Re-examining Archie's law: Conductance description by tortuosity and constriction

TL;DR

This paper re-examines Archie’s law by linking electrical conductance in porous media to microstructural descriptors like tortuosity and constriction, providing a more physical basis for understanding and predicting conductance.

Contribution

It introduces a conductance reduction factor based on tortuosity and constriction, replacing empirical Archie cementation exponent with physically meaningful parameters.

Findings

Global conductance reduction factor equals tortuosity squared divided by constriction.

Tortuosity, constriction, and conductance reduction factor accurately model conductance in idealized media.

Application to Bentheimer sandstone reveals microstructure-related porosity-conductivity correlation.

Abstract

In this article we investigate the electrical conductance of an insulating porous medium (e.g., a sedimentary rock) filled with an electrolyte (e.g., brine), usually described using the Archie cementation exponent. We show how the electrical conductance depends on changes in the drift velocity and the length of the electric field lines, in addition to the porosity and the conductance of the electrolyte. We characterized the length of the electric field lines by a tortuosity and the changes in drift velocity by a constriction factor. Both the tortuosity and the constriction factor are descriptors of the pore microstructure. We define a conductance reduction factor to measure the local contributions of the pore microstructure to the global conductance. It is shown that the global conductance reduction factor is the product of the tortuosity squared divided by the constriction factor, thereby proving that the combined effect of tortuosity and constriction, in addition to the porosity and conductance of the electrolyte, fully describes the effective electrical conductance of a porous medium. We show that our tortuosity, constriction factor, and conductance reduction factor reproduce the electrical conductance for idealized porous media. They are also applied to Bentheimer sandstone, where we describe a microstructure-related correlation between porosity and conductivity using both the global conductance reduction factor and the distinct contributions from tortuosity and constriction. Overall, this work shows how the empirical Archie cementation exponent can be substituted by more descriptive, physical parameters, either by the global conductance reduction factor or by tortuosity and constriction.