Simulation and interpretation of multiphase processes in porous and fractured-porous media

Abstract

A numerical model concept for simulating multi phase flow processes is presented. The conceptual model involves the approximation of heterogeneous porous and fractured porous media, by application of one-, two- and threedimensional elements in space that can be combined arbitrarily in a single model. The mathematical formulation of multiphase flow is valid for both saturated and unsaturated regions, so that dynamic front propagation behaviour as well as different geology-related retention characteristics can be accounted for in the model. For every Finite Element model problems arise when capillary pressure effects can be neglected and the governing equations are of hyperbolic type. To overcome these difficulties, the differential equations were formulated in terms of pressure and saturation as primary variables. To provide an accurate representation of the resulting saturation-front velocities and to avoid numerical oscillations a modified Petrov-Galerkin method was employed. To verify the code, the Buckley-Leverett problem was solved, and together with an adaptive finite element algorithm excellent results were obtained.