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Journal of Mathematical Chemistry

, Volume 57, Issue 2, pp 484–493 | Cite as

Multi-objective optimization of chemical reaction conditions based on a kinetic model

  • K. F. KoledinaEmail author
  • S. N. Koledin
  • A. P. Karpenko
  • I. M. Gubaydullin
  • M. K. Vovdenko
Original Paper
First Online:
  • 31 Downloads

Abstract

The main purpose of the study is to introduce the multi-objective optimization using Pareto approximations to problems of chemical kinetics. We report the setting up and solution of the multi-objective optimization problem for conditions of a chemical reaction on the basis of a kinetic model. The study addresses the reaction of alcohols with dimethyl carbonate catalyzed by cobalt or tungsten carbonyl. The objective functions for optimization of chemical reaction conditions based on a kinetic model are presented. The NSGA-II algorithm was applied to determine the Pareto set and front for the multi-objective optimization problem applied to the reaction of alcohols with dimethyl carbonate for two catalysts, which make it possible to find the compromise values of variable parameters providing extrema of the objective functions.

Keywords

Multi-objective optimization Reaction of dimethyl carbonate with alcohols catalyzed by metal complexes Kinetic model Economic criteria Variable parameters Pareto approximations NSGA-II algorithm Pareto front Pareto set 

List of symbols

DMC

Dimethyl carbonate

DM

Decision maker

t

Time (min)

νij

Stoichiometric coefficients

J

Number of steps

yi

Concentration of a reactant, mol/l

I

Number of compounds

wj

Rate of j-th step (1/min)

kj, k−j

Rate constants of steps (reduced)

Ej

Activation energy of reactions, kcal/mol

G

Universal gas constant, equal to 8.31 J/(mol K) or 0.002 kcal/(mol K)

T

Temperature (K)

αij

Negative elements of the matrix (νij)

βij

Positive elements (νij)

kj0

Pre-exponential factors, 1/min

Z

Optimization function

yct

Amount of the catalyst, mmol

y

Concentration vector of a compound, mol/l

y0

Vector of initial concentrations of compounds, mol/l

η

Weight vector

μ

Additional expenses

t*

Reaction time (min)

B

Productivity [g/(l day)]

N

Number of cycles per day [day−1]

\( \xi_{{X_{i} }} \)

Reactant conversion

\( M_{{X_{i} }} \)

Reactant molar mass [g/mol]

yprod

Reaction product concentrations (mol/l)

ysource

Reactant concentrations (mol/l)

ψ

Variable costs (normalized)

A

Fixed costs (normalized)

Pr

Number of products

Sr

Number of reactants

P

Profitability (normalized)

X*

Desired solution of multi-objective optimization problem over variable parameters

F*

Desired solution of multi-objective optimization problem over objective functions

R|A|

|A|-Dimensional arithmetic space

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Notes

Acknowledgement

The reported study was funded by the President of the Russian Federation SP-669.2018.5 stipends and RFBR according to the research projects No. 18-07-00341, 18-37-00015.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • K. F. Koledina
    • 1
    • 2
    Email author
  • S. N. Koledin
    • 2
  • A. P. Karpenko
    • 3
  • I. M. Gubaydullin
    • 1
    • 2
  • M. K. Vovdenko
    • 1
  1. 1.Institute of Petrochemistry and Catalysis of RASUfaRussian Federation
  2. 2.Ufa State Petroleum Technological UniversityUfaRussian Federation
  3. 3.Bauman Moscow State Technical UniversityMoscowRussian Federation

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