Comparison of REV size and tensor characteristics for the electrical and hydraulic conductivities in fractured rock

International audienceThe representative elementary volume (REV) is a critically important concept in fractured rock investigations as it tells us at what scale the fractured domain can be represented by an anisotropic tensor as opposed to requiring the details of each individual fracture for modelling purposes. Whereas the REV size and corresponding tensor characteristics for the hydraulic conductivity (K) in fractured rock have been the subject of numerous previous investigations, no studies to date have focused on the electrical conductivity (σ). This is despite the fact that geoelectrical measurements are arguably the most popular means of geophysically investigating fractured rock, typically via azimuthal resistivity surveying where the observed electrical anisotropy is commonly used to infer hydraulic characteristics. In this paper, we attempt to fill this void and present a systematic numerical study of the impacts of changes in fracture-network properties on the REV size and equivalent tensor characteristics for both the electrical and hydraulic conductivities. We employ a combined statistical and numerical approach where the size of the REV is estimated from the conductivity variability observed across multiple stochastic fracture-network realizations for various domain sizes. Two important differences between fluid and electric current flow in fractured media are found to lead to significant differences in the REV size and tensor characteristics for σ and K; these are the greater importance of the matrix in the electrical case and the single power instead of cubic dependence of electric current flow upon aperture. Specifically, the REV for the electrical conductivity will always be smaller than that for the hydraulic conductivity, and the corresponding equivalent tensor will exhibit less anisotropy, often with notably different principal orientations. These findings are of key importance for the eventual interpretation of geoelectrical measurements in fractured rock, where we conclude that extreme caution must be taken when attempting to make the link to hydraulic properties