Combining wall interactions, fluid momentum balances and the Maxwell-Stefan equations for gas transport in porous media: An alternative approach

Abstract

This paper presents a modelling framework for incorporating wall interactions into the Maxwell-Stefan equations for ideal gases in porous media. In contrast to already existing models in literature, such as the Dusty Gas, Binary Friction and Modified Binary Friction models, the framework makes use of N−1 (with N being the number of gas species) independent mass balances for the gas species in combination with a total fluid momentum balance. This approach has the advantage that already existing numerical schemes for fluid momentum balances, such as Darcy’s law or the Brinkman equations, can be used with only minor modifications. It also allows for separate initialisation of the velocity and pressure fields, something that is often beneficial when solving convection–diffusion equations numerically. The derived model is validated against both stationary and time-dependent experimental data from literature for binary Ar-He systems in porous media, using Knudsen diffusivities to define the wall friction terms.

Keywords

• Knudsen diffusion
• Maxwell-Stefan diffusion
• Porous media transport
• Darcy’s law
• Dusty gas