Numerical Simulation For Logging Response Based On Integral Equation

In geophysical exploration, electromagnetic(EM) field method has been widely used. The method is judging electricity parameters of rocks and minerals in the earth’s crust the, such as electrical conductivity, etc. It is implemented in reservoir exploration, drilling azimuth orientation, etc. At the same time, the exploitation in oil field is more and more difficult. The industry is not only faced with the problem of conventional logging, but also the problems of solving large scale logging 、 big contrast and anisotropic geological condition in logging while drilling(LWD). So more advanced instruments and equipments are need to be created, this requires a new method for electromagnetic field of study including implement efficient solution’s ability to solve complex formation, which is used to guide instrument design and innovation, the interpretation of the formation, etc. The obtaining and inversion for layers information is based on the forward model. On the above-mentioned background, this paper focus on the forward model. In order to solve the problem given priority to, this paper is based on the anisotropic volume integral equation method of moments(VIE-Mo M), combined with efficient methods which can effectively solves the large scale, big contrast of formation of the problem, and the integral equations under complex tilted anisotropic 2.5D and 3D formation problems. The main contribution of this paper is as follows:1. The common electromagnetic logging response model and modeling method is introduced, the method to obtain the formation parameters and to count voltage of coils, reason of selection of frequency and coil system is explained. 2. The principle of VIE-Mo M is illustrated, along with the discreting and the solving process. impedance matrix elements in anisotropic integral equation with SWG basis function is deduced in the paper independently. Then the method of numerical integration, singularity processed and GMRES method of solving linear equations are stated. 3. When solving large scale logging, in order to solve the VIE-Mo M with many unknowns which consumes a large memory, multi-layer adaptive cross- singular value decomposition(MLACA-SVD) algorithm is introduced. The computational complexity and storage complexity is analyzed. In order to solve the integral equation of the unknown quantity is large, large scale logging consumption causedby large memory of iteration time problem, so the technology of near-field conditions is stated. It effectively speeds up the convergence speed of solving. 4. Based on the above method, through a large number of examples, this paper verifies its correctness and efficiency, It can effectively solves VIE-Mo M in large scale logging and big contrast logging problem. By contrast, we get logging grid subdivision principle in LWD and the low recognition ability with the method. 5. The horizontal and vertical coil are combined to constitute a tilted transmitter coil. Tensor transform method is gained to solve anisotropy in tilted strata. At the same time using the of all kinds of efficient algorithms above to improve the ability of solving the problem of 3-D, effectively simulate resistivity LWD azimuth, to verify the sediment of thin interbed of electric parameters of macro and micro isotropic anisotropic properties. The electric parameters with micro isotropic thin interbed macroscopic anisotropy are analyzed in equivalence. Finally, paper has a synthetic evaluation of simulation and multilayer tilted anisotropic formation LWD response, which provides some guidance for application of resistivity LWD and data processing and interpretation.