A Note on the Interrelationship Between Wetting and Nonwetting Phase Relative Permeability

In a recent publication wetting phase relative permeability was expressedas: (Equation 1) and it was stated that a similar expression applied, mutatis mutandis, tonon-wetting phase relative permeability; i.e., (Equation 2) In Equations (1) and (2), Sw and So are respectively the wetting andnon-wetting phase saturations as a fraction of the pore volume; Pc is thecapillary pressure; I, the wetting phase electrical resistivity index; IN, theanalogous non-wetting phase electrical resistivity index and Krw and Krnw, thewetting and non-wetting phase relative permeabilities. Equation (3) is interesting because it expresses the nonwetting phaserelative permeability of a porous medium at any saturation as a function of thewetting phase relative permeability at that saturation, the saturation itselfand parameters which bear directly on the distribution within the pores of thenon-wetting and wetting phase fluid networks. It is thus inherentlyplausible. Equation (3) is not readily checked against experimental data since fewreliable relative permeability figures have appeared in the literature; also nopublished information exists on the probable relationship between IN and So.However, if the Krw and Krnw figures of Leverett for unconsolidated sands areused in conjunction with the relationship I = Sw-2 for sands of this type, itis possible for Equation (3) to compute IN as a function of So. The results areshown in the accompanying figure and it will be seen that IN = So-1.72. Asynthetic sandstone for which Muskat quotes relative permeability data, alsogives a straight line plot between IN and So if I = Sw-1.8 is assumed. (Aresistivity index exponent of 1.8 appears to be the best average forconsolidated porous media.) T.N. 93