Non-hysteretic functional form of capillary pressure in porous media

Abstract

Models of flow of two immiscible fluids in a porous medium overwhelmingly involve use of an equilibrium correlation between what is identified as capillary pressure and the saturation of one of the fluids. This correlation is said to be hysteretic with the functional relation depending on which of the two fluids has displaced the other in a flow scenario. This correlation was proposed when abilities to investigate porous medium systems experimentally for the distribution of fluids or using computer simulation were limited. Because of advances, we can now assert that the quantity called capillary pressure is ambiguously defined and the alleged hysteretic behaviour, even at equilibrium, is actually due to incompleteness in the functional dependence. We provide a path forward for a theoretically sound formulation that corrects the assertion that capillary pressure is a hysteretic function of saturation, and we advocate for moving beyond ingrained erroneous notions.