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《Chinese Journal of Geophysics》 2007-03

## 3-D numerical mode-matching (NMM) method for resistivity logging responses in nonsymmetric conditions

TAN Mao-Jin~ 1,2,3 ,ZHANG Geng-Ji~2,YUN Hua-Yun~4,ZHAO Wen-Jie~31 Lab. of Computational Geodynamics, Graduate University of Chinese Academy of Science, Beijing 100049, China2 China University of Petroleum, Dongying 257061, China3 Shengli Well Logging Co., SINOPEC, Dongying 257096, China4 Shengli Petroleum Administrative Bureau, SINOPEC, Dongying 257000, China
Three-dimension (3-D) Numerical Mode-Matching (NMM) is selected to deal with resistivity logging responses in nonsymmetric conditions. First, an appropriate Descartes's reference frame is set up—the plane of deviated borehole and normal of formation is regarded as XOY, and formation strike is regarded as Z axis. In the XOY plane, the finite-element method (FEM) is used and a series of 2-D generalized eigenvalue problems are solved; whereas vertical analytic is adopted along Z axis. In analytical section, the medium is sliced into some layers artificially, and the relationship between adjacent layers is derived according to the electromagnetic field continuity, namely boundary transition matrices rather than reflection and transmission matrixes theory in the 2-D NMM method. Finally, a system of linear equations is constructed according to the natural boundary conditions that the top bed has no up-going wave or the bottom bed has no down-going wave, and the potential of every point of formation is solved and the apparent resistivity is computed. In the given formation model, the results of 3-D NMM agree well with previous ones of 2-D NMM and FEM in symmetry conditions. Furthermore, the algorithm also applies to titled formation and elliptical borehole; and some examples illustrate how all kinds of tilt degrees affect logging response results.
【CateGory Index】： P631.84
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