process modelling and model analysis © cape centre, the university of queensland hungarian academy...
DESCRIPTION
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 S u y x y = S[u,d] (SISO, MIMO SS or dynamic) dTRANSCRIPT
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
PROCESS MODELLING AND MODEL ANALYSIS 4
© 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
PROCESS MODELLING AND MODEL ANALYSIS 6
© 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
PROCESS MODELLING AND MODEL ANALYSIS 7
© 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
PROCESS MODELLING AND MODEL ANALYSIS 8
© 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 9
© 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
© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
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
PROCESS MODELLING AND MODEL ANALYSIS 12
© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
3. Data for the problem
Physico-chemical data Reaction kinetics Equipment parameters Plant data
PROCESS MODELLING AND MODEL ANALYSIS 13
© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
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
PROCESS MODELLING AND MODEL ANALYSIS 15
© 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
PROCESS MODELLING AND MODEL ANALYSIS 16
© 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
PROCESS MODELLING AND MODEL ANALYSIS 17
© 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
PROCESS MODELLING AND MODEL ANALYSIS 18
© 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 19
© 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
PROCESS MODELLING AND MODEL ANALYSIS 20
© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
CSTR - Numerical Solution (step 5)
Solution of differential-algebraic equationsusing structuring techniquesusing direct DAE solution
PROCESS MODELLING AND MODEL ANALYSIS 21
© 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 22
© 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
PROCESS MODELLING AND MODEL ANALYSIS 25
© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
For Discussion (1)
Open tank system
PROCESS MODELLING AND MODEL ANALYSIS 26
© CAPE Centre, The University of Queensland Hungarian Academy of Sciences
For Discussion (2)
Closed tank system