摘要
采用模式匹配法研究了非轴对称条件下普通电阻率测井响应.根据非轴对称的地层模型,建立了新型的坐标系,确定在井轴与地层法线所形成的XOY平面上用数值方法,与此面垂直的方向上用解析方法.在XOY平面上的数值分析中,构建了广义特征值问题;在Z轴方向的解析部分中,人为地划分了一些介质层,并根据电磁场在层界面的连续性条件,推导出了各层之间场量的传递关系,从而摒弃了传统上二维模式匹配法中的复杂的反射阵和透射阵理论,完成了三维模式匹配理论.多种地层模型的数值结果对比表明,该方法在轴对称条件下的计算结果和二维模式匹配法的计算结果具有很好的一致性.此外,应用此算法还研究了倾斜地层等各种非轴对称的地层模型电阻率测井响应,系统地考察了井斜角对普通电阻率测井响应的影响.
Abstract 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.
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2007年第3期939-945,共7页
Chinese Journal of Geophysics
关键词
非轴对称条件
电阻率测井响应
三维模式匹配法
广义特征值
Nonsymmetric conditions, Resistivity logging responses, 3-D numerical mode-matching （NMM）method, Generalized eigenvalue problem
