Generalized Archie law — application to petroleum reservoirs

Constantino Tsallis, Evaldo M.F. Curado, Maria do Socorro de Souza, Vera L. Elias, Claudio Bettini, Maximiano S. Scuta and Rodolfo Beer

Physica A: Statistical Mechanics and its Applications, 1992, vol. 191, issue 1, 277-283

Abstract: The experimental formation factor (F) vs. porosity (φ) as well as resistivity index (I) vs. water saturation (Sw) results typically present, in double-logarithmic representation, bendings which we now interpret as crossovers between different fractal-like regimes. We consistently propose for the ratio (rock resistivity)/(brine resistivity) ≡ Rt/Rw = F(φ) I(Sw), where the functional forms of F(φ) and I(Sw) are simply one and the same. This proposal yields F∼φ−m and F∼BFφ−m' in the φ→1 and φ→0 limits respectively, as well as I∼S−nw and I∼BIS−n'w in the Sw→0 limits respectively (m,m'BF,n,n' and BI are rock parameters); hence Archie's law Rt/Rw∼φ−mS−nw is recovered in the (φ,Sw)→(1,1) limit. The agreement between theory and experiments is quite satisfactory for the entire range of (φ,Sw). The use of the present generalized Archie law into electrical resistivity logs improves the precision of the evaluation of the hydrocarbon reserves.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:191:y:1992:i:1:p:277-283

DOI: 10.1016/0378-4371(92)90538-2

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