Mathematical modeling of an unsteady process in a catalyst layer with cylindrical grain shape

The article develops a mathematical model of an unsteady process in a catalyst layer with cylindrical grains. The model includes the diffusion-reaction-convection equations, an equation for calculating the rate of forced convection in grain pores, the heat conductivity equation for the catalyst skeleton, and the equations of heat and mass transfer of gas in the catalyst layer. A computational algorithm based on the splitting by physical processes is constructed for the developed model. The tasks of chemical kinetics are separated into an isolated integration stage and solved by the RADAU5 method with an adaptive step. The diffusion-reaction-convection equations were hyperbolized for reducing the estimated time of slow diffusion processes in grain pores. There is a three-layer scheme explicit in time for these equations. The heat conductivity equation is also explicitly integrated, and the integral source term in it is calculated using the trapezoid method. The transport equations along the length of the catalyst layer are integrated implicitly to expand the range of the algorithm’s stability in case of sharp temperature and concentration fluctuations in the layer. The boundary conditions for the catalyst grain are approximated by the spatial second order of accuracy. The constructed algorithm has been tested on a problem with a known analytical solution and compared with the solution of the Dirichlet problem in a mathematical package. The developed model and algorithm are used to study the modes of a real non-stationary process in the catalyst layer.