The relationship between hydraulic and electrical transport properties in sandstones: An experimental evaluation of several scaling models

The purpose of this paper is to investigate the relationship between the parameters that define the hydraulic and electrical transport in porous rock. We therefore measured the effective pressure dependence of both permeability (k) and (specific) electrical conductivity (σ) of three different types of sandstones (Fontainebleau, Flechtinger, and Eberswalder). The experiments were performed in a high pressure and high temperature (HPT) permeameter at a maximum confining- and pore pressure of 50 MPa and 45 MPa, respectively and a constant temperature of 40 °C. 0.1 molar NaCl-brine was used as the pore fluid. We show that for the present rock–fluid combinations surface conductivity can be neglected. The experiments were complemented with 2D image analysis and mercury porosimetry to derive the average pore radii, the specific inner pore surfaces, and the pore radius distributions of the samples. The experimental and microstructural results were used to relate both transport properties by means of different length scales and to test the associated scaling models based on (1) the equivalent channel concept, (2) statistics and percolation, and (3) an interpretation of mercury porosimetry data. As the principal result, none of these integrated models could adequately reproduce the respective transport property within experimental error margins. Furthermore, it is emphasized that these models are not applicable for effective pressures other than zero unless the concurrent evolution of the microstructure, respectively the length scale, can be characterized. By comparison, it is shown that purely empirical permeability–conductivity relationships can always be adjusted to provide a reasonable description of the coupled k–σ dependence on effective pressure. However, it is implied that the included empirical length parameter is fundamentally different from the ones above as it is a pressure independent constant that contains no true microstructural or physical information.