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 des cribe the displacement patterns that develop when a fluid spreads on an imp ermeable boundary in a porous medium under the influence of gravity (buoyan cy) forces in a drainage process. The approach is intended to simulate appl ications, such as the spreading of a DNAPL in the saturated zone and of a N APL in the vadose zone on top of an impermeable layer, or the classical pro blems of gravity underruning and gravity override in reservoir engineering. As gravity acts in a direction transverse to the main displacement directi on, a novel form of IPG develops. We study numerically the resulting patter ns for a combination of transverse and parallel Bond numbers and interpret the results using the concepts of gradient percolation. A physical interpre tation in terms of the capillary number, the viscosity ratio and the gravit y Bond number is also provided. In particular, we consider the scaling of t he thickness of the spreading gravity 'tongue', for the cases of gravity-do minated 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, w hich cannot be captured by conventional continuum equations. These characte ristics will affect, for example, mass transfer and must be considered in t he design of remediation processes.