Flow and Diffusion of Gases in Porous Media

TLDR

The study develops a generalized gas‑transport framework for porous media based on the dusty‑gas model, treating the medium as a lattice of stationary dust molecules. The authors derive equations for multiple transport regimes—such as isobaric, isothermal diffusion, pressure‑driven diffusion, Poiseuille flow with Knudsen minimum, Kramers–Kistemaker effect, thermal transpiration, and pressure‑dependent thermal‑diffusion factor—by decomposing the problem into special cases of composition, pressure, and temperature gradients. The derived equations also apply to capillaries when geometric parameters are appropriately substituted.

Abstract

A generalized treatment of gas transport in porous media is presented as developed on the basis of the ``dusty-gas'' model, a model in which a porous medium is described as consisting of uniformly distributed, giant molecules (dust) held stationary in space. The problem is broken down into a series of special cases which involve the various combinations of gradients in composition, pressure, and temperature. Equations are given for the description of several well-known phenomena. These include isobaric, isothermal diffusion; diffusion under the influence of a pressure gradient; Poiseuille's flow equation, including the Knudsen minimum; the Kramers—Kistemaker effect; thermal transpiration; and the effect of pressure on the thermal-diffusion factor. The results are likewise applicable to capillaries by a suitable substitution for geometric parameters.