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Efficient finite-volume simulation of the LWD orthogonal azimuth electromagnetic response in a three-dimensional anisotropic formation using potentials on cylindrical meshes

  • Rock Physics and Borehole Geophysics
  • Published:
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Abstract

In this study, the cylindrical finite-volume method (FVM) is advanced for the efficient and high-precision simulation of the logging while drilling (LWD) orthogonal azimuth electromagnetic tool (OAEMT) response in a three-dimensional (3D) anisotropic formation. To overcome the ill-condition and convergence problems arising from the low induction number, Maxwell’s equations are reformulated into a mixed Helmholtz equation for the coupled potentials in a cylindrical coordinate system. The electrical field continuation method is applied to approximate the perfectly electrical conducting (PEC) boundary condition, to improve the discretization accuracy of the Helmholtz equation on the surface of metal mandrels. On the base, the 3D FVM on Lebedev’s staggered grids in the cylindrical coordinates is employed to discretize the mixed equations to ensure good conformity with typical well-logging tool geometries. The equivalent conductivity in a non-uniform element is determined by a standardization technique. The direct solver, PARDISO, is applied to efficiently solve the sparse linear equation systems for the multi-transmitter problem. To reduce the number of calls to PARDISO, the whole computational domain is divided into small windows that contain multiple measuring points. The electromagnetic (EM) solutions produced by all the transmitters per window are simultaneously solved because the discrete matrix, relevant to all the transmitters in the same window, is changed. Finally, the 3D FVM is validated against the numerical mode matching method (NMM), and the characteristics of both the coaxial and coplanar responses of the EM field tool are investigated using the numerical results.

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Acknowledgements

This research was supported jointly by Strategic Pilot Science and Technology Project of Chinese Academy of Sciences (No. XDA14020102), National key research and development plan (No. 2017YFC0601805), National Natural Science Foundation of China (No. 41574110), Youth Foundation of Hebei Educational Committee (No. QN2018217), Hebei Higher Education Teaching Reform Research and Practice(No. 2018GJJG328), Zhangjiakou science and technology bureau(No. 1821011B), Doctoral Fund of Hebei Institute of Architecture and Civil Engineering (No. B-201606), and Academic Team Innovation Ability Improvement Project of Hebei Institute of Architecture and Civil Engineering(TD202011).

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Authors and Affiliations

  1. Hebei Institute of Architecture and Civil Engineering, Zhangjiakou, 075000, China

    Hao-Sen Wang

  2. College of Physics, Jilin University, Changchun, 130012, China

    Hong-Nian Wang & Shou-Wen Yang

  3. College of Geo-exploration Science and Technology, Jilin University, Changchun, 130023, China

    Chang-Chun Yin

Authors
  1. Hao-Sen Wang
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  2. Hong-Nian Wang
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  3. Shou-Wen Yang
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  4. Chang-Chun Yin
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Corresponding author

Correspondence to Hong-Nian Wang.

Additional information

Wang Hao-Sen, lecturer, Hebei Institute of Architecture and Civil Engineering. He received his Ph.D. degree in Jilin University, Changchun, China, in 2016. His research interests include computational electromagnetics and EM inverse imaging.

Wang Hong-Nian, Professor. He received his Ph.D. degree in geophysics from Changchun University of Geoscience, Changchun, China, in 1994. From 1995 to 1997, he was a postdoctoral researcher, and from July 1997 to Sept. 2001, he was an associate professor in the Department of Physics, Jilin University, Changchun, China. From Nov. 2003 to May 2004, he worked as a senior visiting scholar with the Department of Electrical and Computer Engineering, University of Victoria, Victoria, B.C., Canada. Since Oct. 2001, he has been a Professor at the College of Physics, Jilin University, Changchun, China. His research interests include computational electromagnetics and EM inverse imaging.

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Wang, HS., Wang, HN., Yang, SW. et al. Efficient finite-volume simulation of the LWD orthogonal azimuth electromagnetic response in a three-dimensional anisotropic formation using potentials on cylindrical meshes. Appl. Geophys. 17, 192–207 (2020). https://doi.org/10.1007/s11770-020-0818-6

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  • DOI: https://doi.org/10.1007/s11770-020-0818-6

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