3D FV Simulation of the Orthogonal Azimuth Electromagnetic Tool Response Logging While Drilling with Multi Annular Grooves Using Potentials

Abstract In this paper, we use the 3D cylindrical finite volume (3D FV) method to simulate the Orthogonal Azimuth Electromagnetic Tool (OAEMT) responses Logging While Drilling (LWD) according to the special structure of the OAEMT with multi annular grooves. The algorithm allows the solution of the 3D Maxwell’s equation in inhomogeneous media with arbitrary conductivity and magnetic permeability distributions. For improvement of the computational efficiency and the modeling accuracy of the responses of OAEMT with annular grooves filled with ferrite material on steel mandrel in a completely anisotropic media, several techniques are applied: 1) a 3-D cylindrical irregular grid to avoid stair-casing discretization errors in the transmitter, receiver, and mandrel geometries; 2)the electric field continuation to approximate the perfectly electric conducting (PEC) boundary condition for enhancement of the discrete accuracy of the Helmholtz equations on the surface of steel mandrel; 3)the standardization technique to determine the equivalent conductivity and permeability in a non-uniform element; 4) PARDISO direct solver to solve the discrete equation as far as possible for increase of solution stability. We validate the 3D FV results against the numerical mode matching method. The comparisons show very good agreement. Results from 3-D borehole problems in several complex formation conditions involving eccentric tools and dipping beds are given to demonstrate the robustness of the method.