# Dictionary:Archie’s formulas

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

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,*R*_{o}= resistivity of the formation when 100% saturated with formation water,*R*_{w}= resistivity of the formation water,*R*_{t}= 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

- ↑ 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