Modeling the Nonlinear–To–Linear Relationship Between Bulk and Pore Water Electrical Conductivity in Saturated Porous Media Using a Padé Approximant

Abstract

A petrophysical model that accurately relates bulk electrical conductivity (σ) to pore fluid conductivity (σ_w) is critical to the interpretation of geophysical measurements. Classical models are either only applicable over a limited salinity regime or incorrectly explain the nonlinear-to-linear behavior of the σ(σ_w) relationship. In this study, asymptotic limits at zero and infinite salinity are first established in which, σ is expressed as a linear function of σ_w with four parameters: cementation exponent (m), the equivalent value of volumetric surface electrical conductivity (σ_s), the volume fraction of overlapped diffuse layer (ϕ_od) and parameter χ representing the ratio of the volume fraction of the water phase to that of the solid phases in the surface conduction pathway. Subsequently, we bridge the gap between the two extremes by employing the Padé approximant (PA). Given that parameter χ exhibits a marginal influence on the σ(σ_w) curve, based on measurements for 15 samples, we identify its optimal value to be 0.4. After setting the optimal value of χ, we proceed to evaluate the performance of the PA model by comparing its estimates and estimates made by two existing models to measured values from 27 rock samples and eight sediment samples. The comparison confirms that the PA model estimates are more accurate than estimates made by existing models, particularly at low salinity and for samples with higher cation exchange capacity. The PA model is advantageous in scenarios involving the interpretation of electrical data in freshwater environments.