A physically-based model for the electrical conductivity of water-saturated porous media

Electrical conductivity is one of the most commonly used geophysical method for reservoir and environmental studies. Its main interest lies in its sensitivity to key properties of storage and transport in porous media. Its quantitative use therefore depends on the efficiency of the petrophysical relationship to link them. In this work, we develop a new physically based model for estimating electrical conductivity of saturated porous media. The model is derived assuming that the porous media is represented by a bundle of tortuous capillary tubes with a fractal pore-size distribution. The model is expressed in terms of the porosity, electrical conductivity of the pore liquid and the microstructural parameters of porous media. It takes into account the interface properties between minerals and pore water by introducing a surface conductivity. Expressions for the formation factor and hydraulic tortuosity are also obtained from the model derivation. The model is then successfully compared with published data and performs better than previous models. The proposed approach also permits to relate the electrical conductivity to other transport properties such as the hydraulic conductivity.