In petrophysics, Archie's law relates the in-situ electrical conductivity of a sedimentary rock to its porosity and brine saturation:
Here, denotes the porosity, the electrical conductivity of the fluid saturated rock, represents the electrical conductivity of the brine, is the brine saturation, is the cementation exponent of the rock (usually in the range 1.8–2.0 for sandstones), is the saturation exponent (usually close to 2) and is the tortuosity factor.
Reformulated for electrical resistivity, the equation reads
with for the fluid saturated rock resistivity, and for the brine resistivity.
The factor
is also called the formation factor, where is the resistivity of the rock filled with only water .
The factor
is also called the resistivity index.
It is a purely empirical law attempting to describe ion flow (mostly sodium and chloride) in clean, consolidated sands, with varying intergranular porosity. Electrical conduction is assumed not to be present within the rock grains or in fluids other than water.
Archie's law is named after Gus Archie (1907–1978) who developed this empirical quantitative relationship between porosity, electrical conductivity, and brine saturation of rocks. Archie's law laid the foundation for modern well log interpretation as it relates borehole electrical conductivity measurements to hydrocarbon saturations (which, for fluid saturated rock, equals ).
Read more about Archie's Law: Sands With Clay/shaly Sands
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