Upscaling momentum and mass transport under Knudsen and binary diffusion gas slip conditions

Abstract:

Modeling of gas phase flow in porous media is relevant as it is present in a wide variety of applications ranging from nanofluidic systems to subsurface contaminant transport. In this work, we derive a macroscopic model to study slightly compressible gas flow in porous media for conditions in which the tangential fluid velocity undergoes a slip at the solid interface due to Knudsen effects and to mass diffusion in binary conditions. To this end, we use the method of volume averaging to derive the governing equations at the Darcy scale for both mass and momentum transport. The momentum transport model consists on a modification to Darcy’s law due to mass dispersion and to total density gradients. For mass transport, the resulting model is the conventional convection-dispersion equation with two correction terms, one affecting convective transport and the second one affecting mass dispersion due to gas compressibility. The macroscopic model reduces to the one reported by Altevogt et al. (2003) for the case in which gas slip is only due to a concentration gradient and to the one by Lasseux et al. (2014) under Knudsen slip conditions. The model is written in terms of effective-medium coefficients that can be predicted from solving the associated closure problems in representative unit cells. For conditions in which the Péclet number is much greater than one and when the Knudsen number is not exceedingly small compared to the unity, our computations show that the predictions of the longitudinal dispersion may reach an error as high as 60% compared to the predictions obtained by ignoring gas slip.

Altevogt A.S., Rolston D.E., Whitaker S. New equations for binary gas transport in porous media, Part 1: equation development. Advances in Water Resources, Vol. 26, 695-715, 2003.

Lasseux D., Valdés-Parada F.J., Ochoa-Tapia J.A., Goyeau B. A macroscopic model for slightly compressible gas slip-flow in homogeneous porous media. Physics of Fluids, Vol. 26, 053102, 2014.