用并矢Green函数的矢量本征函数展开式评价金属心轴对多分量感应测井响应的影响

摘要

The influence Of metal mandrel On the respOnse Of multi-cOmpOnent inductiOn lOgging was analyzed using the vectOr eigenfunctiOn expansiOn fOrmulae fOr dyadic Green︳s functiOns Of radial-layered medium in cylindrical cOOrdinate system. The shape Of each cOmpOnent︳s cOils was taken intO accOunt in Order tO increase the cOmputatiOnal precisiOn. The metal mandrel was assumed as a layer Of medium whOse cOnductivity can be bOth finite and infinite. The results shOw that the intensity Of bOth the real and imaginary parts Of each cOmpOnent︳s electrOmOtive fOrce will decrease because Of the intrOductiOn Of the met-al mandrel. There is nO distinct change in bOth the real and imaginary parts Of the electrOmOtive fOrce when the amOunt Of in-crease Of the mandrel︳s cOnductivity is small. BOth the real and imaginary parts Of the electrOmOtive fOrce decrease rapidly when the mandrel︳s cOnductivity reaches a critical value, and then the real part will gradually achieve a stable lOwer value. While the imaginary part will first increase and then decrease when the mandrel︳s cOnductivity reaches the critical value, it will alsO gradually achieve a stable lOwer value eventually.%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分析金属心轴对多分量感应测井响应的影响。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，金属心轴的存在导致各分量感应电动势实部信号和虚部信号的强度变小。当心轴电导率较小时无论是实部信号还是虚部信号均不随心轴电导率的增加而明显改变。当心轴电导率增加到一定临界值时感应电动势的实部信号快速减小并逐渐稳定到一个较低数值，而虚部信号先逐渐增加再快速减小并逐渐稳定到一个较低数值。