Efficient and Accurate Electromagnetic Modeling of Triaxial Induction Responses From Multiscale Fractures for Well-Logging Applications

Electromagnetic modeling of triaxial induction responses in fractured formation is of growing importance in well-logging applications. Usually, fractures have a tiny thickness in a scale between micrometers and millimeters, while their length or width is several orders of magnitude larger than their thickness. Such a distinctive multiscale feature generally leads to a very dense mesh, which makes the modeling using the conventional methods, e.g., the finite element method and volume integral equation (VIE), unnecessarily expensive. With the aid of thin dielectric sheet (TDS) approximation for fractures, an efficient and accurate solution is achieved in this paper to model the triaxial induction responses by utilizing the TDS-based surface integral equation (TDS-SIE), which successfully transforms the original VIE into an SIE while guaranteeing a good accuracy. Since the TDS-SIE method only requires surface discretization, unnecessarily dense volume meshes are avoided, and a substantial amount of unknowns can be reduced in numerical simulation. By modeling the triaxial induction responses of both conductive and resistive fractures at the practical scenarios, excellent accuracy, efficiency, and flexibility of the TDS-SIE are demonstrated by comparing the result with that from the semianalytical one-dimensional solution or the VIE method. This provides a valuable solution to characterize near-borehole fractures from induction well-logging data.