3D numerical simulation of controlled source electromagnetic data for hydraulic fracturing-induced anisotropic electric conductivity

Abstract Controlled source electromagnetic (CSEM) methods are sensitive to fluids, offering significant potential in monitoring hydraulic fracturing processes. However, the quantitative interpretation of CSEM data related to hydraulic fracturing requires multi-scale simulations, covering millimeter-scale fractures within kilometer-scale background formations. This entails the design of intricate grids and the solution of large Maxwell equations, which is computationally intensive. This study employs effective medium theory to establish a quantitative relationship between the geometric structure parameters of hydraulic fractures and the anisotropic electrical conductivity. In the forward modeling, the equivalent electrically anisotropic medium that can quantitatively describe the fracture geometric structure is used to replace the fracture medium in the hydraulic fracturing section. Thus, for the multi-scale geoelectric model of hydraulic fracturing, the efficient forward calculation of the CSEM method is realized. This calculation quantitatively considers the geometric structure of hydraulic fractures. Comparisons with the calculation results of series-parallel circuits in layered media and the computational outcomes of a single-fracture model with fine-meshed complex grids verify the accuracy and effectiveness of the equivalent conductivity formulas proposed. Calculations on two multi-stage hydraulic fracturing models indicate that even with similar stimulated volume and fracturing fluid content, fracture deflection significantly influences the distribution of electric field anomalies observed at the surface. This study demonstrates that for interpreting CSEM data in fracturing, fracture-induced anisotropy is a critical factor to consider, in addition to the known effects of steel casings.