Efficient Domain Decomposed Simulations of Induction Well-Logging Tools in a Deviated Borehole.

For designing or calibrating a triaxial induction well-logging tool, efficient simulations of moving the tool in an arbitrary borehole in an invaded layered medium are essential. The computational time of conventional methods is directly proportional to the number of tool positions. In this work, a domain decomposition method (DDM) that utilizes the layered medium Green's functions (LMGFs) and loop-tree (LT) basis functions is proposed; it separates stationary subdomains from the variable subdomain where the tool moves. Efforts are saved in calculating the matrix related to the stationary subdomains. A special stationary subdomain is the boundary surface of the finite-element volume. The combination of the finite-element method (FEM) and the layered medium surface integral equation (SIE) method minimizes the number of unknowns. LT basis functions are used to discretize the equivalent current densities on the boundary to improve numerical accuracy at low frequencies. The accuracy and efficiency of this new method are validated in well-logging simulations with a prototype induction tool including the solenoids, mandrels, and sleeves in a deviated borehole and layered media.