ModelBased Experimental Analysis or A Systems Approach to Mechanistic Process Modeling

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Model-Based Experimental AnalysisorA Systems
Approach to Mechanistic Process Modeling

• Wolfgang Marquardt
• Lehrstuhl für Prozesstechnik
• RWTH Aachen

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Modeling of Product and Process Systems
experimental and theoretical methods tools
product process systems

• kinetic phenomena
• diffusion
• heat and mass transfer
• interface phenomena
• multiphase transport
• (bio-)chemical reaction
• nucleation ...
• multi-phase reaction and separation processes
• fluid, structured functional products
• biological systems

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Integration of Modeling and Experimentation
cf. J.V. Beck, Meas. Sci. Techn. 9 (1998)

• common approach in research and industrial
  practice
• coupled phenomena
• detailed modes, numerical case studies
• comparison of simulation and experimental results
• evaluation of the model, but no model
  identification !
• suggested future approach
• coordinated design of model and experiment
• model refinement based on experimental evidence
• accounting for inevitable measurement errors
• identification of a valid (mechanistic) model
  (structure parameters) !

model-based experimental analysis MEXA valid
models at minimal effort
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Collaborative Research Centre 540

• Model-based Experimental Analysis
• of Kinetic Phenomena in Fluid
• Multi-phase Reactive Systems

• 13 research groups with cross-disciplinary
  expertise
• biotechnolgy (Ansorge-Schuhmacher)
• biochemical engineering (Büchs)
• reaction engineering (Greiner, Leitner)
• thermal separations (Pfennig)
• transport phenomena (Kneer)
• multiphase fluid dynamics (Modigell)
• computational engineering science (Behr)
• process systems engineering (Bardow, Marquardt)
• numerical mathematics (Reusken)
• scientific computing (Bischof, Bücker)
• NMR imaging (Blümich, Stapf)
• optical spectroscopy (Koß, Lucas, Poprawe)

Funded by DFG(Deutsche Forschungs-gemeinschaft)
since 1999 Director W. Marquardt
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MEXA Methodology
measurements
experimental design
iterative model refinement
incremental model identification
a-priori knowledge and intuition
extended understanding
iterative improvement of experiment
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Simultaneous Model Identification
measurements y
model of observations y(x,q,t)
model parameters q

• What if we do not know any candidate model
  structure ?
• How to select a suitable model structure ?
• Is bias due to model structure defects or a lack
  of information content in data ?
• How to deal with very few or very many
  observations ?
• How to deal with convergence robustness
  problems of estimation algorithm?

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Incremental Model Identification
measurements y
model of observations y(x,q,t)
model parameters q

• computationally efficient (minutes rather than
  days)
• numerically robust
• a-priori knowledge can be integrated into the
  identification process
• complex and interacting kinetic phenomena can be
  identified

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Incremental Model Development
Incremental Model Identification
Illustratrion with a CSTR
Illustratrion with reaction kinetcis idenfication
in a CSTR
(Marquardt, 1995)
(Marquardt, 1998)
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Incremental Model Identification
What are the ingredients for implementation ?
model-based design of experiments
high-resolution in-situ measurements
inversion algorithms for operator equations
parameter and structure identification for
algebraic models
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High Resolution Measurement Techniques

• non-invasive, in-situ measurements of field data
• observation of qualitative behavior
• quantitative characterisation of kinetic
  phenomena

interpretation of the primary measurement data,
calibration, quantification of measurement errors
!
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Calibration of Spectroscopic Measurement Data
mixture
xC
xT
pure component toluene
pure component cyclohexane

• simplest case xCspectrum C xT spectrum
  T mixture spectrum
• here nonlinear calibration for high accuarcy
  required during modeling

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Nonlinear Spectral Effects

• effects of interaction
• band shifting
• band shape change,band splitting

0.8
Mixture
EtOH
EtOAc
0.6

• constant integral absorption coefficient

A -
0.4
0.2

• modeling approach
• spectrum is a sum of individual bands
• band shapes Gaussian, Lorentzian, Voigt
• interactions accounted for by corrections

0
0.1
A -
0
D
-0.1
1000
1100
1200
1300
1400
1500
1600
1700
1800
-1
n
cm

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Indirect Hard Modeling of Spectral Data

• Indirect Hard Modeling (IHM)
• reduces calibration effort compared to
  established multivariate methods
• solves problems of establ. methods

Our Analysis Toolbox SPAIX can be applied plug
and play to different spectrometers without
additional reference data, because
all non-linear effects are modeled
phenomenologically
(Alsmeyer, Marquardt, 2004 Alsmeyer, Koß,
Marquardt, 2004 Kriesten, Bardow, Marquardt,
2006)
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Incremental Model Identification
What are the ingredients for implementation ?
model-based design of experiments
high-resolution in-situ measurements
inversion algorithms for operator equations
parameter and structure identification for
algebraic models
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Optimal Experimental Design Idea
parameter estimation objective
set free variables p such that information on
model parameters is maximized

maximize curvature of parameter estimation
objective
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Modeling of Reaction Kinetics

• no. of reactions, stoichiometry and kinetics
  unknown
• isothermal semi-batch CSTR experiments
• concentration measurements (ex-situ, e.g. GC
  in-situ, e.g. Raman/IR spectroscopy)
• a number of simulated semi-batch reactor
  experiments, 60 min (cases noise, sampling )

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Incremental Model Identification
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Concentration Measurements ? Reaction Fluxes
estimated concentration
regularisation
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Incremental Model Identification
target factor analysis Bonvin Rippin, 1990
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Reactionfluxes ? Stoichiometry, Reaction Rates
estimated reaction fluxes
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Incremental Model Identification
measurements
measured concentrations
candidates for
model 1
balances
stoichiometry
fluxes
concentrations
candidates for
balances
model 2
stoichiometry
reaction kinetics
concentrations
fluxes
rates
model 3
kinetic law
stoichiometry
balances
concentrations
fluxes
rates
reaction parameters
model of the reaction
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Identification of Reaction Kinetic Laws
candidate kinetic laws
regression of estimated rates and
concentrationens for each individual reaction
estimated rate kinetic las 4 kinetid law 5
kinetic law 8
?
simultaneous identification for promising model
candidates
best model structure with statistically optimal
parameters
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Iterative Model lmprovement
measurements
Reaktionsparameter
model structure and parameters q
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Iterative Improvement - Example
scenario 3600 data points in each experiment
(Ts1 s), 5 noise
stoichiometry
kinetic law
validation
parameters
-
1 P D PAA 2 D D DHA 3 D OL
1
N/A
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Incremental vs. Simultaneous Model Identification
Incremental Method
Simultaneous Method
CPU Time
Ident. Corr.
Reso- lution
Ident. Corr.
CPU Time
Reso- lution
Models
Models
STDV 2
3 sec
1
30 min
100
3 sec
100
3600
1.7 d
30 sec
1
15 sec
100
30 sec
100
3600
3.8 h
5 min
7
6 sec
100
5 min
100
3600
1.7 h
STDV 10
3 sec
40 min
100
100
3 sec
100
3600
1.6 d
30 sec
160
3 min
50
30 sec
50
3600
3.9 h
5 min
200
2 min
10
5 min
10
3600
1.1 h
60 min
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Incremental vs. Simultaneous Identification
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Asymmetric Multi-phase Catalysis in scCO2
catalytic hydration of olefins
chemo-catalysis Greiner, Leitner modelling,
spectral calibration Kriesten, Michalik,
Marquardt
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Enzymatic catalysis in Two-phase Systems
organic solvent
Raman spectroscopy
hydrogel
educts
products
confocal 3-photonslaser scanning microscopy
modelling Michalik, Marquardt measurements
Koß, Lucas / Poprawe bio-catalysis
Ansorge-Schumacher, Büchs, Spieß
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MEXA for Investigation of Diffusive Transport

• Why studying diffusion ?
• detrimental for product and process design
• very high experimental effort
• very few multi-component diffusion data available
• validity of diffusion models still a matter of
  debate

selectivity of heterogeneously catalyzed
reactions(Pantelides Urban, 2004)

• a good model problem
• for the development of
• MEXA methodology

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Incremental Model Identification
measurements y
binary diffusion
model for fluxes
model F(x,?)
parameters ?
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Incremental Model Identification
Dik(x, ?)
Ji(z,t)
model discrimination
transport laws
x(z,t)
model
balance equations 1D
sequence of inverse problems
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Quaternary Diffusion
- 9
Marquardt, LPT

• concentration measurements with Raman
  spectroscopy and
• model-based design and evaluation of diffusion
  experiments
• (cyclohexane toluene dioxane chlorobutane)

matrix of Ficksdiffusion coefficients
thermodynamical factor accuracy improvements
electrolytes
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Kinetic Phenomena in Falling Film Reactors

• falling films are all around - falling film
  cooler
• - falling film evaporator
• falling film absorber
• falling film reactors
• transport phenomena are hardlyunderstood,
  interaction between
• - fluid dynamics with free surface
• - heat and mass transfer
• - chemical reaction
• first milestone modelling of heat transfer
  with effective transport coefficients

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Heat Transfer through Falling Film
measurement data
measured temperature field
model 1
energy bal.
heat flux
temperatures
transportlaw
energy bal.
model 2
eff. heat conduction
temperatures
heat flux
constitutive equation
transportlaw
model 3
energy bal.
eff. heat conductiont
temperatures
heat flux
parameters
Model structure and parameters
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Experimental Set-up
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Mathematical Problem Formulation
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Heat Flux Estimates from Experimental Data
measured temperature distributions
estimated heat flux distribution
(Groß, Soemers, Mhamdi, Al-Sibai, Reusken,
Marquardt, Renz, 2005)
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Towards Inverse Transport Problems

• CG method for the solution of inverse problem
  embeds DROPS (Reusken u.a., SFB 540) ein.
• DROPS employs
• adaptive multi grid methods,
• finite element discretization,
• levelset method
• and facilitates the numerical simulation
• of multi-phase flow problems in 3D
• at high resolution
• of the phenomena at the phase interface,
• efficient and error-controlled
• with
• appropriate flexibility
• for model extensions.

a droplet rising in a stagnant liquid Pfennig,
Reusken u.a., CRC 540
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MEXA Business Process Evaluation

• method integration has high potential !
• optimal experimental design reduces effort
• structure identification leads to mechanisms
• improvement of method integration in
  particular for distributed problems

• incremental refinement has high potential !
• homogenous reactions, multi-component diffusion,
  diffusion bioreaction in gels
• drastic reduction of experimental and engg.
  effort
• significantly improved transparency
• further development for CFD problems

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Lessons Learned

• accept interactions between kinetic phenomena in
  experiments,
• butisolate them during identification by a
  suitable decomposition strategy
• high precision calibration of high-resolution
  measurements
• (PIV, LIC, LCSM, NMR imaging, Raman / IR
  spectroscopy etc.)
• often is a difficult modeling problem in itself
• statistics of measurement errors need to be
  included in the analysis
• flux estimation is the key to reliable
  identification
• tremendous improvements are possible by
  systematic cross-disciplinary linking of process
  systems and experimental skills