圆柱分层各向异性地层中偏心线圈电磁场闭合解  

Closed-form of electromagnetic representation for eccentric coil in cylindrically layered anisotropic formation

作　　者：陈华 洪德成[2] 武圣哲 CHEN Hua;HONG Decheng;WU Shengzhe(College of Science in China University of Petroleum(East China),Qingdao 266580,China;Internal Center for Computational Method and Software,College of Physics,Jilin University,Changchun 130012,China)

机构地区：[1]中国石油大学(华东)理学院,山东青岛266580 [2]吉林大学物理学院计算方法与软件国际中心,吉林长春130012

出　　处：《中国石油大学学报（自然科学版）》2022年第4期41-51,共11页Journal of China University of Petroleum(Edition of Natural Science)

基　　金：国家自然科学基金项目(41874132);中国石油重大科技项目(ZD2019-184-001)。

摘　　要：圆柱状分层介质中电磁场解析算法是电法测井快速正演模拟及井眼环境校正基础,推导倾斜线圈在最内层偏心时电磁场解析解闭合表达式。在频率-波数域中,利用Graf定理将电磁场的驻波和外行波由仪器坐标系转换成地层坐标系,然后引入无数值溢出的新型广义反射系数描述电磁场不同角模量在偏心边界处的耦合。针对共轴倾斜线圈系给出其偏心时接收线圈电压解析解,并分析线圈水平放置时电压表达式的退化过程。通过将背景场与反射场分离,减小被积函数收敛区间,提高接收线圈电压数值积分的稳定性及计算精度。结果表明:仪器居中时水平发射-水平接收线圈电压与地层电导率各向异性无关,而偏心时会受各向异性影响;水平发射-倾斜接线圈的偏心角不同导致其与井眼边界朝向不同,电压随偏心角变化明显;倾斜发射-倾斜接收线圈电压受仪发射线圈倾斜角、地层电导率各向异性及偏心角影响很大。In this paper,we present a closed-form analytical solution for an eccentric tilted coil that is embedded in the innermost layer of a cylindrical anisotropic formation.Such a solution is the basis of fast forward modeling and borehole correction for electric logging.In the frequently-wavenumber domain,the representation of electromagnetic field in the tool coordinate system is firstly transformed into the formation coordinate system based on Graf s theorem,and then,the non-overflow generalized reflection/transmission coefficient is introduced to describe the electromagnetic coupling between different harmonic components at the cylindrical boundary.The voltage expression on the eccentric tilted coil voltage is given,and its process of simplification is also analyzed while the coil is placed horizontally.Both accuracy and stability for voltage calculating are improved by separating the background field from the reflection field.The numerical results show that the anisotropy affects obviously the voltage of the horizontal transmitter-horizontal receiver in the eccentric situation;the eccentric angle affects the obvious voltage of the horizontal transmitter-tilted receiver due to different direction to the borehole boundary;the relative dip of coils,the anisotropy and the eccentric angle affect the voltage of the tilted transmitter-tilted receiver,which make the response more complex in the eccentric scenarios.

关 键 词：圆柱状分层 各向异性地层 偏心电流源 倾斜线圈 方位电磁波 

分 类 号：P631.9[天文地球—地质矿产勘探]