Coil System Design for Multi-Frequency Resistivity Logging Tool Based on Numerical Simulation

A coil-type resistivity logging tool has been proposed for multi-frequency operation (250 kHz to 8 MHz) based on electromagnetic wave propagation. Different frequencies are matched with specific transmission coils, while the same two reception coils are used to achieve a consistent depth of investigation (D_OI). By analyzing the electromagnetic attenuation and phase difference of induced signals at different frequencies, the complex resistivity can be jointly inverted. The coil systems were designed with four D_OI options (0.3 m, 0.5 m, 1 m, and 1.5 m) and six measurement frequencies (250 kHz, 500 kHz, 1 MHz, 2 MHz, 4 MHz, and 8 MHz). Their detection performance was evaluated using the finite element method on the COMSOL platform. For higher frequencies or a deeper D_OI, a coil system with a larger source-receiver distance was selected. These designed coil systems can provide qualitative identification of formations with thicknesses greater than 0.05 m and quantitative identification of formations with thicknesses greater than 1.5 m. In the single-transmission, dual-reception coil system, response signals are distorted at the formation boundary, and this distortion increases with the source-receiver distance. Adding a secondary transmission coil can reduce the distortion of response signals at the formation interface without increasing the overall length of the coil system. This research enriches the theoretical framework of complex resistivity spectrum (CRS) logging and contributes to the commercial development of CRS logging tools.