Relating permeability and electrical conductivity in partially saturated porous media by means of the Johnson–Koplik–Schwartz characteristic length

Abstract

In this work, we revisit the seminal concept of Johnson-Koplik-Schwartz (JKS) length Λ, i.e. a characteristic length representing an effective pore size which controls various transport-related properties of porous media, such as, the permeability and the electrical conductivity. We present a novel closed-form equation that predicts the behavior of Λ in partially saturated media, for different saturation states. Using previous models in the literature that predict the intrinsic and relative electrical conductivities under partially saturated conditions, we infer the JKS length Λ and the electrical formation factor F as functions of water saturation and properties associated with the pore-size distribution of the probed porous medium. The proposed method permits to estimate the effective permeability and the relative permeability directly from electrical conductivity measurements, thus opening new-avenues for the remote characterization of partially saturated media. We believe that this new model will prove useful for various characterization and modeling applications from reservoir (CO2 or hydrogen storage) to vadose zone studies.