ABSTRACT: In this work, the issue of stability for two-phase incompressible flow in homogeneous porous media out of the Darcy regime (i.e. when inertia must be taken into account) is considered. The development is based on a macroscopic model derived by upscaling the pore-scale Navier-Stokes equations, assuming that the inertial correction is quadratic in the filtration velocity, as widely admitted with the classical Darcy-Forchheimer model.
Starting from the momentum and mass balance equations in each phase, a 1D linear stability analysis is performed in the framework of negligible capillary pressure. The analysis is carried out using an extended Buckley-Leverett type of solution including inertia. A flow-rate dependent stability criterion is obtained from this analysis. Some numerical simulations are presented confirming the predicted stability criterion.