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 S u y x y = S[u,d] (SISO, MIMO SS 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

PROCESS MODELLING AND MODEL ANALYSIS 6 © CAPE Centre, The University of Queensland Hungarian Academy of Sciences   Clear description of system   establish underlying assumptions   Statement of modelling intention   intended goal or use   acceptable error   anticipated 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

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

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 transfer ASSUMPTIONS

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

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: k 0, E,  H R   Physico-chemical properties   specific 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

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

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

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

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 equations   using structuring techniques   using 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

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   conditions   Constraints   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

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