Fast and accurate simulation of electromagnetic telemetry in deviated and horizontal drilling

Electromagnetic (EM) telemetry systems are widely used for measurement-while-drilling (MWD), especially in unconventional drilling. In this paper, a numerical method for the simulation of EM telemetry systems in deviated and horizontal drilling is introduced. The underground formation is assumed to be horizontally layered media, and the long, metal drill string acts as an antenna that may be treated as a thin wire excited by a gap voltage source located near the drill bit. The numerical model employs the electric field integral equation (EFIE) and the method of moments (MoM) to obtain a linear system for the axial current distribution on the drill string, which is subdivided into several one-dimensional segments. By using the thin wire kernel, near-field interactions can be evaluated accurately and efficiently, while also reducing problem dimensionality and singularity order of the homogeneous medium contribution to the layered medium Green's function (LMGF). The latter typically takes the form of a dyadic spectral domain integral, the asymptotics of whose integrands may be estimated and combined with Kummer's method to accelerate its evaluation, with the asymptotic correction terms evaluated in closed or easily evaluated forms. Numerical results are presented to verify the fast and accurate performance of the proposed approach. Results for signal voltage receivability by a surface antenna are also presented and discussed.