The flow of two or more gases through a porous medium is usually modelled using an Advective-Diffusive Model (ADM) which involves the linear addition of the diffusive flux, calculated using Fick’s Law, and the advective flux, calculated using Darcy’s Law. A more accurate approach is to use a Dusty-Gas Model (DGM) that includes advection, normal diffusion and Knudsen diffusion (where molecule-wall collisions dominate), together with couplings between these various transport mechanisms. It is so called because the grains of the porous medium are thought of as large dust molecules that are fixed in space and treated as a component of the gas mixture.
The DGM has been implemented in QPAC by Fintan O’Brien during his professional placement year at Quintessa, which formed part of his physics degree at the University of Bath under the supervision of Kate Thatcher. The implementation has been compared with equivalent results for the ADM and validated by comparison with the results of experiments carried out by Evans, Watson and Truitt (1962, 1963). In these experiments, a thin graphite septum separates two regions: on one side there is initially only helium; and on the other only argon. As shown in the following Figures, in contrast to the ADM, the DGM accurately represents the transport of helium and argon through porous graphite for the experimental conditions.
ADM mole flux data-model comparison for the general case of advection and diffusion
DGM mole flux data-model comparison for the general case of advection and diffusion
References
Evans R. B., Watson G. M. and Truitt J. (1962) Interdiffusion of Gases in a Low Permeability Graphite at Uniform Pressure. Journal of Applied Physics 33: 2682-2688.
Evans R. B., Watson G. M. and Truitt J. (1963) Interdiffusion of Gases in a Low Permeability Graphite. II. Influence of Pressure Gradients. Journal of Applied Physics 34: 2020-2026.