Computational Modeling Technique for Numerical Simulation of Immiscible Two-phase Flow Problems Involving Flow and Transport Phenomena in Porous Media With Hysteresis

摘要

Numerical methods are necessary, and are extremely important, in developing an understanding of the dynamics of multiphase flow of fluids in porous media applications to maximize hydrocarbon recovery as well as to simulate contaminant transport of soluble or insoluble species in groundwater contamination problems. This work deals with a problem very common in water-flooding process in petroleum reservoir to motivate the proposed modeling: the flow of two immiscible and incompressible fluid phases. The system of equations which describe this type of flow is a coupled, highly nonlinear system of time-dependent partial differential equations. The equation for the invading fluid (e.g., water phase) is a convection-dominated, degenerate parabolic partial differential equation whose solutions typically exhibit sharp moving fronts (e.g., moving internal layers with strong gradients) and it is very difficult to approximate numerically. We propose a two-stage numerical method to describe the injection problem for a model of two-phase (water-oil) flow in a porous rock, taking into account both gravity and hysteresis effects for solving transport flow problems in porous media. Indeed, we also investigate the Riemann problem for the one-dimensional, purely hyperbolic system, associated to the full differential model problem at hand. Thus, the use of accurate numerical methods in conjunction with one-dimensional semi-analytical Riemann solutions might provide valuable insight into the qualitative solution behavior of the full nonlinear governing flow system.