Linking drainage front morphology with gaseous diffusion in unsaturated porous media: A lattice Boltzmann study

The effect of drainage front morphology on gaseous diffusion through partially saturated porous media is analyzed using the lattice Boltzmann method (LBM). Flow regimes for immiscible displacement in porous media have been characterized as stable displacement, capillary fingering, and viscous fingering. The dominance of a flow regime is associated with the relative magnitudes of gravity, viscous, and capillary forces, quantifiable via the Bond number Bo, capillary number Ca, and their difference, Bo-Ca. Forced drainage from an initially saturated two-dimensional (2D) porous medium was simulated and the resulting flow patterns were analyzed and compared with theoretical predictions and experimental results. The LBM simulations reproduced expected flow morphologies for a range of drainage velocities and gravitational forces (i.e., a range of capillary and Bond numbers). Furthermore, measures of drainage front width as a function of the dimensionless difference Bo-Ca correspond well with scaling laws derived from percolation theory. Effects of flow morphology on residual fluid entrapment and gaseous diffusion were assessed by running LBM diffusion simulations through the partially saturated domain for a range of water contents. The effective diffusion coefficient as a function of water content was estimated for three regimes: stable drainage front, capillary fingering, and viscous fingering. Significant reductions in gaseous diffusion coefficient were found for viscous fingering relative to stable displacement, and to a lesser extent for capillary fingering, indicating that wetting phase distribution with a high degree of fingering in the 2D domain severely restricts connectivity of gas diffusion pathways through the medium. The study lends support for the use of LBM in design and management of fluids in porous media under variable gravity, and enhances the understanding of the role of dynamic fluid behavior on macroscopic transport properties of partially saturated porous media.