基于电阻率敏感性函数的随钻电磁波测井探测特性研究

为研究地层电性变化时不同区域对电磁波测井响应的贡献分布，从响应信号对地层参数求偏导的角度，给出一种新的电阻率敏感性函数定义，引入模式匹配法对纵向成层、径向非均匀介质敏感性分布进行快速模拟；通过对敏感性函数纵、横向积分给出了单发双收线圈系纵、横向探测范围，研究了井眼、频率、背景地层电阻率等对探测特性的影响.结果表明：敏感性函数能够定量表征响应对地层纵向与径向微观与宏观敏感性，幅度比与相位差敏感性分布形态类似，幅度比较广较深，而相位差分辨率高，敏感范围小；敏感性函数进行径向积分后可表征仪器的探测深度，与伪几何因子对比达到了同样的效果；背景地层电阻率在1~100 Ωm变化时，工作频率2 MHz下幅度比探测深度约为0.6~2.3 m，相位差为0.3~0.8 m，幅度比50%纵向积分敏感性层厚约为0.3~1.6 m，相位差约为0.2~0.6 m；异常体与背景地层电阻率对比度在1~50变化时，引起的探测深度与敏感性层厚差异约为0.1~0.2 m，远小于地层电阻率的影响.

Research on detection characteristics of electromagnetic logging while drilling based on resistivity sensitivity function

In order to investigate the electromagnetic logging response contribution from different spatial domain with different electrical properties, a new sensitivity function is defined by taking partial derivative of response with respect to formation properties, and numerical mode matching method is introduced to compute the sensitivity function distribution of vertical layered and horizontal inhomogeneous medium. The vertical and horizontal integration of this sensitivity function has been used to illustrate the vertical and horizontal detection range of one transmitter and two receivers coil array in electromagnetic logging while drilling, and the influence of frequency, background formation resistivity and resistivity contrast are discussed. The results show that this definition of sensitivity function can quantitatively describe micro and macro sensitivity distribution of electromagnetic logging response with respect to properties of abnormal bodies in horizontal and vertical direction. The shape of sensitivity distribution of amplitude ratio and phase difference are alike, response contribution is mostly from the region between transmitter and receiver, sensitivity region of amplitude ratio is larger and deeper than that of phase difference, phase difference sensitivity is more centralized around borehole with a smaller region which represent good vertical resolution; the horizontal sensitivity function is used to determine depth of investigation, and has achieved desired effect compared with pseudo geometric factor. The variety of main contribution region caused by the change of resistivity is simulated by sensitivity function, and when frequency is 2 MHz, results show that investigation depth calculated by amplitude ratio sensitivity function is about 0.6 to 2.3 m with background formation resistivity varying from 1 to 100 Ωm, phase difference is about 0.2 to 0.6 m; when resistivity contrast between abnormal body and background formation changes from 1 to 50, the difference caused by resistivity contrast is about 0.1 to 0.2 m, which is far less than the influence caused by background resistivity.