| With the rapid progress of the oil industry and the increasingly complicated geologic status of reservoir, many new logging methods come forth continuously. Logging while drilling method is one of the most rapidly developing method. New logging environments and methods bring new challenges to the logging researchers, such as new electromagnetic LWD instruments capability, the response of electromagnetic LWD instruments in highly deviated or horizontal wells, the different detection ability between the traditional induction logging tools and electromagnetic LWD instruments. Numerical simulation can serve as an efficient tool to solve these problems. The objective of this dissertation is to attempt to provide a feasible methodological platform by the study of numerical simulation in 1D, 2D and 3D formation models.In chapter 2 and 3, the electromagnetic distribution formulate of radially layered and stratified formation is introduced with high efficient algorithm. The transmitting coils of induction logging instruments are simplified as series of magnetic dipoles, electromagnetic wave is resolved as TE and TM wave in horizontal layers, and the analysis results which include integration of Bessel function are obtained in the dissertation. Improved Gauss numerical integral method is used to calculate the infinite integration of Bessel function instead of traditional Fourier-Henkel transform method. The numerical simulation method is effective to analysis the effect of the shoulder and the borehole deviation on the response of LWD electrical instruments.The widely used 2D algorithm is introduced in chapter 4. Successive method and numerical model matching method are addressed. The successive method is meaningful to the inversion of induction logging data. Amplitude basis function and slope basis function built by Mr. Zhang Geng-ji are used in the method of NMM. New basis function guarantee the continuity of the field itself and its first-order derivation, so only a small quantity of basis function are needed to get a high accuracy. The simulation results show that NMM is the most effective algorithm to simulate the response of low frequency induction logging and high frequency electromagnetic LWD instruments by choosing proper mesh and proper amount of basis functions. In chapter 5 a 3D algorithm for electromagnetic LWD simulation in frequency domain is introduced. The difference equations to calculate the electromagnetic response are deserved from Maxwell's equations by using staged-grid finite difference method. A new mesh generation method is adopted according to the geometric characteristics of deviated well models with borehole and invasion. The mirror symmetry of the electric field is involved to largely reduce the computation scale. The large scale complex equations are stored by one-dimensional variant-banded and are solved by the method of improved incomplete Choleskey conjugate gradient and the response of electromagnetic LWD tool is deserved. The simulation results show that the algorithm can solve the 3D problem effectively by contrast with analytical results, but the adoption principle of background conductivity should be further studied.Taking EWR-Phase4 as an example, various influence factors are studied on the basis of several numerical simulation methods in chapter 6. The research contents include that the choosing of work frequency, the investigation ability, the influence of shoulder and thickness, borehole, mud-filtrate invasion, deviation of borehole, dielectric constant and anisotropy. The study can provide theoretical basis for the instrument manufacture and logging data interpretation.A new research idea of compensated tools is proposed in chapter 7. Borehole slump has great influence on the response of electromagnetic tools because of the characteristics of the tools, especially when the mud is salty. It is necessary to compensate the logging data. Traditional compensation method makes the tool one time longer. A new compensation method is proposed which can reduce the length of tools greatly on the basis of reciprocity principle of electromagnetic.
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