用并矢Green函数的矢量本征函数展开式模拟多分量感应测井仪器的刻度

Simulating multi-component induction logging tool's calibration by vector eigenfunction expansion formulae for dyadic Green's functions

基于圆柱坐标系下径向成层介质中并矢Green函数的矢量本征函数展开式,模拟含金属心轴多分量感应测井的刻度。为提高计算精度,考虑各分量线圈系的具体形状。将金属心轴作为一层介质处理,既可以考虑其电导率有限,也可以考虑其电导率为无穷大的情况。计算结果表明,无论金属心轴存在与否,同一组线圈系的刻度电动势随刻度环中心点轴向坐标的变化规律完全相同,只是金属心轴的存在导致刻度电动势实部信号和虚部信号的强度均变小。不同分量、不同接收线圈阵列的刻度电动势随刻度环中心点轴向坐标的变化关系完全不同,且接收阵列越远,刻度电动势的最大值越小,其所对应的刻度环位置越远。

The multi-component induction logging tools calibration was simulated based on the vector eigenfunction expansion formulae for dyadic Greens functions of radial-layered medium in cylindrical coordinate system,in which the influence of the metal mandrel was considered. The shape of each components coils was taken into account in order to increase the computational precision. The metal mandrel was taken as a layer of medium and whose conductivity was set both finite and infinite. The results show that the relationship between the calibrated electromotive force of the same coil group and the axial coordinate of the calibration loops center is exactly the same,no matter whether the metal mandrel exists or not; on the other hand,the intensity of both the real part and imaginary part of the calibrated electromotive force will decrease when the metal mandrel is considered. The relationship between the calibrated electromotive force and the axial coordinate of the calibration loops center varies for different components or different receiver arrays. The maximum value of the calibrated electromotive force will become smaller and the corresponding position of the calibration loops center will become more distant when the receiver array is further far away from the transmitter coil.