Application of Hyperbolization in a Diffusion Model of a Heterogeneous Process on the Spherical Catalyst Grain

The article investigates an application of hyperbolization for parabolic equations to material and thermal balance equations in a mathematical model of oxidative regeneration of the spherical catalyst grain with detailed kinetics. The initial spherical grain model is constructed using a diffusion approach. It is a nonlinear system of differential equations in a spherical coordinate system. The material balance of the gas phase is described by diffusion-convection-reaction equations with source terms for the concentrations of the substances of the gas phase; the balance of the solid phase is represented by nonlinear ordinary differential equations. The thermal balance equation of the catalyst grain is a thermal conduction equation with an inhomogeneous term corresponding to grain heating during a chemical reaction. The slow processes of heat and mass transfer in combination with the fast chemical reactions cause significant difficulties in the development of a computational algorithm. Hyperbolization of the parabolic equations is used to avoid the computational complexity. It consists in the introduction of a second time derivative multiplied by a small parameter to extend the stability area of the computational algorithm. An explicit three-layer difference scheme is constructed for the modified model. It is implemented in the form of a software module. The convergence of the thus developed algorithm is analyzed. A comparative analysis of the new computational algorithm with a previously constructed one is carried out. The new algorithm has an advantage while maintaining the order of accuracy. The new algorithm resulted in profiles of distributions of the temperature and substances along the radius of the catalyst grain.