Cylindrical FDTD analysis of LWD tools through anisotropic dipping-layered earth media

Electrical logging-while-drilling (LWD) tools are commonly used in oil and gas exploration to estimate the conductivity (resistivity) of adjacent earth media. In general, earth media exhibit anisotropic conductivities. This implies that when LWD tools are used for deviated and horizontal drilling, the resulting borehole problem may include dipping-layered media with dipping beds having full 3 x 3 conductivity tensors. To model this problem, we describe a 3-D cylindrical finite-difference time-domain (FDTD) algorithm extended to fully anisotropic conductive media and implemented with cylindrical perfectly matched layers to mimic open-domain problems. The 3-D F algorithm is validated against analytical results in simple to formations, showing good agreement, and used to simulate the response of LWD tools through anisotropic dipping beds for various values of anisotropic conductivities and dipping angles.