n

The exponent, n, in the relation of water saturation, S_w, to resistivity index, I (I = S_w^-n) for a sample of rock. It expresses the effect on the resistivity of desaturating the sample, or replacing water with a non-conductive fluid. In petrophysically simple, water-wet rocks (Archie rocks), n is constant for different values of S_w, and a single average n can be found for a particular reservoir or formation. A typical value is 2. In more complex rocks, n changes with S_w, although often being about 2 near S_w = 1. In rocks with conductive minerals, such as shaly sands, n becomes increasingly lower as S_w is reduced. This change is negligible for high-salinity waters, but increases as the salinity is reduced. In shaly-sand saturation equations, such as Waxman-Smits, dual water, SGS and CRMM, n is the intrinsic n, determined with high-salinity water or with the clay effects removed. The variation of I with S_w is then predicted, with varying success, by the different equations. In carbonates with multiple pore types, such as fractures, vugs, interparticle porosity and microporosity, n may change as each pore type is desaturated. A different n may be used for a different range of S_w. In all cases, n increases if any pores are oil-wet. Values up to 8 have been reported in very oil-wet rocks.