Complex conductivity measurements and fractal nature of porosity

Abstract

Complex resistivity measurements were performed on 22 saturated samples (sandstones, slate, shale, and granites) at room temperature and pressure over a frequency range from 1 Hz to 5 MHz, using a two‐terminal sample holder. Although low‐frequency measurements (from 1 Hz to 1–10 kHz) are perturbed by electrode polarization phenomena, we observed classical behavior for 20 samples, i.e., behavior that can be fitted to a Cole and Cole response function, and different behavior for the other two (two slates). These two last samples exhibit an almost constant imaginary part of the complex resistivity. Since the frequency dependence is caused by interfacial effects, it is possible to characterize the internal surface area from electrical measurements. We use models developed by Le Méhauté and Crépy (1983) and Po Zen Wong (1987) to calculate the fractal dimension d of the internal surface area from experimental data. An independent measurement confirms that the specific surface area correlates with d. The two models contradict each other, however, and we suggest that Le Méhauté and Cré py’s model is appropriate to describe the observed behavior. Fractal dimension varies between 2.02 (Fontainebleau sandstone) and 2.94 (shale).