Conceptual Approach in Multi-Objective Optimization of Packed Bed Membrane Reactor for Ethylene Epoxidation Using Real-coded Non-Dominating Sorting Genetic Algorithm NSGA-II

Matthew J. Palys; Stanislav Y. Ivanov; Ajay K. Ray

doi:10.1515/ijcre-2016-0041

Article

Conceptual Approach in Multi-Objective Optimization of Packed Bed Membrane Reactor for Ethylene Epoxidation Using Real-coded Non-Dominating Sorting Genetic Algorithm NSGA-II

Matthew J. Palys , Stanislav Y. Ivanov and Ajay K. Ray

Published/Copyright: June 14, 2016

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From the journal International Journal of Chemical Reactor Engineering Volume 15 Issue 1

Abstract

An isothermal plug flow reactor model with extended Fick diffusion model for transport through the porous membrane is utilized for simulation of ethylene oxide formation in a packed bed membrane reactor (PBMR). The model was verified and validated using published experimental data from an existing lab-scale unit. Sensitivity analysis was performed to determine robustness of the model. A conceptual approach on operation and design stage multi-objective optimization study is discussed. Real-coded NSGA-II is used and effect of its parameters on optimization of reactor performance is also studied. The results of three two-objective operation-stage (with 4 decision variables) and one two-objective design-stage (with 6 decision variables) optimization case studies are presented. Good convergence to a Pareto optimal solution is achieved for all cases. Significant improvement over current experimental operation is observed in terms of increase in conversion of ethylene, selectivity to ethylene oxide and ethylene oxide product flow rate.

Keywords: ethylene epoxidation; multi-objective optimization; membrane reactor; NSGA-II

Nomenclature

Fi: molar frow rate of species i, mmol/min
Ii: ith objective function
LR: membrane length, m
Nt,i: molar flux of species i through membrane, mol/(m2s)
Npop: size of population in NSGA-II
Ngen: number of generation in NSGA-II
PBMR: packed bed membrane reactor
PBMR-E: вЂ“ packed bed membrane reactor with ethylene fed into tube side
P: total pressure, Pa
pcross: probability of crossover
pmut: probability of mutation
Pi: partial pressure of species i, bar
Qfeed: volumetric feed rate into reactor, std.cm3/min
Rg: universal gas constant, J/(molв€™K)
ri: rate of reaction i, mol/(kgв€™s)
rw: inner radius of shell, m
SC2H4O: selectivity to etylene oxide, %
T: temperature, K
Qfeed: volumetric feed rate into reactor, std.cm3/min
XC2H4: conversion of ethylene, %
YC2H4O: yield of ethylene oxide, %
yi: molar fraction of species i
z: axial coordinate, m
Greek letters
α: distribution index for simulated mutation operation
σ: distribution index for the simulated crossover operation

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Appendix A

Mathematical model of PBMR

The mathematical model assumes plug flow in shell side. The flow through the membrane is equally divided along its length and transport of ethylene through membrane is convective only. Pressure drop in the tube or shell side is neglected. Molar species balance in the shell side:

dFs,C2H4dz=2πrsNt,C2H4+π(rw2−rs2)ρbed(−r1−r2)

dOs,O2dz=2πrsNt,O2+π(rw2−rs2)ρbed(−1/2r1−3r2)

dFs,N2dz=2πrsNt,N2

dFs,C2H4Odz=2πrsNt,C2H4O+π(rw2−rs2)ρbedr1

dFs,CO2dz=2πrsNt,CO2+π(rw2−rs2)ρbed(2r2)

dFs,H2Odz=2πrsNt,H2O+π(rw2−rs2)ρbed(2r2)

with Nt,i=Ft,i2πrtL

where r1 and r2 are reaction rates for eqs (1) and (2), respectively (Figure 1) given by:

r1=1.33⋅105exp(−60700RgT)PEPO0.58(1+6.50PE)2

r2=1.80⋅106exp(−73200RgT)PEPO0.30(1+4.33PE)2

XC2H4+XO2+XN2+XC2H4O+XCO2+XH2O=1.0

Appendix B

$Figure 11: Effect of Number of Generations Ngen${N_{gen}}$ on NSGA-II convergence.$

Figure 11:

Effect of Number of Generations Ngen on NSGA-II convergence.

$Figure 12: Effect of Crossover Probability pcross${p_{cross}}$ on NSGA-II convergence.$

Figure 12:

Effect of Crossover Probability pcross on NSGA-II convergence.

$Figure 13: Effect of Mutation Probability pmut${p_{mut}}$ on NSGA-II convergence.$

Figure 13:

Effect of Mutation Probability pmut on NSGA-II convergence.

Published Online: 2016-6-14

Published in Print: 2017-1-1

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Articles in the same Issue

https://doi.org/10.1515/ijcre-2016-0041

Keywords for this article

ethylene epoxidation; multi-objective optimization; membrane reactor; NSGA-II