PROCESS MODELLING AND MODEL ANALYSIS

© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

A Model Building Framework

PROCESS MODELLING AND MODEL ANALYSIS 2

© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

An Overview

The process system (SISO, MISO,MIMO) The modelling goal A systematic approach The necessary ingredients

PROCESS MODELLING AND MODEL ANALYSIS 3

© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

The Process System

Inputs, u Outputs, y States, x Disturbances, d

Su yx

y = S[u,d]

(SISO, MIMOSS or dynamic)

d

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

The Modelling Goal

Flowsheeting simulation (rating) design optimization

Process control prediction regulation identification diagnosis

Application areas

Performance specifications

real, integer or Boolean indices

PROCESS MODELLING AND MODEL ANALYSIS 5

© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

A Systematic Modelling Procedure

Problem definition

Controlling factors

Problem data

Model construction

Model solution

Model verification

Model calibration &

validation

1

2

4 7

5

3 6

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

Clear description of systemestablish underlying assumptions

Statement of modelling intention intended goal or useacceptable erroranticipated inputs/disturbances

1. Problem Definition

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

Definition Example (Step 1) CSTR description

details lumped ? dynamic

Goal (intent) inlet change range +/-10% accuracy control design

in-flow

out-flow

f, C Ai

f, C A , C B

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

A Systematic Modelling Procedure

Problem definition

Controlling factors

Problem data

Model construction

Model solution

Model verification

Model calibration &

validation

1

2

4 7

5

3 6

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

2. Controlling Factors / Mechanisms

Chemical reaction Mass transfer

convective, evaporative, ...

Heat transfer radiative, conductive, …

Momentum transferASSUMPTIONS

PROCESS MODELLING AND MODEL ANALYSIS 10

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Mechanisms - CSTR (step 2)

Chemical reaction A P Perfect mixing No heat loss (adiabatic)

PROCESS MODELLING AND MODEL ANALYSIS 11

© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

A Systematic Modelling Procedure

Problem definition

Controlling factors

Problem data

Model construction

Model solution

Model verification

Model calibration &

validation

1

2

4 7

5

3 6

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

3. Data for the problem

Physico-chemical data Reaction kinetics Equipment parameters Plant data

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Data - CSTR (step 3)

Reaction kinetics data: k0 , E, HR

Physico-chemical propertiesspecific heats, enthalpies, …

Equipment parameters: V

PROCESS MODELLING AND MODEL ANALYSIS 14

© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

A Systematic Modelling Procedure

Problem definition

Controlling factors

Problem data

Model construction

Model solution

Model verification

Model calibration &

validation

1

2

4 7

5

3 6

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

4. Model construction

Assumptions Boundaries and balance

volumes Conservation equations

mass energy momentum

Constitutive equations reaction rates transfer rates property relations balance volume relations control relations &

equipment constraints Characterizing Variables Conditions (ICs, BCs) Parameters

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

CSTR Model (step 4)

Assumptions A1: perfect mixing A2: first order reaction A3: adiabatic operation A4: equal inflow, outflow A5: constant properties

Equations conservation

constitutive

HfHfdtdH

rVffdtdm

i

AAA

i

ˆˆ

AA

AiA

P

iPi

AA

ARTE

fCf

fCfTcH

TcH

VCmCekr

i

ˆ

ˆ

0

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

CSTR Model (step 4)

Initial Conditions

Parameters and inputs 10% accuracy

30% - 500% accuracy

i

AA

TT

CCi

)0(

)0(

PiiA cTCfV ,,,,

RHEk ,,0

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

A Systematic Modelling Procedure

Problem definition

Controlling factors

Problem data

Model construction

Model solution

Model verification

Model calibration &

validation

1

2

4 7

5

3 6

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

5. Model solution

Algebraic systems Ordinary differential equations Differential-algebraic equations Partial differential equations Integro-partial differential equations

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CSTR - Numerical Solution (step 5)

Solution of differential-algebraic equationsusing structuring techniquesusing direct DAE solution

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

A Systematic Modelling Procedure

Problem definition

Controlling factors

Problem data

Model construction

Model solution

Model verification

Model calibration &

validation

1

2

4 7

5

3 6

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

6. Model verification

Structured programming approach Modular code Testing of separate modules Exercise all code logic

conditionsConstraints

Quality documentation

PROCESS MODELLING AND MODEL ANALYSIS 23

© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

A Systematic Modelling Procedure

Problem definition

Controlling factors

Problem data

Model construction

Model solution

Model verification

Model calibration &

validation

1

2

4 7

5

3 6

PROCESS MODELLING AND MODEL ANALYSIS 24

© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

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

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

For Discussion (1)

Open tank system

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© CAPE Centre, The University of Queensland Hungarian Academy of Sciences

For Discussion (2)

Closed tank system