Macroscale modeling the methanol anomalous transport in the porous pellet using the time-fractional diffusion and fractional Brownian motion: A model comparison

Abstract

In this paper, we present physically-based macroscale models for the simulation of the mass transport process through the solid porous media. The models are based on the standard diffusion, time-fractional diffusion, and the fractional Brownian motion diffusion equations respectively. For the experimental verification of the developed models, the transport process in zeolite ZSM-5 pellet was studied using the methanol as a probing agent. Treating the experimental data by the second Fick's law of diffusion demonstrated no correspondence between the methanol transport and the Fickian concept. Therefore, the models, based on the time-fractional diffusion and the fractional Brownian motion, were adopted for a description of the experimental mass transfer kinetic. Both models provided an excellent correspondence between the experimental data and the relevant asymptotic solutions. For the time-fractional diffusion model, the asymptotic analysis of the experimental data revealed the equivalence of the anomalous diffusion exponents measured at the short and the long times. In contrast, the anomalous diffusion exponents estimated in the frame of the fractional Brownian motion model are different for the short and the long times. These findings allowed us to speculate on the applicability of the certain anomalous diffusion model in the experimental scenario studied. The obtained conclusions are additionally supported by an analysis of the mass transfer data presented in the literature.