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
The resisitivity index I, is defined as
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.
In this form, the desired, but unknown water saturation Sw may be solved from log measurements of porosity , 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.
- Archie's law — Archie's equation on Wikipedia