Macroscopic Model for Passive Mass Dispersion in Porous Media Including Knudsen and Diffusive Slip Effects - Valdés-Parada, Francisco J.; Lasseux, Didier (Frontiers in Water, 2021)
In this work, a macroscopic model for incompressible and Newtonian gas flow coupled to Fickian transport of a passive solute in rigid and homogeneous porous media is derived, using the volume averaging method. At the pore-scale, both momentum and mass transport phenomena are coupled, not only by the convective mechanism in the mass transport equation, but also by the solid-fluid interfacial boundary condition. This boundary condition is a generalization of the Kramers-Kistemaker slip condition that includes the Knudsen effects. The resulting upscaled model, applicable in the bulk of the porous medium, corresponds to: 1) A Darcy-type model that involves an apparent permeability tensor, complemented by a dispersive term and 2) A macroscopic convection-dispersion equation for the solute, in which both the macroscopic velocity and the total dispersion tensor are influenced by the slip effects taking place at the pore-scale. The different regimes of application of the model, in terms of the Péclet number values, are discussed as well as its extents and limitations. This new model generalizes previous attempts that only include either Knudsen or diffusive slip effects in porous media.