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

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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.

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Abbreviations

DMC:

Dimethyl carbonate

DM:

Decision maker

t :

Time (min)

νij :

Stoichiometric coefficients

J :

Number of steps

y i :

Concentration of a reactant, mol/l

I :

Number of compounds

wj :

Rate of j-th step (1/min)

k j, k −j :

Rate constants of steps (reduced)

E j :

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)

α ij :

Negative elements of the matrix (νij)

β ij :

Positive elements (νij)

k 0 j :

Pre-exponential factors, 1/min

Z :

Optimization function

y ct :

Amount of the catalyst, mmol

y :

Concentration vector of a compound, mol/l

y 0 :

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]

y prod :

Reaction product concentrations (mol/l)

y source :

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

References

  1. P.T. Anastas, J.C. Warner, Green chemistry: theory and practice (Oxford University Press, New York, 1998)

    Google Scholar 

  2. F. Arico, P. Tundo, Russ. Chem. Rev. 79(6), 479 (2010)

    Article  CAS  Google Scholar 

  3. A.G. Shaikh, Chem. Rev. 96, 951 (1996)

    Article  CAS  PubMed  Google Scholar 

  4. R.I. Khusnutdinov, N.A. Shchadneva, Y.Y. Mayakova, Russ. J. Org. Chem. 50(6), 790–795 (2014)

    Article  CAS  Google Scholar 

  5. K.F. Koledina, S.N. Koledin, N.A. Schadneva, Y.Y. Mayakova, I.M. Gubaydullin, Reac Kinet Mech Cat 121(2), 425–428 (2017)

    Article  CAS  Google Scholar 

  6. K.F. Koledina, S.N. Koledin, N.A. Shchadneva, I.M. Gubaidullin, Russ. J. Phys. Chem. A 91(3), 444–449 (2017)

    Article  CAS  Google Scholar 

  7. R.Z. Zainullin, K.F. Koledina, A.F. Akhmetov, I.M. Gubaidullin, Kinet. Catal. 58(3), 279–289 (2017)

    Article  CAS  Google Scholar 

  8. E. Hairer, G. Wanner, Solving ordinary differential equations II, 2nd edn. (Springer, New York, 1996)

    Book  Google Scholar 

  9. L.F. Shampine, R.M. Corless, J Comp Appl Math 125(1–2), 31–40 (2000)

    Article  Google Scholar 

  10. M.M. Canedo, J.L. González-Hernández, J. Math. Chem. 49(1), 163–184 (2011)

    Article  CAS  Google Scholar 

  11. K.F. Koledina, I.M. Gubaidullin, Rus J Phys Chem A 90(5), 914–921 (2016)

    Article  CAS  Google Scholar 

  12. I.M. Gubaydullin, K.F. Koledina, L.V. Sayfullina, Eng J 18(1), 13 (2014)

    Article  Google Scholar 

  13. L.F. Nurislamova, I.M. Gubaydullin, K.F. Koledina, R.R. Safin, React. Kinet. Mech. Catal. 117(1), 1–14 (2016)

    Article  CAS  Google Scholar 

  14. A.P. Karpenko, Modern algorithms of search optimization. Algorithms inspired by nature: a tutorial (MSTU Publishing House. N.E. Bauman, Moscow, 2014)

    Google Scholar 

  15. M. Abramson, A. Charles, J.E. Dennis, J. Digabel, S. Digabel, SIAM J. Optim. 20(2), 948–966 (2009)

    Article  Google Scholar 

  16. D. Kalyanmoy, A. Pratap, S. Agarwal, T. Meyarivan, IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  17. P. Alonso, F. Argüeso, R. Cortina, J. Ranilla, A.M. Vidal, J. Math. Chem. 51(4), 1153–1163 (2013)

    Article  CAS  Google Scholar 

  18. P. Alonso, F. Argüeso, R. Cortina, J. Ranilla, A.M. Vidal, J. Math. Chem. 50(2), 410–420 (2012)

    Article  CAS  Google Scholar 

Download references

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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Authors and Affiliations

  1. Institute of Petrochemistry and Catalysis of RAS, 141 Oktyabrya Prospect, Ufa, Bashkortostan Republic, Russian Federation, 450075

    K. F. Koledina, I. M. Gubaydullin & M. K. Vovdenko

  2. Ufa State Petroleum Technological University, Cosmonavtov str. 1, Ufa, Bashkortostan Republic, Russian Federation, 450062

    K. F. Koledina, S. N. Koledin & I. M. Gubaydullin

  3. Bauman Moscow State Technical University, 2nd Baumanskaya str. 5, Moscow, Russian Federation, 105005

    A. P. Karpenko

Authors
  1. K. F. Koledina
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  2. S. N. Koledin
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  3. A. P. Karpenko
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  4. I. M. Gubaydullin
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  5. M. K. Vovdenko
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Correspondence to K. F. Koledina.

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Koledina, K.F., Koledin, S.N., Karpenko, A.P. et al. Multi-objective optimization of chemical reaction conditions based on a kinetic model. J Math Chem 57, 484–493 (2019). https://doi.org/10.1007/s10910-018-0960-z

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  • DOI: https://doi.org/10.1007/s10910-018-0960-z

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