Articles | Volume 8, issue 4
Solid Earth, 8, 805–816, 2017
Solid Earth, 8, 805–816, 2017

Research article 26 Jul 2017

Research article | 26 Jul 2017

A new theoretical interpretation of Archie's saturation exponent

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

Abstract. This paper describes the extension of the concepts of connectedness and conservation of connectedness that underlie the generalized 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 generalized Archie's law. In the generalized 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 = GrefSini. 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.

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 two 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 describing their connectedness also sums to unity.