hysys rto refguide

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Copyright Notice

2002 Hyprotech Ltd. All rights reserved.

Hyprotech Ltd is the owner of, and have vested in them, the copyright and all other intellectual propertyrights of a similar nature relating to their software, which includes, but is not limited to, their computerprograms, user manuals and all associated documentation, whether in printed or electronic form (theSoftware), which is supplied by us or our subsidiaries to our respective customers. No copying or

reproduction of the Software shall be permitted without prior written consent of Hyprotech Ltd., Suite 800,707 - 8thAvenue SW, Calgary AB, T2P 1H5, Canada, save to the extent permitted by law.

Hyprotech reserves the right to make changes to this document or its associated computer programwithout obligation to notify any person or organization. Companies, names, and data used in examplesherein are fictitious unless otherwise stated.

Hyprotech does not make any representations regarding the use, or the results of use, of the Software, interms of correctness or otherwise. The entire risk as to the results and performance of the Software isassumed by the user.

HYSYS, HYSYS.RTO, HYSYS Dynamics, HYSYS.Plant, HYSYS.Process, HYSYS.Refinery, HYSYS.Concept,HYSYS OTS Environment, HYSYS.RTO, Economix, HTFS TASC and MUSE, DISTIL, HX-NET, HYPROP III,and HYSIM are registered trademarks of Hyprotech Ltd.

Microsoft Windows, Windows 95/98, Windows NT, Windows 2000, Visual Basic, and Excel are registeredtrademarks of the Microsoft Corporation.

Documentation Credits

Authors of the current release, listed in order of historical start on project (2002-1998):

Colleen Kachmarski, BAC; Nana Nguyen, BSc; Conrad Gierer, BASc; Lisa Hugo, BSc, BA; Ian McKay, BSc.

Since software is always a work in progress, any version, while representing a milestone, is nevertheless buta point in a continuum. Those individuals whose contributions created the foundation upon which this

work is built have not been forgotten. The current authors would like to thank the previous contributors. Aspecial thanks is also extended by the authors to everyone who contributed through countless hours ofproof-reading and testing.

Contacting Hyprotech

Hyprotech can be conveniently accessed via the following:

Web site: www.hyprotech.com

Information and Sales: [email protected]

Documentation: [email protected]

Training: [email protected]

Technical Support: [email protected]

Detailed information on accessing Hyprotech Technical Support can be found in the Technical Supportsection of the Get Startedmanual.
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Table of Contents

1 Introducing HYSYS.RTO..............................................1-1

1.1 Welcome to HYSYS.RTO.....................................................1-3

2 Using HYSYS.RTO.......................................................2-1

2.1 Role of the Sub-Flowsheet ...................................................2-3

2.2 Optimization Objects.............................................................2-5

2.3 Collection Utilities .................................................................2-6

2.4 Optimizer Interface ...............................................................2-62.5 Data Reconciliation/Parameter Estimation Problem.............2-7

2.6 Optimization Problem ...........................................................2-8

2.7 Creating a Collection Utility...................................................2-9

3 Optimizer .....................................................................3-1

3.1 Optimizer Interface ...............................................................3-3

4 Derivative Utility .........................................................4-1

4.1 HYSYS.RTO Variables - Properties......................................4-3

4.2 HYSYS.RTO Constraints - Properties ..................................4-9

5 ESTIM DRU Overview..................................................5-1

5.1 The Problem .........................................................................5-3

5.2 The Solution..........................................................................5-3

5.3 The Benefits..........................................................................5-4

5.4 ESTIM DRU Facilities...........................................................5-5

5.5 Using ESTIM DRU................................................................5-6

5.6 Configuring a Fitting Problem .............................................5-10

5.7 Estim Data Set Analysis .....................................................5-19

5.8 Optimization Objects...........................................................5-20

5.9 General Notes.....................................................................5-25

5.10 ESTIM DRU Diagnostic File Output....................................5-26


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6 Data Reconciliation Utility..........................................6-1

6.1 Heat Exchanger Network Data Reconciliation......................6-3

7 Derivative Utility & Optimizer.....................................7-1

7.1 The Derivative Utility.............................................................7-3

7.2 Optimizer ............................................................................7-12

A HYSYS.RTO+ Example ................................................A-1

A.1 Data Reconciliation Example............................................... A-3

A.2 Install Data Reconciliation Utility.......................................... A-5

Index.............................................................................I-1


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Introducing HYSYS.RTO 1-1

1-1

1 Introducing HYSYS.RTO

1.1 Welcome to HYSYS.RTO .................................................................3


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1-2

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Introducing HYSYS.RTO 1-3

1-3

1.1 Welcome to HYSYS.RTOHYSYS.RTO is a real-time on-line optimization software package that

combines the following two proven technologies:

Rigorous first principal models and thermodynamic methods (fromHYSYS).

Optimization and data reconciliation routines (from RTO).

Optimization within HYSYS is based on a simultaneous modular

approach. A flowsheet model is developed as a collection of Sub-

flowsheets (SFS or the modular blocks) are connected through streams.

Within each SFS are a collection of unit operations and streams that are

appropriate to be solved together. During the course of the optimizationrun, each Sub-flowsheet is solved using one of the standard HYSYS

solvers (non-sequential modular or one of the available column

solvers).

When the model is being posed to the optimizer, each product stream

from one SFS that serves as a feed stream to another SFS is "torn". The

act of tearing the stream creates a collection of connection equations

which the optimizer solves as part of its calculations. In the case of

nested Sub-flowsheets, the tearing occurs at the terminal locations (i.e.,

between the stream which is calculated as the product of one unit

operation, and the stream which feeds the next unit operation). There

are no intermediate tears constructed.

Recycle locations in the flowsheet should be defined at the transition

across a Sub-flowsheet boundary. This additional transfer basis allows

the flowsheet to be initialized correctly, and then have the recycle

replaced by connection equations when the model is posed to the

optimizer.

Within each of the Sub-flowsheets are a number of decision variables,

true process constraints and objective function variables. These are

individually selected and configured by the user and are automatically

associated with the corresponding block when the problem is posed tothe optimizer.


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1-4 Welcome to HYSYS.RTO

1-4

Upon configuration of the flowsheet, Derivative Utilities can be attached

to the various Sub-flowsheet operations. These utilities allow the tearing

of the appropriate streams to be invoked, and the various optimization

objects (decision variables, constraints, objective function variables)

collected into lists which are then provided to the optimizer.

When the optimizer is invoked, it accesses these lists from each of the

utilities to construct its solution matrix. During the course of its

solution, the optimizer configures the necessary information from each

of the objects to determine aspects such as step size, derivative

evaluations etc.

In the simultaneous modular approach, the blocks are treated as a

matrix of variables (decision and tear) and constraints (true process

constraints and connection equations). The derivatives that theoptimizer then sees from any block are of the entire constraints vector

with respect to each individual variable within the block. If the block

contains variables which are part of the objective function, the gradient

is also determined for each of the variables.

During the optimization, values are returned to the flowsheet through

the utilities to be evaluated by the models, with the calculated results

(tear equation residuals, process constraint values, objective function,

etc.) returned to the optimizer. The interaction between the optimizer

and the flowsheet continues until the defined solution criteria is met.


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Using HYSYS.RTO 2-1

2-1

2 Using HYSYS.RTO

2.1 Role of the Sub-Flowsheet..............................................................3

2.1.1 Simultaneous Modular Optimization.........................................4

2.1.2 Implementation in HYSYS.RTO ...............................................4

2.1.3 Overview ..................................................................................4

2.2 Optimization Objects .......................................................................5

2.3 Collection Utilities............................................................................6

2.4 Optimizer Interface ..........................................................................6

2.5 Data Reconciliation/Parameter Estimation Problem ....................7

2.5.1 General Procedure...................................................................7

2.6 Optimization Problem......................................................................8

2.6.1 General Procedure...................................................................8

2.6.2 Flowsheet Tearing ....................................................................8

2.7 Creating a Collection Utility............................................................9

2.7.1 Derivative Utility......................................................................11

2.7.2 Optimization Objects ..............................................................14

2.7.3 Optimization Object Installation..............................................15


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2-2

2-2


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Using HYSYS.RTO 2-3

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2.1 Role of the Sub-FlowsheetIn the standard HYSYS modeling environment, the sub-flowsheet lets

you provide a logical grouping of operations to facilitate understanding

of the process behaviour. In addition, it provides the mechanism to

encapsulate a solver (i.e., the Column sub-flowsheet) or to use different

fluid packages (thermodynamics, component slates, etc.) within a

simulation.

For optimization, the sub-flowsheet provides the same benefits plus a

number of additional capabilities for the simultaneous modular

approach. Foremost, it provides a location where the standard

propagation of information can be broken. Once a model is torn foroptimization, information does not propagate from one sub-flowsheet

to another. This limits calculations to only those needed at a point in

time.

Similarly, by selecting the structure of the Sub-flowsheets appropriately,

unnecessary equations are never posed to the optimizer. In addition, if

derivatives are being generated numerically, the potential for noise in

the generated derivatives is minimized by constructing suitably sized

Sub-flowsheets.

For operations that deliver analytical derivatives, these must be

encapsulated within a single sub-flowsheet. For example, HYSYS

columns being solved by the Newton solver are able to deliver the

Jacobian matrix to the optimizer directly. Extension unit operations that

deliver analytical derivatives are handled in the same manner.


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2-4 Role of the Sub-Flowsheet

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2.1.1 Simultaneous Modular OptimizationSimultaneous Modular Optimization (SMO) is a hybrid between

Sequential Modular and Open Equation forms of optimization. It uses

modular solvers to solve the unit operations themselves, and the

Optimizer solver to solve both the Optimization and connection

equation problems.

2.1.2 Implementation in HYSYS.RTO

In HYSYS.RTO, the SMO is facilitated by the development ofOptimization Objects (which provide a generic interface to flowsheet

variables), configuration utilities (Data Reconciliation and Derivative)

and flowsheet tearing. The act of tearing the flowsheet blocks the

propagation of information across the torn location, creating a set of

connections equations which are exposed to the Optimizer for solution

as part of the optimization problem.

2.1.3 OverviewFor the HYSYS user, the key pieces to configuring an optimization or

data reconciliation problem are:

Optimization Objects A generic set of objects used to identify theunderlying flowsheet variable and provide the necessaryconfiguration information for use by Optim or Estim.

Collection Utilities Utilities used to identify the "pieces" of theflowsheet which are to be exposed to Optim or Estim.

Optimand Estimparameters Tolerances and flags.

The mechanics for creating either a Data Reconciliation or Optimization

problem are essentially identical. The only differences are as follows:

Optimization object types being used

Optim or Estim properties

Tolerances and flags being configured

Specific procedures to the type of problem being solved


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Using HYSYS.RTO 2-5

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2.2 Optimization ObjectsOptimization objects are the mechanism of identifying the flowsheet

variables which are to be considered as part of the problem. The

optimization and data reconciliation routines have the ability to set and

retrieve flowsheet values as well as the necessary configuration

parameters through the optimization object. While there are a number

of different optimization object types, they all serve the same basic

function.

The primary differences between the optimization objects are the

properties they contain, and how Optimor Estimtreats them. For

flowsheet optimization, there are: Optimization Variable Decision variables for the optimization that

must be specified (blue) variables.

Constraints True process constraints, bounded variables that areinstantiated by the user. These must be calculated (black) variables.

Objective Function Variables A variable that is part of the overallobjective function. Each variable has its own defining equation, theresults of which are combined into a single flowsheet objectivefunction. These must be calculated (black) variables.

For Data Reconciliation and Parameter Estimation, there are:

DCS Tags Variables for which you have a set of measurements,which are used to calculate offsets in the measurements and updatefitting parameters. These can be either specified or calculatedvariables.

Fitting Parameters Variables whose value is to be directlyadjusted to match the supplied data. These must be specified (blue)variables.

There is a third type of Optimization Object used for Data Reconciliation

called a DRU Stream (Data Reconciliation Utility Stream). This is

essentially a data holder, i.e., it allows for multiple sets of stream data,

each corresponding to a different data set, to be supplied by you. These

values are taken as supplied, no offsetting is calculated for these

streams.


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2-6 Collection Utilities

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2.3 Collection Utilities

Derivative and Data Reconciliation UtilityThere are two utilities used by HYSYS.RTO to provide the primary

interface between the flowsheet model and the solver:

Data Reconciliation Utility

Derivative Utility.

Their primary purpose is to collect appropriate optimization objects

which are then exposed to the solvers.

These utilities are first "attached" with unit operation(s) within the

flowsheet model. Then, based on the types of optimization objects that

utility type is interested in, it collects those objects of the correct types

which are attached to variables that are related to the targeted unit

operations and their corresponding streams.

It is the corresponding lists of "variables" and "constraints" that are

exposed to Optim.

2.4 Optimizer InterfaceThe Optimizerinterface in HYSYS provides the collection points for the

utilities within the flowsheet. Depending on the mode, the Optimizer

invokes either Estim(Data Reconciliation and Parameter Fitting) or

Optim(Optimization) and provides the necessary interfaces back into

the process model.


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Using HYSYS.RTO 2-7

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2.5 Data Reconciliation/ParameterEstimation Problem

2.5.1 General Procedure1. Build the flowsheet.

2. Install aData Reconciliationutility.

3. Select the unit operations from the flowsheet that are associatedwith the variables to be fit, or for which you have measured the data.The streams that are attached to the unit operations areautomatically obtained at the same time.

4. Install Fitting Parametersfrom the Utilityand attach them to theappropriate flowsheet variables to be fit.

5. Supply appropriate values for the Fitting Parameters.

6. Install DCS Tags and attach them to flowsheet variables for whichyou have measured data.

7. Supply required values for the Tags.

8. Supply the measured data.

9. If necessary, turn on the multiple data set option for attachedstreams, and supply corresponding data.

10. Set the appropriate Estimproperties and tolerances and flags.

11. Invoke the HYSYS Optimizer F5and turn on DataReconciliationmode.

12. Identify the utility containing the unit operations and streams beingreconciled.

13. Start the data reconciliation.


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2-8 Optimization Problem

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2.6 Optimization Problem

2.6.1 General Procedure1. Build the flowsheet.

2. Install a Derivativeutility.

3. SelectFlowsheet Wide for the Unit Operation.

4. InstallOptimizationVariablesfrom the utility and attach them to theappropriate flowsheet variables.

5. Supply appropriate values for the Optimization Variables.6. Install Constraintsand attach them to appropriate flowsheet

variables.

7. Supply required values for the Constraints.

8. Install the objective function object(s) and attach them toappropriate flowsheet variables.

9. Configure the appropriate prices for the objective function objects.

10. Invoke the Optimizer F5and select Optimization.

11. Change appropriate Optimproperties and tolerances and flags.

12. Start the Optimization.

2.6.2 Flowsheet TearingThere is an additional feature available for optimization which involves

Flowsheet Tearing. With this approach, specific streams in the flowsheet

are "torn" and appropriate connection equations written. These

additional variables and constraints are passed to the Optimizerto be

solved as part of the optimization problem. Typically, this approach

requires multiple derivative utilities to be constructed.


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Using HYSYS.RTO 2-9

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2.7 Creating a Collection UtilityUtilities are created from the FlowSheet Tools Menu Bar, or by using the

CTRLUhot key combination. This produces a view containing the

available and installed utilities in the flowsheet. Select Derivative Utility

(as shown in Figure 2.1) orData Recon Utility, and click theAdd Utility

button. This displays the corresponding Utility property view.

Utility Property ViewBoth the Data Reconciliation and Derivative Utilityproperty viewscontain a number of tabs, that are organized around the optimization

object types (variables, constraints, fitting parameters, DCS Tags, etc.).

Both utilities contain a similar section at the top of the view that

provides access, on every tab, to the features for unit operation

attachment and optimization object creation for the problem. While

optimization objects can be created from the flowsheet prior to

installing a utility, it is recommended that this be done from this

location. Once unit operations are selected, optimization objects that

are created, are tested as to whether they are associated with the

attached operations and streams.

Figure 2.1


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2-10 Creating a Collection Utility

2-10

Immediate feedback is provided when the objects are created and added

directly to the lists contained within the utility, and are displayed

directly on the property view. Information can either be supplied as

objects are added, or at any time prior to running the solver.

The tabs of the Derivative Utility are defined as follows:

Figure 2.2

Tab Description

Structural Non-Zeroes

Assign variable/constraint associations such that a Jacobianelement is always assigned to the pair regardless of theJacobian Tolerance.

IndependentVariables

Access the collection of variables (optimization Variables,Connection Equation Variables, and Solution Variables)associated with the utility

Constraints/Objective Function

Access the collection of dependent variables (Constraints,Technical Constraints, Solution Constraints and ObjectiveFunction variables) associated with the utility.

Derivative Analysis Access the numerical perturbation mechanism to allowexamination of the sparsity pattern and Jacobian values,gradient and model noise which will be generated by thegradient calculations of the solution.


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2.7.1 Derivative Utility

Configuration GroupAt the top of the Derivative Utility property view is the Derivative Utility

Configuration group, which is displayed on every tab. This provides

access to the following options:

Figure 2.3

Field Description

Unit Operation Selection Select the unit operation(s) for the given utility.

Add Add variables, constraints and objective function objects.

Master/Run Time Toggle Switch between Master and Run Time lists for displaypurposes. The Master List is all variables or constraintsthat are attached to utility. During the set up phase of anoptimization problem, each variable and constraint isevaluated for its current parameter settings. Those whichdo not qualify for the current problem (i.e., the OptimizeFlag is false) are not included in the list of variables andconstraints exposed to the Optimizer, which is the Run

Time list. This button lets you switch between lists (evenwhen the problem is running).


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Unit Operation Selection

There are three modes for the derivative utility and they are as follows:

It is best to select the desired unit operation prior to installing any of the

remaining optimization objects. Part of the procedure for attaching the

unit operation to the utility is to obtain all existing optimization objects

(of the appropriate type) from the simulation case.

For example, if the Specific Unit Operradio button is selected, the view

displays as shown in the figure below.

Select the target unit operations from the Objectcolumn of the view.Note that Sub-flowsheets (i.e., Columns), are to be selected as an Object,

not as a Flowsheet. When a Unit Operation is selected, the utility

displays all optimization objects currently installed in the simulation

case which are associated (attached to) the unit operation(s) and their

associated streams.

Mode Selection

FlowsheetWide

Use when minimal flowsheet tearing is being employed, and nospecial derivative and solution mechanisms (such as extensionoperations) are being used. In this mode, a single derivative utility isused for the entire flowsheet.

Specific UnitOperation

Typically this is a sub-flowsheet, which is torn on both the feeds andproducts. The sub-flowsheet typically contains several unitoperations which are solved either using the HYSYS standardsolver, or one of the column solvers.

ExtensionOperation

Used when the sub-flowsheet contains an extension operationwhich is solved using the available OLE functions to allow the solverto solve the model equations as part of the optimization problem

Figure 2.4


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Object and Property Filters

In Optim, there are only variables and constraints. However, to assistwith the interpretation of the optimization problem, these lists are

divided according to the source of the attached variable. On the

corresponding tabs of the utility, there are radio buttons which filter the

objects into these types.

For theVariablestab, the Independent Propertiescan be selected by

using the following radio buttons:

Figure 2.5

Variable Description

Optimization Variable True decision variables

Tear Variables Variables created by the tearing of a flowsheet stream

Solution Variables Variables created to support an extension operation whichis to be solved as par t of the optimization problem


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Further filtering is provided to indicate which of the given object

properties are as follows:

All of the appropriate optimization object types are displayed on the tab

in a worksheet format. In addition to the properties, the view displays

the flowsheet object and variable that each optimization object is

associated with. Values that can be specified are indicated in blue, whilecalculated variables are displayed in black.

Unit conversion is provided for each of the appropriate object property

combinations.

2.7.2 Optimization ObjectsThe Optimizationobject types which are used for optimization

problems are as follows:

Radio Button Description

Input Required user input.

Output Values output from Optim.

Results Values resulting from the optimization problem.

All Access to all properties. There are a number of internal properties(i.e., Sparse Column), contained inside of the optimization object,but are used as internal values for the solution.

Type Description

OptimizationVariable

Decision variables for the optimization that must be specified(blue) variables.

Constraints True process constraints, bounded variables and areinstantiated by the user. These must be calculated (black)variables.

Objective FunctionVariables

A variable which is part of the overall objective function. Eachvariable has its own defining equation, the results of which arecombined into a single flowsheet objective function. Thesemust be calculated (black) variables.


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2.7.3 Optimization Object InstallationOptimization objects appropriate for the utility (in the case of the

Derivativeutility - Optimization Variables, Constraintsand Objective

Functionvariables) can be added directly from the view. Use the drop-

down list in the upper right corner of the Derivative Utility

Configurationgroup, to select one of the three options. By selecting the

appropriate option and clicking theAddbutton, the corresponding

selection view is displayed:

By making the selection as shown (Flowsheet, Object, Variable and

Variable Specifics), the Optimization Variable is created and added to

the utilities collection.

Figure 2.6


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By default, the new object is given the next available name. However,

you can edit the name of the object directly from the utility view by

highlighting the name in the Object Name column and typing a new

string, as shown below

Constraints and Objective Function Objects are added in a similar

manner. When an object of a given type is added, the utility

automatically switches to the appropriate tab and filter type.

Specified Versus Calculated ValuesWhen you install a variable or constraint, you must examine the status

of the Current Value property. Variables must display a status of Blue

(specifiable), while Constraints must display a status of Black(calculated).

Figure 2.7


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Units and Delta Properties

All communication with Optim for property values is conducted inHYSYS internal units. However, you can input your values in any

necessary unit set, the conversion is handled internally. There are

certain properties (typically span or range type properties) which are

handled differently based on the variable type they are attached to (i.e.,

pressure and temperature). When you input a value for these types of

property/variable combinations, the input is converted automatically to

Delta; i.e., a Range for a temperature variable of 1 C displays as 1.8 F if

the unit set is changed.

The only location where the chosen Units set influences the problem is

with respect to the Objective Function object. The default formula for anObjective Function object is variable value X price. The calculations

performed for determining the individual contribution of that object to

the overall objective function are done in display units. For example, if

the objective function object is attached to a LiquidVolumeFlow

variable, and the current display units are in Barrels/Day, then the actual

display value (1000 bbl/day) is used in determining the contribution to

the objective function. You can create a new unit set (Tools/Preferences)

for this purpose.

If you store a case and then reload it from disk, you should ensure

that the correct units set is being used prior to running theoptimization problem.


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Derivative Analysis

The Derivative Analysistab of the utility property view provides accessto the Jacobian and Gradient calculation mechanism used during the

solution. Examine different perturbation sizes and single and two sided

gradient calculations to see their impact on the calculated Jacobian and

gradient for the variables.

Filtering is provided to allow examination of subsets of the overall

variable and constraint lists. In addition, examine the model noise to

determine if tighter solution tolerances on the individual unit

operations (i.e., Columns) are necessary. Typically, a tighter solution

tolerance requires more individual calculations at any phase, but

improves the quality of the Jacobian being returned to Optim andreduces the time of the overall problem solution.

When the calculations are complete, examine both the individual

Jacobian elements, or the Gradient, as well as the noise of the model.

While the default solution tolerances for unit operations is valid for

modelling purposes, experience shows that a tighter tolerance is more

appropriate for Jacobian evaluations (where small changes are being

Figure 2.8


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sensical response, without impacting the conditioning of the

optimization problem (i.e., a desired very small range to work with on

the variable itself).


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Optimizer 3-1

3-1

3 Optimizer

3.1 Optimizer Interface ..........................................................................3

3.1.1 Calculations............................................................................23

3.1.2 Results ...................................................................................23


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3-2

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Optimizer 3-3

3-3

3.1 Optimizer InterfaceWhile the derivative utilities are used for collecting and configuring the

individual optimization objects for the problem, the Optimizer collects

all of the utilities and exposes the combined list of variables and

constraints to Optim. In addition, this is where you set the tolerances,

flags and settings for the Optimization problem in its entirety. The

Optimizer is accessed by pressing the F5key.

The radio button selection provided along the bottom of the view

provides access to the available options:

Default the existing HYSYS Optimizer

Optimization access to Optimization (Optim)

Data Recon access to Data Reconciliation (Estim)

Model used specifically for Real Time applications

Figure 3.1


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3-4 Optimizer Interface

3-4

Depending on the radio button selected, additional tabs are displayed

on the view. A number of tabs (Testing, Properties, Transferand Object

Transfer) relate solely to the Real Time interfaces and should not be

used. All of the necessary configuration for the Optimization Problem

can be accessed through the Optim Configurationtab.

There are three pieces of the Configuration:

SetUp Identifying the optimization algorithm to be used, type ofperturbations, level of diagnostics, etc.

Tolerances Access to the various solution tolerances and Optimparameters.

Flags Access to the various Optim configuration options which areBooleans.

Optim Configuration Set Up Inputs (Set Up Radio Button)These inputs consist of the following Optimizer properties:

Algorithm

The algorithm used by the Optimizer, is one of the following:

SS_LP single-shot linear programming algorithm.

MDC_SLP sequential linear programming algorithm.

MDC_SQP two-phase sequential quadratic programmingalgorithm with large-scale sparse matrix handling features.

NAG_SQP single-phase sequential quadratic programmingalgorithm.

Suggested Default: MDC_SQP


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Optimizer 3-5

3-5

LP Options

Used to select the options to be used with the SS_LP algorithm. Selectone of the following:

None No option.

Initialize A single run of the linear programming algorithm isconducted, and the Objective Valueproperty of the Optimizer isreset to 0.0.

Intercepts The Optimizer Fix Variable Spansflag is switched onprior to carrying out the SS_LP optimization.

Gradients The Optimizer constraint and objective functiongradients are re-evaluated prior to carrying out the SS_LPoptimization. Otherwise, the gradients used during the SS_LPoptimization are those found at the previous point.

Gradient Calculations

This option specifies if one-sided or two-sided gradient calculations are

used:

1-sided Causes forward differences to be used when constructinggradient approximations.

2-sided Causes central differences to be used. This optionrequires twice as many function evaluations at a given solution, butmay provide a more accurate estimate of the constraint andobjective gradients, particularly for highly non-linear problems, orproblems featuring large amounts of noise.

In both cases, the perturbation size used for the Optimizer internal

variables is given by the Optimizer Perturbation property.

Suggested Default:1-sided

The SS_LP algorithm is not included in the current version.


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3-6

Diagnostic Print Level

Select one of the following options: None No Optimizer diagnostic file is produced.

Partial_1, Partial_2, or Partial_3 Increasing levels of Optimizeroutput in the diagnostic file.

Full The maximum amount of useful information in the Optimizerdiagnostic file.

Excessive Only used for debugging the Optimizer.

Suggested Default:Partial_2

Max. Iterations

This parameter fulfils the following two roles:

When Algorithmis set to MDC_SQP / MDC_SLP, this parametergives the maximum number of Optimizer iterations allowed toimprove an already feasible solution.

When Algorithmis set to NAG_SQP, this parameter gives themaximum number of major iterations. A major iteration in this caseconsists of a sequence of minor iterations which minimize a linearlyconstrained subproblem.

Suggested Default:50

Max. Feasible Point

This parameter also fulfils two roles:

When Algorithmis set to MDC_SQP / MDC_SLP, this parametergives the maximum number of Optimizer iterations allowed to findthe first feasible solution.

When Algorithmis set to NAG_SQP, this parameter gives themaximum number of minor iterations. A minor iteration in this caserepresents a sequence of local improvements to the linearizedproblem within a major iteration.

Suggested Default:20


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Max. Constraint Relaxations

This parameter relates to the Relax Violated Constraintsflag. This flag isused to drive the Optimizer constraint bounds to their extreme values

allowed by the Optimizer tolerances. This is done to help the feasible

point search part of the MDC_SQP algorithm find the first feasible

solution. TheMax. Constraint Relaxationsparameter gives a limit for the

number of times this can occur.

Suggested Default: 0

Max. Hessian Resets

The MDC_SQP algorithm operates using an approximation to the

matrix of second derivatives of the objective function. On some

problems, it is necessary to reset this approximation to the diagonal

matrix arising from the FPS Hessian Diagonal parameter (during the

FPS search) or to the diagonal matrix arising from the OPT Hessian

Diagonal parameter (during the OPT search). The Max. Hessian Resets

parameter gives a limit on the number of times this can be done.

This is useful if the algorithm suffers from step convergence meaning it

is not used when the algorithm converges according to other criteria.

Suggested Default:0

Verify

In the NAG_SQP algorithm, you can carry out numerical checking on

gradient elements. Setting Verify to -1 switches off this checking. The

extent of the numerical checking conducted by the NAG_SQP algorithm

depends on the setting for Verify. Refer to the following table:

Suggested Default:-1

Value Description

0 Results in a check on the gradients at the first feasible point.

1 Results in a check of the Optimizer objective gradients

2 Results in a check on the Optimizer constraint gradients

3 Checks both types of gradient. The checking takes place at the start of theoptimization.


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DV_Level

Used to specify which gradients should be estimated by the NAG_SQPalgorithm. Refer to the following table:

This parameter is only to be used for debugging the Optimizer.

Suggested Default:3

Objective Value

This displays the current plant model objective function value as

calculated by the Optimizer.

Termination Reason

An output from the optimization run, which is one of the following:

OK Used by the FPS to indicate a feasible termination of thisphase.

Impossible This output signifies either a non-implementedOptimizer algorithm is selected, or the algorithms could not find asolution to the linearized problem. In this case, the problemconstraint/variable bounds and feasibility tolerance parametersshould be checked.

No variables The number of variables in the problem is zero.

Step convergence During the Optimizer OPT phase ofMDC_SQP, the stepping back procedure has resulted in a stepcollapse to below the Stepsolution tolerance.

Cost convergence During the Optimizer OPT phase ofMDC_SQP, two successive objective function values have returneda difference in cost less than the Costsolution tolerance. Note thatonly feasible points are considered for this test.

Flat A special case of cost convergence in which the objectivefunction gradient is zero. Usually indicates an incorrectly defined (orscaled) objective function.

Value Description

0 Both missing constraint gradients and missing objective gradients areestimated.

1 Missing constraint gradients are estimated

2 Missing objective gradients are estimated.

3 No action is taken.


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Gradient convergence Occurs when the gradient of theLagrangian function for the given optimization problem is less thanthe Gradientsolution tolerance.

Globally infeasible This occurs when the feasible region cannotbe seen from the FPS starting point (i.e., even the linearization ofthe problem does not yield a feasible solution).

The MDC_SQP Optimizer expands the variable local bounds (theMinimumand Maximumproperties of the variables) out to the globalbounds (the Global Minimumand Global Maximumproperties of thevariables) to attempt to solve the linearized problem with thesebounds. If this still yields no solution, the FPS phase conducts asequence of steps aimed at minimizing the constraint violations.

An objective function is constructed which contains the sum of theconstraint violations, and this function is minimized, producing afeasible solution to the problem (if one exists).

Infeasible In the FPS phase of the optimization, if a step collapse

takes place while looking for a feasible point, then the problem isconsidered to be infeasible due to this. This is not the same asGlobally infeasible.

Unbounded This occurs when the objective function isunbounded below (or is badly scaled), i.e., can be reduced withoutlimit. This usually indicates incorrectly set constraint and/or variablebounds.

Time out (feasible) This report is generated by the OPT phase ofthe MDC_SQP Optimizer, when the number of Optimizer iterationsduring the OPT phase exceeds the Optimizer Max. Iterationsparameter.

Time out (infeasible) This report is similar to the Time out(feasible) report, except occurs during the FPS phase, when thenumber of iterations exceeds the Max. Feasible Pointparameter.

Not converged A report solely from the NAG_SQP algorithm.

Not run Set during the Optimizer initialisation phase. This isreported in the Optimizer screen while the Optimizer is initializing.

Stopped Occurs when the you stop the Optimizer using thecontrol box on the Optimizer screen (beside the spreadsheetbutton).

Actual Optimizer

This is output from the Optimizer. It gives the number of iterations the

Optimizer has conducted after finding the first feasible solution, when

the MDC_SQP/SLP algorithms are used. When the NAG_SQP algorithmis used, this returns the number of major iterations used.


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Feasible Point Iterations

This is output from the Optimizer. It gives the number of iterations theOptimizer has conducted in order to find the first feasible solution,

again when the MDC_SQP/SLP algorithms are used. When NAG_SQP is

used, this returns the number of minor iterations from the last major

iteration (in this case the usefulness of this parameter is limited).

Solution Phase

This is output from the Optimizer. It describes the current phase of the

Optimizer search, which is one of:

Initialize A report that the Optimizer is initializing the diagnosticsfile, and preparing to carry out the FPS search.

Results Reported when the Optimizer is writing the final solutionto the diagnostics file and completing any post-optimizationcalculations.

Setup The Optimizer variables and constraints are beinginspected and set-up internally by the Optimizer using the user-supplied data.

FPS The beginning of the FPS phase of the Optimizer.

FPS Deriv The Optimizer is calculating the gradients of theconstraints and objective function during the FPS phase. Thisoccurs every time the Optimizer adjusts the current solution toimprove the feasibility of the current point.

FPS Visible The Optimizer has successfully solved the linearizedproblem during the FPS phase.

FPS Invisible The linearized problem at the current solution in theFPS phase cannot be solved.

FPS Shrink The Optimizer is stepping back during the FPSphase. This occurs when the projected point in the FPS is lessfeasible than the current point, and so the projected point isadjusted.

Optim The Optimizer is preparing to enter the FPS phase.

OPT Deriv The Optimizer is calculating the constraint andobjective function gradients during the OPT phase.

OPT Search The Optimizer has successfully found a new,improved solution which remains feasible, and has moved the

current solution to this point. OPT Shrink The Optimizer is stepping back in the OPT phase.

This occurs if either the projected solution is infeasible, or theobjective function has increased.


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Gradient Evaluations

This reports the number of gradient (constraint and objective function)evaluations during the course of the optimization. At present, this gives

the correct number only when theNumerical Gradientsflag is checked.

Model Evaluations

This reports the number of plant model evaluations during the course of

the optimization. At present, this gives the correct number only when

theNumerical Gradientsflag is checked.

Code Version

The current version of the Optimizer.

Total CPU Time

This reports the total time taken during both phases of the

Optimization, in minutes and seconds.

Start ObjectiveThis gives the plant model cost function value at the starting point,

before carrying out any optimization.


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Optim Configuration Tolerance Inputs (Tolerance Radio

Button)This section contains the tolerances to be used for generating

approximations to the objective and constraint functions, controlling

the path taken to Optimizer feasible/optimal solutions, and for

determining whether an optimum point has been reached:

Sigma

This tolerance is not currently used.

Linesearch Tolerance

This is used by the NAG_SQP algorithm to control the accuracy of the

linesearch phase.

Suggested Default:0.8

Function Precision

Gives the precision to which functions are to be evaluated by the

NAG_SQP algorithm. Used when constructing default Optimizer control

parameters.

Suggested Default:10-8


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Optimality Tolerance

Gives the accuracy with which the linearized problem is solved by theMDC_SQP algorithm. This parameter is a tolerance below which any

changes to the cost function of the linearized problem are considered to

have caused cost convergencewhen solving the linearized problem.

Suggested Default:1.e-8

Row Tolerance

A tolerance used with the NAG_SQP algorithm which gives the feasibility

tolerance within which linear constraints are to be satisfied. If a linear

constraint violates a bound by a value not greater than the Row

Tolerance(in absolute terms) the constraint is considered to be feasible

by NAG_SQP.

In the current version of the Optimizer all constraints are considered to

be non-linear, and so this property is not used.

Nonlinear Row Tolerance.

As for Row Tolerance, except this applies to constraints defined as non-

linear.


Step

The step convergence limit used in the MDC_SQP algorithm. If the

algorithm at any point makes a step which is less than the Step

tolerance, the algorithm is considered to have converged on step.



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Gradient

The tolerance which is the maximum value of the Lagrangian functiongradient for which the MDC_SQP algorithm is considered to have

converged on Lagrangian gradient. A value of 0.0 forces convergence of

either the Stepor Costkind.


Cost

This is the maximum magnitude of change in scaled objective function

between Optimizer steps for which the Optimizer is considered to have

converged on cost.


Zeta

The tolerance which is used in conjunction with the constraint Scale

properties to define the feasibility tolerance for constraints in the

MDC_SQP algorithm. The feasibility tolerance for an individual

constraint isZeta * Scale, for the given constraint. A value of 1.0 means

that the feasibility of the individual constraints is controlled uniquelythrough the individual constraint Scaleproperty.

Suggested Default: 1.0

Bind

A tolerance used with the NAG_SQP algorithm and in the solution of the

linearized problem in the MDC_SQP algorithm. This tolerance gives a

value which is the maximum absolute difference between a constraint

and one of its bounds below which the constraint is considered to bebinding (active) in the linearized problem.

In general, the solution of the linearized problem satisfies the constraint

MinimumandMaximumproperty bounds, whereas the solution of the

true non-linear problem satisfies the bounds (Minimum - Zeta * Scale,


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Maximum + Zeta * Scale) for the given constraint. In this way, by

enforcing tighter bounds in the linearization, there is a greater

likelihood of the problem remaining feasible when the non-linearities

are re-introduced.


Perturbation

The change in the scaled variables during gradient evaluation. An

individual variable in the Optimizer is scaled according to the variable

Minimumproperty, and the variable Spanproperty (or the Range

property if the Optimizer Fix Variable Spansproperty is checked).

In general, the Optimizer scales the problem variables vto produce a set

of internal scaled variablesx, according to the formula.

Where minis the variableMinimumproperty, and Sis the variable

Rangeproperty if the Optimizer Fix Variable Spansflag property is

checked (the variable Spanproperty otherwise). This allows equalmagnitude gradients to be produced for all internal variablesx,

regardless of the magnitude of the external (model) variables v, by

suitable choice of the variable Rangeproperties.

The perturbation which is applied to the external variables vis therefore

, where is the Optimizer Perturbationproperty.


Max. Iteration StepCalculated by the Optimizer, this gives the current maximum step under

consideration for projecting the current point to the new point. The size

of this parameter is based on the current history of the optimization run.

(3.1)xjvj mi n

S-------------------=

S


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Base Search Step

The upper limit for Max. Iteration Step. When the Optimizer finds asequence of good linear approximations to the constraints and

simultaneously improves the objective function, the Max. Iteration Step

can be reset to the Base Search Step.


Max. Allowed Move

This parameter gives the maximum allowable change in a scaled

(internal Optimizer) variable over the entire course of an optimization

run. A value of 1.0 indicates a 100% change in the variable.


FPS Hessian Diagonal

These give the starting values of the diagonal elements of the

approximated Hessian matrices before the FPS phase of the Optimizer,

of the MDC SQP algorithm.


OPT Hessian Diagonal

These give the starting values of the diagonal elements of the

approximated Hessian matrices before the FPS and OPT phases of the

Optimizer respectively, of the MDC SQP algorithm.



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Jacobian Elimination

The value below which entries in the Jacobian matrix are deemed to bepure model noise, and are set to zero (or when the Optimizer Sparse

Jacobianflag is checked, are excluded from the Jacobian sparsity pattern

and hence never re-evaluated in future).


Max. CPU Usage

This parameter is not currently used.

Objective Scale Factor

This is used for scaling the objective function (and its gradient). The

given function is divided by the Objective Scale Factor.


Major Damping Parameter

Used in the NAG_SQP algorithm to restrict the effects of major iterationvariable moves of the scaled variables and the Lagrange multipliers. A

value of 2.0 restricts the variable move to 200%.


Minor Damping Parameter

Used in NAG_SQP to restrict the effects of minor iteration variable

moves. As Major Damping Parameter.



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Penalty Parameter

This is used solely in the NAG_SQP algorithm. It is used for forcingconvergence of the linearized constraints solved in each NAG_SQP

minor iteration to their non-linear versions which are actually evaluated

in the major iterations. The larger the Penalty Parameterthe slower the

algorithm converges upon a feasible solution, however, this may be

necessary for highly non-linear constraints.


Scaling Type

The scaling algorithm to be used by the NAG_SQP algorithm. When set

to 0, no scaling is done. Otherwise the NAG_SQP algorithm attempts to

scale the Jacobian matrix in order to make the matrix coefficients as

close to 1 as possible. To scale the rows only, the parameter should be set

to 1. To scale the rows and columns, the parameter should be set to 2.


Flow Field / Gradient Evaluation

Not used.


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Optim Configuration Flag Inputs (Flag Radio Button)

This section contains the Optimizer properties used for controlling thenature of the Optimizer search, for specify methods for handling the

constraints, for initializing and terminating the Optimizer, and for

specifying the nature of the gradient calculations.

Omit Tech. Constraints

Indicates whether the technical constraints (specifications) are to be

omitted entirely from the constraint residuals when searching for a

feasible point. Technical constraints are used to obtain a valid model

solution, e.g. pressure drop or mass balance residuals. Processconstraints relate to the actual process being modelled, e.g. vessel

pressure or unit throughput limits.

Suggested Default:unchecked

Relax Violated Constraints

If the MDC_SQP algorithm cannot find a feasible point, one method of

proceeding is to relax the constraints. This property is therefore a flag

indicating whether all of the constraints (unchecked) or only those

which are currently violated (checked) are to be relaxed, duringconstraint relaxation. The maximum number of relaxation steps is given

by theMax. Constraint Relaxationsparameter.

Relaxing the violated constraints within the context of the MDC_SQP

algorithm means the constraint bounds in the linearized problem

(usually set to the constraintMinimumandMaximumproperties) are

expanded out to the bounds (Minimum - Zeta * Scale, Maximum + Zeta

* Scale) for the given constraint.

Thus, under normal circumstances the linearized problem is solved to a

much higher tolerance level than the true non-linear problem (whichimproves the chances of the current solution remaining feasible upon

introducing the non-linearities back into the problem). However, when

the Optimizer relaxes the violated constraints, both problems are solved

to the same tolerance (the capacity of the solution of the linearized

problem to satisfy the non-linearities is therefore much reduced).



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Recentre

This is checked for testing purposes, in which case the Optimizer reflectsthe effects created by an on-line Optimizer. The Optimizer variable soft

limits (theMinimumandMaximumproperties) are re-calculated so

that at the start of optimization, the current value of the variable lies

mid-way between the soft limits, while ensuring that the soft limits do

not fall out of range of the global limits.


Restricted Step

Used to indicate to MDC_SQP that theMax. Allowed Moveparameter is

to be used to limit the overall change in the Optimizer variables brought

about during optimization. When this flag is checked, the optimization

algorithm reduces the upper bound of each optimization variable by the

Max. Allowed Moveparameter, and increases the lower bound by the

same amount.


Include Fixed Constraints

If this is checked then Optimizer variables that have their Optimize Flag

property checked are nevertheless included in the optimization. This

acts on every variable, and its Optimizeflag property is checked.

Otherwise, such variables remain with fixed values during the

optimization.


NAG Calculated Gradients

If this flag is checked when the NAG_SQP algorithm is being used, then

the NAG_SQP algorithm itself carries out numerical calculation of any

gradient elements needed.



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Fix Variable Spans

This flag indicates whether the Span(i.e.Maximum - Minimum) of theOptimizer variables is to be calculated and stored, or taken directly from

the stream Rangeproperty (which is user-specified for each variable).


Sparse Jacobian

Checked when the user wants the Optimizer to calculate the Jacobian

matrix of constraint gradients in sparse form (by storing only the

nonzero elements, which usually indicates constraint-variable

functional dependence). This is done once, at the start of the

optimization, and establishes which Jacobian elements are stored for

the rest of the optimization (the sparsity pattern).


Numerical Gradients

Used to indicate to the Optimizer the origin of the gradient elements for

the constraints and objective function.

If the flag is checked, the Optimizer carries out numericalcalculation of the gradients by direct perturbation of variables usingthe method specified in the Gradient Calculationflag.

If it is unchecked, the Optimizer obtains the gradient elements fromHYSYS.RTO using the same method. The main difference is that inthe latter case certain gradient elements may be computedanalytically, and are therefore potentially more accurate.


Include Scales

Whether the constraint Scale properties are to be included when

normalizing the Jacobian matrix of constraint gradients and calculating

the bounds for the linearized subproblems in the MDC_SQP algorithm.



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Adjust Scaling

Not used.

Pert_Reset

Used at the start of optimization to indicate that the gradient calculation

process removes noise elements (checked) or not (unchecked).

When calculating the gradient functions by perturbing Optimizer

variables, model noise is introduced into the gradient elements, which

can mislead the Optimizer. When perturbing variable vj, if it does not

affect constraint ci, the corresponding noise can be removed from the

gradients by recalculating the constraint functions after removing the

perturbation from the variable.

This recalculation is done once for each variable, (i.e., for the first

gradient calculation) and is used for establishing the sparsity pattern of

the Jacobian matrix. The sparsity pattern is stored for use during the rest

of the optimization, if the Sparse Jacobianproperty flag of the Optimizer

is checked.

The advantages of this method are as follows:

Removes noise terms which can mislead the Optimizer.

Does not need theJacobian Eliminationtolerance parameter, whichmay be difficult to set.

Is required once only (the efficient sparse storage of the Jacobianeliminates this kind of noise from all future Optimizer steps).

The disadvantages are as follows:

For certain models it may take much more CPU time to carry out theextra plant model evaluations, compared with the use of theJacobian Eliminationtolerance method.

The presence of structural zeros in the Jacobian matrix are ignored.A structural zero is a forced presence of a Jacobian element, which,during first pass evaluation of the Jacobian, is zero and thereforecould be excluded from the sparsity pattern.

This flag should be checked along with the Sparse Jacobianflag, since it

takes advantage of the removal of model noise in terms of future

computation of gradients and their storage. However, it is still possible

to use this method with a dense Jacobian matrix (where all zero

elements are retained during optimization).


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If empty or invalid values are entered, the Optimizer uses a set of in-

built default values.

3.1.1 CalculationsThe Optimizer controls the running of the continuous optimization

algorithms. A description of the techniques used is given in the

Continuous Optimizer Overview.

3.1.2 ResultsThe results produced at the end of the optimization run are as follows:

A price for the current model data

Values of the Optimizer constraints and variables

Shadow prices for the constraints and variables, if they exist

A termination reason

A feasibility flag for the model data at termination of the Optimizer

Iterations taken

CPU time taken


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Derivative Utility 4-1

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4 Derivative Utility

4.1 HYSYS.RTO Variables - Properties.................................................3

4.1.1 Inputs: Object Object Name - Range .......................................4

4.1.2 Inputs: Global Minimum - Price ................................................6

4.1.3 Inputs: Sparse Column - Jac Num ...........................................7

4.1.4 Calculations..............................................................................8

4.2 HYSYS.RTO Constraints - Properties ............................................9

4.2.1 Inputs: Object Name - Maximum............................................10

4.2.2 Inputs: Scale - Sparse Row....................................................11

4.2.3 Inputs: Current Bias1...........................................................13

4.2.4 Calculations............................................................................14


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4.1 HYSYS.RTO Variables -Properties

The Variables in a HYSYS.RTO optimization problem are held in a

Derivative Utility. This is used for holding all of the data used for

defining the HYSYS.RTO Optimizer constraints and variables.

For detailed information on the Optimizer properties, see the Optimizer

Properties document[3].

The Optimizer contains a number of properties used for specifyingand controlling an optimization problem for a given HYSYS.RTOcase.

The Optimizer is also associated with a Derivative Utilitywhichcontains, a list of Independent Propertiesand DependentProperties. The Independent Propertiesare the variables in theplant model that are changed to satisfy the Dependent Properties(the constraints on the plant model) simultaneously minimizing theplant model cost function.

Figure 4.1


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4-4 HYSYS.RTO Variables - Properties

4-4

This document has the following styles:

All properties of the Optimizer/Variables/Constraints are shown initalic.

Important notes are shown in bold.

4.1.1 Inputs: Object Object Name - RangeThe Independent Propertieshave a number of inputs and they are

described following the figure below:

The Independent Propertiesinputs are as follows:

Object Name The name of the HYSYS.RTO object which is usedas optimizer variable.

Attached Object The object (e.g., Stream or Unit Op, etc.) that isattached or associated with the listed variable.

Attached Property The property relating to the Attached Objectand variable.

Start Value The starting value for the property of the Object Namein the plant model.

Figure 4.2


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Status The current status of the variable, which is calculated bythe Optimizer. Unlike constraints, variables are not allowed to moveout of their bounds. The Statusproperty is set to one of:

Not Evaluated The status of the variable is not evaluated bythe Optimizer.

InactiveThe variable Output property lies between the Minimumand Maximumproperties, but not on one of the bounds.

EqualityThe maximum and minimum properties of the variable,Minimumand Maximum, are equal, and the Outputproperty has thesame value as well.

Active LowThe variable Outputproperty value is equalto that ofthe Minimum.

Active HighThe variable Outputproperty value is equalto that ofthe Maximum.

Current Value The current value for the property of the ObjectName in the plant model.

Optimize Flag Determines if the variable is to be used in theoptimization process. If this flag is not set, no attempt is made by theOptimizer to include this variable into optimization process.

Minimum The lowerbound property for the variable during theoptimization process. This value might be different from its globalminimum, if the change in the variable is restricted to its allowedamount, set by the maximum rate of change, during the period in theoptimization process.

Maximum The upperbound property for the variable during theoptimization process. This value might be different from its globalmaximum, if the change in the variable is restricted to its allowedamount, set by the maximum rate of change, during the period in theoptimization process.

Range A user-specified alternative for the span. The purpose ofthe range is to scale the gradients of the cost function andconstraints, to give similar gradient magnitudes for each variable.The gradients of the objective function (and constraints) varyinversely with the variable ranges.


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4.1.2 Inputs: Global Minimum - Price

Global Minimum Represents the absolute minimum value for

which the variable is operated. This value is user-specified. Global Maximum Represents the absolute maximum value for

which the variable is operated. This value is also user-specified.

Span The difference between the Global Minimumand GlobalMaximumvalues for the variable and is calculated by the variableset-up. The role of the span is to convert every variable into therange (0, 1), to use uniform numerical perturbations andconvergence tests.

Output It is the current value of the variable in the plant model.The output value is determined by the optimizer during theoptimization process.

Price The shadow price (Lagrange multiplier) for the givenvariable, calculated by the Optimizer. The shadow price is used to

estimate the effect which small changes to variable bounds have onthe plant cost function.

Figure 4.3


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4.1.3 Inputs: Sparse Column - Jac Num

Sparse Column The column occupied by the given variable in the

Jacobian matrix. Unused variables are given a sparse column of 0. Old Var Value This is the cached value of variable prior to

perturbation, during gradient calculation.

Delta Var The change in variable after perturbation, duringgradient evaluation.

Gradient

Tear Variable

Jac Offset The Jacobian Offset.

Jac Num The Jacobian Number.

Figure 4.4


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4-8

4.1.4 CalculationsThe following properties are set by the user before an optimization run:

Global Minimum

Global Maximum

Range

Start value

Sparse Column

The following properties are Initialized by the HYSYS.RTO model before

an optimization run:

Minimum

Maximum

Span

The following properties are updated by the HYSYS.RTO model during


Old Var Val

Delta Var

The following properties are updated by the Optimizer during and after


Status

Price

Output


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4.2 HYSYS.RTO Constraints -Properties

The constraints in a HYSYS.RTO optimization problem are held in a

Derivative Utilityand are used for holding all data used for defining the

HYSYS.RTO Optimizer constraints and variables. For details about the

Optimizer properties, see the Optimizer Properties document[3].

The Optimizer contains a number of properties used for specifying and

controlling an optimization problem for a given HYSYS.RTO case. It is

associated with a Derivative Utilitythat contains a list of Independent

Propertiesand Dependent Properties. The Independent Propertiesare the

variables in the plant model that are changedto satisfy the Dependent

Properties(the constraints on the plant model) simultaneously

minimizing the plant model cost function.

Properties of the Optimizer/Variables/Constraints are shown in italic

and important notes are bold.

Figure 4.5


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4-10 HYSYS.RTO Constraints - Properties

4-10

4.2.1 Inputs: Object Name - Maximum

The Dependent Propertieshave a number of inputs and they are as

follows:

Object Name The name of the HYSYS.RTO object to beconstrained.

Attached Object The object (e.g. Stream or Unit Op, etc.) that isattached or associated with the listed variable.

Property The property related to the Attached Object andvariable.

Current Value The current value for the property of the objectName.

Use Flag Determines whether the constraint is to be used in theoptimization. If this flag is not set, no attempt is made by theOptimizer to satisfy this constraint.

Minimum The lowerbound for the constraint, which is user-specified.

Maximum The upperbound for the constraint, which is also user-specified.

Figure 4.6


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4.2.2 Inputs: Scale - Sparse Row

Scale A user-supplied number that gives the scale on which the

feasibility of the constraint is measured. This property is used inconjunction with the Optimizer Zeta property, which is a relativefeasibility tolerance. In general, a constraint is said to be feasible if:

Where Minimum and Maximum are the lower and upper boundproperties respectively, of the constraint, and Current is its currentvalue (equivalent to Hooked Property for constraints which have theUse Flag checked).

Minimum Chi Square Determines whether or not a chi-squaretest is done for the constraint.

Figure 4.7

Mi ni mu m Sc al e Ze ta C ur re nt M ax im um S ca le Z et a+


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Status The current status of the constraint, which is calculated bythe Optimizer. The Status property is set to one of:

Not EvaluatedThe status of the constraint has not been evaluated

by the Optimizer. InactiveThe constraint Currentproperty lies between the

Minimumand Maximumproperties, but is neither Active High norActive Low.

Violated LowThe constraint Currentproperty is less thanMinimum - Scale x Zeta, where Scaleis the constraint Scalepropertyand Zetais the Optimizer Zetatolerance property.

Violated HighThe Currentproperty is greater than Maximum +Scale x Zeta.

Active LowThe constraint Currentproperty is less than Minimum+ Scale x Zeta, but greater than Minimum - Scale x Zeta.

Active HighThe constraint Currentproperty is greater thanMaximum - Scale x Zeta, but less than Maximum + Scale x Zeta.

Normalization When the Jacobian matrix is first calculated (firstpass evaluation) the Normalizationproperty for the constraint is setto be the largest Jacobian entry in the row ( Sparse Row) of theJacobian matrix corresponding to this constraint. This number isused to normalize the rest of the given Jacobian row, for allremaining Optimizer search steps (i.e., is not recalculated).

Base Value When calculating the gradient of a given constraintwith respect to each variable, the internal scaled variable isperturbed away from the current point by adding the numberspecified in the Optimizer Perturbationproperty. The new value ofthe constraint is found corresponding to the new variable value, andthe change in constraint, divided by the change in the variable, is thecorresponding Jacobian element.

The constraint Baseproperty stores the pre-perturbation value ofthe constraint. Under certain circumstances, however, the Baseproperty itself can change duringthe Jacobian calculation. This isdue to the fact that removing a perturbation from a perturbedvariable, and re-running the plant model, will not reproduce theprevious Baseproperty within the constraint Currentproperty; this isdue to noise in the model arising from non-zero convergencetolerances (i.e., the de-perturbed constraint Currentdiffers slightlyfrom the pre-perturbed Current).

Therefore, under certain circumstances (when the Pert_Reset flagproperty of the Optimizer is checked) the Optimizer will remove theperturbation from the variable, re-run the plant model, and then re-set the Baseproperty of the constraint to match the re-calculatedCurrentproperty. This eliminates associated noise from the

Jacobian matrix. This method is discussed in more detail in theOptimizer Properties document[3], in the Pert_Resetsection.


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4-13

Price The shadow price (Lagrange multiplier) for the givenconstraint, calculated by the Optimizer. If a feasible solution is foundby the Optimizer, then a simple interpretation of the Lagrange

multiplier is that it gives the gradient of the cost function along thecorresponding constraint normal. Thus, the shadow price indicatesthe approximate change to the objective function when increasing(i.e., relaxing) the given active bound by a unit amount.

Hard Constraint A user-specified flag that indicates whether theconstraint is a technical one, i.e., is a process specification such asa mass balance or a temperature, as opposed to purely aneconomic constraint.

Off Flag A user-specified flag that indicates whether the constraintis in the 'off' state, or not. This is often used when related items ofequipment are being constrained, which themselves have an on-offbehaviour.

Sparse Row The number of the row in the Jacobian matrix whichis occupied by the given constraint.

4.2.3 Inputs: Current Bias1

Current The current value the constraint possesses in the plantmodel.

Figure 4.8


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4-14

Old Cons Value The value of the constraint prior to perturbationof a variable, during gradient calculation.

Bias1

Delta Cons The change in constraint after perturbing a variable,during gradient evaluation.

4.2.4 CalculationsThe following properties are updated by the HYSYS.RTO model during


Base Value

Old Cons Val

The following properties are updated by the Optimizer during and after


Status

Normalization

Price

Sparse Row

Current


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ESTIM DRU Overview 5-1

5-1

5 ESTIM DRU Overview

5.1 The Problem .....................................................................................3

5.2 The Solution .....................................................................................3

5.3 The Benefits .....................................................................................4

5.4 ESTIM DRU Facilities .......................................................................5

5.4.1 Error Detection/Correction........................................................5

5.4.2 Model Updating ........................................................................5

5.4.3 Utilities......................................................................................5

5.5 Using ESTIM DRU ............................................................................6

5.5.1 Measurement Problem.............................................................6

5.5.2 Basic Methods..........................................................................7

5.6 Configuring a Fitting Problem ......................................................10

5.6.1 Configuration Tab ...................................................................11

5.6.2 Results Tab.............................................................................14

5.6.3 Stream Initialization Tab .........................................................16

5.6.4 Parameter Fit Tab ...................................................................17

5.6.5 DCS Tags Tab ........................................................................18

5.7 Estim Data Set Analysis ................................................................19

5.8 Optimization Objects .....................................................................20

5.8.1 Connection Tab ......................................................................21

5.8.2 Properties Tab ........................................................................225.8.3 Transfer Tab............................................................................25

5.9 General Notes.................................................................................25


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5-2

5-2

5.10 ESTIM DRU Diagnostic File Output............................................26

5.10.1 Initial Problem Parameters...................................................275.10.2 Iteration Output ....................................................................29

5.10.3 Final Output .........................................................................31


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5-3

5.1 The ProblemModern instrumentation and distributed control and management

information systems produce a wealth of plant data. The plant

operator/manager has a problem making sense of all this data where:

It may be inconsistent or inaccurate.

It may not give a complete or understandable indication of plantperformance.

In addition, plant models can only be configured to a specific

operational instance, whereas the performance of actual equipment

varies as conditions change and equipment degrades. Thus, the model

behaviour may start to diverge from actual plant behaviour.

5.2 The SolutionThe ESTIM DRU addresses these issues and produces concise

information to aid decision making and aid model tuning and off-line

investigation.

Firstly, it can perform data reconciliation. Measurements are subject to

error and, therefore, provide inconsistent information. ESTIM DRU can

detect and correct measurement errors, thereby providing a consistent

and accurate data set.

Secondly, a model representing a specific item of plant can be updated

whereby ESTIM DRU is able to reconcile model and actual plant values,

to ensure that the model continues to represent actual plant

performance.


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5-4 The Benefits

5-4

5.3 The BenefitsThe ESTIM DRU brings real benefits by ensuring good representation of

plant equipment, and providing indications of poor plant data as an aid

to decision making in the following areas:

Identification of process unit performance, in particular conditionmonitoring.

Identification and quantification of instrument errors.

This leads to improvements due to:

Better process operation in general.

More effective and efficient equipment maintenance and/or

replacement. More effective and efficient instrument maintenance.

Improved plant model representation.

ApplicationsCurrent applications of the ESTIM DRU include:

Compressor model updating/condition monitoring

Catalyst performance monitoring/updating

Thermal cracker model updating

Steam system data reconciliation

Gas turbine model parameter updating

Heat exchanger fouling effect updating

Reactor model parameter updating

Boiler model updating and condition monitoring

General network reconciliation (e.g., oil & gas fields, steam systems,etc.)

In fact, anywhere where plant measurements are available around

process equipment, the ESTIM DRU can be applied.


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5-5

5.4 ESTIM DRU Facilities

5.4.1 Error Detection/CorrectionNo measurement is perfect, so by using a number of sets of data and

statistical routines, the ESTIM DRU sorts the good from the bad and

only uses good data. This is a pre-requisite for model updating and the

essence of data reconciliation.

5.4.2 Model UpdatingThe ESTIM DRU can update the parameters of even the most complex

model.

5.4.3 UtilitiesThe ESTIM DRU invokes a number of statistical and optimizationroutines to perform the following tasks:

Parameter Estimation Calculation of model parameters whichmay change with time, such as reaction rate coefficients, heattransfer coefficients, etc.

Data Reconciliation Model based reconciliation of over-determined systems, such as steam system mass balancing, wherethere are many flow-meters, or estimation of power output of aturbine with both steam flow and driven load being measured.

Bad Data Elimination Results of data reconciliation calculationscan be examined statistically to determine whether bad data ispresent, and if so eliminate the bad data.


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5-6 Using ESTIM DRU

5-6

5.5 Using ESTIM DRUThe ESTIM DRU comes in the form of a tool kit, comprised of the

following:

A set of related screens in HYSYS for attaching an ESTIM DRU to aHYSYS plant model simulation case.

Demonstration examples describing how to use the DRU[1]. This letsyou configure plant model updating and data reconciliation routineswithin the HYSYS environment without recourse to programming orexpert assistance.

5.5.1 Measurement ProblemMeasurement devices are often assumed to have zero bias and random

error

hysys rto refguide

Documents