Search

Modelling the relationships among bulk conductivity, electrolyte conductivity, porosity and fractional electrolyte‐saturation continues to be based on empirical relationships such as Archie's law or the Bruggeman correlation. Several authors have attempted to connect such empirical models to first principles. This article presents a complete first principles‐based description of conductivity in partially saturated porous media. A geometrical factor is introduced which, together with porosity and saturation, describes the conductivity of partially saturated porous media. This geometrical factor is separated into two intrinsic geometrical descriptors of the electrolyte distribution accounting for tortuosity and constriction. This tortuosity and constriction factor are obtained from integration over the electrical field lines traversing the electrolyte. Bulk and saturation‐dependent conductance descriptions are illustrated using three‐dimensional pore space models and simulated fluid distributions. Describing conductance through porosity, saturation and a geometrical factor, decomposed into separate terms accounting for tortuosity and constrictivity, permits more insightful understanding of conductance in partially saturated porous media. Use and efficacy of this full conductance description is illustrated throughout this article. [ABSTRACT FROM AUTHOR]

The petroleum industry's standard porosity-resistivity model (i.e., Archie's law), although it is fit for its purpose, remains poorly understood after seven decades of use. This results from the choice of the graphical display and trend formula used to analyze Archie's seminal porosity-resistivity data, taken in the Nacatoch sandstone, a petroliferous clastic formation in the Gulf of Mexico coastal area. Archie's model accurately predicts the conductivity-brine volume trend for this sandstone. Not all rocks follow the same porosity-resistivity trends observed in the Nacatoch sandstone, but those that do are defined as Archie rocks. Archie's Nacatoch sandstone data set has significant irreducible scatter, or noise. Data with significant scatter cannot be used to uniquely define a trend. Alternative graphical analyses of Archie's Nacatoch sandstone data indicates that Archie could have analyzed these data differently had it occurred to him to do so. A physics-based porosity-conductivity model, a "geometrical factor theory" (GFT), is preferred as an alternative to the Archie model because it has a physical interpretation. In this model, the bulk conductivity of an Archie rock is the product of three factors: brine conductivity, fractional brine volume, and an explicit geometrical factor. The model is offered in the form of a theorem, proved in three steps, to make our arguments as explicit and transparent as possible. The model is developed through its culmination as a saturation equation to illustrate that it is a complete theory for Archie rocks. The predictive power of the Archie model and GFT are similar, but unlike the adjustable parameters of the Archie model (m, n, and a), all of the parameters of GFT have a priori physical interpretations. Through a connection to site percolation theory, GFT has promise to connect porosity-conductivity interpretation to circuit theory first principles. [ABSTRACT FROM AUTHOR]