| The finite element method (FEM) has become a powerful tool for numerical solutions to a wide range of problems. In this dissertation, FEM was applied to solving subsurface well logging problems. Special features of the problem were the following: low frequency electromagnetic (EM) waves were transmitted in a lossy medium; electric conductivity was a tensor quantity and may have a high contrast between different media; logging tools were complicated and focusing conditions were added for constraints; simulation range was up to 10,000 feet. Three applications have been discussed in this dissertation: the simulation of AC laterolog tools; the simulation of EM telemetry systems, and the simulation of through casing resistivity tools. Only vertical wells were considered in this dissertation.;The accomplishments of this dissertation were: (1) FEM formulations suited for the alternating current (AC) well logging tools were developed based on Maxwell's equations and cylindrical coordinates. Several sets of formulations were illustrated based on magnetic field (H), electrical field (E), and rhoH. (2) Innovative formulations for FEM source models were formulated for AC well logging tools. The application of these source formulas made simulations of different AC well logging tools practical, flexible and accurate. (3) Four FORTRAN codes were developed for AC laterolog tools, EM telemetry systems and through casing resistivity tools. Modules and subroutines were well constructed for future development of the code. (4) The direct solver --- the Frontal Solver code was upgraded for the AC situation; it could also self-adjust to different logging tools and users did not need to change it for different tool structures. This solver was also very fast.;The codes have been tested, validated, and delivered to well logging consortium members. The Groningen effect was analyzed for AC laterolog tools. Frequency, invasion and media anisotropy effects were discussed for both the AC laterolog tool and the through-casing resistivity tool. The effect of frequency, drill bit depth, casing, formation resistivity, source gap thickness, and borehole fluid type on the receiver voltage and system impedance were evaluated for the EM telemetry system. |
