A simplified 3D finite difference method for electromagnetic logging while drilling simulation in symmetrical models

Electromagnetic (EM) Logging While Drilling (LWD) plays an increasingly significant role in oil and gas exploration and development. Fast and accurate simulation of EM LWD is essential for optimizing tool parameters and data processing. As the depth of investigation increases, EM LWD simulation and inversion in complex geological structures become more important, while the computational cost of three-dimensional (3D) simulations remains a major challenge. In this paper, we present a simplified 3D finite-difference frequency domain method for symmetric geological models. In such models, the electromagnetic field generated by a magnetic dipole source exhibits symmetry in all directions. Leveraging this symmetry, we reduce the computational domain by half, centering it on the symmetry plane, and impose new boundary conditions based on the symmetry of the electric field. Compared to conventional methods, the proposed approach reduces the number of unknowns by half, significantly improving computational efficiency. Numerical simulations show that the results from the proposed method agree well with both analytical solutions and finite element simulations. We further apply the method to analyze borehole effects, mud invasion, and near-wellbore anomalies. The numerical results indicate that in a 12-inch diameter borehole, EM LWD apparent resistivity curves are influenced by borehole effects, deviating from those obtained under borehole-free conditions. The impact of the borehole and mud invasion varies with tool frequency and transmitter-receiver (TR) spacing: shorter TR spacings and higher frequencies are more susceptible to these effects, whereas longer TR spacings and lower frequencies exhibit greater stability.