On the interaction between gravity forces and dispersive brine fronts in micro-heterogeneous porous media

The concepts of homogenization theory are employed to derive a macro-scale brine transport equation for micro-heterogeneous porous medium of layered structure under assumptions of validity of classical Darcy's law and Fick's law at the local scale. Derived macro-scale model is analogous to the so-called phase field equations. The obtained results are verified with direct numerical experiment.