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Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method

Published online by Cambridge University Press:  03 June 2015

Zhonghua Ma ,
Dejun Liu ,
Hui Li  and
Xinsheng Gao
Zhonghua Ma*
Affiliation:
College of Geophysics and Information Engineering, China University of Petroleum, 18 Fuxue Road, Changping District, Beijing 102249, China LandOcean Energy Services Co., Ltd, Beijing 100084, China
Dejun Liu*
Affiliation:
College of Geophysics and Information Engineering, China University of Petroleum, 18 Fuxue Road, Changping District, Beijing 102249, China
Hui Li*
Affiliation:
College of Geophysics and Information Engineering, China University of Petroleum, 18 Fuxue Road, Changping District, Beijing 102249, China
Xinsheng Gao*
Affiliation:
College of Geophysics and Information Engineering, China University of Petroleum, 18 Fuxue Road, Changping District, Beijing 102249, China
*
URL:http://cii.cup.edu.cn/Showteacher.aspx?id=liudejun, Email: mazhonghua1983@yahoo.com.cn
Corresponding author. Email: liudj01@yahoo.com.cn
Email: toobage@163.com
Email: shengxingao@163.com
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Abstract

A novel, highly efficient and accurate adaptive higher-order finite element method (hp-FEM) is used to simulate a multi-frequency resistivity logging-while-drilling (LWD) tool response in a borehole environment. Presented in this study are the vector expression of Maxwell’s equations, three kinds of boundary conditions, stability weak formulation of Maxwell’s equations, and automatic hp-adaptivity strategy. The new hp-FEM can select optimal refinement and calculation strategies based on the practical formation model and error estimation. Numerical experiments show that the new hp-FEM has an exponential convergence rate in terms of relative error in a user-prescribed quantity of interest against the degrees of freedom, which provides more accurate results than those obtained using the adaptive h-FEM. The numerical results illustrate the high efficiency and accuracy of the method at a given LWD tool structure and parameters in different physical models, which further confirm the accuracy of the results using the Hermes library (http://hpfem.org/hermes) with a multi-frequency resistivity LWD tool response in a borehole environment.

Keywords

35Q6135Q8674S05Resistivity logging-while-drillinghigher-order finite element methodadaptiveexponential convergencenumerical simulation
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 4 , August 2012 , pp. 439 - 453
Copyright
Copyright © Global-Science Press 2012

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