Numerical solution of hyperbolic models of transport in bidisperse solids

Abstract

This article considers the numerical solution of generalized transport models for adsorption that include the presence of finite local relaxation times. Such models arise in adsorption problems where the small diffusivity in micropores can lead to local nonequilibrium even at the macroscopic process time scale. We consider the important case of a bidisperse-structured adsorbent, the transport in which is a problem of long-standing interest to chemical engineers. In the formulation considered, the microparticle model involves a non-linear hyperbolic differential equation with source terms, and in the macroparticle model the differential equation involves a singularly perturbed parabolic diffusion problem. There are some difficulties in solving these equations due to the hyperbolic nature of the microparticle transport, conventionally assumed to obey the Fickian model leading to a parabolic diffusion equation. In this paper, an efficient numerical technique is presented to simulate these processes. A combination of the upwind method and fitted mesh collocation method is applied to solve the problem. Numerical solutions were found to match the analytical solution of the traditional model when the adsorption isotherm is linear, for macropore diffusion control or micropore diffusion control. Simulations of the adsorption and desorption dynamics are also presented for a Langmuir isotherm. The numerical scheme offers a more generalized alternative that can be used for both the model forms, with and without consideration of finite local relaxation times.