Numerical simulation of two-phase flow in porous media using a wavelet based phase-field method

An understanding of the transport and dynamics of two fluids in porous media, as well as the bubbly flow regime, is important for many engineering applications, such as enhanced oil recovery (EOR) method, drilling technology, multiphase production system, etc. In this respect, the dependence of capillary stresses on the excess free-energy of a thin interfacial layer formed by two immiscible fluids is not fully clear, particularly in porous media. Of particular interests are the closure models for interphase forces which often hinder the reliable prediction of the homogeneous flow regime. This article presents a multiphase Computational Fluid Dynamics (CFD) study of bubbles in homogeneous porous media to model the flow of oil and gas, and investigates a closure model that is based on the Allen-Cahn phase-field method, where the capillary stress is derived from the excess free-energy. The governing dynamics is simulated with the volume averaged Navier-Stokes equations extended for multiphase flow in porous media. The equations have been discretized by a wavelet transform method to accurately capture the topological change of the fluid-fluid interface. To validate the closure model for interphase forces, the results of the present phase-field method have been compared with that from experiments, as well as from reference numerical models. An excellent agreement among the results from present phase-field simulations, experiments, and some reference numerical simulations has been observed. The terminal velocity of the rising gas bubble in a liquid saturated porous medium, as well as in a pure liquid has been investigated. The bubble rising velocity in both cases have been compared with respect to the theoretical and experimental results. The study illustrates how the bubble dynamics in porous media depend on the excess free energy of a thin interfacial layer formed by two immiscible fluids.