Simulation of two-phase flow in porous media with sharp material discontinuities

•New FEM-FVM hybrid scheme that permits decoupling of saturation and pressure across strong material discontinuities for two-phase flow simulation.•Through the introduction of an additional degree of freedom of fluid pressure, scheme permits the simulation of transient flow barriers, which form when the non-wetting phase builds up upstream of capillary interfaces.•Local conservation of phase volume is guaranteed Capillary hold-up and non-wetting phase breakthrough are reproduced in 1D, 2D and 3D examples. Geologic boundaries juxtaposing fine- against coarse-grained rock, have a profound impact on multiphase flow, giving rise to a spectrum of non-linear flow behaviors, ranging from capillary filtration, capillary holdup and the formation of transient ’vapour locks’, to spontaneous imbibition. Although these discontinuities tend to be small-scale features, their impact is felt on the large scale where they are challenging to model with regard to both, spatial discretization and dynamic flow simulation. We develop a new numerical scheme to handle jump discontinuities in pressure and saturation, embedding boundaries into a hybrid FE-FVM model of immiscible two-phase flow in porous media. The integration of interface conditions is an extension of the discontinuous finite element finite volume method (DFEFVM). A unique feature of it is that saturation at the interface is computed locally without constructing a system of equations, and, in contrast with other schemes, it offers sufficient degrees of freedom to accommodate disequilibrium in pressure. A range of test cases including gravity, capillary pressure and material discontinuities are presented to verify, validate and show the effectiveness of the new simulation method.