Fractal model used for heterogeneously isothermal nth-order reaction

Abstract

This paper uses the fractal diffusion–reaction model (OP diffusion–reaction model) to describe the diffusion and reaction of gases in a mesoporous catalyst. We obtain an approximate solution of the OP diffusion–reaction model by using first approximation. Based on the first approximate and multi-step first approximation, we propose two formulas for the effectiveness factor expressed in general form and use them for an nth-order reaction. The catalytic kinetics could be qualitatively and quantitatively analyzed in detail with these two formulas. We determine the pre-exponential factor of the effective diffusivity and the pre-exponential factor of the fractal rate coefficient. We compare experimental data for the kinetics of an ethylene hydrogenation reaction on Ni/Al2O3 with values calculated from the OP diffusion–reaction model and Fick's diffusion–reaction model. The results show quantitative differences between the effectiveness factors obtained with these two models. There are no qualitative differences between them, but the OP diffusion–reaction model gives a more realistic description of heterogeneous catalysis in a porous catalyst because its calculated results fit better to the experimental data. The effective diffusivity is related to the temperature, molecular weight of gases and structure of the porous material, and it describes diffusional behavior in real catalytic porous particles for each particle size more effectively because it does not depend on the tortuosity factor.