Archie equation

In the petrophysics describes the Archie Equation purely empirically the relationship between the in-situ - conductivity of the rock and the conductivity of the water with which the pores are completely saturated. The equation only applies to "clay-free" rocks. The equation is applied to borehole measurements in oil exploration and for monitoring salt mines and landfills .

{\ displaystyle {\ frac {\ rho _ {b, s}} {\ rho _ {W}}} = {\ frac {a} {\ phi ^ {m}}} = F}

(1. Archie equation)

${\ displaystyle \ rho _ {b, s}:}$ specific resistance of the saturated rock
${\ displaystyle \ rho _ {W}:}$ specific resistance of the pore water
${\ displaystyle \ phi:}$ Porosity (pore volume / total volume, decreasing with increasing cementation )
a : Tortuosity factor or cementation axis segment (0.6 to 1)
m : cementation exponent (1.3 for sand, 1.8 to 2 for sandstone )
F : Formation factor, summarizes the influence of the pore geometry.

If the pore volume is only partially filled with the aqueous phase , this has a similar effect as a correspondingly smaller porosity: ${\ displaystyle S_ {W} <1}$

{\ displaystyle {\ frac {\ rho _ {b}} {\ rho _ {W}}} = {\ frac {a} {\ phi ^ {m} S_ {W} ^ {n}}}}

(2nd Archie equation)

The saturation exponent n is usually fixed at values close to 2.0. That and how the axis section a changes depends on whether the aqueous phase wets the stone and displaces air or whether petroleum wets the stone and is displaced in volume by the aqueous phase.

swell

GE Archie: The electrical resistivity log as an aid in determining some reservoir characteristics . In: Petroleum Transactions of AIME . 146, 1942, pp. 54-62.
GE Archie: Electrical resistivity an aid in core-analysis interpretation . In: American Association of Petroleum Geologists Bulletin . 31, No. 2, 1947, pp. 350-366.
GE Archie: Introduction to petrophysics of reservoir rocks . In: American Association of Petroleum Geologists Bulletin . 34, No. 5, 1950, pp. 943-961.
GE Archie: Classification of carbonate reservoir rocks and petrophysical considerations . In: American Association of Petroleum Geologists Bulletin . 36, No. 2, 1952, pp. 278-298.
Malcolm H. Rider: The Geological Interpretation of Well Logs , Second. Edition, Whittles Publishing Services, 1999, ISBN 0954190602 , p. 288.
Darwin V. Ellis: Well Logging for Earth Scientists . Elsevier, 1987, ISBN 0-444-01180-3 .
Darwin V. Ellis, Julian M. Singer: Well Logging for Earth Scientists , Second. Edition, Springer, 2008, ISBN 1402037384 , p. 692.
MH Waxman, LJM Smits: Electrical conductivities in oil-bearing shaly sands . In: PES Journal . 8, No. 2, 1968, pp. 107-122. doi : 10.2118 / 1863-A .
WO Winsauer, Shearing, HM, Jr., Masson, PH, and Williams, M .: Resistivity of brine saturated sands in relation to pore geometry . In: AAPG Bulletin . 36, No. 2, 1952, pp. 253-277.