Resistivity index of fractional wettability porous media

The effects of fractional wettability on electrical resistivity index curves of porous media are investigated using pore network models. A bond percolation-and-fractal roughness model is used to simulate the oil/water drainage of the conventional porous plate method in pore networks composed of randomly distributed `strongly water-wetʹ and `strongly oil-wetʹ capillaries. Based on universal scaling laws of percolation quantities, effective medium approximation and fractal geometry, approximate analytic relationships are developed with respect to the dependence of the resistivity index, capillary pressure and saturation exponent on certain microstructural properties of the pore space and surface fractional wettability over the various water saturation regions. The simulated data are fitted to two-exponent power laws, which in turn are evaluated as macroscopic conceptual models of the resistivity index. At high water saturations, the saturation exponent becomes a strongly increasing function of the fraction of oil-wet pores when the value of this parameter exceeds the percolation threshold of the lattice network and oil percolates spontaneously through network joining clusters of oil-wet pores. At intermediate water saturations, the saturation exponent is a moderately increasing function of the fraction of oil-wet pores, whereas the slope of the capillary pressure curve remains almost unaltered to variations of wettability. At low water saturations, as the fraction of oil-wet pores becomes quite large, permanent trapping of water may occur with result that both the saturation exponent and the slope of the capillary pressure curve tend to infinity at the limit of irreducible water saturation. The exponents of the phenomenological models of the resistivity index change significantly with fractional wettability and are consistent with the values of the saturation exponent obtained with the approximate analytic relationships.