Based On Electrical Logging Response Of The Integral Equation Method For Numerical Computing Research

With the increasing development of electrical well-logging technology, conventionnal induction logging technology can not meet the needs of oil exploration. Logging-While-Drilling(LWD) has become one of the most popular technology because of the accurate measurement, geo-steering drilling in real time. In this dissertation, we have developed a numerical modeling code of well-logging response based on the volume-surface integral equation. Three topics are included in the contents,Firstly, we systematically introduce the basic principle of the coupled equation for solving EM characteristics of a mixed conducting and dielectric target. Numerical method for solving such problem-Method of Moments (MOM) and some key technologies will be given.Secondly, details of the multilevel adaptive cross approximation (MLACA) which is applied to reduce memory and CPU time are inctroduced, including mathematical principle, numerical implementation and error analysis. Besides, preconditioning technique is used to accelerate the convergence rate of the iterations.Thirdly, we will give the basic principle of LWD, and then study the difference between magnetic dipole and real coil that serve as the excitation source. For induction logging measurements, compared with the wavelength of electromagnetic waves and the distance between transmitter and receiver coils, the coil radius can be ignored. Therefore, the coil antenna can be adequately approximated as a magnetic dipole source. However, for LWD tools, the distance between transmitter and receiver coils is shorter and all coils are wrapped on the mandrel, in order to simulate the role of mandrel, we can not approximate them as magnetic dipole.Finally, the response characteristics in different inhomogeneous formation are modeled and calculated. Many factors are taken into consideration. They include different truncated radii, shoulder, mandrel, invasion, dipping beds and others.