三轴各向异性层状介质磁偶极子源电磁场递推算法及应用

许孝凯, 赵伟娜, 张晋言, 董经利, 孙清溪, 王磊

许孝凯,赵伟娜,张晋言,等. 三轴各向异性层状介质磁偶极子源电磁场递推算法及应用[J]. 石油钻探技术,2024, 52(1):130-139. DOI: 10.11911/syztjs.2023117
引用本文: 许孝凯,赵伟娜,张晋言,等. 三轴各向异性层状介质磁偶极子源电磁场递推算法及应用[J]. 石油钻探技术,2024, 52(1):130-139. DOI: 10.11911/syztjs.2023117
XU Xiaokai, ZHAO Weina, ZHANG Jinyan, et al. Recursive algorithm for electromagnetic fields from magnetic dipole in layered triaxial anisotropic medium and its application [J]. Petroleum Drilling Techniques,2024, 52(1):130-139. DOI: 10.11911/syztjs.2023117
Citation: XU Xiaokai, ZHAO Weina, ZHANG Jinyan, et al. Recursive algorithm for electromagnetic fields from magnetic dipole in layered triaxial anisotropic medium and its application [J]. Petroleum Drilling Techniques,2024, 52(1):130-139. DOI: 10.11911/syztjs.2023117

三轴各向异性层状介质磁偶极子源电磁场递推算法及应用

详细信息
    作者简介:

    许孝凯(1985—),男,山东东营人,2007年毕业于中国石油大学(华东)勘查技术与工程专业,2012年获中国石油大学(华东)地质资源与地质工程专业博士学位,高级工程师,主要从事地球物理测井方面的研究。E-mail:xuxiaokai@foxmail.com

  • 中图分类号: P631.8+13

Recursive Algorithm for Electromagnetic Fields from Magnetic Dipole in Layered Triaxial Anisotropic Medium and Its Application

  • 摘要:

    为快速、精确模拟复杂三轴各向异性介质中的电磁波测井响应规律,研究了一种适用于水平层状地层的磁偶极子源电磁场伪解析递推算法。该算法通过双重傅里叶变换,将空间域的三维电磁场正演转换为一系列对一维谱域场的求解,将地层上、下界面位置引入谱域电磁场通解公式,克服了传统方法存在的数值溢出问题;进一步利用传播矩阵方法,递推获得各个地层界面处的幅度系数;针对积分核函数存在的强烈振荡问题,提出了一种双重正余弦数值滤波积分方法,实现了谱域到空间域电磁场的准确、快速转换。模拟结果表明:三轴各向异性导致电测井响应更为复杂,传统各向异性电测井解释模型不再适用。新递推算法是复杂各向异性储层测井响应分析的基础,也为电性参数准确提取和精准地质导向提供了正演手段。

    Abstract:

    In order to quickly and accurately simulate the response of electromagnetic (EM) wave logging in complex triaxial anisotropic media, a pseudo-analytical recursive algorithm for the EM fields generated by magnetic dipole was developed, which was suitable for horizontal layered strata. By using the dual Fourier transform technique, the algorithm transformed the forward modeling of the three-dimensional EM field into a series of solutions of a one-dimensional spectral field. The upper and lower boundary positions were introduced into the general expressions of the spectral field, which avoided the numerical overflow problem in traditional algorithms. The propagation matrix method was then adopted to recursively derive the amplitude coefficients at each boundary. To handle the strong oscillation of the integral kernel function, a dual sine/cosine numerical filtering integral technique was developed to achieve the accurate and fast conversion between EMs from the spectral domain to the spatial domain. The simulation results show that the existence of triaxial anisotropy makes the electrical logging response more complex, and the traditional anisotropic electrical logging interpretation model is no longer applicable. The new recursive algorithm is the basis of complex anisotropic reservoir logging response analysis and provides a forward modeling method for accurate extraction of electrical parameters and accurate geosteering.

  • 图  1   多层三轴各向异性地层模型示意

    Figure  1.   Layered formation model with triaxial anisotropy

    图  2   无限厚双轴各向异性地层模型及双重积分核函数分布

    Figure  2.   Infinitely thick formation model with biaxial anisotropy and double integral kernel function distribution

    图  3   2层介质伪解析解与商业软件计算结果的对比

    Figure  3.   Result comparison by pseudo-analytical method and commercial software in two layered formation

    图  4   多分量感应测井结构及地层模型

    Figure  4.   Multi-component induction logging structure and formation model

    图  5   VTI介质多分量感应测井的同轴和共面分量在俄克拉荷马地层模型中的响应

    Figure  5.   Coaxial and coplanar components of multi-component induction logging in a VTI Oklahom formation model

    图  6   HTI介质多分量感应测井的同轴和共面分量在俄克拉荷马地层模型中的响应

    Figure  6.   Coaxial and coplanar components of multi-componentinduction logging in a HTI Oklahoma formation model

    图  7   不同地层随钻方位电磁波测井的响应

    Figure  7.   Logging-while-drilling azimuthal EM wave logging responses in three-layered anisotropic formations

    表  1   2种积分方法精度与速度的对比

    Table  1   Accuracy and speed comparison of two integral methods

    方法采样点数量误差,%相对耗时
    高斯积分1 2000.004 0219.50
    2 0000.000 3610.00
    数值滤波810.006 01.00
    2410.002 58.85
    6010.001 655.10
    下载: 导出CSV

    表  2   不同地层模型围岩的电导率

    Table  2   Conductivities of surrounding rock in different formation models

    地层模型σx/(S·m−1σy/(S·m−1σz/(S·m−1
    各向同性0.250.250.25
    VTI0.250.250.10
    HTI0.250.100.25
    各向异性0.200.100.05
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-09-26
  • 修回日期:  2023-11-09
  • 网络出版日期:  2023-11-21
  • 刊出日期:  2024-01-24

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