Modeling and Parameter Estimation of Batch Solid-Liquid ...egon.cheme.cmu.edu/ewo/docs/Dow_EWO_F16_YajunWang.pdf · Modeling and Parameter Estimation of Batch Solid-Liquid Reactors

Modeling and Parameter Estimation of Batch Solid-Liquid Reactors

Yajun Wang, Lorenz T. Biegler

Carnegie Mellon University

Mukund Patel, Yisu Nie, John Wassick

The Dow Chemical Company

08/18/2016

ConclusionsResultsParameterEstimation

Reactor Model

Reaction Mechanism

Problem StatementProblem

Statement

Problem Statement• Batch reactor

Preparation

Reaction

Solvent

Solid W

Liquid X

2

Solvent and reactant materials

Reactor discharge

Vent

Agitator

Reactor jacket

Cooling water inlet

Cooling water outlet


Reactor Model

Reaction Mechanism

Problem StatementProblem

Statement

Solid-liquid Reactions

W(s) + X(l) Y(s/l) + Z(s)→

• Surface reaction, dissolution, diffusion -- where does the reaction occur, on the solid surface or in the liquid phase?

• Different particle shapes and sizes -- how to incorporate reaction surface?

• Product effects – where are the products, accumulating on the reaction surface or cracking off?

Solid and liquid reactants react to generate solid or liquid products

3


Reactor Model

Reaction Mechanism

Problem Statement

Reaction Mechanism

Reaction Mechanism 1Shrinking particle model

4

Reactant reactantreactantFluid film

bic

sic

Liquid reactant diffuses onto the particle surface

Solid-liquid reaction

Reaction


Reactor Model

Reaction Mechanism

Problem Statement

Reaction Mechanism

Shrinking particle model

• Pseudo-steady state is assumed on the reaction surface.

Reaction rate Rk is a function of surface concentration of the liquid reactant

• Total surface area is related to total amount and the shape of particles.

σ is the specific surface area with the unit [m2/kg]. a is a dimensionless shape factor.

5

1/ 1 1/0a a

s s sS M N Nσ −=

1(c ) 0

Kb s

dl l l lk kk

k c Rυ=

− + =∑

Reaction Mechanism 1

Fick’s Law


Reactor Model

Reaction Mechanism

Problem Statement

Reaction Mechanism

Shrinking particle model

6

1/ 1 1/0 0

1 1

1/ 1 1/0 0

1 1

Solid: (c )

Liquid: (c )

aks s k

aks s k

EK Ka a ss RT

sk k sk s s s s k lk k

EK Ka a sl RT

lk k lk s s s s k lk k

dN SR M N N k edtdN SR M N N k edt

α

α

υ υ σ

υ υ σ

−−

= =

−−

= =

= =

= =

∑ ∑

∑ ∑

b ll

l

NcV

=

1(c ) 0

Kb s

dl l l lk kk

k c Rυ=

− + =∑

0

(c ) k

ak

sk k l

ERT

k k

R k

k k e

α

−

=

=


Surface reaction rate depends on surface concentration of the liquid reactant.

Surface area Reaction rate


Reactor Model

Reaction Mechanism

Problem Statement

Reaction Mechanism

Reaction Mechanism 2Dissolution model

7

Reactant reactantreactant

Solid particles dissolve into solvent

Liquid – liquid reaction


Reactor Model

Reaction Mechanism

Problem Statement

Reaction Mechanism

• Assume dissolution is the rate limiting step. (Reaction is much faster than dissolution.)

• Dissolution rate constant is Arrhenius type.

8

sdN kSdt

= − 1/ 1 1/0a a

s s sS M N Nσ −=

0

aERTk k e

−=

1/ 1 1/0 0

1

1/ 1 1/0 0

1

Solid:

Liquid:

as s

as s

EKa as RT

sk s s s sk

EKa al RT

lk s s s sk

dN M N N k edtdN M N N k edt

υ σ

υ σ

−−

=

−−

=

=

=

∑

∑


Surface area Dissolution rate

Dissolution rate doesn’t depend on surface concentration of the liquid reactant.

Dissolution model


Reactor Model

Reaction Mechanism

Problem Statement

Reactor Model

Batch Reactor Model Lumped parameters A, B, D, E, F and heat transfer coefficient U are to be estimated.

9


Reactor Model

Reaction Mechanism

Problem Statement

Reactor Model

Batch Reactor Model

Surface concentration of liquid reactant

F=0 Dissolution modelF>0 Shrinking particle modelOne formulation for two mechanisms

10


Reactor Model

Reaction Mechanism

Problem Statement

Parameter Estimation

Parameter EstimationWeighted least-square formulation (WLS)

Measured output errors

• End-point concentrations• Reactor temperatures

+ Smaller problem to solve.- Ignoring input measurement errors.- Fewer degree of freedom, less control.

11


Reactor Model

Reaction Mechanism

Problem Statement



+ Considering both input and output measurement errors. + Doing parameter estimation and data reconciliation at the same time.+ More control of the problem, better data fitting. - More decision variables, larger problem to solve.

12

Measured output errors Measured input errors

Errors-in-variables-measured formulation (EVM)

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


Reactor Model

Reaction Mechanism

Problem Statement Results 13

Comparison of WLS & EVM

Fitting by EVM is much better than it by WLS.Accumulated squared error of EVM is smaller than 1/3 of 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

tem

pera

ture

Reactor temperature

PredictData

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 timeS

cale

d te

mpe

ratu

re

Reactor temperature

PredictData

WLS EVM


Reactor Model

Reaction Mechanism


Estimation ResultsEstimated parameter values and confidence levels by EVM

Large confidence level indicates the parameter is not estimable.


Reactor Model

Reaction Mechanism


Parameter Selection• Get rid of parameters with large confidence level D

• Simplify heat transfer coefficient

0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.750

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Scaled temperature

Heat tranfer coefficient

Sca

led

U


Reactor Model

Reaction Mechanism

Problem Statement Results

Modified estimation results

Small confidence level of all parameters.

Estimation Results

16


Reactor Model

Reaction Mechanism


Estimation Results

17

Fitting of jacket temperature(measured inputs)

Fitting of reactor temperature(measured outputs)

Data fitting

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

tem

pera

ture

Reactor temperature

PredictData

0 0.2 0.4 0.6 0.8 10

0.5

1Jacket inlet temperature

PredictData

0 0.2 0.4 0.6 0.8 10

0.5

1

Scaled time

Jacket outlet temperature

Sca

led

tem

pera

ture


Reactor Model

Reaction Mechanism


Estimation Results

18

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Scaled time

Sca

led

mol

ar a

mou

ntComponent molar amounts vs. reaction time

X (Liquid reactant)W (Solid reactant)Y (Product)

Reaction profiles W(s) + X(l) Y(s/l) + Z(s)→


Reactor Model

Reaction Mechanism

Problem Statement Conclusions

Conclusion and Future work• Shrinking particle and dissolution models of solid-liquid

reactions are explored and an uniform dynamic model isimplemented for both mechanisms.

• Parameter estimation is conducted based on limitedindustrial data. EVM method leads to better data fitting ofboth jacket temperatures and reactor temperatures.

• An analysis of estimation results is presented to enhanceproblem estimability.

------------------------------------------------------------------------------------• More data is going to be collected to validate the model.• Recipe optimization and process control are going to be

implemented after model validation.

19


Reactor Model

Reaction Mechanism

Problem Statement Conclusions

References• Forryan, Claire L., et al. "Heterogeneous kinetics of the dissolution of an inorganic

salt, potassium carbonate, in an organic solvent, dimethylformamide." The Journal of Physical Chemistry B 109.16 (2005): 8263-8269.

• 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.

• Zavala, Victor M., and Lorenz T. Biegler. "Large-scale parameter estimation in low-density polyethylene tubular reactors." Industrial & engineering chemistry research 45.23 (2006): 7867-7881.

• Bard, Yonathan, and Yonathan Bard. Nonlinear parameter estimation. No. 04; QA276. 8, B3.. 1974.

• Biegler, Lorenz T. Nonlinear programming: concepts, algorithms, and applications to chemical processes. Vol. 10. SIAM, 2010.

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Modeling and Parameter Estimation of Batch Solid-Liquid ...egon.cheme.cmu.edu/ewo/docs/Dow_EWO_F16_YajunWang.pdf · Modeling and Parameter Estimation of Batch Solid-Liquid Reactors