Two-phase flow in porous media: dynamic capillarity and heterogeneous media

We investigate a two-phase porous media flow model, in which dynamic effects are taken into account in phase pressure difference. We consider a one-dimensional heterogeneous case, with two adjacent homogeneous blocks separated by an interface. The absolute permeability is assumed constant, but different in each block. This may lead to the entrapment of the non-wetting phase (say, oil) when flowing from the coarse material into the fine material. We derive the interface conditions coupling the models in each homogeneous block. In doing so, the interface is approximated by a thin porous layer, and its thickness is then passed to zero. Such results have been obtained earlier for standard models, based on equilibrium relationship between the capillary pressure and the saturation. Then, oil is trapped until its saturation on the coarse material side of the interface exceeds an entry value. In the non-equilibrium case, the situation is different. Due to the dynamic effects, oil may still flow into the fine material even after the saturation drops under the entry point, and this flow may continue for a certain amount of time that is proportional to the non-equilibrium effects. This suggests that operating in a dynamic regime reduces the account of oil trapped at interfaces, leading to an enhanced oil recovery. Finally, we present some numerical results supporting the theoretical findings. Keywords: Dynamic capillary pressure; Immiscible flow; Heterogeneity; Trappin