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Model reduction and optimization of reactive batch distillation based on the adaptive neuro-fuzzy inference system and differential evolution

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Abstract

This paper considers the application of the adaptive neuro-fuzzy inference system (ANFIS) instead of the highly nonlinear model of a reactive batch distillation column for optimization. The architecture has been developed for fuzzy modeling that learns information from a data set, in order to compute the membership function and rule base in accordance with the given input–output data. In this work, the differential evolution algorithm has been employed for optimization of operation policy of reactive batch distillation for producing ethyl acetate. In optimization, minimal batch time and high purity of product are considered, and reflux ratio and final batch time are taken as decision parameters. The results show that the reduced model (ANFIS) is able to properly create a robust model of the reactive batch distillation, and CPU use is reduced to 1/18,000 of that of a real mathematical model. The highest yield and mole fraction of ethyl acetate were achieved through the use of the obtained optimization policy.

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Abbreviations

AcOH:

Acetic acid (–)

EtOH:

Ethanol (–)

EtAc:

Ethyl acetate (–)

d :

Column diameter (cm)

WHS:

Weir height (cm)

WLS:

Weir length (cm)

Q R :

Reboiler heat input (kJ/h)

M :

Molar liquid holdup on tray (kmol)

MV:

Volumetric liquid holdup on tray (cm3)

V :

Vapor flow rates (kmol/h)

MwAve :

Average molecular weight (kg/kmol)

DensityAve :

Average density (kg/m3)

D :

Distillate flow rates (kmol/h)

R ij :

Chemical reaction rates for jth component on ith tray (1/h)

NP:

Number of population (–)

pi :

Target vector (–)

pz :

Mutant vector (–)

pu :

Trail vector (–)

CR:

Crossover (–)

U:

Dimension space (decision variables) (–)

Rfmin :

Reflux minimum (–)

Rfmax :

Reflux maximum (–)

\( \bar{X}_{\text{EtAc}}^{{}} \) :

Average mole fraction of ethyl acetate at final batch time (–)

\( X_{\text{EtAc}}^{\min } \) :

Minimum mole fraction of ethyl acetate at final batch time (–)

MSE:

Mean squared error (–)

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Authors and Affiliations

  1. School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, 71345, Iran

    S. M. Khazraee, A. H. Jahanmiri & S. A. Ghorayshi

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  1. S. M. Khazraee
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  2. A. H. Jahanmiri
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  3. S. A. Ghorayshi
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Correspondence to A. H. Jahanmiri.

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Khazraee, S.M., Jahanmiri, A.H. & Ghorayshi, S.A. Model reduction and optimization of reactive batch distillation based on the adaptive neuro-fuzzy inference system and differential evolution. Neural Comput & Applic 20, 239–248 (2011). https://doi.org/10.1007/s00521-010-0364-x

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