Simulation of Electromagnetic Wave LWD tool response based on a volume integral equation method

An efficient volume integral equation (VIE) method based on piecewise constant basis functions (PWCBF) is presented for simulation of Electromagnetic Wave Logging-While-Drilling (EM LWD) tool response. The use of the basis allows a geometric discretization of nonconformal meshes, which leads to much flexibility in geometric modeling, but a hypersingular integral involving in the gradient-gradient operator applied on the Green´s function must be handled. Examples of applying the VIE into modeling of EM LWD tool response are presented, which show the accuracy and efficiency of the scheme. An analytical method based on spherical functions expansion is used to obtain the exact electric fields radiated from transmitter coil of LWD tool in comparison with magnetic dipole approximation.