An advanced hybrid-dimensional discrete fracture-matrix model for coupled simulation of water flow and electrical current in variably saturated fractured porous media

In the unsaturated zone of fractured and karstified media, although the fractures and incipient karst conduits generally account for a minor volume in the bulk geologic formations, they contribute significantly to the flow and transport properties. The reason is due to the significant difference (i.e., several orders of magnitude) of permeability in comparison with the surrounding porous matrix. Thus, the simulation of groundwater flow in such heterogeneous porous media requires knowledge of geometry and hydrodynamical characteristics of the fractures. However, identifying fractures and incipient karst conduits in the unsaturated zone has been a challenge in hydrogeology. Electrical resistivity tomography (ERT) as a non-invasive geophysical method has the potential to deliver vast information rapidly in a relatively economical way related to fractures and incipient karst conduits. However, the sole use of ERT for the interpretation of geological formation and hydrodynamic properties of fractured domains is not possible as it may lead to ambiguity of interpretations. The main goal of this work is to investigate the performance of coupling water flow and electrical current for fracture characterization. Thus, we develop a new numerical model for the simulation of coupled water flow and electrical current. In this model, the fractures or incipient karst conduits are simulated with the discrete fracture matrix approach which is known to be the most accurate approach for addressing flow in fractured domains as it considers fractures without any simplification. This approach is applied for both electrical current and water flow. The hybrid dimensional approach, which assumes 1D fractures in a 2D porous matrix is used to improve the computational efficiency of the developed model. The partial differential equations describing the flow and electrical current are solved using the mixed hybrid finite element method for space discretization and the method of lines for time integration. These numerical techniques have been selected to ensure an accurate solution to the nonlinear problem in a time-efficient and effective way. The newly developed model is validated for simplified test cases against the results obtained by an equi-dimensional approach based on the conforming finite element method (i.e., using COMSOL Multiphysics®). The effect of major fracture orientation and length on the temporal response of bulk resistivity during a percolation scenario has been studied numerically. In addition, the effect of injection of electrical dipole has been simulated and discussed for the same problem. The results show that the proper placement of the electrical dipole can significantly affect the resolution of the fracture signature response and the bulk resistivity measured on the surface of the domain through time.