电磁波电阻率仪器的基本理论及其在随钻测量中的应用

The basic theory of electromagnetic wave resistivity instrument and its application to measurement of while-drilling

采用递推矩阵方法计算径向成层介质的Green函数并将其作为电磁波电阻率仪器的基本理论.根据圆柱形层界面处电场和磁场的连续性条件得到确定待定系数的矩阵方程组并通过递推方法快速求解.只需改变方程组中源项元素的位置,就可以方便地得到当源点和场点在任意层时的Green函数,形式简洁、易于编程.采用将变型Bessel函数的指数项单独列出的方式有效地解决了Green函数计算中的上溢问题.用上述Green函数对随钻电磁波电阻率测量仪器进行数值模拟,分析了钻铤的影响规律、井眼校正方法、仪器的径向探测特性和垂向分辨率.所得到的结论可为随钻电磁波电阻率测量仪器的研制和使用提供理论指导.

A recursive matrix method is adopted for the computation of Green＇s function in radial stratified media, which can he taken as the basic theory of electromagnetic wave resistivity instrument. A matrix equation group for computing the coefficients is obtained according to the continuity condition of electric and magnetic fields on the cylindrical interface, which can be quickly solved by the reeursive method. The Greenrs function with the source point and field point in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the equation group, and the obtained Greenrs function is terse in form and is easy to be programmed.The problem of overflow during the computation of Green＇s function has been successfully solved by subtracting the exponential term from the modified Bessel functions. The obtained Green＇s function is applied to numerical modeling of electromagnetic wave resistivity MWD instrument, and the influence of the drill collar, the borehole-correction method, the radial characteristics of investigation and the vertical resolution of the tool are analysed. The obtained conclusions can provide theoretical guide for the manufacture and application of the electromagnetic wave resistivity MWD instrument.