Résumé
The study of fractured rocks is extremely important in a variety of research fields and applications such as hydrogeology, hydrocarbon extraction and long-term storage of toxic waste. As fractures are highly conductive structures in comparison to the surrounding rock, their presence can be either an advantage or a drawback. For hydrocarbon extraction, fractures allow for quick and easy access to the resource whereas for toxic waste storage their presence increases the risk of leakage and migration of pollutants. In both cases, the identification of fracture network characteristics is an essential step. Recently, we have developed an approach for modeling electric current flow in 2D fractured media. This approach is based on a discrete-dual-porosity model where fractures are represented explicitly, the matrix is coarsely discretized into blocks, and current flow exchange between the fractures and matrix is analytically evaluated at the fracture-scale and integrated at the block-scale. Although this approach has shown much promise and has proven its efficiency for 2D simulations, its extension to 3D remains to be addressed. To this end, we assume that fractures can be represented as two-dimensional finite planes embedded in the surrounding matrix, and we express analytically the distribution of electric potential at the fracture scale. This fracture-scale expression takes into account the electric-current-flow exchange with the surrounding matrix and flow conservation is enforced at the fracture intersections. The fracture-matrix exchange is then integrated at the matrix-block scale where the electric current flow conservation at the block boundaries is formulated with a modified finite volume method. With the objective of providing a low-computational-cost modeling approach adapted to 3D simulations in fractured media, our model is (i) validated and compared to existing modeling approaches and, (ii) used to evaluate the impact of the presence of fractures on equivalent properties and synthetic simulations of electrical surveys.