张烨^1,,
林蔺²,
陈桂波¹,
李强³
1. 长春理工大学 理学院, 长春 130022
2. 东北电力大学 理学院, 长春 132012
3. 中国石油长城钻探工程有限公司测井技术研究院, 北京 100124

基金项目: 国家自然科学基金青年基金（41404109）资助


详细信息

作者简介: 张烨, 男, 长春理工大学, 讲师, 主要研究方向为非均质与各向异性介质中电磁场数值模拟.E-mail:zhangye84829@163.com

中图分类号: P631

收稿日期:2017-03-13
修回日期:2017-09-26
上线日期:2018-04-05

Study on the 3D frequency domain coupled potential forward modeling of crosswell electromagnetic response in transversely isotropic formation

ZHANG Ye^1,,
LIN Lin²,
CHEN GuiBo¹,
LI Qiang³
1. College of Science, Changchun University of Science and Technology, Changchun 130022, China
2. College of Science, Northeast Electric Power University, Changchun 132012, China
3. Institute of Logging Technology, CNPC Greatwall Drilling Company, Beijing 100124, China


MSC: P631

--> Received Date: 13 March 2017
Revised Date: 26 September 2017
Available Online: 05 April 2018


摘要
摘要:本文针对电导率横向同性地层中三轴发射-接收线圈系的井间电磁响应，开展三维正演算法及模拟研究.首先将发射线圈简化为三轴正交磁偶极子源.为克服低频电磁产生的数值迭代收敛缓慢问题，利用低感应数预处理方法将频域Maxwell方程组转化为基于矢势与标势的Helmholtz方程.采用非等间距的Yee氏交错网格、电导率的体积加权平均技术以及积分形式的有限差分格式实现对控制方程的离散化.借助于不完全LU分解预处理的稳定双共轭梯度法计算井间电磁响应的数值解，并通过与有限元软件COMSOL的数值结果对比验证本文模型与算法的有效性.数值计算结果表明：在横向同性地层的垂直井模型中，测井响应横向分量xx和yy能反映出地层电导率各向异性信息，但横向探测能力较差.轴向分量zz虽只反映地层水平电阻率信息，但具有较好的横向探测能力，且对地层中异常体非常敏感，而交叉分量xz、zx则具备较强的层边界识别能力.
关键词: 井间电磁测井/
横向同性地层/
耦合势有限体积差分/
三轴线圈系

Abstract:In this paper, a three-dimensional forward algorithm and simulation for the crosswell electromagnetic responses of the triaxial coils system in the transversely isotropic (TI) formation are presented. The transmit coils are simplified to the triaxial perpendicular magnetic dipole source firstly. To solve the problem of low convergence caused by low electromagnetic frequency, low induction number (LIN) preconditioner is applied to transform Maxwell equations to the Helmholtz equations. Conductivity volume weighted average, non-uniform Yee's grid and integral finite difference scheme are used to discrete the governing equations. Incomplete LU factorization preconditioning technique and bi-conjugate gradient stabilized method are applied to obtain the numerical solution of cross-well electromagnetic responses, and the numerical results given by the finite element software Comsol verify the validity of the proposed model and algorithm. The numerical results show that the lateral components xx and yy can reflect the formation anisotropy information in the vertical well model of TI formation, but its lateral detection ability is poor. Although the axial component zz only reflects the horizontal resistivity information, it has a good ability of lateral detection and is very sensitive to the anomalies in the formation. The cross components xz, zx have a strong ability to identify the boundary layer.
Key words:Crosswell electromagnetic logging/
Transversely isotropic formation/
Coupled potentials finite volume difference/
Triaxial coils



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