# 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

${\displaystyle F={\frac {R_{0}}{R_{\mathrm {w} }}}={\frac {a}{\phi ^{m}}}}$

The resisitivity index I, is defined as

${\displaystyle I={\frac {R_{\mathrm {t} }}{R_{0}}}={\frac {1}{S_{\mathrm {w} }^{n}}}}$

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.

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

In this form, the desired, but unknown water saturation Sw may be solved from log measurements of porosity ${\displaystyle \phi }$, 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.