TCAT Analysis of Capillary Pressure in Non-equilibrium, Two-fluid-phase, Porous Medium Systems

Standard models of flow of two immiscible fluids in a porous medium make use of an expression for the dependence of capillary pressure on the saturation of a fluid phase. Data to support the mathematical expression is most often obtained through a sequence of equilibrium experiments. In addition to such expressions being hysteretic, recent experimental and theoretical studies have suggested that the equilibrium functional forms obtained may be inadequate for modeling dynamic systems. This situation has led to efforts to express relaxation of a system to an equilibrium capillary pressure in relation to the rate of change of saturation. Here, based on insights gained from the thermodynamically constrained averaging theory (TCAT) we propose that dynamic processes are related to changes in interfacial area between phases as well as saturation. A more complete formulation of capillary pressure dynamics is presented leading to an equation that is suitable for experimental study.