Effects of pore-scale geometry and wettability on two-phase relative permeabilities within elementary cells

We study the relative role of the complex pore space geometry and wettability of the solid matrix on the quantification of relative permeabilities of elementary cells of porous media. These constitute a key element upon which upscaling frameworks are typically grounded. In our study we focus on state immiscible two-phase flow taking place at the scale of elementary cells. Pressure-driven two-phase flow following simultaneous co-current injection of water and oil is numerically solved for a suite of regular and stochastically generated two-dimensional explicit elementary cells with fixed porosity and sharing main topological/morphological features. We show that the relative permeabilities of the randomly generated elementary cells are significantly influenced by the formation of preferential percolation paths, called principal pathways, giving rise to a strongly nonuniform distribution of fluid fluxes. These pathways are a result of the spatially variable resistance that the random pore structures exert on the fluid. The overall effect on relative permeabilities of the diverse organization of principal pathways, as driven by a given random realization at the scale of the elementary cell, is significantly larger than that of the wettability of the host rock. In contrast to what can be observed for the random cells analyzed, the relative permeabilities of regular cells display a clear trend with contact angle at the investigated scale.