Simulação numérica do escoamento trifásico em reservatórios de petróleo

Abstract

The mathematical model for three-phase flow in porous media is described by at least three partial differential equations. These equations are often non-linear and with the presence of heterogeneous coefficients, which makes it very hard to obtain an analytical solution. The nonlinearities and the coupling between the equations can be treated in different forms, raising different ways for solving the model. In this work, the traditional solutions are reviewed, including IMPES and fully implicit, together with the Finite Volume Method for the model discretization. A third option for the solution is examined, here called Sequential Picard-Newton method, in two versions: simultaneous and detached. This new strategy represents this work main contribution. The analyzed model consists in the isothermal and immiscible flow of oil, water and gas, taking into account the three fluids compressibilities and also considering the porous media to be compressible. As application examples, three-phase flow in porous media is considered under different scenarios, including the presence of production wells and the alternate injection of water and gas (WAG), capillary effects and also gravitational effects. Sequential Picard-Newton method, in both versions, was capable of producing similar results as shown by the traditional methods and, for the numerical experiments presented here, with a significant reduction in simulation time.