Numerical studies of gravity destabilized percolation in 2D porous media

Two dimensional simulations of percolation are realized on square networks of pore throats with a random capillary pressure distribution. We analyse the influence of a destabilizing gravity field (g) and of the standard deviation of the distribution of the capillary pressure thresholds (W<Subscript>t</Subscript>). The fragmentation process is not taken into account in this study. For an increase of g or/and when W<Subscript>t</Subscript> decreases, two transitions are analyzed with three different regimes displacement patterns: Invasion percolation, invasion percolation in a gradient, and invasion in a pure gradient. The transitions are controlled both by the ratio g/W<Subscript>t</Subscript> and by the sample size (L). A scaling law between the saturation at the percolation threshold and g/W<Subscript>t</Subscript> allows delineating the three regimes in agreement with theoretical argument of the percolation in a gradient. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006