Microscale heterogeneous pore occupancy with variable background resistance

Fluid flow through porous media often involves the spontaneous displacement of one immiscible fluid by another. On the level of adjacent channels, a pore doublet model can estimate the relative flow rates in the two channels and the final fluid occupancy of the pair. Pore doublet models nominally capture the dominant roles of capillarity and viscosity, by describing the flow using hydraulic circuit theory. However, this approach neglects the more complex fluid flow in the region where the immiscible fluids meet, and therefore the applicability of this model for low aspect-ratio pores commonly seen in natural media is questionable. We show that for large channel aspect ratios, the numerical results replicate the traditional pore doublet models; however, as the aspect ratio approaches unity, the accuracy of these models break down. We quantify the effect of complex flow on the final fluid occupancy, which we link to the excess energy dissipation rate from the flow near the immiscible interface. Our results indicate that a minimal 1D pore doublet model may be sufficient to model global dynamics, including the fraction of residual oil that remains trapped in a reservoir, where the pore diameter and length are comparable.