Resistivity index of fractional wettability porous media

The effects of fractional wettability on electrical resistivity index curve s of porous media are investigated using pore network models. A bond percol ation-and-fractal roughness model is used to simulate the oil/water drainag e of the conventional porous plate method in pore networks composed of rand omly distributed 'strongly water-wet' and 'strongly oil-wet' capillaries. B ased 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, capillar y pressure and saturation exponent on certain microstructural properties of the pore space and surface fractional wettability over the various water s aturation regions. The simulated data are fitted to two-exponent power laws , which in turn are evaluated as macroscopic conceptual models of the resis tivity index. At high water saturations, the saturation exponent becomes a strongly increasing function of the fraction of oil-wet pores when the valu e of this parameter exceeds the percolation threshold of the lattice networ k 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 th e slope of the capillary pressure curve remains almost unaltered to variati ons of wettability. At low water saturations, as the fraction of oil-wet po res becomes quite large, permanent trapping of water may occur with result that both the saturation exponent and the slope of the capillary pressure c urve tend to infinity at the limit of irreducible water saturation. The exp onents of the phenomenological models of the resistivity index change signi ficantly with fractional wettability and are consistent with the values of the saturation exponent obtained with the approximate analytic relationship s. (C) 1999 Elsevier Science B.V. All rights reserved.