Hysteretic behavior of electrical conductivity in packings of particles

Abstract

We address the problem of predicting saturation-dependent electrical conductivity {\sigma} in packings of spheres during drainage and imbibition. The effective-medium approximation (EMA) and the universal power law of percolation for {\sigma} are used, respectively, at higher and low water saturations to predict the conductivity, with the crossover between the two occurring at some intermediate saturation Swx. The main input to the theory is a single parameter that we estimate using the capillary pressure data. The predictions are compared with experimental, as well as numerical data for three distinct types of packings. The results for drainage in all the packings indicate that the universal power law of percolation is valid over the entire range of Sw. For imbibition, however, the universal power law crosses over to the EMA at Swx = 0.5. We also find that the effect of the pore-size distribution on the {\sigma}-Sw relation is minimal during both drainage and imbibition.