Revisiting the Johnson-Koplik-Schwartz characteristic length to relate transport properties in partially saturated porous media, insights from a fractal-based petrophysical approach

In petrophysics, characteristic lengths are used to relate fundamental transport properties of porous media. However, these characteristic lengths have mostly been defined and tested in fully saturated conditions, with few exceptions. This contribution revisits the seminal work of Johnson-Koplik-Schwartz (JKS) length, which represents an effective pore size controlling various transport-related properties of porous media, such as permeability and electrical conductivity. A novel closed-form equation is presented to predict the behavior of this characteristic length 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 as functions of water saturation and properties associated with the pore-size distribution of the considered porous medium. The proposed method allows for the direct estimation of effective and relative permeability through electrical conductivity measurements. This creates new opportunities for remotely characterizing partially saturated media. We believe that this new model has potential for various applications in reservoir (CO2 or hydrogen storage) and vadose zone studies.