轴对称连续电性模型激电测井二维有限元数值模拟

Two-dimensional finite element numerical simulation of an axially symmetric continuous electrical model of excited electrical loggin

激电测井是将电极排列置于钻孔中进行探测的一种测井方法,由于电极排列接近目标体,使得观测的异常信号较强,能够较好地划分目标体的埋藏深度。为了提高激电测井正演精度和方便激电测井电极排列的优化设计,笔者研究了轴对称连续电性介质模型的激电测井曲线二维有限元数值模拟方法。首先在轴对称坐标系下推导了稳恒电流激励异常电位满足的边值问题和变分问题,然后,根据轴对称连续电性介质模型,推导了激电测井曲线二维有限元数值模拟的理论公式,并在此基础上编制了激电测井二维有限元模拟程序,可用于模拟二极、三极和四极观测装置的激电测井曲线。最后,通过模型算例检验了程序的正确性,并分析了不同网格单元剖分尺度对激电测井曲线形态特征的影响,以及不同观测装置、不同极距下测井曲线的响应特征。研究为激电测井的电极排列设计提供了有利的辅助工具。

Excitation logging is a method in which the electrode arrangement is placed in the borehole for detection.Because the electrode arrangement is close to the target body,it strengthens the observed anomalous signal and can better deline-ate the burial depth of the target body.In order to improve the accuracy of radical logging orthorectification and facilitate the optimal design of the electrode arrangement of the radical logging,this paper investigates the two-dimensional finite element numerical simulation method of the radical logging curve in the axisymmetric continuous electrical medium model.Firstly,the axisymmetric coordinate system derives the side value problem and the variational problem satisfied by the anomalous potential of the steady current excitation.Then,the theoretical formulation of the two-dimensional finite element numerical simulation of the excitation logging curve is derived based on the axisymmetric continuous dielectric model.On this basis,the excitation logging's two-dimensional finite element simulation program is prepared,which can be used to simulate the excitation logging curve of the two-pole,three-pole,and four-pole observation devices.Finally,the correctness of the program is checked by modeling examples,and the effects of different grid cell dissection scales on the morphological characteristics of the radical log-ging curve and the response characteristics of the logging curve with different observation devices and different pole distances are analyzed.The research in this paper provides a favorable auxiliary tool for the design of electrode arrangement of the excita-tion logging.