Introduction

Contents:

1- Design, Modeling, Simulation, Optimization,

Their Applications and Relations

1-1- Design (Determination of equipment size, …)

(Cost, Capability, Maintenance, Safety)

Steps:

Conceptual Design

Basic Design

Detail Design

1-2- Modeling

Definition

Programming

Using software

1-3- Simulation

1-4- Optimization

1-5- Applications and Relations

Contents (continue):2- Modeling and Engineering Problem solving

2-1- Physical Model2-2- Mathematical Model2-3- Numerical Model2-4- Modeling Using Software

3- Types of Modeling 3-1- Steady State3-2- Pseudo Steady State3-3- Unsteady State

4- Modeling procedure

5- Programming and Using of Software

Lumped model

1 D Model

2 D Model

3 D Model

4 D Model

1- Design, Modeling, Simulation, Optimization, Their

Applications and Relations

1-1- Design (Determination of equipment size, …)

(Cost, Capability, Maintenance, Safety)

Design Steps:

Conceptual Design

Basic Design

Detail Design

1- Design, Modeling, Simulation, Optimization, Their

Applications and Relations

1-1- Design (Determination of equipment size, …)

(Cost, Capability, Maintenance, Safety)

Design Steps:

Conceptual Design

Basic Design

Detail Design

1- Design, Modeling, Simulation, Optimization, Their

Applications and Relations

1-2- Modeling

Modeling is a fundamental and quantitative way to understand complex systems and phenomena.

A model is an imitation of reality.

Model:

“A model (M) for a system (S)

and an experiment (E) is

anything to which E can

be applied in order to answer questions

(P) about S”

“A Processes Engineering Model is

typically a mathematical representation (M)

of a physical system (S) for a specific

purpose (P) and experiment (E)”

Model

The Process Modeling

1- Design, Modeling, Simulation, Optimization, Their

Applications and Relations1-3- Simulation

Process simulation is used for the design, development, analysis, and optimization of technical processes

Simulation is also used for scientific modeling of natural systems or human systems in order to gain insight into their functioning

Simulation can be used to show the eventual real effects of alternative conditions and courses of action. Simulation is also used when the real system cannot be engaged, because it may not be accessible, or it may be dangerous or unacceptable to engage, or it is being designed but not yet built, or it may simply not exist

It is mainly applied to

Chemical plants Chemical processes

Safety engineering Testing

Training (Flight Simulators) Education

video games (war Games) power stations

and similar technical facilities.

1- Design, Modeling, Simulation, Optimization, Their

Applications and Relations

1-3- Simulation

Simulation Steps:

1- Design, Modeling, Simulation, Optimization, Their

Applications and Relations

1-4- Optimization

In mathematics, computer science and economics, optimization, or mathematical programming, refers to choosing the best element from some set of available alternatives.

In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. This formulation, using a scalar, real-valued objective function, is probably the simplest example; the generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, it means finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains.

1- Design, Modeling, Simulation, Optimization, Their

Applications and Relations

1-4- Optimization

optimization techniquesOptimization methods are crudely divided into two groups:SVO - Single-variable optimizationMVO - Multi-variable optimization

For twice-differentiable functions, unconstrained problems can be solved by finding the points where the gradient of the objective function is zero (that is, the stationary points) and using the Hessian matrix to classify the type of each point. If the Hessian is positive definite, the point is a local minimum, if negative definite, a local maximum, and if indefinite it is some kind of saddle point.The existence of derivatives is not always assumed and many methods were devised for specific situations. The basic classes of methods, based on smoothness of the objective function, are:Combinatorial methodsDerivative-free methodsFirst-order methodsSecond-order methods

1- Design, Modeling, Simulation, Optimization, Their

Applications and Relations

1-5- Applications and

Relations

2- Engineering Problem solving and Modeling

2-1- Engineering Problem Solving

2-2- Physical Model

2-3- Mathematical Model

2-4- Numerical Model and Programming

2-5- Modeling Using Software

2-1- The Engineering Skills:

1) How to represent a design problem

2) How to generate possible ideas for designs

3) How to effectively conduct a search for a

solution

4) How to plan and schedule activities

5) How to make efficient use of resources

6) How to organize the components and activities

of a team design project

2-1-1- Problem Solving Steps:

The strategy has eight steps- seven working steps and

one motivational step- listed below:

1) I can (positive attitude)

Try to view each problem as a challenge, and don’t give up too easily.

2) Define

Identify the “Knowns”, Identify the “Unknowns”, State in simpler terms,

Develop a diagram, schematic, or visual representation for the problem

3) Explore (pre-planning and we double-check that we understand the

problem)

You think about what the problem is actually asking you to solve, what

additional information you might need, and general strategies that might

be applicable

Dose the problem makes sense?

Assumptions

What are the key concepts and possible approaches

What level of understanding is tested?

2-1-1- Problem Solving Steps (cont.):

4) Plan

Main goal (unknown), subgoals (Unknown), Initial Values (Known) and

assumptions

5) Implement

Solve the equations

6) Check

7) Generalize

some questions:

What specific facts have you learned about the content?

Could this problem have been solved more efficiently?

Could you have applied something you learned in solving this problem

to another problem that you’d seen in the past?

Were there any problems or bugs that you encountered that you

should remember, in case you run into them again?

8) Present the results

Show your work

Give good directions

Be neat

2-1-2- Problem Solving Steps (Example):

How much CO2 does a typical passenger car produce per year? (p:113)

2-2- Physical Model

A physical model (most commonly referred

to simply as a model, however in this sense it

is distinguished from a conceptual model) is

a smaller or larger physical copy of an

object. The object being modeled may be

small (for example, an atom) or large (for

example, the Solar System).

2-3- Mathematical Model

A mathematical model is a description of a system using mathematical language.

The process of developing a mathematical model is termed mathematical

modeling (also written modeling).

Mathematical models are used not only in the natural sciences (such as physics,

biology, earth science, meteorology) and engineering disciplines, but also in the

social sciences (such as economics, psychology, sociology and political science);

physicists, engineers, statisticians, operations research analysts and economists

use mathematical models most extensively.

Mathematical models can take many forms, including but not limited to

dynamical systems, statistical models, differential equations, or game theoretic

models.

These and other types of models can overlap, with a given model involving a

variety of abstract structures.

2-4- Numerical Model and Programming

- Drive Required Equations in General Form

-Consider Boundary and Initial Conditions

- Prepare Flowchart of Program

- Write Program

- Get Results

- Compare with Available Data (*)

2-5- Modeling Using Software

-Select a proper and User Friendly Software

- Find Its Tutorial Help and Examples

- Run Simple Models or Programs

- Run Your Program or Model

-Get Results

- Compare with Available Data

3- Types of Modeling

Steady State

Pseudo Steady State

Unsteady State

Lumped model

1 D Model

2 D Model

3 D Model

4 D Model

4- Modeling procedure

The Process System A Process Model

4-1- Model

SISO: Simulation interoperability Standards Organization

MIMO: multiple-input and multiple-output

SS: steady state

m: model

4-2- Goals for Process Modeling

Flow Sheeting

Design

Optimization

Process Control

Prediction

Regulation

Identification

Diagnosis

4-3- Model Building White-box modeling

A white-box model (also called glass box or clear box) is a system where all necessary information is available.

Black-box modeling

A black-box model is a system of which there is no a priori information available.

Grey-box modeling

Real process systems

4-4- Systematic Modeling Procedure

1. Problem Definition

Clear description of system

input/output

spatial distribution

time characteristics

etc

Statement of modeling intention

intended goal or use

acceptable error

anticipated inputs/disturbances

1. Problem Definition (cont.)

CSTR descriptiondetails

lumped ?

dynamic

Goal (intent)inlet change range

± 10% accuracy

control design

Definition Example (Step 1)

2. Controlling Factors / Mechanisms

Chemical reaction

Mass transfer

convective, evaporative, ...

Heat transfer

radiative, conductive, …

Momentum transfer

ASSUMPTIONS

2. Controlling Factors / Mechanisms

Mechanisms - CSTR (step 2)

Chemical reaction A P

Perfect mixing

No heat loss (adiabatic)

3. Data for the problem

Physico-chemical data

Reaction kinetics

Equipment parametersV

Plant data

RHEK ,,0

4. Model construction

Assumptions

Boundaries and balance

Volumes

Characterizing Variables

Conservation equationsmass

energy

momentum

Constitutive equations reaction rates

transfer rates property relations

balance volume relations

control relations &

equipment constraints

Conditions (ICs, BCs)

Parameters

4. Model construction (cont.)

Assumptions A1: perfect mixing

A2: first order reaction

A3: adiabatic operation

A4: equal inflow, outflow

A5: constant properties

CSTR Model (step 4)

Equations conservation

constitutive

4. Model construction (cont.)

Initial Conditions

Parameters and inputs

10% accuracy

30% - 50% accuracy

CSTR Model (step 4)

• Industrial measured data is

± 10 to 30%

• Estimated parameters from

laboratory or pilot plant data is

±5 to 20%

• Reaction kinetic data is

± 10 to 50 % (if nothing else is specified)

5. Model solutionWhat variables must be chosen in the model to satisfy the

degrees of freedom?

Is the model solvable?

What numerical (or analytic) solution technique should be

used?

Can the structure of the problem be exploited to improve the

solution speed or robustness?

What form of representation should be used to disp1ay the

results (2D graphs, 3D visualization)?

How sensitive will the solution output be to variations in the

system parameters or inputs?

5. Model solution (cont.)

Mechanistic

Empirical

Stochastic

Deterministic

Lumped parameter

Distributed parameter

Linear

Nonlinear

Continuous

Discrete

Hybrid

Based on mechanisms/underlying phenomena

Based on input-output data, trials or experiments

Contains model elements that are probabilistic in nature model

Based on cause-effect analysis

Dependent variables not a function of spatial position

Dependent variables are a function of spatial position

Superposition principle applies

Superposition principle does not apply

Dependent variables defined over continuous space-time

Only defined for discrete values of time and/or space

Containing continuous and discrete behavior

Type of model Criterion of classification

Model Classification

5. Model solution (cont.)

Algebraic systems

Ordinary differential equations

Differential-algebraic equations

Partial differential equations

Integro-differential equations

5. Model solution (cont.)Type of model Equation

Steady-state

problem

types

Dynamic problem

Deterministic

Stochastic

Lumped parameter

Distributed

parameter

Linear

Nonlinear

Continuous

Discrete

Nonlinear algebraic

Algebraic/difference

equations

Algebraic equations

EPDEs

Linear algebraic equations

Nonlinear algebraic

equations

Algebraic equations

Difference equations

ODEs/PDEs

Stochastic ODEs or difference

equations

ODEs

PPDEs

Linear ODEs

Nonlinear ODEs

ODEs

Difference equations

6. Model verification

Model Verification

Model Validation

Reality

Conceptual Model Computerised Model

6. Model verification (cont.)

Verification is determining whether the model is behaving correctly.Is it coded correctly and giving you the answer you intended? This is not the same as model validation where we check the model against reality.You need to check carefully that the model is correctly implemented. Structured programming using top-down algorithm design can help here as well as the use of modular code which has been tested thoroughly.This is particularly important for large-scale models.

6. Model verification (cont.)

Structured programming approach

Modular code

Testing of separate modules

Exercise all code logic

conditions

constraints

Verification is determining whether the model is behaving correctly. Is it coded correctly and giving you the answer you intended? This is not the same as model validation where we check the model against reality. You need to check carefully that the model is correctly implemented. Structured programming using top-down algorithm design can help here as well as the use of modular code which has been tested thoroughly. This is particularly important for large-scale models.

7. Model calibration/validation

Generate plant data

Analyze plant data for quality

Parameter or structure estimation

Independent hypothesis testing for validation

Revise the model until suitable for purpose

For Discussion (1)

Open tank system

For Discussion (2)

Closed tank system

5- Programming and Using of Software

5-1 ProgrammingSelect Proper Language and Learn It

5-2 Using Software

Select Proper and User Friendly Software

Find Tutorial Help and Examples