Efficient Simulation of LWD Azimuthal Propagation Resistivity Tool in Layered TI Formation Based on 3-D Finite Volume Method of Coupled Potentials in the Half Space and Continuation Technique

Abstract

In this paper, we improve the three-dimensional (3-D) finite volume algorithm of coupled potentials on cylindrical grids to enhance the simulation efficiency of the logging while drilling (LWD) azimuthal propagation resistivity tool (APR). In general, the spatial distributions of both formation conductivity and electromagnetic (EM) fields excited by the axial direction transmitters are symmetric on both sides of the vertical section of the APR instrument axis in the inclined borehole. We thus try to decompose the whole solution domain into two symmetric sub-regions. Then, we introduce appropriate boundary conditions on the joint surface of sub-regions. The problem on solving the EM fields in the 3-D full space is converted to that in the half space. The 3-D finite volume method of coupled potentials is applied to solve the EM fields in one of the sub-regions in cylindrical coordinates. According to the EM symmetry, we continue the numerical results in the half space into another half space to acquire EM fields in full space. Finally, we apply the numerical results of the new algorithm to study and investigate tool responses in several different cases such as different formation resistivity, tool eccentricity, etc. The comparison of results obtained in the half space with those in the full space validates the effectiveness of the new method, and the forward simulation efficiency in half space has been improved by more than 4 times.

Keywords

• Logging while drilling (LWD)
• LWD azimuthal electromagnetic wave tool
• Maxwell’s equation
• finite-volume method
• inhomogeneous anisotropic media