Conservative numerical methods to solve the two-phase flow in porous media including foam displacemen

Abstract

This thesis is dedicated to numerically analyzing how heterogeneity, gravity, and surfactant adsorption affect foam displacement in a porous medium saturated with gas and water. The presence of foam in the water-gas mixture acts to control the mobility of the gas phase, contributing to reducing the effects of viscous fingering and gravity override. In order to model these phenomena, a fractional flow formulation based on the global pressure concept is employed, resulting in a system of partial differential equations that describe two coupled problems of distinct mathematical nature. The numerical methodology is based on splitting the system of equations into two subsystems that group equations of the same kind and on applying a hybrid finite element method to solve the hydrodynamic problem and a high-order finite volume method to solve the transport equations. Numerical results validate and show the proposed algorithm’s efficiency compared with laboratory results and numerical techniques usually used for multiphase flows. Furthermore, computer simulations in complex scenarios involving heterogeneities, gravity, gas compressibility, and adsorption phenomena show the remarkable ability of foam to increase sweep efficiency when compared to flow in the absence of foam.