The Spreading of Immiscible Fluids in Porous Media under the Influence of Gravity

We use an approach based on invasion percolation in a gradient (IPG) to describe the displacement patterns that develop when a fluid spreads on an impermeable boundary in a porous medium under the influence of gravity (buoyancy) forces in a drainage process. The approach is intended to simulate applications, such as the spreading of a DNAPL in the saturated zone and of a NAPL in the vadose zone on top of an impermeable layer, or the classical problems of gravity underruning and gravity override in reservoir engineering. As gravity acts in a direction transverse to the main displacement direction, a novel form of IPG develops. We study numerically the resulting patterns for a combination of transverse and parallel Bond numbers and interpret the results using the concepts of gradient percolation. A physical interpretation in terms of the capillary number, the viscosity ratio and the gravity Bond number is also provided. In particular, we consider the scaling of the thickness of the spreading gravity ‘tongue’, for the cases of gravity‐dominated and viscous‐unstable displacements, and of the propagating front in the case of stabilized displacement at relatively high rates. It is found that the patterns have percolation (namely fractal‐like) characteristics, which cannot be captured by conventional continuum equations. These characteristics will affect, for example, mass transfer and must be considered in the design of remediation processes.