Dictionary: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,

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

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

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

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,
• 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.

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