Stabilized Finite Element Methods for Three-Phase Porous Media Flows

Abstract

This work presents a stabilized finite element method for the simplified black-oil model, which is of great importance in reservoir simulation. This model considers that the three fluids, water, oil and gas are incompressible and assumes no mass transfer among phases. We apply a stabilized finite element method, using the CAU shock-capturing technique, to discretize the equations in space. A segregated solution technique is used to solve the coupled differential equation system. We simulate a one-dimensional gas-water injection case in a petroleum reservoir. The results obtained in this work are compared with the analytical solution and also with other numerical solution computed with a coupled multiscale technique. We can conclude that the computational strategy utilized in this work yields results comparable to those obtained with the coupled multiscale method.