Mathematical Modeling of Unsteady Combustion of Coke Sedimentations in a Catalyst Layer with Spherical Grains

• Published in: Computational mathematics and mathematical physics Vol. 65; no. 6; pp. 1441 - 1452
• Main Author: Yazovtseva, O. S.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.06.2025; Springer Nature B.V
• Subjects: Algorithms; Boundary conditions; Burnout; Catalysts; Chemical reactions; Coke; Combustion; Computational Mathematics and Numerical Analysis; Differential equations; Diffusion; Finite volume method; Forced convection; Heat balance; Mass transfer; Material balance; Mathematical models; Mathematical Physics; Mathematics; Mathematics and Statistics; Ordinary differential equations; Runge-Kutta method; Solid phases; Thermodynamics; Transport equations; Vapor phases; mathematical modeling; numerical methods; hyperbolization; chemical kinetics; oxidative regeneration
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542525700514

A mathematical model of coke deposit burning out from a layer of aluminosilicate cracking catalyst with spherical grains taking into account heterogeneous detailed chemical reactions is developed. The model is a system of equations of mathematical physics with initial boundary conditions. The material balance of the grain is described by nonstationary diffusion–convection–reaction equations subject to boundary conditions of mass transfer for substances of the gas phase of the reaction and ordinary differential equations to take into account the dynamics of mass fractions of the solid phase of the reaction. The heat balance of the catalyst layer corresponds to the nonstationary heat equation with a source term. To describe the gas motion in the catalyst layer, the transport equations are used taking into account the velocity of the reaction mixture and its mass transfer with the catalyst layer. An explicit-implicit computational algorithm is developed for the constructed mathematical model. It is based on splitting by physical processes. The concentration dynamics is calculated using the three-stage fifth-order Runge–Kutta method. The diffusion–convection–reaction equations containing the second spatial derivative are hyperbolized in order to increase the calculation time step. The forced convection is calculated conservatively. The resulting difference scheme for the material balance equations of the catalyst grain is based on the finite volume method and is three-layered in time. The transport equations for describing the gas motion in the catalyst layer and the boundary conditions for the grain are approximated implicitly to reduce the effect of sharp fluctuations in temperature and substance concentrations on the stability of the algorithm as a whole. Comparison of the calculation results with experimental data for the material balance and theoretical estimates for temperature revealed the validity of the mathematical model and computational algorithm.