In Russian

Abstract

For the first time, it is demonstrated that the methanol diffusion in the H-ZSM-5/Al 2 O 3 catalyst pellet is anomalous and is described by the time-fractional diffusion equation. The regime of the methanol transport is sub-diffusive. The aim of the present work is a description of the experimental data of the methanol transport through the pellet of the zeolite-containing catalyst for olefins synthesis form the methanol based on the solutions of the diffusion equation of the second Fick’s law of diffusion and the time-fractional diffusion equation. In this work, the mesoporous catalyst based on zeolite H-ZSM-5 and alumina with zeolite/alumina ratio 3/1 by mass is used. The methanol transport has been studied using the developed method of mass transfer process investigation in the porous solid media in flow regime. The method is based on the porous sample saturation by a pulse of the adsorbate. The porous sample is installed to the diffusion cell. Adsorbate quantity evolution versus time is chromatographically analyzed. The porous sample is installed to the diffusion cell so that half of its surface is impermeable for adsorbate which allows applying the von Neumann boundary conditions to sole the diffusion equation. The investigation resulted in the obtaining the relative concentration decay versus time on the boundary of the catalyst pellet. The obtained experimental dependences are analyzed on the whole temporal scale using the analytic solution of the diffusion equation based on the second Fick’s law of diffusion. However, the correspondence between the theoretical solution and the experimental data is very poor. The asymptotic analysis of the experimental data in the long-time range linearized in the logarithmic coordinates according to the solution of the standard diffusion equation has demonstrated that the equation for the second Fick’s law of diffusion is inapplicable to a description of the obtained experimental data because the slope of the experimental data is far from the theoretical one which is equal to unity. On the other, an hand analysis of the experimental data in the long-time range linearized in the logarithmic coordinates according to the solution of the time-fractional diffusion equation revealed the high correlation between the theoretical solution and the experimental data. The calculated values of the fractional order and the fractional diffusion coefficient are independent on the experimental conditions. This means that these characteristics are individual for each pair of the porous media and diffusate and may be associated with the methanol adsorption on the active sites on the surface of the catalyst. The fractional order value is lower than unity, which reveals the presence of the sub-diffusive regime of transport, which is slower comparing to the standard diffusion. Based on the analysis of the methanol mass transfer in the pellet of the zeolite-containing catalyst, it is found that the solution of the time-fractional diffusion equation gives good fit to the experimental data comparing to the solution of the standard diffusion equation. The values of the diffusion coefficients and the fractional orders calculated on the long times are equal to the values estimated for the whole temporal range. It is found that the methanol transfer in the catalyst pellet occurs in the slow sub-diffusive regime. The experimental evidence of the presence of an anomalous diffusion is fundamental for the theoretical understanding the mass transfer process and modeling as well as for application during solving the engineering problems.