Archie's law

Relationship between the electrical conductivity of a rock and its porosity In petrophysics, Archie's law is a purely empirical law relating the measured electrical conductivity of a porous rock to its porosity and fluid saturation. It is named after Gus Archie (1907–1978) and laid the foundation for modern well log interpretation, as it relates borehole electrical conductivity measurements to hydrocarbon saturations. Statement of the law The in-situ electrical conductivity ( C t {\displaystyle C_{t}} ) of a fluid-saturated, porous rock is described as C t = 1 a C w ϕ m S w n {\displaystyle C_{t}={\frac {1}{a}}C_{w}\phi ^{m}S_{w}^{n}} where ϕ {\displaystyle \phi \,\!} denotes the porosity C w {\displaystyle C_{w}} represents the electrical conductivity of the aqueous solution (fluid or liquid phase) S w {\displaystyle S_{w}} is the water saturation, or more generally the fluid saturation, of the pores m {\displaystyle m} is the cementation exponent of the rock (usually in the range 1.8–2.0 for sandstones) n {\displaystyle n} is the saturation exponent (usually close to 2) a {\displaystyle a} is the tortuosity factor. This relationship attempts to describe ion flow (mostly sod