A new theoretical interpretation of Archie's saturation exponent

Paul W J Glover

doi:10.5194/se-8-805-2017

Abstract

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.

Highlights

There is no well-accepted physical interpretation of the saturation exponent other than qualitatively as some measure of the efficiency with which electrical flow takes place within the water occupying a partially saturated rock
Some might say that the meaning is not important as long as one can reliably obtain the water saturation of reservoir rocks with sufficient accuracy to calculate reserves
Even a tiny uncertainty of, say, 0.01 in a saturation exponent of 2 (i.e. 0.5 % or 2 ± 0.01) would result in an error in the reserves of about USD ±254.36 billion; the equivalent of 82 Queen Elizabeth class aircraft carriers or one mission to Mars. This calculation has been carried out by calculating the percentage change in hydrocarbon saturation resulting from an error of 2 ± 0.01 in the value of the saturation exponent

Summary

Introduction

There is no well-accepted physical interpretation of the saturation exponent other than qualitatively as some measure of the efficiency with which electrical flow takes place within the water occupying a partially saturated rock. The classical Archie’s laws (Archie, 1942) link the electrical resistivity of a rock to its porosity, to the resistivity of the water saturating its pores, and to the fractional saturation of the pore space with the water They have been used for many years to calculate the hydrocarbon saturation of the reservoir rock and hydrocarbon reserves. Despite its importance to reserves calculations, the physical meaning of the saturation exponent is difficult to understand from a physical point of view, which leads to petrophysicists not giving it the respect it deserves It is common, for example, to hear that, in the absence of laboratory measurements, the saturation exponent has been taken to be equal to 2, which it has just been noted is bound to lead to gross errors. The purpose of this paper is to investigate the elusive physical meaning of the saturation exponent, where it is shown that the saturation exponents are intimately linked to the phase exponents in the generalized Archie’s model

Traditional interpretations

The generalized Archie’s law

Origin of the saturation exponent

Physical interpretation of the saturation exponent

Conclusions