Random walker derivation of Archie's law

TL;DR

This paper provides a theoretical derivation of Archie's law, explaining how the electrical resistivity of electrolyte-saturated rocks relates to porosity, which is crucial for oil and gas exploration.

Contribution

It offers a theoretical justification for Archie's law, connecting empirical observations to fundamental principles.

Findings

Archie's law is derived from first principles.

The derivation confirms the power-law relationship.

The work enhances understanding of resistivity-porosity correlation.

Abstract

Theoretical justification is provided for Archie's law. This phenomenological equation, having the form of a power law, relates the measured electrical resistivity of electrolyte-saturated rock samples to their connected porosity. Historically it has been important for oil and gas exploration.