Using the total chemical potential to generalize the capillary pressure concept and therefrom derive a governing equation for two-phase flow in porous media

Abstract

This work presents a governing equation (GE) for two-phase flow in porous media connecting capillary pressure to frictional pressure loss and external chemical potential supplied to a system in either stationary or diffusive equilibrium. It is based on the difference between non-wetting and wetting phase chemical potential (physically, pressure or energy density), which leads to a generalization of the capillary pressure concept. The difference in phase internal chemical potentials is characterized by changes in both interfacial areas and entropy densities due to variation in fluid saturations and is balanced by the system external chemical potential supplied. A definition of the capillary pressure concept is formulated based on the diffusive equilibrium criterion. The GE can explain the origin of the dynamic capillary pressure term, hysteresis, and connect the shift in the capillary pressure curve upon injecting water phases with varying salinities to all the other chemical potentials acting. It can connect, constrain, and potentially quantify all effects which can be formulated in terms of chemical potentials since it is based on a balance equation all two-phase flow systems must obey when either in stationary or diffusive equilibrium.