Footprints of spontaneous fluid redistribution on capillary pressure in porous rock

Pore-scale imaging of two-phase flow in porous media shows that pore filling occurs as cooperative events with accompanying spontaneous fluid redistribution in other parts of the pore space. We present a level set method that controls saturation quasi-statically to model experiments controlled by low, constant flow rates and demonstrate that our method can describe the observed displacement mechanisms. The level set approach determines states of capillary equilibrium, which generally are different for displacement protocols constrained by saturation and pressure. Saturation-controlled simulations of drainage in sandstone show spontaneous fluid redistributions with abrupt pressure jumps and cooperative behavior, including snap-off and interface retraction events, consistent with experimental observations. Drainage capillary pressure curves are lower when saturation, rather than pressure, controls displacement. Remarkably, these effects are less significant for imbibition processes where the development of hydraulically connected wetting phase moderates the cooperative behavior and associated pressure jumps.