Numerical Simulation of One-Dimensional Two-Phase Flow in Porous Media

The flow of two immiscible fluids in porous media is described by two coupled non-linear partial differential equations of the parabolic type. In this paper a numerical algorithm to simulate one-dimensional two-phase flow is presented. Cell-centered finite volume method and a generalized two-level scheme with weighting parameter are applied for the discretization in space and time, respectively. The performance of the algorithm is tested for different values of the weighting parameter in the time-discretization scheme and for various methods of approximation of the average conductivities between two adjacent gridblocks. The results are compared with an analytical solution for the horizontal flow and with a reference numerical solution performed on a dense grid for the vertical flow.