Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes
In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius ∼27 mm). Fine grids and large computational models are required to model th...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2016
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| Online Access: | http://hdl.handle.net/1721.1/105375 https://orcid.org/0000-0001-7081-258X |
| _version_ | 1826195097313607680 |
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| author | Tao, Guo Wang, Hua Shang, Xuefeng Fang, Xinding Burns, Daniel R |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Tao, Guo Wang, Hua Shang, Xuefeng Fang, Xinding Burns, Daniel R |
| author_sort | Tao, Guo |
| collection | MIT |
| description | In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius ∼27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is >30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(MPML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d[subscript 0]. The optimal parameter space for the maximum value of the linear frequency-shifted factor (α[subscript 0]) and the scaling factor (β[subscript 0]) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to <1% using the optimal PML parameters, and the error will decrease as the PML thickness increases. |
| first_indexed | 2024-09-23T10:06:57Z |
| format | Article |
| id | mit-1721.1/105375 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:06:57Z |
| publishDate | 2016 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1053752022-09-30T19:01:11Z Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes Tao, Guo Wang, Hua Shang, Xuefeng Fang, Xinding Burns, Daniel R Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Massachusetts Institute of Technology. Earth Resources Laboratory Wang, Hua Shang, Xuefeng Fang, Xinding Burns, Daniel R In acoustic logging-while-drilling (ALWD) finite difference in time domain (FDTD) simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns (radius ∼27 mm). Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole (the difference is >30 times), the stability and efficiency of the perfectly matched layer (PML) scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain (FDTD) in the ALWD simulation, including field-splitting PML (SPML), multiaxial PML(MPML), non-splitting PML (NPML), and complex frequency-shifted PML (CFS-PML). The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one d[subscript 0]. The optimal parameter space for the maximum value of the linear frequency-shifted factor (α[subscript 0]) and the scaling factor (β[subscript 0]) depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to <1% using the optimal PML parameters, and the error will decrease as the PML thickness increases. National Natural Science Foundation (China) (Grant 41174118) Postdoctoral Fellowship of China (Grant 2013M530106) China Scholarship Council (Grant 2010644006) Major State S&T Special Project (Grant 2008ZX05020-004) 2016-11-21T15:33:14Z 2016-11-21T15:33:14Z 2014-03 2013-10 2016-08-18T15:46:57Z Article http://purl.org/eprint/type/JournalArticle 1672-7975 1993-0658 http://hdl.handle.net/1721.1/105375 Wang, Hua et al. “Stability of Finite Difference Numerical Simulations of Acoustic Logging-While-Drilling with Different Perfectly Matched Layer Schemes.” Applied Geophysics 10.4 (2013): 384–396. https://orcid.org/0000-0001-7081-258X en http://dx.doi.org/10.1007/s11770-013-0400-6 Applied Geophysics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Editorial Office of Applied Geophysics and Springer-Verlag Berlin Heidelberg application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Tao, Guo Wang, Hua Shang, Xuefeng Fang, Xinding Burns, Daniel R Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes |
| title | Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes |
| title_full | Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes |
| title_fullStr | Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes |
| title_full_unstemmed | Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes |
| title_short | Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes |
| title_sort | stability of finite difference numerical simulations of acoustic logging while drilling with different perfectly matched layer schemes |
| url | http://hdl.handle.net/1721.1/105375 https://orcid.org/0000-0001-7081-258X |
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