Multiscale direct numerical modeling of pore-scale and darcy-scale multiphase flow in porous media

Abstract

Improving our understanding about the evolution of multiphase flow in porous media is crucial for many applications such as extraction of hydrocarbons and geothermal energy from subsurface reservoirs, ground-water remediation, CO2 capture and storage, and transport of contaminants in aquifers and soil. Although such applications have implications at very large length scales, e.g., in the orders of kilometers, they strongly depend on the complex physics and dynamics that mainly occur at the pore-scale. Studying multiphase flow at the pore-scale using direct numerical modeling requires developing accurate numerical frameworks that not only honor conservation laws of mass, momentum, and energy, but also can precisely represent and track fluid-fluid interfaces in space and time in the presence of complex embedded solid geometries. In this dissertation, we consider incompressible and immiscible two-phase flows under isothermal conditions and in electrokinetic equilibrium. We solve for the conservation of mass and momentum, and using an immersed boundary approach account for the presence of embedded solid boundaries. We use a two-phase flow modeling approach based on the level-set method to capture the interfacial dynamics of the flow. Using our numerical framework, we first validate recent experimental works on phase separation in the form of pinch-off at the pore-scale, then we extend such experimental observations to a wide range of wettability conditions. For the phase separation in the form of pinch-off, we provide a quantitative study of the emerging length and time scales and their dependence on the wettability conditions, capillary effects, and viscous forces. Afterward, we present a subgrid thin-film model in order to resolve the interfacial dynamics of thin-films on curved solid surfaces in porous media. We couple a Navier-Stokes solver with a topology-preserving level-set method and a sub-grid thin-film model in order to simulate immiscible two-phase pore-scale flows in the presence of thin-films on curved solid surfaces. We validate our proposed subgrid thin-film model for the cases of static and dynamic fluid-fluid interfaces in capillary tubes (both drainage and imbibition) in the presence of curved solid surfaces. We compare the thin-film profile obtained by the subgrid thin-film model versus the profile numerically resolved by refined computational grid cells spanning the subgrid resolution of the thin-film and achieve a great agreement. Subsequently, we consider granular porous media with homogeneous and heterogeneous wettability conditions. We investigate the influence of capillary and viscous forces as well as wettability conditions on the interfacial dynamics, displacement efficiency, phase trapping phenomenon, and interfacial instabilities. For the heterogeneous wettability conditions, we consider granular media with mixed-wet conditions as well as fractional (patterned) wettability conditions. Finally, at the end of this dissertation, we present a physics-constrained super-resolution framework that can super-resolve numerical simulation data in both space and time. We test the robustness of our proposed super-resolution framework for super-resolving simulation data obtained for a turbulent flow case of Rayleigh-Bénard convection problem as well as a case of two-phase flow interfacial dynamics in porous media for a subsurface reservoir