Vol. 24, No. 1 (2025), Sim24391 https://doi.org/10.24275/rmiq/Sim24391

Application of a genetic algorithm for optimization of periodic polymerization processes

 

Authors

E.N. Miftakhov, S.I. Mustafina, A.A. Akimov

Abstract

A numerical algorithm for optimal composition search of the initial reaction mixture using heuristic optimization methods is developed and evaluated for its effectiveness in investigating polymer synthesis processes. The methodology, based on a kinetic approach grounded in the method of moments, presents all main stages of the research. A genetic algorithm is proposed for solving the optimization problem of the formed unified model description of the process, with its implementation steps contributing to finding the global optimum. The software implementation of this algorithm and the computational experiments conducted for the production process of 1,4-cis-polyisoprene in the presence of a catalytic system based on neodymium chloride solvates allowed the identification of the initial reaction mixture composition, which contributes to achieving a final conversion of 72% over 85 minutes for a polymer product with a weight-average molecular weight of 680·103 g/mol. The proposed algorithm successfully copes with multi-factor optimization tasks.

Keywords

genetic algorithm, optimization, polymerization, heuristic method.

References
  • Albani, V., De Cezaro, A., Zubelli, J. P. (2016). On the choice of the Tikhonov regularization parameter and the discretization level: a discrepancy-based strategy. Inverse Problems and Imaging 10(1), 1-25. https://doi.org/10.3934/ipi.2016.10.1
  • Almufti, S. M., Shaban, A. A., Ali, Z. A., Ali, R. I., Dela Fuente, J. A. (2023). Overview of Metaheuristic Algorithms. Polaris Global Journal of Scholarly Research and Trends 2, 10-32. https://doi.org/10.58429/pgjsrt.v2n2a144
  • Antipina, E. V., Miftakhov, E. N., Mustafina, S. A. (2020). Search for the optimal value of the initial concentration of diisobutylaluminum hydride for regulating the molecular weight of polyisoprene on a neodymium-containing catalytic system. Vestnik TvGU. Series “Chemistry” 3(41), 52–64. https://doi.org/10.26456/vtchem2020.3.6
  • Aris, R. (1989). Analysis of processes in chemical reactors. L.: Chemistry.
  • Berlin, A. A., Patlazhan, S. A., Kravchenko, I. V., Prochukhan, K. Yu., Prochukhan, Yu. A. (2019).  Intensification of Fast Chemical Processes at Interfaces of Two-Component Liquid Media in Tubular Turbulent Reactors. Russian Journal of Physical Chemistry B 13(1), 19-26. https://doi.org/10.1134/S0207401X19010059
  • Gao, J., Penlidis, A. (2002). Mathematical modeling and computer simulator/database for emulsion polymerizations. Progress in polymer science 27(3), 403-535.  https://doi.org/10.1016/S0079-6700(01)00044-2
  • Greene, J. P. (2001). Microstructures of Polymers, Automotive Plastics and Composites (pp. 27-37). William Andrew Publishing.
  • Guzman-Lucero, D., Palomeque-Santiago, J.F., Vega-Paz, A., Guzman-Pantoja, J., Likhanova, N.V., Guevara-Rodríguez F.J. (2024). Dosage of monomers in a polymerization reaction. Revista Mexicana de Ingeniería Química 23(3). https://doi.org/10.24275/rmiq/Poly24316
  • Hamielec, A. E., Macgregor, J. F., Penlidis, A. (1987). Multicomponent free‐radical polymerization in batch, semi‐ batch and continuous reactors. Macromolecular and Materials Chemistry 10(1), 521-570. https://doi.org/10.1002/masy.19870100126
  • Holland, J. H. (1992). Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. University of Michigan Press.
  • Kasat, R. B., Ray, A. K., Gupta S. K. (2003). Applications of Genetic Algorithm in Polymer Science and Engineering. Materials and Manufacturing Processes 18(3), 523–532. https://doi.org/10.1081/AMP-120022026
  • Katoch, S., Chauhan, S. S., Kumar, V. (2021) A review on genetic algorithm: past, present, and future. Multimedia Tools and Applications 80(5), 8091-8126. https://doi.org/10.1007/s11042-020-10139-6
  • Kim, C., Batra, R., Chen, L., Tran, H., Ramprasad, R. (2021). Polymer design using genetic algorithm and machine learning. Computational Materials Science 186.  https://doi.org/10.1016/j.commatsci.2020.110067
  • Luciani, C. V, Choi, K. Y. (2021). Mathematical modeling of free radical solution terpolymerization reactions in a batch and continuous flow stirred tank reactors. Macromolecular Theory and Simulations 30. https://doi.org/10.1002/mats.202000094
  • Miftakhov, E. N., Mustafina, S. A., Nasyrov, I. Sh., Daminov, A. Kh. (2021). Kinetic heterogeneity of polymer products obtained in the presence of microheterogenic catalytic systems based on gel chromatograms. Periódico Tchê Química 18(38), 27-37. http://dx.doi.org/10.52571/PTQ.v18.n38.2021.03_MIFTAKHOV_pgs_27_37.pdf
  • Miftakhov, E. N., Mustafina, S. A., Nasyrov, I. Sh., Faizova, V. Yu. (2022). Kinetic heterogeneity of the catalytic system based on gadolinium chloride solvate in 1,4-cis-polyisoprene production. Russian Journal of Applied Chemistry 95(3), 423-429. https://doi.org/10.1134/S1070427222030120
  • Miftakhov, E. N., Mustafina, S. I., Akimov, A. A., Mustafina, S.A. (2024). Simulation approach to study kinetic heterogeneity of gadolinium catalytic system in the 1,4-cis-polyisoprene production. e-Polymers 24(1). https://doi.org/10.1515/epoly-2023-0131
  • Miftakhov, E. N., Mustafina, S. I., Morozkin, N. D., Nasyrov I. Sh., Mustafina, S. A. (2023). Evaluating the efficiency of the tube turbulent apparatus influence on kinetics of polymer production processes. Engineering Technologies and Systems 33(3), 388–402. https://doi.org/10.15507/2658-4123.033.202303.388-402
  • Miftakhov, E. N., Nasyrov, I. Sh., Mustafina, S. A., Zakharov, V. P. (2021).  Study of kinetics of isoprene polymerization in the presence of neodymium-containing catalytic systems modified in turbulent flows. Russian Journal of Applied Chemistry 94(1), 77-83. https://doi.org/10.1134/S1070427221010110
  • Nasyrov, I. Sh., Zhavoronkov, D. A., Shurupov, O. K., Zakharova, E. M., Vasiliev, V. A., Zakharov, V. P. (2021). Characteristics of Stereoregular cis-1,4-Polyisoprene Obtained under the Conditions of a Large-Tonnage Production Process on Titanium and Lanthanide Catalysts Modified in Turbulent Flows. Russian Journal of Applied Chemistry 94(6), 741-747. https://doi.org/10.1134/S1070427221060070
  • Panteleev, A. V., Skavinskaya, D. V., Aleshina, E. A. (2024). Metaheuristic algorithms for searching for optimal program control. Moscow: Infra-M.
  • Pereira, R.V., Giudici, R. (2023). Mathematical modeling of emulsion copolymerization regarding particle size distribution and average molecular weights. Chemical Engineering Science 265. https://doi.org/10.1016/j.ces.2022.118234
  • Piña-Victoria, J.C., Barrales-Cortés, C.A., Tamayo-Galván, V.E., Viveros-García, T. (2024). Isomerization of citronellal to isopulegol. Activity and diastereoselectivity on sulfated and phosphated zirconia. Revista Mexicana de Ingeniería Química 23(3). https://doi.org/10.24275/rmiq/Cat24272
  • Rawlings, J. B., Ekerdt, J. G. (2002). Chemical Reactor Analysis and Design Fundamentals. Madison: Nob Hill Publishing.
  • Simon, D. (2013). Evolutionary Optimization Algorithms. Wiley, John Wiley & Sons Limited.
  • Tanaka, R., Yuuya, K., Sato, H., Eberhardt, P., Nakayama, Y., Shiono, T. (2016). Synthesis of stereodiblock polyisoprene consisting of cis-1,4 and trans-1,4 sequences by using a neodymium catalyst: change of the stereospecificity triggered by an aluminum compound. Polymer Chemistry 7(6), 1239–1243. doi: https://doi.org/10.1039/C5PY01872B
  • Tikhonov, A. N., Arsenin, V. Ya. (1986). Methods for solving ill-posed problems. M.: Science.
  • Usmanov, T. S., Yagola, A. G., Usmanov, S. M., Monakov, Yu. B. (2005). Determination of catalyst active sites distributions in ionic polymerization. Inverse Problems in Science and Engineering 13(2), 101-107. https://doi.org/10.1080/10682760410001697822
  • Yigit, Y., Kilislioglu, A., Karakus, S., Baydogan, N. (2019). Determination of the intrinsic viscosity and molecular weight of Poly (methyl methacrylate) blends. Journal of Investigations on Engineering & Technology 2(2), 34-39.
  • Zakharov, V. P., Mingaleev, V. Z., Berlin, A. A., Nasyrov, I. Sh., Zhavoronkov, D. A., Zakharova, E. M. (2015). Kinetic inhomogeneity of titanium- and neodymium-based catalysts for the production of cis-1,4-polyisoprene. Russian Journal of Physical Chemistry B, 9, 300–305. https://doi.org/10.1134/S199079311502013X
  • Zakharov, V. P., Mingaleev, V. Z., Zakharova, E. M., Nasyrov, I. Sh., Zhavoronkov, D. A. (2013). Improvement of the neodymium catalyst preparation step in isoprene rubber production. Russian Journal of Applied Chemistry 86(6), 909-913. https://doi.org/10.1134/S1070427213060219
  • Zamora Cisneros, D.U., Ruiz Martínez, R.S. (2023). Simulation investigation of oxydehydrogenation of ethane in an industrial-scale turbulent fluidized bed over MoVTeNbO catalyst. Revista Mexicana de Ingeniería Química 22(2). https://doi.org/10.24275/rmiq/Cat2312