In this study, the cylindrical finite-volume method (FVM) is advanced for the efficient and high-precision simulation of the logging while drilling (LWD) orthogonal azimuth electromagnetic tool (OAEMT) response in a three-dimensional (3D) anisotropic formation. To overcome the ill-condition and convergence problems arising from the low induction number, Maxwell’s equations are reformulated into a mixed Helmholtz equation for the coupled potentials in a cylindrical coordinate system. The electrical field continuation method is applied to approximate the perfectly electrical conducting (PEC) boundary condition, to improve the discretization accuracy of the Helmholtz equation on the surface of metal mandrels. On the base, the 3D FVM on Lebedev’s staggered grids in the cylindrical coordinates is employed to discretize the mixed equations to ensure good conformity with typical well-logging tool geometries. The equivalent conductivity in a non-uniform element is determined by a standardization technique. The direct solver, PARDISO, is applied to efficiently solve the sparse linear equation systems for the multi-transmitter problem. To reduce the number of calls to PARDISO, the whole computational domain is divided into small windows that contain multiple measuring points. The electromagnetic (EM) solutions produced by all the transmitters per window are simultaneously solved because the discrete matrix, relevant to all the transmitters in the same window, is changed. Finally, the 3D FVM is validated against the numerical mode matching method (NMM), and the characteristics of both the coaxial and coplanar responses of the EM field tool are investigated using the numerical results.

在这项研究中，改进了圆柱有限体积法（FVM），可对三维（3D）各向异性地层中随钻测井（LWD）正交方位角电磁工具（OAEMT）响应进行高效，高精度的模拟。为了克服低感应数引起的不适和收敛问题，将麦克斯韦方程重新组合为混合的亥姆霍兹方程，用于圆柱坐标系中的耦合势。电场连续法用于近似理想导电（PEC）边界条件，以提高金属心轴表面亥姆霍兹方程的离散精度。在基地上 Lebedev在圆柱坐标系中的交错网格上的3D FVM被用于离散混合方程，以确保与典型的测井工具几何形状具有良好的一致性。非均匀元素中的等效电导率通过标准化技术确定。直接求解器PARDISO用于有效解决多发射器问题的稀疏线性方程组。为了减少对PARDISO的调用次数，整个计算域被划分为包含多个测量点的小窗口。由于改变了与同一窗口中所有发射器相关的离散矩阵，因此可以同时解决每个窗口中所有发射器产生的电磁（EM）解决方案。最后，针对数字模式匹配方法（NMM）对3D FVM进行了验证，