A multi-region model for reaction–diffusion process within a porous catalyst pellet

• A meso-scale multi-region model is developed for a single porous catalyst pellet.
• The numerical methods are proposed for multi-scale reaction–diffusion problems.
• The model is validated against the alkylation of benzene over H-ZSM-5 crystal particles.
• The effects of volume fraction, size, and spatial distribution of H-ZSM-5 crystal particles are studied.

In this paper, a multi-region model based on the unified Maxwell–Stefan diffusion theory is developed to investigate the reaction–diffusion processes within catalyst pellets formed by micro-pore particles and meso/macro-pore support. The corresponding partial differential equation (PDE) systems, describing chemical reactions, bulk diffusion, Knudsen diffusion, surface diffusion and viscous flow, are converted to ODE systems based on finite volume method (FVM). The resulting multi-scale ODE systems are solved by reduced storage matrix method, where a quasi-stationary state assumption is adopted in the numerical solution to solve multi-scale problem in which the diffusivities of micro-pores and meso/macro-pores are significantly different. The alkylation of benzene over a single multi-porous pellet formed with H-ZSM-5 crystal particles was simulated as an example. The effects of volume fraction, size and spatial distribution of H-ZSM-5 crystal particles on the effectiveness factor of the catalyst pellet were then investigated and discussed. It is shown that the multi-region model is a potential bottom to up tool for reaction–diffusion processes in catalyst pellet exhibiting multi-scale time characteristic.