Three-dimensional simulation of eccentric LWD tool response in boreholes through dipping formations

We simulate the response of logging-while-drilling (LWD) tools in complex thee-dimensional (3-D) borehole environments using a finite-difference time-domain (FDTD) scheme in cylindrical coordinates. Several techniques are applied to the FDTD algorithm to improve the computational efficiency and the modeling accuracy of more arbitrary geometries/media in well-logging problems: (1) a 3-D FDTD cylindrical grid to avoid staircasing discretization errors in the transmitter, receiver, and mandrel geometries; (2) an anisotropic-medium (unsplit) perfectly matched layer (PML) absorbing boundary condition in cylindrical coordinates is applied to the FDTD algorithm, leading to more compact grids and reduced memory requirements; (3) a simple and efficient algorithm is employed to extract frequency-domain data (phase and amplitude) from early-time FDTD data; (4) permittivity scaling is applied to overcome the Courant limit of FDTD and allow faster simulations of lower frequency tool; and (5) two locally conformal FDTD (LC-FDTD) techniques are applied to better simulate the response of logging tools in eccentric boreholes. We validate the FDTD results against the numerical mode matching method for problems where the latter is applicable, and against pseudoanalytical results for eccentric borehole problems. The comparisons show very good agreement. Results from 3-D borehole problems involving eccentric tools and dipping beds simultaneously are also included to demonstrate the robustness of the method.