On the dynamics and kinematics of two‐fluid‐phase flow in porous media

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AbstractA model formulated in terms of both conservation and kinematic equations for phases and interfaces in two‐fluid‐phase flow in a porous medium system is summarized. Macroscale kinematic equations are derived as extensions of averaging theorems and do not rely on conservation principles. Models based on both conservation and kinematic equations can describe multiphase flow with varying fidelity. When only phase‐based equations are considered, a model similar in form to the traditional model for two‐fluid‐phase flow results. When interface conservation and kinematic equations are also included, a novel formulation results that naturally includes evolution equations that express dynamic changes in fluid saturations, pressures, the capillary pressure, and the fluid‐fluid interfacial area density in a two‐fluid‐system. This dynamic equation set is unique to this work, and the importance of the modeled physics is shown through both microfluidic experiments and high‐resolution lattice Boltzmann simulations. The validation work shows that the relaxation of interface distribution and shape toward an equilibrium state is a slow process relative to the time scale typically allowed for a system to approach an apparent equilibrium state based upon observations of fluid saturations and external pressure measurements. Consequently, most pressure‐saturation data intended to denote an equilibrium state are likely a sampling from a dynamic system undergoing changes of interfacial curvatures that are not typically monitored. The results confirm the importance of kinematic analysis in combination with conservation equations for faithful modeling of system physics.