Archie equation

There are two equations that Archie (1942) proposed that may be combined into a single equation, which is generally know as "the Archie equation" for determining water saturation.

The formation volume factor F, is defined as


 * $$F=\frac{R_0}{R_\mathrm{w}}= \frac{a}{\phi^m}$$

The resisitivity index I, is defined as


 * $$I= \frac{R_\mathrm{t}}{R_0}=\frac{1}{S^n_\mathrm{w}}$$

the ratio of the actual resistivity of the formation, Rt, and the value that is should have if its pore space is completely filled with formation water, R0.


 * $$S_\mathrm{w}=\left[ \frac{a R_\mathrm{w}}{\phi^{m}R_\mathrm{t}} \right]^\frac{1}{n}$$

In this form, the desired, but unknown water saturation Sw may be solved from log measurements of porosity $$\phi$$, and formation resitivity Rt, when values are known for the cementation exponent m, a value for a if other than unity, the saturation exponent, n, and the formation water resistivity Rw at formation temperature.

In general, n, the saturation exponent is taken to be 2, and a to be 1. Cementation exponent varies from 1.5 - 2.5.