3-D Finite Volume Modeling for LWD Azimuthal Propagation Resistivity Tool With Multiple Annular Antenna Recesses Using Coupled Potentials on Cylindrical Grids

The sensors of logging-while-drilling (LWD) azimuth propagation resistivity (APR) tool are usually installed in the annular antenna recesses filled with ferrite or other magnetic materials on the grooved metal mandrel. In this article, we will improve the 3-D finite volume method (3-D FVM) on cylindrical grids to solve the Helmholtz equations about coupled potentials for precise simulation of the tool responses with multiple antenna recesses. The irregular and novel Yee's staggered grids are designed to conform to the grooved mandrel surface. The electrical continuation technique is adopted to approximate the perfectly electrical conductor (PEC) boundary condition on the mandrel surface for efficient enhancement of the discretization precision of the potentials around the mandrel. The equivalent conductivity and permeability in heterogeneous elements are determined by the volume average. After that, the parallel direct sparse solver (PARDISO) is used to solve the discretized equation about coupled potentials for effectively ensuring the accuracy and stability of numerical solutions. Finally, we validate the 3-D FVM against results by the hybrid algorithm in homogeneous formation. Through numerical results, we further investigate the influence of both the mandrel and antenna recesses on the LWD tool responses, and its response characteristics in several different environments.