A new theoretical interpretation of Archie’s saturation exponent

Paul W. J. Glover
School of Earth and Environment, University of Leeds, UK

Received: 23 Jan 2017 – Accepted for review: 08 Feb 2017 – Discussion started: 15 Feb 2017

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 G_{i}=G_{ref} S_{i}^{ni}. This leads naturally to the idea of the term S_{i}^{ni}. 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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