Two-Phase Flow in Heterogeneous Porous Media with Non-Equilibrium Nonlinear Effects

In this work, we consider a two-phase flow in heterogeneous porous media with non-equilibrium and nonlinear effects. The mathematical model is described by a coupled nonlinear system of equations for pressure, velocity, and saturation with a flow model that includes a specific time-dependent relationship of velocity and pressure. For a numerical solution, we construct a finite-volume approximation by space for flow and transport processes in heterogeneous porous media with an upwind scheme for a transport equation. We present a time approximation scheme based on the implicit approximation by time for pressure equation and explicit approximation of the saturation equation. Careful approximation of the flow term in the two-phase flow model with non-equilibrium and nonlinear effects is considered. Results are presented for two types of heterogeneous permeability with high-contrast properties in the two-dimensional formulation. Numerical investigation is presented for varying parameters of the rheological flow model.