Residual water saturation, electrical conductivity, and rough rock/pore interfaces

In this paper, we model the roughness of the pore/rock interface in terms of a random surface; we construct the surface by assigning random heights to the vertices of a triangular lattice. A completely wetting fluid preferentially lies along the concave creases of the surface and forms connected pathways that span the surface. A wetting fluid with finite contact angle does not necessarily form continuous pathways in this model. Electrical conductivity for the completely wetting case is simply proportional to the wetting-fluid saturation at very low saturations; this result agrees with recent experimental studies.