Advective-diffusive gaseous transport in porous media: the molecular diffusion regime

Abstract

Traditional mathematical models for advective-diffusive transport in porous media fail to represent important physical processes when fluid density depends on composition. Such is the case for gas mixtures comprised of species with differing molecular masses, such as found in the vadose zone near chlorinated hydrocarbon sources. To address problems of this nature, a more general advection-diffusion (A-D) model is presented, which is valid for porous media with permeabilities exceeding 10-10 cm2 (where Klinkenberg and Knudsen effects are negligible). The new mathematical model is derived by thermodynamic means, based on identifying the meaning of Darcy's advective reference velocity in terms of a weighted average of species drift velocities~ The resulting model has no additional parameters, and introduces no additional complexity or nonlinearity when compared to the traditional A-D model most commonly used in hydrology and environmental science. Because the form of traditional A-D models is retained, the new formulations fit readily into existing numerical simulators for the solution of subsurface transport problems. The new model is equivalent to the Dusty-Gas Model of Mason et al. (1967) for cases where the molecular diffusion regime prevails and pressure, temperature, and forced diffusion are negligible. Further support of the model is provided by hydrodynamic analysis, accounting for the diffusive-slip flux identified by Kramers and Kistemaker (1943). The new model is analytically compared to two existing A-D models, one from the hydrology literature, where Darcy's law is assumed to yield a mass-average velocity, and one from the chemical engineering literature, where Darcy's law is assumed to yield a mole-average velocity. Significant differences are shown to exist between the three transport models. The new model is shown to match closely with the experimental data of Evans et al. (1961a), while the existing A-D models are shown to fail in this regard.