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Solid Earth An interactive open-access journal of the European Geosciences Union

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doi:10.5194/se-2017-5
© Author(s) 2017. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
15 Feb 2017
Review status
This discussion paper is under review for the journal Solid Earth (SE).
A new theoretical interpretation of Archie’s saturation exponent
Paul W. J. Glover School of Earth and Environment, University of Leeds, UK
Abstract. This paper describes the extension of the concepts of connectedness and conservation of connectedness that underlie the generalised Archie`s law for n phases to the interpretation of the saturation exponent. It is shown that the saturation exponent as defined originally by Archie arises naturally from the generalised Archie’s law. In the generalised Archie`s law the saturation exponent of any given phase can be thought of as formally the same as the phase (i.e., cementation) exponent, but with respect to a reference subset of phases in a larger n-phase medium. Furthermore, the connectedness of each of the phases occupying a reference subset of an n-phase medium can be related to the connectedness of the subset itself by Gi=Gref Sini. This leads naturally to the idea of the term Sini. for each phase i being a fractional connectedness, where the fractional connectednesses of any given reference subset sum to unity in the same way that the connectednesses sum to unity for the whole medium. One of the implications of this theory is that the saturation exponent of any phase can be now be interpreted as the rate of change of the fractional connectedness with saturation and connectivity within the reference subset.

Citation: Glover, P. W. J.: A new theoretical interpretation of Archie’s saturation exponent, Solid Earth Discuss., doi:10.5194/se-2017-5, in review, 2017.
Paul W. J. Glover
Paul W. J. Glover
Paul W. J. Glover

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Short summary
Electrical flow through porous media depends on the amount of conductive material available and how that material is connected. This has conventionally been described by 2 laws invented by Archie in 1942 which allowed only one conducting material and one non-conducting material. This paper contends that both laws arise from a single underlying law which allows for any number of materials, where their fractions sum to unity and a parameter that describes their connectedness also sums to unity.
Electrical flow through porous media depends on the amount of conductive material available and...
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