体面积分方程矩量法及其在电法测井中的应用

发布时间：2018-04-20 11:00

本文选题：体面积分方程 + 矩量法　；参考：《电子科技大学》2015年硕士论文

【摘要】：地球物理测井中,大斜度井、水平井占据的比重越来越大,仪器响应在这些测井环境中不同于直井环境,传统的基于直井的测井解释和数值模拟方法变得不再适用。因此,进行电法测井的正演数值模拟研究,用于解释和分析测井仪器在这些测井环境中响应和异常现象,这对于仪器的研发和工程实际应用具有重要意义。基于以上原因,本文对体面积分方程矩量法进行了研究,并用于电法测井的数值模拟。传统的基于SWG基函数的体积分方程,需要处理边界面电荷,几何建模要共形剖分。而本文采用的基于分片常数基的非共形体积分方程,不需处理边界面电荷;采用非共形网格剖分使几何建模更为灵活;只是需要处理双梯度Green函数的超强奇异性积分,本文采用了高阶奇异值提取法很好地处理了该积分奇异性问题。本文主要内容如下:1.详细推导了体积分、面积分、体面积分方程的矩量法求解过程,采用高阶奇异值提取法解决了三类积分方程中涉及的奇异性及近奇异性积分;建立了基于分片常数基的体积分方程,并结合面积分方程建立了的体面积分方程,用该方程精确计算了金属介质组合目标的近场以及介质内部的场,实现了很好的精度;2.采用点匹配法测试非共形体积分方程,实现了阻抗矩阵的快速填充并达到了很好的精度,并且将点匹配法的体积分方程与迦辽金法匹配的面积分方程组合实现了混合两种测试方法的体面积分方程,并在算例中验证了其精度;3.用基于球函数展开的解析方法求解了环形线圈的近场;4.对比了水平线圈和倾斜线圈在各向异性地层中的响应差异;对各向同性地层中,不同的倾斜线圈系的测井响应进行了数值仿真,发现幅度比和相位差变化复杂,出现两者变化趋势不一致的情况;实现了对地层倾斜、井斜的三维测井问题的计算;5.对井眼和钻铤作纵向截断,其网格相对于井眼边界地层非共形剖分,采用井眼内网格随测量点移动的计算模式来数值模拟仪器在井眼中移动测量的过程,实现一套网格的多次使用。
[Abstract]:In geophysical logging, the proportion of high deviated wells and horizontal wells is increasing, and the tool response is different from that of vertical wells in these logging environments. The traditional logging interpretation and numerical simulation methods based on vertical wells are no longer applicable. Therefore, the forward numerical simulation of electrical logging is used to interpret and analyze the response and abnormal phenomena of logging tools in these logging environments, which is of great significance for the research and development of tools and the practical application in engineering. Based on the above reasons, the method of moment of the decent integral equation is studied and applied to the numerical simulation of electric logging. The traditional volume fractional equation based on SWG basis function needs to deal with the boundary surface charge, and the geometric modeling needs conformal dissection. The non-conformal integral equation based on piecewise constant basis does not need to deal with the boundary surface charge, the geometric modeling is more flexible by using non-conformal mesh generation, and the super-singularity integral of the bigradient Green function only needs to be dealt with. In this paper, the high order singular value extraction method is used to deal with the singularity of the integral. The main contents of this paper are as follows: 1. The method of moment for solving volume integral, area fraction and decent integral equation is derived in detail. The singularity and near singularity integral of three kinds of integral equations are solved by the method of high order singular value extraction. The volume fraction equation based on the piecewise constant basis is established, and the decent integral equation based on the area integral equation is established. The near field and the internal field of the combined target in the metal medium are accurately calculated by this equation, and the good precision is achieved. The point matching method is used to test the integral equations of non-conformal bodies. The impedance matrix is filled quickly and the precision is very good. The volume fraction equation of point matching method and the area integral equation of Galerkin method are combined to realize the decent integral equation of mixed two test methods, and its accuracy is verified by an example. An analytical method based on spherical function expansion is used to solve the near field of annular coil. The responses of horizontal coils and tilting coils in anisotropic formations are compared, and the logging responses of different tilting coils in isotropic formations are simulated. It is found that the amplitude ratio and phase difference change are complex. The result shows that the variation trend of the two is not consistent, and the 3-D logging problem of formation inclination and well inclination is realized. The borehole and drill collar are truncated longitudinally, and the meshes are not conformal in relation to the borehole boundary formation. The calculation model of the movement of the borehole meshes with the measured points is adopted to numerically simulate the process of the instrument moving and measuring in the borehole. To achieve a set of grid multiple use.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.811

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