Advancing and Applying Microscale Models for Two-Fluid Flow in Porous Media: From Equilibrium States to Geometric State Equation Parameterization

Two-fluid-phase porous medium flow systems are a category of complex scientific problems of concern to society. Examples include enhanced oil and gas recovery, remediation of subsurface contamination, and sequestration of carbon dioxide. These problems are challenging. They require consideration of physical processes spanning spatial scales from micrometers to kilometers and temporal scales from fractions of a second to centuries. Despite the importance of these complex problems, the standard macroscale modeling approach has several limitations. The model lacks an explicit connection to small-scale physics, relies on empirically obtained closure relationships, and is not constrained by the second law of thermodynamics. Advances in microscale understanding are used to refine a new generation of macroscale models. This work demonstrates the ability of high-fidelity microscale lattice-Boltzmann simulations to capture critical two-fluid displacement behaviors and also discusses the computational limitations of this approach. To address some of these limitations, a new algorithm is proposed for approximating microscale equilibrium fluid distributions. It is shown that equilibrium interfaces in pore spaces between spheres can be well approximated using constant mean curvature n-noids. An alternative macroscale model derived under the thermodynamically-constrained averaging theory (TCAT) framework is described. The TCAT model resolves limitations of the traditional model. However, this model is not closed. To address the closure problem, microscale simulations were used to develop and parameterize a theoretical capillary pressure state equation that incorporates interfacial areas, mean curvatures, and Gaussian curvatures, applies under both dynamic and equilibrium conditions, and eliminates the hysteresis characteristic of traditional capillary pressure-saturation closures. Lastly, it is shown that this state equation can be accurately parameterized using a relatively small number of data points, improving the feasibility of macroscale TCAT two-fluid porous medium flow modeling.