Geometry and dynamics of invasion percolation with correlated buoyancy

We study an invasion percolation model for drainage where the disorder comes partly from capillary thresholds and partly from height differences in a rough self-affine landscape. As a function of the buoyancy, the geometry of the invaded clusters changes dramatically. Long-range correlations from the fracture topography induce a double cluster structure with strings and compact blobs. A characteristic length is introduced comparing the width of the capillary threshold distribution and gravity effects at the pore scale. We study electrical properties of percolating clusters. Current distributions along percolating clusters are shown to be multifractal and sensitive to the buoyancy.