Coarse-graining of diffusion–reaction models with catalyst archipelagos

Abstract

We consider the problem of diffusion and reaction in a supported catalyst in which the active sites are located on the crystallites that are distributed in the form of islands (archipelagos) on the pore walls. We determine the coarse-grained mesoscale kinetic constants in terms of the true crystallite scale constants, catalyst activity distribution, pore size and species molecular diffusivities. We analyze the effect of different catalyst archipelagos on the mesoscale rate constants. We also develop a two-mode coarse grained model to describe diffusion and reaction accurately in such systems and develop criteria under which the pore and crystallite scale gradients can be neglected. A significant result is that for moderately fast reactions, the kinetics is disguised in the coarse-grained model if a single pore space averaged concentration mode is used. However, the true kinetics may be represented accurately with the use of two concentration modes, the second mode being the activity weighted concentration.