Non-equilibrium model of three-phase flow in porous media in presence of capillary and gravity forces

In this work a generalized non-equilibrium model of three-phase flow in porous media including gravity as well as capillary terms is developed and used for analysis of Riemann’s problem in several three-phase systems. The proposed model uses the extension of Barenblatt model to three-phase systems considering dynamic effects in both relative permeability and capillary pressure functions. We compare the solution of the Riemann’s problem when non-equilibrium effects are included. While equilibrium formulation develops unstable oscillatory solution in the elliptic region, non-equilibrium solution is smooth and stable. The results of this work might be helpful to better understanding the behavior of three-phase flow in porous media.