Saturation front evolution for liquid infiltration into a gas filled porous medium with counter-current flow

The infiltration of liquid into a gas saturated porous network is investigated. Particular attention is paid to the situation in which a pressure gradient in the porous medium drives a gas flow upwards, while a more dense liquid infiltrates down into the reservoir due to gravity. There are two flows in opposite directions. A model is proposed, based upon a compressible gas phase and an incompressible liquid phase. The volume fluxes in each phase are assumed to be governed by Darcy type flow laws, modified to include the permeability caused by both the solid matrix and the impeding of the gas flow by the liquid phase. Isothermal flows are examined in the absence of phase changes. The proposed model is an extension of the traditional Buckley-Leverett model and is used to consider a variety of flows, including carbon sequestration in a porous medium below the seabed and rainfall infiltration into a lava dome.