各向异性介质多分量感应测井三维Born几何因子理论研究

几何因子理论被广泛运用于感应测井仪器设计、响应特征分析及高分辨率曲线处理, 现有的感应测井几何因子主要适用于二维各向同性介质, 难以满足各向异性介质多分量感应测井的研究需要. 本文基于Born近似方法将Born几何因子扩展至各向异性介质, 推导了各向异性介质多分量感应测井三维Born几何因子表达式, 随后进一步考察了多分量感应测井对地层各向异性的敏感性和探测能力. 数值模拟结果表明, 各向异性系数越大, 多分量感应测井几何因子空间分布越复杂, 其对各向异性的敏感性越高. 多分量感应测井仪器在不同倾斜角度对各向异性均具有较高的敏感性. 直井条件下, xx共面分量受各向异性影响严重, 井斜角在40°–60°时, xz/zx交叉分量对各向异性的敏感性高, 水平井中zz同轴分量则对各向异性的探测能力最强. 各向异性介质三维Born几何因子弥补了现有几何因子理论的不足, 可为国内新型多分量感应测井仪器研发及储层各向异性评价方法的发展提供有利条件.

Three dimensional Born geometrical factor of multi-component induction logging in anisotropic media

Geometrical factor has been widely used in the design of induction tool and analysis of complex logging responses, as well as the high resolution processing of logging data. Works in this area are usually limited to two-dimensional isotropic medium and are only available to cases of coaxial transmitter and coaxial receiver coupling. For a more thorough understanding of multicomponent induction logging in the presence of transverse anisotropy, a knowledge of anisotropic geometrical factor is often necessary. In this paper, the two-dimensional and isotropic geometrical factors are extended to the anisotropic media using Born approximation, and the expressions of 3D Born geometrical factors for multicomponent induction logging are derived. Then the sensitivity and detectability of coaxial, coplanar and cross-coupling measurements are investigated. Numerical results show that with increasing coefficients of conductivity anisotropy, the spatial distribution of geometrical factors becomes increasingly complicated, and more sensitivity information can be detected by multicomponent induction tools. The multicomponent induction tool is sensitive to conductivity anisotropy at arbitrary dipping angles. In vertical wells, coplanar measurements are significantly affected by the conductivity anisotropy. Compared with coaxial and coplanar measurements, cross-coupling component offers superior sensitivity information to the conductivity anisotropy with the dipping angle being 40～ 60°. In horizontal wells, coaxial measurements are the most sensitive to the conductivity anisotropy. The extended 3D Born geometrical factor directly exhibits the anisotropy sensitivity in terms of spatial contribution, and has made up for the shortage of previous geometrical factors. The new geometrical factor will create favorable conditions for the development of new multicomponent induction tool and the interpretation of anisotropic formations.