DOI: https://doi.org/10.26089/NumMet.v26r209

Mathematical modeling of a non-stationary chemical process in a cylindrical catalyst grain

Authors

  • Olga S. Yazovtseva
  • Elizaveta E. Peskova

Keywords:

mathematical modeling
numerical methods
chemical kinetics
catalytic process

Abstract

The article is devoted to the development and analysis of a mathematical model of a nonstationary process in a cylindrical catalyst grain in two statements: a two-dimensional axisymmetric formulation and in three-dimensional cylindrical coordinates. Computational algorithms are based on the finite volume method with splitting by physical processes. Regularization by B. N. Chetverushkin was applied for two-dimensional and three-dimensional spatial problems to reduce the calculation time in the parabolic equations of the models. A significant acceleration in the operation of the algorithm for hyperbolic problems in comparison with parabolic ones has been revealed. The deviation of the solutions of perturbed hyperbolic systems from the solutions of the original parabolic ones is analyzed. The data on the oxidative regeneration of the cracking catalyst grain obtained using the developed model and the constructed algorithm are checked for adequacy by comparison with the data obtained from the stoichiometric reaction equation. A good consistency of calculated and theoretical data on oxygen consumption has been obtained.

Downloads

Published

2025-04-04

Issue

Vol. 26 (2025): Issue 2.

Section

Methods and algorithms of computational mathematics and their applications

Author Biographies

Olga S. Yazovtseva

National Research Mordovia State University,
• Senior Researcher

Elizaveta E. Peskova

National Research Mordovia State University,
• Senior Researcher

References

  1. I. P. Mukhlenov, Catalyst Technology(Khimiya, Leningrad, 1989) [in Russian].
  2. L. S. Eshchenko, Technology of Catalysts and Adsorbents(BSTU Press, Minsk, 2015) [in Russian].
  3. S. I. Reshetnikov, R. V. Petrov, S. V. Zazhigalov, and A. N. Zagoruiko, “Mathematical Modeling of Regeneration of Coked Cr-Mg Catalyst in Fixed Bed Reactors,” Chem. Eng. J. 380, Article Number 122374 (2020).
    doi 10.1016/j.cej.2019.122374
  4. M. G. Slin’ko, “Modeling of Chemical Reactors,” (Nauka, Novosibirsk, 1968) [in Russian].
  5. C. Kern and A. Jess, “Regeneration of Coked Catalysts -- Modelling and Verification of Coke Burn-off in Single Particles and Fixed Bed Reactors,” Chem. Eng. Sci. 60 (15), 4249-4264 (2005).
    doi 10.1016/j.ces.2005.01.024
  6. S. G. Zavarukhin and V. O. Rodina, “Effect of Intradiffusion Resistance on the Chemical Process in a Nonspherical Catalyst Pellet,” Kinet. Catal. 62 (4), 551-556 (2021).
    doi 10.1134/S0023158421040133
  7. O. A. Malinovskaya, V. S. Beskov, and M. G. Slin’ko, Modeling of Catalytic Processes on Porous Granules (Nauka, Novosibirsk, 1975) [in Russian].
  8. J. P. Wakefield, A. M. Lattanzi, M. B. Pecha, et al., “Fast Estimation of Reaction Rates in Spherical and Non-Spherical Porous Catalysts,” Chem. Eng. J. 454, Part 1, Article Number 139637 (2023).
    doi 10.1016/j.cej.2022.139637
  9. R. A. Buyanov, Coking of Catalysts(Nauka, Novosibirsk, 1983) [in Russian].
  10. V. P. Zhdanov, “Catalytic Conversion of Hydrocarbons and Formation of Carbon Nanofilaments in Porous Pellets,” Catal. Lett. 153 (4), 978-983 (2022).
    doi 10.1007/s10562-022-04039-7
  11. V. P. Zhdanov, “Kinetics and Percolation: Coke in Heterogeneous Catalysts,” J. Phys. A: Math. Theor. 55 (17), Article Number 174005 (2022).
    doi 10.1088/1751-8121/ac5d81
  12. B. N. Chetverushkin, O. G. Olkhovskaya, and V. A. Gasilov, “An Explicit Difference Scheme for a Nonlinear Heat Conduction Equation,” Mat. Model. 34 (12), 3-19 (2022) [Math. Models Comput. Simul. 15 (3), 529-538 (2023)].
    doi 10.1134/S2070048223030031
  13. E. E. Myshetskaya and V. F. Tishkin, “Estimates of the Hyperbolization Effect on the Heat Equation,” Zh. Vychisl. Mat. Mat. Fiz. 55 (8), 1299-1304 (2015) [Comput. Math. Math. Phys. 55 (8), 1270-1275 (2015)].
    doi 10.1134/S0965542515080138
  14. O. S. Yazovtseva, “Application of Hyperbolization in a Diffusion Model of a Heterogeneous Process on the Spherical Catalyst Grain,” Numer. Anal. Appl. 17 (4), 384-394 (2024).
    doi 10.1134/S1995423924040074
  15. O. Yazovtseva, I. Gubaydullin, E. Peskova, and A. Usmanova, “Parallel Algorithm for Computer Simulation of Burning Off Sulfurous Deposits from a Cylindrical Catalyst Grain,” in Communications in Computer and Information Science (Springer, Cham, 2024), Vol. 2241, pp. 211-223.
    doi 10.1007/978-3-031-73372-7_15
  16. O. S. Yazovtseva, I. M. Gubaydullin, E. E. Peskova, et al., “Computer Simulation of Coke Sediments Burning from the Whole Cylindrical Catalyst Grain,” Mathematics 11 (3), 669-1-669-15 (2023).
    doi 10.3390/math11030669
  17. R. M. Masagutov, B. F. Morozov, and B. I. Kutepov, Regeneration of Catalysts in Oil Processing and Petrochemistry(Khimia, Moscow, 1987) [in Russian].
  18. O. S. Yazovtseva, I. M. Gubaydullin, and I. G. Lapshin, “Averaging of the Model of a Chemical Process in a Catalyst Layer with a Spherical Grain,” Numerical Methods and Programming 25 (4), 413-426 (2024).
    doi 10.26089/NumMet.v25r431

License

Copyright (c) 2025 О. С. Язовцева, Е. Е. Пескова

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.