Résumé
Quantification of fluid flow in fractured media is critically important for a wide variety of research fields and applications. To this end, applied geophysical methods are of significant interest because (i) they allow for subsurface physical property estimation in a non-invasive and cost-effective manner; and (ii) many of these methods are sensitive to the presence of fractures. A number of empirical studies have suggested that measurement of the directionally dependent characteristics of the electrical resistivity in fractured rock, for example via azimuthal resistivity surveying, may provide an inexpensive means of obtaining important information regarding the corresponding hydraulic conductivity tensor such as dominant orientation and degree of anisotropy. However, theoretical and numerical work to further investigate these findings has been extremely limited due to a lack of appropriate modeling tools. Here we explore numerically, in the context of stochastically generated fracture networks, the question of whether information regarding the electrical resistivity tensor can be used as a proxy for information about the hydraulic conductivity. Electric current flow is modeled using the recently developed discrete-dual-porosity approach of Roubinet and Irving (2014), whereas groundwater flow is simulated using a discrete-fracture-network model. In our analysis, we compare: (i) the size of domain required to obtain a representative elementary volume (REV) for each parameter; and (ii) the corresponding tensor properties. Quite importantly, we find that the REV size for the electrical conductivity is notably smaller than that for the hydraulic conductivity because of the homogenizing effect of matrix current flow in the former case. In addition, we find that differences in the dependence of each parameter on fracture aperture can lead to strong discrepancies between their tensor characteristics.