A numerical investigation of the acoustic mode waves in a deviated borehole penetrating a transversely isotropic formation
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Abstract
A 2.5-dimensional method in frequency wave-number domain is developed to investigate the mode waves in a deviated borehole penetrating a transversely isotropic formation. The phase velocity dispersion characteristics of the fast and slow flexural mode waves excited by a dipole source are computed accurately at various deviation angles for both hard and soft formations. The sensitivities of the flexural mode waves to all elastic constants in a transversely isotropic formation are calculated. Numerical results show that, for a soft formation, the fast flexural mode wave is dominated by c 66 at high deviation angles and low frequencies, while the slow flexural mode wave is dominated by c 44 at the same conditions. Waveforms in time domain are also presented to support the conclusions.
Keywords
deviated borehole transverse isotropy acoustic mode waves dispersion curve sensitivity analysisReferences
- 1.Tsang L, Rader D. Numerical evaluation of the transient acoustic waveform due to a point source in a fluid-filled borehole. Geophysics, 1979, 44: 1706–1720ADSCrossRefGoogle Scholar
- 2.Kurkjian A L. Numerical computation of individual far-field arrivals excited by an acoustic source in a borehole. Geophysics, 1985, 50: 852–866ADSCrossRefGoogle Scholar
- 3.Sinha B K, Norris A N, Chang S K. Borehole flexural modes in anisotropic formations. Geophysics, 1994, 59: 1037–1052ADSCrossRefGoogle Scholar
- 4.Chi S H, Tang X M. Stoneley-wave speed modeling in general anisotropic formations. Geophysics, 2006, 71: F67–F77ADSCrossRefGoogle Scholar
- 5.Berryman J G. Long-wave elastic anisotropy in transversely isotropic media. Geophysics, 1979, 44: 896–917ADSCrossRefGoogle Scholar
- 6.Chan A K, Tsang L. Propagation of acoustic waves in a fluid-filled borehole surrounded by a concentrically layered transversely isotropic formation. J Acoust Soc Am, 1983, 74: 1605–1616ADSCrossRefGoogle Scholar
- 7.White J E, Tongtaow C. Cylindrical waves in transversely isotropic media. J Acoust Soc Am, 1981, 70: 1147–1155ADSCrossRefGoogle Scholar
- 8.Schmitt D P. Acoustic multipole logging in transversely isotropic poroelastic formations. J Acoust Soc Am, 1989, 86: 2397–2421ADSCrossRefGoogle Scholar
- 9.Zhang B X, Dong H F, Wang K X. Multipole sources in a fluid-filled borehole surrounded by a transversely isotropic elastic solid. J Acoust Soc Am, 1994, 96: 2546–2555ADSCrossRefGoogle Scholar
- 10.Ellefsen K J. Elastic Wave Propagation Along A Borehole in An Anisotropic Medium. Dissertation for the Doctoral Degree. Massachusetts: Massachusetts Institute of Technology, 1990. 228–231Google Scholar
- 11.Leslie H D, Randall C J. Multipole sources in boreholes penetrating anisotropic formations: Numerical and experimental results. J Acoust Soc Am, 1992, 91: 12–27ADSCrossRefGoogle Scholar
- 12.Wang X M, Hornby B, Dodds K. Dipole sonic response in deviated boreholes penetrating an anisotropic formation. In: SEG Annual Meeting. Salt Lake City: Society of Exploration Geophysicists, 2002. 1–4Google Scholar
- 13.Sinha B K, Şimşek E, Liu Q H. Elastic-wave propagation in deviated wells in anisotropic formations. Geophysics, 2006, 71: D191–D202ADSCrossRefGoogle Scholar
- 14.Lin W J, Wang X M, Zhang H L. Acoustic wave propagation in a borehole penetrating an inclined layered formation (in Chinese). Chin J Geophys, 2006, 49: 234–246CrossRefGoogle Scholar
- 15.He X, Hu H S, Guan W. Fast and slow flexural waves in a deviated borehole in homogeneous and layered anisotropic formations. Geophys J Int, 2010, 181: 417–426ADSCrossRefGoogle Scholar
- 16.Yan S G, Song R L, Lv W G, et al. Numerical simulation of acoustic fields excited by cross-dipole source in deviated wells in transversely isotropic formation (in Chinese). Chin J Geophys, 2011, 54: 2412–2418MATHGoogle Scholar
- 17.Wang R J, Qiao W X, Jv X H, et al. Acoustic multipole logging in deviated wells penetrating transversely isotropic formations: A numerical study. In: SEG Annual Meeting. Houston: Society of Exploration Geophysicists, 2013. 1–4Google Scholar
- 18.Kimball C V, Marzetta T L. Semblance processing of borehole acoustic array data. Geophysics, 1984, 49: 274–281ADSCrossRefGoogle Scholar
- 19.Ekstrom M P. Dispersion estimation from borehole acoustic arrays using a modified matrix pencil algorithm. In: Conference Record of the Twenty-Ninth Asilomar Conference on Signals, Systems and Computers. Pacific Groov: IEEE, 1995. 449–453Google Scholar
- 20.Ellefsen K J, Cheng C H, Toksöz M N. Applications of perturbation theory to acoustic logging. J Geophys Res, 1991, 96: 537–549ADSCrossRefGoogle Scholar
- 21.Norris A N, Sinha B K. Weak elastic anisotropy and the tube wave. Geophysics, 1993, 58: 1091–1098ADSCrossRefGoogle Scholar
- 22.Zhang B X, Wang K X. Theoretical study of perturbation method for acoustic multipole logging in anisotropic formation. J Acoust Soc Am, 1996, 99: 2674–2685ADSCrossRefGoogle Scholar
- 23.Zhu Z Y, Chi S H, Toksöz M N. Sonic logging in deviated boreholes penetrating an anisotropic formation: Laboratory study. Geophysics, 2007, 72: E125–E134ADSCrossRefGoogle Scholar
- 24.Wang R J, Qiao W X, Jv X D, et al. Experimental study of the acoustic field in the borehole surrounded by HTI formations excited by dipole sources with different orientations (in Chinese). Chin J Geophys, 2013, 56: 707–717Google Scholar
- 25.Mace B R, Duhamel D, Brennan M J, et al. Finite element prediction of wave motion in structural waveguides. J Acoust Soc Am, 2005, 117: 2835–2843ADSCrossRefGoogle Scholar
- 26.Komatitsch D, Martin R. An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation. Geophysics, 2007, 72: SM155–SM167ADSCrossRefGoogle Scholar
- 27.Li Y F, Matar O B. Convolutional perfectly matched layer for elastic second-order wave equation. J Acoust Soc Am, 2010, 127: 1318–1327ADSCrossRefGoogle Scholar
- 28.Liu L, Lin W J, Zhang H L, et al. Simulation of 2.5-dimensional borehole acoustic waves with convolutional perfectly matched layer. In: The Proceedings of Symposium on Piezoelectricity, Acoustic Waves and Device Applications (SPAWDA). Changsha: IEEE, 2013. 1–4Google Scholar
- 29.Ellefsen K J, Cheng C H, Toksöz M N. Effects of anisotropy upon the normal modes in a borehole. J Acoust Soc Am, 1991, 89: 2597–2616ADSCrossRefGoogle Scholar
- 30.Auld B A, Sun C P. Acoustic Fields and Waves in Solids (in Chinese). Beijing: Science Press, 1982. 70–82Google Scholar
- 31.Thomsen L. Weak elastic anisotropy. Geophysics, 1986, 51: 1954–1966ADSCrossRefMATHGoogle Scholar
- 32.Tang X M, Cheng C H, Zhao X M. Quantitative Borehole Acoustic Methods (in Chinese). Beijing: Petroleum Industry Press, 2004. 48–49Google Scholar