有限元感应测井模拟的背景场选择方法研究

在感应测井的有限元模拟中,为了消除源的奇异性,一般将总场分解为背景场和散射场.本文定量研究了不同背景场选择方法对计算精度的影响.首先,分析了在均匀和径向分层介质中不同背景电导率对长短源距线圈系有限元模拟结果的影响;其次,利用三层介质模型对比了选择源点附近和线圈系中点附近地层电导率作为背景电导率的结果.研究结果表明,如果在选择背景场时,只考虑源附近的散射场梯度而不同时考虑源和接收器附近的散射场梯度,计算误差明显增大.在此基础上提出一种利用Gianzero几何因子计算的视电导率作为背景电导率的新的背景场方法.该方法综合考虑了围岩、井眼、线圈距等因素,特别是在介质分界面处,可有效减小计算误差,并取得了满意的精度.本研究为复杂环境下的感应测井模拟的背景场选择提供了指导和依据.

Research on selection method of background field for finite element simulation of induction logging

With the development of petroleum industry, accurate and fast numerical simulation methods are needed to achieve reliable inversion of the measured response of induction logging in complex media. Thereinto,the choice of the background field plays an important role in the forward modeling of electromagnetic.Thus, the objectives are to quantitatively compare the effects of different background fields on the calculation accuracy.#br#The finite element method is employed to carry out simulation of induction logging. In order to eliminate the singularities, total field is usually decomposed into two parts, background field and scattered field. Analytical method is generally available for the former one, which reflects the drastic change of the field. While for the latter one, due to its character of gentle change, finite element method with sparse grid would be enough. We performed comparisons between results obtained from different background conductivities in several models to find out how background field affects the numerical accuracy.Then, we propose a new method in which use the apparent conductivity calculated by Gianzero geometry factor as the background conductivity.#br#The main results are as following: (1) in the homogeneous media, error becomes smaller as the background conductivity matches the media's. And taking smaller background conductivity usually gains better results; (2) in the radial layered medium, when the mud is fresh and using short spacing, mud and formation are both used as background field in the calculation. And results turn out the error of former is smaller than the latter's. When the mud is salty, similar results are obtained except the scaleof error.(3) in the three layered model, we choose formation conductivity near the source and near the midpoint of transmitter-receiver as background conductivity respectively. The results reveal that error greatly increases without taking scattering field gradient near the source and receiver into consideration simultaneously. (4) we compare the results from Gianzero geometry factor background and cosine background, and the test shows that Gianzero background field has higher precision with long spacing or thin formation.Moreover, Gianzero method is more efficiency due to its concise expression and no need to calculate hankel function transform.#br#In the simulation of induction logging, background field exerts a significant influence upon the calculation accuracy, and the results can deviate markedly due to the improper conductivity value. For the complex inhomogeneous earth model, such as sand-shale interbedded layers, constant background conductivity cannot ensure the accuracy when the transmitter and receiver are not in the same layer, especially there are thin layers.Besides, ideal background field should take the distribution of field near the transmitter and receiver into account simultaneously. Only in this way can the increase of gradient of scattered field near the receiver be avoided, which is caused by only considering the decrease of gradient of field near the transmitter.The main differences between Gianzero geometry factor background and other step type background are that the Gianzero geometry factor background is more smooth and gentle, and can take many factors into account, such as surrounding rock, borehole, transmitter-receiver interval. When the tool intersects bed boundary ,the results of Gianzero background field are more accurate.