Fast simulation of EM telemetry in vertical drilling: A semi-analytical finite-element method with virtual layering technique

The electromagnetic (EM) telemetry systems, employed for real-time data transmission from the borehole and the earth surface during drilling, are widely used in measurement-while-drilling (MWD) and logging-while-drilling (LWD). Several numerical methods, including the method of moments (MoM), the electric field integral equation (EFIE) method, and the finite-element (FE) method have been developed for the simulation of EM telemetry systems. The computational process of these methods is complicated and time-consuming. To solve this problem, we introduce an axisymmetric semi-analytical FE method (SAFEM) in the cylindrical coordinate system with the virtual layering technique for rapid simulation of EM telemetry in a layered earth. The proposed method divides the computational domain into a series of homogeneous layers. For each layer, only its cross-section is discretized, and a high-precision integration method based on Riccati equations is employed for the calculation of longitudinally homogeneous sections. The block-tridiagonal structure of the global coefficient matrix enables the use of the block Thomas algorithm, facilitating the efficient simulation of EM telemetry problems in layered media. After the theoretical development, we validate the accuracy and efficiency of our algorithm through a series of numerical experiments and comparisons with the Multiphysics modeling software COMSOL. We also discussed the impact of system parameters on EM telemetry signal and demonstrated the applicability of our method by testing it on a field dataset acquired from Dezhou, Shandong Province, China.