Effectiveness factor for zeolite catalysed isomerization reactions

Abstract

We analyze the influence of diffusion on the reversible isomerization reaction A 1↔A 2, occurring within a zeolite catalyst, of spherical, cylindrical, and slab geometries. The intra-crystalline diffusion process is described by the Maxwell–Stefan (M–S) equations. Two different guest–host confinement scenarios are examined. For strongly confined guest molecules, the M–S diffusivities Đ i decrease with loading inside the zeolite. For weakly confined guest molecules, the M–S diffusivities Đ i are independent of the loading. The correlation effects, typical of zeolite diffusion, are described by introducing an exchange coefficient Đ 12 in the M–S diffusion formulation. For facile exchange, D ̵ 12→∞ , correlation effects are washed out. For finite exchange, a logarithmic interpolation formula is used to calculate Đ 12 from the two pure component M–S diffusivities Đ i . Analytic expressions for the effectiveness factor are derived for a variety of confinement and exchange scenarios. In the development of the analytic solution we assume Langmuirian behavior of the pure components and that the mixture sorption loadings can be calculated from the multicomponent Langmuir isotherm. By means of a variety of numerical examples, we stress the various characteristic features of intra-crystalline diffusion influences in zeolite catalysis. The effectiveness factor is found to a strong function of (a) molecular loadings and mixture composition, (b) ratio of diffusivities of the participating species, and (c) the reaction equilibrium constant. Only for the case of low loadings of weakly confined guest molecules and vanishing correlation effects, is the classical formula for the effectiveness factor valid.