The impact of buoyancy on front spreading in heterogeneous porous media in two-phase immiscible flow

We study the influence of buoyancy and spatial heterogeneity on the spreading of the saturation front of a displacing fluid during injection into a porous medium saturated with another, immiscible fluid. To do so we use a stochastic modeling framework. We derive an effective large-scale flow equation for the saturation of the displacing fluid that is characterized by six nonlocal flux terms, four that resemble dispersive type terms and two that have the appearance of advection terms. From the effective large-scale flow equation we derive measures for the spreading of the saturation front. A series of full two-phase numerical solutions are conducted to complement the analytical developments. We find that the interplay between density and heterogeneity leads to an enhancement of the front spreading on one hand and to a renormalization of the evolution of the mean front position compared with an equivalent homogeneous medium. The quantification of these phenomena plays an important role in several applications, including, for example, carbon sequestration and enhanced oil recovery.