# Dictionary:Archie’s formulas

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{{#category_index:A|Archie’s formulas}} (ar’ chēz) Empirical relationships between the formation factor F (sometimes FR), porosity φ, water saturation Sw, and resistivities R. In clean granular rocks,

FIG. A-17. Archie’s formula for different lithologies. [1]

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

${\displaystyle S_{\mathrm {w} }^{n}={\frac {R_{\mathrm {o} }}{R_{\mathrm {t} }}}}$

where

• a = proportionality constant varying from 0.6 to 1.5,
• m = cementation factor that varies between 1.3 and 3,
• n = saturation exponent, often assumed to be 2,
• Ro = resistivity of the formation when 100% saturated with formation water,
• Rw = resistivity of the formation water,
• Rt = true resistivity of the formation.

Archie’s law assumes that m=2 and a=1.
The Humble formula assumes that m=2.15 and a=0.65.
Values of a and m for different lithologies are shown in Figure A-17.
Named for Gus E. Archie, American engineer and geologist.

## References

1. Keller, G. R., 1987, Rock and mineral properties: in Nabighian, M. N., Ed., Electromagnetic methods in applied geophysics—Theory, 1: Soc. Expl. Geophys., 13–52. http://dx.doi.org/10.1190/1.9781560802631.ch2