Numerical Simulation, Response Analysis, and Physical Experiment of Induction Logging in an Inclined Fractured Formation

The majority of previous studies of induction logging in fractured formations have typically focused on the variation in spatial resistivity distribution around the wellbore. However, the effect of cumulative charge on the boundaries of an inclined fracture with a distinct morphology on induction logging has rarely been discussed. In this work, the 3-D finite element method (3-D FEM) is adopted to investigate the dual-induction logging response of inclined fractures in formations of different resistivities considering the volume contribution and charge contribution. First, induction logging theory is studied, and a 3-D fractured formation model considering cumulative charges is established. Second, the induction logging responses under various fracture resistivities, apertures, dip angles, and formation resistivities are simulated and analyzed. Subsequently, the corresponding logging response characteristics are studied, and the different response laws of inclined fractures in high- and low-resistivity formations are systematically summarized. Third, a 1:5 miniaturized dual-induction logging instrument was designed and manufactured. Furthermore, two devices were built to measure the induction logging response of the inclined fracture (simulated by nanoscale silver film or metal wire mesh) in low- and high-resistivity formations. The results of the physical experiments are consistent with the numerical results, validating the accuracy of the numerical simulation. Both the results reveal that due to the existence of cumulative charge layers on the upper and lower inclined fracture boundaries, the induction logging response rules of the conductive fractures in high-resistivity formations differ from those in low-resistivity formations, and hence, they should be treated differently.