Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T16:18:48.428Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Chimedsurong, Z. and Wang, H., Forward modeling of induction well logging tools in dipping boreholes and their response, Chinese. J. Comput. Phys., 20 (2003), pp. 161–168.Google Scholar
[2]Chen, X., Liu, D. and Ma, Z., Numerical simulation of electric field in resistivity LWD using High accuracy self-adaptive hp-FEM, Chinese. J. Comput. Phys., 28 (2011), pp. 50–56.Google Scholar
[3]Pardo, D., Two-dimensional high accuracy simulation of resistivity logging while drilling (LWD) measurements using a self adaptive goal oriented finite element method, SIAM. J. Appl. Math., 66 (2006), pp. 2085–2106.CrossRefGoogle Scholar
[4]Lee, H. O., Cylindrical FDTD Analysis of LWD Tools Through Anisotropic Dipping Layered Earth Media, M.S. Thesis, The Ohio State University, 2005.Google Scholar
[5]Tan, M., Gao, J., Wang, X. and Zhang, S., Numerical simulation of the dual laterolog for carbonate cave reservoirs and response characteristics, Appl. Geophys., 8 (2011), pp. 79–85.Google Scholar
[6]Lovell, J. R., Finite Element Methods in Resistivity Logging, Ph.D Thesis, Delft University of Technology, 1993.Google Scholar
[7]Chen, Q., Pardo, D., Li, H. and Wang, F., New post-processing method for interpretation of through casing resistivity (TCR) measurements, J. Appl. Geophys., 74 (2011), pp. 19–25.CrossRefGoogle Scholar
[8]Dubcova, L., Solin, P., Cerveny, J. and Kus, P., Space and time adaptive two-mesh hp-finite element method for transient microwave heating problems, Electromagnetics., 30 (2010), pp. 23–40.Google Scholar
[9]Vejchodsky, T., Solin, P. and Zitka, M., Modular hp-FEM system HERMES and its application to the Maxwell’s equations, Math. Comput. Simul., 76 (2007), pp. 223–228.CrossRefGoogle Scholar
[10]Solin, P., Segeth, K. and Dolezel, I., Higher-Order Finite Element Methods, Chapman & Hall/CRC Press, Philadelphia, 2002.Google Scholar
[11]Demkowicz, L., Computing with hp-Adaptive Finite Elements: One and Two Dimensional Elliptic and Maxwell Problems, Chapman & Hall/CRC Press, Boca Raton, 2006.Google Scholar
[12]Solin, P., Cerveny, J. and Dolezel, I., Arbitrary-level hanging nodes and automatic adap-tively in the hp-FEM, Math. Comput. Simul., 77 (2008), pp. 117–132.CrossRefGoogle Scholar
[13]Pardo, D., Demkowicz, L., Torres-Verdin, C. and Paszynski, M., A self-adaptive goal-oriented hp finite element method with electromagnetic applications, part II: electrodynamics, Comput. Methods. Appl. Mech. Eng., 196 (2007), pp. 3585–3597.Google Scholar
[14]Solin, P., Cerveny, J., Dubcova, L. and Andrs, D., Monolithic discretization of linear ther-moelasticity problems via adaptive multimesh hp-FEM, J. Comput. Appl. Math., 234 (2010), pp. 2350–2357.CrossRefGoogle Scholar
[15]Solin, P., Dubcova, L., Cerveny, J. and Dolezel, I., Adaptive hp-FEM with arbitrary-level hanging nodes for Maxwell’s equations, Adv. Appl. Math. Mech., 2 (2010), pp. 518–532.Google Scholar