Abstract: Complex resistivity well logging (CRWL) is a new well logging method for differentiating and evaluating the saturation of rock formation through its frequency dispersion character. The current tool used in the field is actually the modified dual laterolog tool. The tool can be used to measure deep and shallow laterologs at two different frequencies. The ratio of low frequency (0～200Hz) to high frequency (1～20k) is used to evaluate the formation. The bigger ratio means the higher oil saturation. CRWL has been used in some oil fields for several years and a lot of data has been collected. However,some eata are vague and need to be clarified through more theoretical studies. In this paper,we start from Maxwell equation for electromagnetic field.Considering the boundary condition and specific well logging environment,we deduce Maxwell equation into a boundary value of Laplace equation.Using the variational method,we get the variational formula to satisfy the finite element method. In 2D formation model,we use finite element method (FEM) to simulate the CRWL response at different frequencies working in DLL mode. The results show that the responses agree with DLL when the frequency is near zero,and the readings of response reduce when the frequency increases. When the formation has some extant frequency dispersion,the readings of different frequencies will disperse. Then,the readings of complex resistivity logs at different frequencies can be used to differentiate oil layer from the water layer. Also they can be used to evaluate the saturation of a formation.

Key words: complex resistivity well logging (CRWL), frequency dispersion, Dual Laterolog (DLL), numerical simulation

摘要： 在二维地层模型条件下,应用有限元方法模拟了双侧向模式的复电阻率测井仪器在不同频率下的响应,结果表明当频率很低时,复电阻率测井的响应接近双侧向测井的响应;随着频率的提高,复电阻率测井的响应幅度降低。当地层具有一定的频散效应时,可以利用不同频率下的复电阻率测井响应直观地区分油水层。

关键词: 复电阻率测井, 频散, 双侧向测井, 数值模拟