Evaluation of data needed to parameterize a new hysteretic-free state equation involving capillary pressure in two-fluid-phase porous medium systems

The traditional modeling approach for two-fluid-phase flow within porous medium systems includes an empirical and hysteretic closure relation for the pressure difference between connected fluid phases, which is usually called capillary pressure. A hysteretic-free state equation has recently been shown to exist for such systems. This expression applies for both equilibrium and dynamic states. We use data from microscale lattice Boltzmann simulations to obtain macroscale volume fractions, interfacial areas, interfacial curvatures, and specific Euler characteristics in terms of the nonwetting fluid phase for natural and synthetic media. We show that a relatively small number of easy to generate states is sufficient to determine the parameters in this state equation, and we compare both linear and nonlinear forms of this equation. Guidance is provided on a general approach to determine the parameters needed to apply this state equation, and we show the advantages of this state equation compared to long-standing, traditional approaches.