Parametric Analysis of Capillary Flow in Dual-Layer Porous Media: Implications for Energy and Environmental Applications

The capillary-driven flow in homogeneous porous media typically follows the dif- fusive behavior described by Washburn’s law. However, in heterogeneous porous systems—ranging from 3-Dimensional (3-D) paper-based microfluidic devices to layered petroleum reservoirs—this law fails to explain capillary-controlled dis- placement adequately. In this study, we demonstrate that at the Darcy scale, the existing analytical solutions for spontaneous imbibition in homogeneous media do not capture the full physics across varying wetting conditions. We also look into how various layer characteristics in a two-layered medium impact interlayer cross-flow and alter flow behavior as a result. Specifically, we employ a Darcy scale numerical model that includes capillary pressure (Pc) - saturation (Sw) curves, relative permeability (kr), and permeability (k) as flow parameters inside the layers of the porous medium. The findings show that, contrary to previous assumptions, cross-flow between the layers is not limited to the area close to the imbibition front. By comparing imbibition in the interacting and non-interacting porous layers, we demonstrate that (a) variations in porosity lead to cross-flow, which causes the layers’ saturation profiles to converge to the saturation profile seen in an averaged porous medium, and (b) when porosity and capillary pres- sure are correlated, the high porosity layer displays the leading front, (c) when porosity and permeability are correlated, the flow is dominated due to the per- meability of the layers; the interaction in layers causes the fronts to come closer, (d) when porosity, permeability and capillary pressure are correlated, a contrast- ing behavior is observed where the fluid front leads in the low permeability layer except near the front, and (e) when different wetting porous layers interact, the cross-flow causes the front in both layers to coincide at same location. These findings provide information for creating a novel model that forecasts the general course of capillary driven flow in multilayer porous media.