Numerical scheme for coupling two-phase compositional porous-media flow and one-phase compositional free flow

We present the numerical implementation of a model that couples single-phase free and two-phase porous-media flow and transport with the focus on the treatment of the interface conditions. The model concept is based on the two-domain approach and on non-isothermal compositional submodels. These are coupled by interface conditions accounting for mass, momentum and energy transfer, and guaranteeing continuity of fluxes. A vertex-centred finite-volume scheme is used throughout the domain and a global matrix is solved for the whole system incorporating the coupling matrices. The fluxes at the interface are calculated indirectly via a flux balance from the adjacent finite-volume boxes. Numerical examples, representing evaporation from partially saturated porous media influenced by an ambient air flow, illustrate the evolution of saturation and temperature in a reference case and demonstrate the coupling concept. Furthermore, the effect of temperature, Beavers-Joseph coefficient and permeability on the evaporation process are examined with a series of simulations. In the presented set-ups, the choice of the Beavers-Joseph coefficient has a negligible influence on the evaporation rate across the interface.