Influence of Fracture Geometry on the Krauklis Wave in Finite Fractures
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 147, Issue 2
Abstract
Study of the Krauklis wave in fractured media reveals the potential for characterizing fracture geometry. In this paper, a finite element scheme is proposed to simulate the Krauklis wave in fractures with different geometries. The influence of fracture geometry on the propagation properties of the Krauklis waves is evaluated. Here, fracture geometry refers to the fracture shape, width, and length. First, a series of numerical models containing a single water-filled fracture is set up, in which the fracture shape can be an ellipse or rectangle, its width varies from 5 to 10 mm, and its length varies from 2 to 3 m. The proposed finite element scheme is applied to simulate Krauklis waves. From these simulation results, the Krauklis wave signals inside the fractures are extracted, and a velocity estimation method is developed and implemented to estimate the average velocity within the finite length fractures. For comparison, the theoretical velocity is solved from a dispersion equation, in which the fracture is assumed to be an infinite thin fluid layer. It is shown that the rectangular fractures generate stronger amplitude and higher velocity waves than the elliptical ones. The amplitude varies along the fracture and can be significantly affected by the fracture geometry. Furthermore, the velocity increases with the fracture width, whereas the fracture length does not affect the velocity for both elliptical and rectangular fractures. These effects indicate that Kraulklis waves are rich in information about fracture geometry, and this is valuable when applied to the quantitative characterization of fractures.
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Acknowledgments
This research is supported by the National Natural Science Fund Projects (41804105 and U19B6003), Fundamental Research Funds for the Central Universities (2462018YJRC008), and Major National Project Program (2017ZX05018005).
References
Chao, M., Y. Gao, and C. Lu. 2019. “Numerical modeling of elastic wave in frequency-domain by using staggered grid fourth-order finite-difference scheme.” Adv. Geo-Energy Res. 3 (4): 410–423. https://doi.org/10.26804/ager.2019.04.08.
Chouet, B. 1981. “Ground motion in the near field of a fluid-driven crack and its interpretation in the study of shallow volcanic tremor.” J. Geophys. Res. Solid Earth 86 (Jul): 5985–6016. https://doi.org/10.1029/JB086iB07p05985.
Chouet, B. 1986. “Dynamics of a fluid-driven crack in three dimensions by the finite difference method.” J. Geophys. Res. Solid Earth 91 (Dec): 13967–13992. https://doi.org/10.1029/JB091iB14p13967.
Chouet, B. 1988. “Resonance of a fluid-driven crack: Radiation properties and implications for the source of long-period events and harmonic tremor.” J. Geophys. Res. Solid Earth 93 (May): 4375–4400. https://doi.org/10.1029/JB093iB05p04375.
Ding, P., S. Qin, H. Liu, B. Di, and X. Li. 2019a. “Experimental observation of Krauklis wave amplitude variation based on single fracture physical model.” [In Chinese.] Chin. J. Geophys. 62 (12): 4794–4804. https://doi.org/10.6038/cjg2019M0321.
Ding, P., D. Wang, G. Di, and X. Li. 2019b. “Investigation of the effects of fracture orientation and saturation on the Vp/Vs ratio and their implications.” Rock Mech. Rock Eng. 52 (9): 3293–3304. https://doi.org/10.1007/s00603-019-01770-3.
Ferrazzini, V., and K. Aki. 1987. “Slow waves trapped in a fluid-filled infinite crack: Implication for volcanic tremor.” J. Geophys. Res. Solid Earth 92 (Aug): 9215–9223. https://doi.org/10.1029/JB092iB09p09215.
Frehner, M. 2014. “Krauklis wave initiation in fluid-filled fractures by seismic body waves.” Geophysics 79 (1):27–35. https://doi.org/10.1190/geo2013-0093.1.
Frehner, M., and S. M. Schmalholz. 2010. “Finite-element simulations of Stoneley guided-wave reflection and scattering at the tips of fluid-filled fractures.” Geophysics 75 (2): 23–36. https://doi.org/10.1190/1.3340361.
Frehner, M., S. M. Schmalholz, E. H. Saenger, and H. Steeb. 2008. “Comparison of finite difference and finite element methods for simulating two-dimensional scattering of elastic waves.” Phys. Earth Planet. Inter. 171 (1–4): 112–121. https://doi.org/10.1016/j.pepi.2008.07.003.
Korneev, V. 2008. “Slow waves in fractures filled with viscous fluid.” Geophysics 73 (1): 1–7. https://doi.org/10.1190/1.2802174.
Korneev, V., G. Goloshubin, B. Kashtan, V. Troyan, R. Shigapov, A. Bakulin, M. Frehner, and S. Shapiro. 2012. “Krauklis wave-half a century after.” In Proc., Saint Petersburg 2012-5th Saint Petersburg Int. Conf. & Exhibition 2012: Making the Most of the Earth’s Resources, 246–251. Amsterdam, Netherlands: European Association of Geoscientists and Engineers.
Krauklis, P. 1962. “About some low frequency oscillations of a liquid layer in elastic medium.” [In Russian.] PMM 26 (6): 1111–1115.
Krüger, O. S., E. H. Saenger, and S. A. Shapiro. 2005. “Scattering and diffraction by a single crack: An accuracy analysis of the rotated staggered grid.” Geophys. J. Int. 162 (1): 25–31. https://doi.org/10.1111/j.1365-246X.2005.02647.x.
Liang, C., O. O’Reilly, E. H. Dunham, and D. Moos. 2017. “Hydraulic fracture diagnostics from Krauklis-wave resonance and tube-wave reflections.” Geophysics 82 (3): 171–186. https://doi.org/10.1190/geo2016-0480.1.
Lipovsky, B. P., and E. M. Dunham. 2015. “Vibrational modes of hydraulic fractures: Inference of fracture geometry from resonant frequencies and attenuation.” J. Geophys. Res. Solid Earth 120 (2): 1080–1107. https://doi.org/10.1002/2014JB011286.
Liu, H., P. Ding, J. Wei, and X. Li. 2019. “Properties of Krauklis wave in fluid filled fractures.” Eur. Assoc. Geosci. Eng. 2019 (1): 1–5. https://doi.org/10.3997/2214-4609.201900816.
Luo, C., X. Li, and G. Huang. 2017. “Application of oil–water discrimination technology in fractured reservoirs using the differences between fast and slow shear-waves.” J. Geophys. Eng. 14 (4): 723–738. https://doi.org/10.1088/1742-2140/aa664f.
Nakagawa, S., S. Nakashima, and V. Korneev. 2016. “Laboratory measurements of guided-wave propagation within a fluid-saturated fracture.” Geophys. Prospect. 64 (1): 143–156. https://doi.org/10.1111/1365-2478.12223.
Qin, X., X. Li, S. Chen, and Y. Liu. 2018. “The modeling and analysis of frequency-dependent characteristics in fractured porous media.” J. Geophys. Eng. 15 (5): 1943–1952. https://doi.org/10.1088/1742-2140/aac130.
Shih, P. J. R., and M. Frehner. 2016. “Laboratory evidence for Krauklis-wave resonance in fractures and implications for seismic coda wave analysis.” Geophysics 81 (6): 285–293. https://doi.org/10.1190/geo2016-0067.1.
Wang, D., P. Ding, and J. Ba. 2018. “Analysis of dynamic fracture compliance based on poroelastic theory. Part II: Results of numerical and experimental tests.” Pure Appl. Geophys. 175 (8): 2987–3001. https://doi.org/10.1007/s00024-018-1818-9.
Zienkiewicz, O. C., and R. L. Taylor. 2000. The finite element method fifth edition volume 1: The basis. Oxford, UK: Butterworth-Heinemann.
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Journal of Geotechnical and Geoenvironmental Engineering
Volume 147 • Issue 2 • February 2021
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© 2020 American Society of Civil Engineers.
History
Received: Nov 6, 2019
Accepted: Jul 15, 2020
Published online: Nov 24, 2020
Published in print: Feb 1, 2021
Discussion open until: Apr 24, 2021
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