Modelling the complex problem of intracrystalline diffusion and first-order phenomena in microporous solid particles under constant-volume/variable-concentration conditions

Microporous solids with pore diameters comparable to effective molecular cross-sections are mainly used as both stereo-selective absorbents and shape-selective catalysts. Often complex phenomena govern the overall rate of processes of both physical adsorption and catalytic reaction. Transport and reaction rates are usually determined independently of each other. In contrast to this procedure, this paper describes a way to model such phenomena comprising internal diffusion in microporous particles coupled with any first-order rate process inherent both in the physical system, i.e. sorption system with nonlinear sorption isotherm and any particle size distribution, and the experimental apparatus characteristics. Modelling and complete solution of the models for both constant and variable boundary conditions were carried out by means of non-linear Volterra integral equations. It becomes possible to determine both the diffusion coefficients and rate constants of constituents of a complex process using only one experimental arrangement. The approach is incorporated into the software ZEUS (zeolite uptake simulator).