Water Saturation from Resistivity

How Much of the Pore Is Water?

Porosity tells us how much pore space there is; saturation tells us what fills it. The water saturation $S_w$ is the fraction of the pore volume occupied by water, and the hydrocarbon saturation is $1 - S_w$. Even in a good oil zone some water clings to the grains as irreducible water, so $S_w$ rarely falls below 0.1 to 0.2. Getting $S_w$ right is getting the oil volume right.

Archie's Law

We cannot measure saturation directly downhole, but we can measure resistivity, and brine conducts while hydrocarbons resist. Archie's law turns one into the other: $S_w = \left(\frac{a,R_w}{\phi^m,R_t}\right)^{1/n}$, where $R_t$ is the measured resistivity, $R_w$ the brine resistivity, and $a$, $m$, $n$ are calibration constants (the tortuosity factor, the cementation exponent, and the saturation exponent). The Pickett plot below makes it visual: on log porosity against log resistivity, lines of constant $S_w$ are straight.

Calibration Matters

Drag $m$ and $n$ and watch the saturation lines swing. The water saturation you read, and therefore the oil volume you book, is only as good as these parameters, which come from special core analysis. A cementation exponent off by 0.2 can shift the computed hydrocarbon volume by a large fraction. This sensitivity is a major source of uncertainty in volumetrics, and a reason petrophysics and core work earn their keep.