Analysis of Capillary Pressure Relations for Two-Fluid-Phase Porous Medium Systems

The standard approach for modeling two-fluid-phase porous medium systems includes using an empirical and hysteretic relationship between fluid-fluid pressure differences and fluid saturations. Recent work has resulted in a theoretically derived alternative that applies for both equilibrium and dynamic conditions over the entire state space without hysteresis. Given the widespread use of the standard model, a question arises over the accuracy of popular empirical representations of the state of two-fluid porous medium systems in comparison to the theoretically derived representation. Why have the standard empirical approaches had some utility and under what conditions are the errors in such approaches most significant? We examine datasets of systems using methods analogous to standard experimental approaches, examine states not typically included in standard approaches, interpret the fidelity with which empirical approaches represent the known system state, and identify conditions for which empirical approaches are apt to deviate most significantly from the true description of the system state.