Automation of search for optimal values of the ethylene oligomerization process parameters

A mathematical description of the process of ethylene oligomerization on a NiO/B₂O₃-Al₂O₃ catalyst in a liquid heptane solvent is given. Problems of optimal process control are formulated. The temperature and time of the process are taken as control parameters. An algorithm is proposed for solving the problem of optimal control of the industrially significant catalytic process of ethylene oligomerization. The search for solutions to the formulated problems is carried out using a genetic algorithm with real coding. For each of the problems under consideration, a method is proposed for representing a mathematical analogue of a population on the basis of which a solution is searched. A step-by-step algorithm for determining the optimal parameters for the ethylene oligomerization process is presented. A special feature of the algorithm is the simultaneous search for the values of a continuous control parameter (temperature) and a discrete control parameter (process time). A program (application) has been developed to determine the optimal values of process parameters. The application allows the user to select an optimal control problem, set the values of the genetic algorithm parameters to find a solution, and visualize the results obtained. A computational experiment was carried out for the process of ethylene oligomerization. The optimal duration of the process under isothermal conditions was calculated, at which the highest concentration of C₄ hydrocarbons is achieved. The optimal temperature conditions and duration of the ethylene oligomerization process were determined to ensure the maximum concentration of C₆ hydrocarbons. The conducted numerical experiments demonstrated lower resource consumption compared to the methods of uniform search and variations in the control space. The proposed algorithm can be used to study the patterns of catalytic processes without resorting to laboratory experiments associated with additional material and time costs.

1. Dzhambekov A.M., Shcherbatov I.A. Optimal control of the process of catalytic reforming of petrol fractions. Transactions of the TSTU, 2017, vol. 23, no. 4. pp. 557–571. (in Russian). https://doi.org/10.17277/vestnik.2017.04.pp.557-571

2. Antipina E.V., Mustafina S.A., Antipin A.F. Theoretical optimization of regular parameters of a catalytic reaction with a variable reaction volume. Herald of Tver State University. Series: Chemistry, 2022, no. 2(48), pp. 67–78. (in Russian). https://doi.org/10.26456/vtchem2022.2.8

3. Charitopoulos V.M., Papageorgiou L.G., Dua V. Multi-parametric mixed integer linear programming under global uncertainty. Computers & Chemical Engineering, 2018, vol. 116, pp. 279–295. https://doi.org/10.1016/j.compchemeng.2018.04.015

4. Charitopoulos V.M., Papageorgiou L.G., Dua V. Closed-loop integration of planning, scheduling and multi-parametric nonlinear control. Computers & Chemical Engineering, 2019, vol. 122, pp. 172–192. https://doi.org/10.1016/j.compchemeng.2018.06.021

5. Ziyatdinov N.N., Emel’yanov I.I., Tuen L.Q. Method for the synthesis of optimum multistage heat exchange network. Theoretical Foundations of Chemical Engineering, 2018, vol. 52, no. 6, pp. 943–955. https://doi.org/10.1134/s0040579518060167

6. Fu K., Zou Y., Li S. Iterative unit-based Adaptive dynamic programming with application to fluid catalytic cracker unit. Proc. of the 2019 Chinese Automation Congress (CAC), 2019, pp. 5010– 5015. https://doi.org/10.1109/CAC48633.2019.8996670

7. Cao X., Jia S., Luo Y., Yuan X., Qi Z., Yu K.-T. Multi-objective optimization method for enhancing chemical reaction process. Chemical Engineering Science, 2019, vol. 195, pp. 494–506. https://doi.org/10.1016/j.ces.2018.09.048

8. Kozuch D.J., Stillinger F.H., Debenedetti P.G. Genetic algorithm approach for the optimization of protein antifreeze activity using molecular simulations. Journal of Chemical Theory and Computation, 2020, vol. 16, no. 12, pp. 7866–7873. https://doi.org/10.1021/acs.jctc.0c00773

9. Antipina E.V., Mustafina S.A., Antipin A.F. Algorithm of solving a multiobjective optimization problem on the basis of a kinetic chemical reaction model. Optoelectronics, Instrumentation and Data Processing, 2021, vol. 57, no. 6, pp. 668–674. https://doi.org/10.3103/S8756699021060029

10. Trokoz D.A. Parametric optimization method for wide neural networks using genetic algorithms. Izvestia of Samara Scientific Center of the Russian Academy of Sciences, 2021, vol. 23, no. 2, pp. 51–56. (in Russian). https://doi.org/10.37313/1990-5378-2021-23-2-51-56

11. Stastny J., Skorpil V., Balogh Z., Klein R. Job shop scheduling problem optimization by means of graph-based algorithm. Applied Sciences, 2021, vol. 11, no. 4, pp. 1921. https://doi.org/10.3390/app11041921

12. Gulbaz R., Siddiqui A.B., Anjum N., Alotaibi A.A., Althobaiti T., Ramzan N. Balancer genetic algorithm–a novel task scheduling optimization approach in cloud computing. Applied Sciences, 2021, vol. 11, no. 14, pp. 6244. https://doi.org/10.3390/app11146244

13. Jalali Z., Noorzai E., Heidari S. Design and optimization of form and facade of an office building using the genetic algorithm. Science and Technology for the Built Environment, 2020, vol. 26, no. 2, pp. 128–140. https://doi.org/10.1080/23744731.2019.1624095

14. Xie L., Chen Y., Chang R. Scheduling optimization of prefabricated construction projects by genetic algorithm. Applied Sciences, 2021, vol. 11, no. 12, pp. 5531. https://doi.org/10.3390/app11125531

15. Migov D.A., Volzhankina K.A., Rodionov A.S. Genetic algorithms for drain placement in wireless sensor networks optimal by the reliability criterion. Optoelectronics, Instrumentation and Data Processing, 2021, vol. 57, no. 3, pp. 240–249. https://doi.org/10.3103/S8756699021030110

16. Volkov A.A., Buluchevskiy E.A., Lavrenov A.V. Kinetics of ethylene oligomerization on NiO/B2O3-Al2O3 in liquid phase. Journal of Siberian Federal University. Chemistry, 2013, vol. 6, no. 4, pp. 352–360. (in Russian)