Physical Explanation of Archie's Porosity Exponent in Granular Materials: A Process-Based, Pore-Scale Numerical Study

The empirical Archie's law has been widely used in geosciences and engineering to explain the measured electrical resistivity of many geological materials, but its physical basis has not been fully understood yet. In this study, we use a pore-scale numerical approach combining discrete element-finite difference methods to study Archie's porosity exponent m of granular materials over a wide porosity range. Numerical results reveal that at dilute states (e.g., porosity phi > similar to 65%), m is exclusively related to the particle shape and orientation. As the porosity decreases, the electric flow in pore space concentrates progressively near particle contacts and m increases continuously in response to the intensified nonuniformity of the local electrical field. It is also found that the increase in m is universally correlated with the volume fraction of pore throats for all the samples regardless of their particle shapes, particle size range, and porosities. Plain Language Summary In many topical areas in Earth science and engineering such as groundwater hydrology and petroleum explorations, the electrical resistivity data are widely used to estimate the porosity and/or water/oil content in the subsurface with an empirical relationship that originated in the 1940s of the last century. This relation, known as Archie's law, relates a material's resistivity at saturation to its porosity and the pore fluid resistivity with a power function. As an empirical parameter, the exponent of the function varies considerably among different geological materials, and therefore, the estimated porosity/fluid content is significantly affected by the chosen value. At present, a physical understanding of the exponent is still limited mainly due to the lack of the detailed information on the complex geometry of the pore space. Here we use computational simulations to obtain the microscale geometrical characteristics of synthetic granular materials and to analyze the dominant parameter(s) impacting the exponent. We also provide a pore-scale, mechanistic explanation for the changes in the exponent of granular materials subjected to geological compaction. The findings from this study would help develop a physics-based approach to determine the value of the exponent in the modeling of the resistivity of various Earth materials in practice.