A numerical algorithm to solve the two-phase flow in porous media including foam displacement

Abstract

This work is dedicated to simulating the Enhanced Oil Recovery (EOR) process of foam injection in a fully saturated reservoir. The presence of foam in the gas-water mixture acts in controlling the mobility of the gas phase, contributing to reduce the effects of fingering and gravity override. A fractional flow formulation based on global pressure is used, resulting in a system of Partial Differential Equations (PDEs) that describe two coupled problems of distinct kinds: elliptic and hyperbolic. The numerical methodology is based on splitting the system of equations into two sub-systems that group equations of the same kind and on applying a hybrid finite element method to solve the elliptic problem and a high-order finite volume method to solve the hyperbolic equations. Numerical results show good efficiency of the algorithm, as well as the remarkable ability of the foam to increase reservoir sweep efficiency by reducing gravity override and fingering effects.