How Does the Background Field Affect the Numerical Accuracy of the Finite Element Simulation of Induction Logging?

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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.

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. As well, 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.

Recently, researchers from the Institute of Acoustics of the Chinese Academy of Sciences performed comparisons between results obtained from different background conductivities in several models to find out how background field affected the numerical accuracy. Based on that, they proposed a new method in which they used the apparent conductivity calculated by Gianzero geometry factor as the background conductivity.

During their research, in the homogeneous media, error became smaller as the background conductivity matched the media's. And taking smaller background conductivity usually gained better results.

Meanwhile, in the radial layered medium, when the mud was fresh and using short spacing, mud and formation were both used as background field in the calculation. Results turned out the error of former was smaller than the latter's. When the mud was salty, similar results were obtained except the scaleof error.

In the three layered model, formation conductivity was chosen near the source and near the midpoint of transmitter-receiver as background conductivity respectively. The results revealed that error greatly increased without taking scattering field gradient near the source and receiver into consideration simultaneously.

In the following, researchers compared the results from Gianzero geometry factor background and cosine background, and the test showed that Gianzero background field had higher precision with long spacing or thin formation. Moreover, Gianzero method was more efficiency due to its concise expression and no need to calculate hankel function transform.

As well in the simulation of induction logging, background field exerted a significant influence upon the calculation accuracy, and the results could deviate markedly due to the improper conductivity value. For the complex inhomogeneous earth model, such as sand-shale interbedded layers, constant background conductivity could not ensure the accuracy when the transmitter and receiver were not in the same layer, especially there were thin layers.

Besides, ideal background field should take the distribution of field near the transmitter and receiver into account simultaneously. Only in this way could the increase of gradient of scattered field near the receiver be avoided, which was 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 were that the Gianzero geometry factor background was more smooth and gentle, and could take many factors into account, such as surrounding rock, borehole, transmitter-receiver interval. When the tool intersected bed boundary, the results of Gianzero background field were more accurate.

References:

WANG Jian, CHEN Hao, WANG Xiuming, ZHANG Lei. Research on Selection Method of Background Field For Finite Element Simulation of Induction Logging. Chinese Journal Of Geophysics-Chinese Edition (Vol. 58, No. 6, pp. 2177-2187, June 2015). DOI: 10.6038/cjg20150630

Contact:

WANG Jian

Institute of Acoustics, Chinese Academy of Sciences, 100190 Beijing, China

Email: wangjianshinian@163.com

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