Résumé
The identification of fractures and the characterization of their properties are of critical importance in a wide variety of research fields and applications. To this end, geophysical methods are of significant interest as they can provide information regarding the spatial distribution of a number of subsurface physical properties in a rapid and noninvasive manner. Electrical resistivity surveying, in particular, has been shown in several previous investigations to exhibit sensitivity to the presence of fractures, suggesting that geoelectrical experiments may contain important information regarding how fractures are distributed and connected in the subsurface. However, a lack of suitable numerical modeling tools for electric current flow in fractured media has prevented a detailed and systematic exploration of this concept. To address this issue, we present a novel discrete-dual-porosity modeling approach that is specifically tailored to the electrical resistivity problem. With our approach, an analytical formulation for fracture-matrix current flow exchange at the fracture scale is integrated into a discrete-fracture-network model, which is then combined with a block-scale finite-volume representation of the rock matrix. Our methodology allows for low-cost and accurate simulation of electric current flow through both the fractures and matrix, and is readily applicable to complex fracture networks at relatively large scales. Although formulated here in two dimensions, this work represents an important first step toward investigating the effect of fracture-network characteristics on bulk electrical properties, as well as toward the simulation of geoelectrical survey data in realistic fractured-rock environments.