Modeling and Parameter Estimation of Batch Solid-Liquid ...egon.cheme.cmu.edu/ewo/docs/Dow_Wang_Yajun_EWO_2017.pdf · Modeling Conclusions & Significance Parameter Estimation Industrial

Parameter estimation and model discrimination of batch solid-liquid reactors

Yajun Wang, Lorenz T. Biegler

Carnegie Mellon University

Mukund Patel, John Wassick

The Dow Chemical Company

March 2017

Enterprise-wide Optimization Meeting

Problem Statement & Motivation

Reactor Modeling

Significance & Potential Impact

Parameter Estimation

Industrial Case Study


• Batch reactor

Preparation

Solid-liquid Reaction

Solvent

Solid W

Liquid X

2

Solvent and reactant

materials

Reactor discharge

Vent

Agitator

Reactor

jacket

Cooling water

inlet

Cooling water

outlet W(s) + X(l) Y(s/l) + Z(s)

• Unknown reaction mechanism –

• Limited information –

Surface reaction, dissolution, diffusion

Different particle shapes and sizes

Product effects

Lack of concentration measurements

An over-parameterized model without enough data


Reactor Modeling




Reaction Mechanisms

Shrinking particle model (SPM)

3

Reactant reactant Fluid

film

b

lc

s

lc

Liquid reactant diffuses onto the particle surface

Solid-liquid reaction

Solid product breaks off from reaction surface.

Dissolution model (DM)

Reactant reactant

Solid particles dissolve into solvent

Liquid–liquid reaction

Products precipitate into solid phase.

Assume dissolution is the rate limiting step.

Reaction rate of SPM depends on liquid reactant concentration while DM doesn’t.


Reactor Modeling




Batch Reactor Model

4

• Model indicator

F=0 DM

F>0 SPM

• Parameters

1/ 1 1/

0

0

a ass s

s

aMS N N

R

Total surface area is related to total amount and the shape of particles[1].

[1] Salmi, Tapio, et al. "New modelling approach to liquid–solid reaction kinetics: From ideal particles to real particles." Chemical

Engineering Research and Design 91.10 (2013): 1876-1889.

1/ 1 1/

0 0

0

1/ 1 1/

0 0

0

(c )a

s s

a

s s

E

a a ss s RTs s s s l

s

E

a as s RTs s s

s

dN aMSR N N k e

dt R

dN aMkS N N k e

dt R

SPM

DM


Reactor Modeling





5

Estimability evaluation

Simultaneous estimation

Estimation quality analysis

Posterior probability share

Sensitivity coefficient matrix

QR transformation with column permutation

Rank parameters by their individual variance contribution Estimable?

YES EVM formulation > WLS formulation

• Data reconciliation

• Parameter estimation

Small Confidence

interval?

Reduce parameter set/ Simplify model

YES

NO

NO

Estimation covariance matrix

Reduced Hessian – confidence region

Model Validation


Bayes’ theorem

• Fitting

• Number of parameters

Validation by unseen batch data

Cross validation


Reactor Modeling





Estimability evaluation

• Parameter rankings at different points are different • All parameters are included in the estimation

Rank parameters by QRcp of scaled sensitivity matrix

6

Solid-liquid batch reactor

• Jacket temperatures • Inlet flowrates • Reactor weights

• Reactor temperatures • Concentrations

• Batch k k = 1 … NS • Measured input ukj* • Measured output ηki* • Normally distributed measurements


Reactor Modeling




7

Measured output errors

Simultaneous estimation -- EVM

• EVM does parameter estimation and data reconciliation

simultaneously

• Better output data fitting Accumulated squared errors of EVM is

reduced by 44% compared with WLS

• Intensive computational load EVM has 15771 variables and

13830 equation constraints


Measured input errors

• Reactor temperatures • End-point concentrations • Jacket temperatures • Weights and flowrates

0 0.2 0.4 0.6 0.8 10.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

Scaled time

Sca

led

te

mp

era

ture

Reactor temperature

Predict

Data

WLS

0 0.2 0.4 0.6 0.8 10.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

Scaled time

Sca

led

te

mp

era

ture

Reactor temperature

Predict

Data

EVM


Reactor Modeling




8

Industrial Case Study Estimation quality analysis

• Set Cb,X = Cs,X

• Set F = 0 dissolution model

• Fix parameter UA

Linearly temperature-dependent U



Reactor Modeling




9

Industrial Case Study Estimation results

Unseen data

Model Validations

1 2 3 4 5 6 7 8 90.09

0.095

0.1

0.105

0.11

0.115

0.12

Iteration

Pa

ram

ete

r A

3

Estimated value in each iteration

Average of 9 estimations

Estimated value by all data

New data 9-fold cross validation


Reactor Modeling

Conclusions & Significance



Conclusions & Significance

• Discussed two potential models for a solid-liquid reaction in a batch

reactor

• Built a uniform dynamic model with an indicating parameter to

discriminate two mechanisms

• Introduced a parameter estimation procedure

• Applied parameter estimation to the solid-liquid batch reactor model

• Conducted model validation to examine the model capability of

predicting system behaviors

Optimal control will be conducted based on estimated model to

reduce the batch time

10

Documents

Modeling and Parameter Estimation of Batch Solid-Liquid ...egon.cheme.cmu.edu/ewo/docs/Dow_Wang_Yajun_EWO_2017.pdf · Modeling Conclusions & Significance Parameter Estimation Industrial