growth 128

Streams continuous batch charge 322 defining feed 13 displaying distribution data 67 distributions 64 fortran utilities 454–59 initializing attributes 465 manipulating 286 MIXED variables 370 processing in user models 353 RBatch 322 time-averaged continuous

reactor product 323 time-averaged continuous vent

product 323 time-varying continuous feed

323 variables for data regression 338

Structure of components 22 of monomers 15 of oligomers 15, 23

of polymers 15–19, 19, 23 of segments 15, 24 property–end-use relationship 72

Styrene 195 Subroutines

fortran arguments 435–59 including user basis 157, 281 including user kinetic 157 including user rate constant 157,

280 local work arrays 151, 275 updating component list 150 user 136–51, 265–76 user basis 136, 263, 266 user forms 152 user gel effect 186 user kinetic (example) 358 user kinetics 145 user property (example) 363 user rate constant 140, 270

support, technical 3 Suspension polymerization 82 Synthesis

monomer 283 polymer 284

T

tacticity 34 TDB See Terminal double bond technical support 3 Temperature

in RBatch 319 in RCSTR 297 in RPlug 309

Templates custom 373 fortran 374 simulation 373

Terminal double bond reactions 235

terminal double bonds 34 Terminal models

free-radical 165 Ziegler-Natta 231

Terminal monomer loss 100 Termination

between chain radicals 177 bimolecular 177 by combination 176 disproportionation 176 free-radical polymerization 174–

75

546 Index

inhibition 177 Tetrafluroethylene 195 Thermal initiation reaction 169 Thermoplastics 16 Thermosets 16 Tips

configuration 373 data regression 345–47

Transesterification 88 Trommsdorff effect 185 Troubleshooting

Aspen Polymers 374–77 convergence (RBatch) 324–27 convergence (RCSTR) 307–9 convergence (RPlug) 315–19 data regression convergence

345–47 diagnostic messages 356 RBatch common problems 327 RCSTR common problems 308 RPlug common problems 318 simulation engine 376 user interface 374

U

Unimodal distributions 54 Unit operation models 11 Unit operations

Aspen Plus models 351–57 available models 351–57 basic models 286 calculations 356 diagnostics 356 distillation models 287, 293 Dupl 288–90 equilibrium reactor models 296 features 285 Flash2 290 Flash3 290 fractionation models 287 FSplit 291 Heater 291 input variables 338 kinetic reactor models 296–327 mass-balance reactor models

294–96 Mixer 291 Mult 291 Pipe 292

property calculations 356 Pump 292 RadFrac 293 RBatch 319–27 RCSTR 296–309 reactor models 288, 294 reports 357 REquil 296 results variables 338 RGibbs 296 RPlug 309–19 RStoic 294 RYield 295 Sep 293 Sep2 293 steady-state models 286–330 stream processing 353 treatment of component

attributes 328–30 user model calculations 352–57 user model structure 351 user models 351–57 variables for data regression 338

USER 351, 357 User attributes

properties tracked 45 User fortran

arguments 435–59 linking 374 templates 374

User models about 351–65 calculations 352–57 component list 150 diagnostics calculations 356 integer parameters 151, 275 kinetic 357–61 packed vectors 151, 275 physical property 361–65 property calculations 356 real parameters 151, 275 reports 357 stream processing 353 structure 351 unit operation 351–57 unit operation calculations 356 USER block 351 USER2 block 351

User profiles for emulsion polymerization 214

Index 547

specifying 193 User prop-sets 73 User reactions

adding step-growth 155 assigning rate constants for

step-growth 156 editing step-growth 155 for polyesters 106 nylon-6 109 nylon-6,6 116 specifying rate constants for

step-growth 155 specifying step-growth 154 step-growth polymerization 134–

36 User routines

fortran linking 374 User subroutines

segment-based power-law model 265–76

step-growth polymerization 136–51

USER2 about 351 model routine 354

V

Vacant sites 44, 226 Variables

accessing flowsheet 369–71 indirect manipulation 339 input 338, 341, 342 results 338, 341, 342 standard deviations 343

Vectors packed 151, 275

Viewing emulsion reactions 216 flowsheet variables 369–71 free-radical reactions 190 ionic reactions 253 segment-based reactions 278 step-growth reactions 153 Ziegler-Natta reactions 238

Vinyl chloride 195 Vinylacetate 195 Viscosity

as polymer property 8 intrinsic 74 zero-shear 74

VOLL 458 Volume

in RBatch 321

W

web site, technical support 3 Weight average

chain length 61 degree of polymerization 55

X

XATOWT 453 XATOXT 453

Z

Z-average degree of polymerization 55

Z-average degree of polymerization 34

Zero-shear viscosity 74 Ziegler-Natta

component attributes 44 Ziegler-Natta catalysts

about 24 attributes 44 component attributes 32 dead sites 44 inhibited sites 44 occupied sites 44 potential sites 44 properties tracked 44 specifying 24 vacant sites 44

Ziegler-Natta polymerization accessing model 237 adding reactions 238 applications 220 assigning rate constants 239 built-in reaction listing 238 catalyst preactivation 232 catalyst reactions 225 catalyst site activation 232 catalyst states 225 catalyst types 221 chain initiation 232 chain transfer to small molecules

233 cocatalyst poisoning 235 copolymerization steps 231 editing reactions 239 ethylene processes 222 gas-phase process 222, 223 industrial processes 221

548 Index

input language 499–509 kinetics scheme 225–35 kinetics scheme (figure) 227 liquid process 223 model 220–40 model assumptions 235 model features 235 nomenclature 229 phase equilibria 235 polyethylene processes 222 polypropylene process types 223 propagation 233 properties calculated 236 propylene processes 223, 224 rate calculations 236 rate constants 231 rate expressions 231 reactions 227 site deactivation 234 site inhibition 234 site types 226 slurry process 222, 223 solution process 222 specifying model 237 specifying reacting species 237 steps 230 terminal double bond 235

aspen polymers+vol1v7 1-usr

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