We numerically simulate filtration noise within the framework of the earlier proposed model for the generation of acoustic noise as a result of excitation of relaxation self-oscillations. The simulation is performed for typical parameters of reservoir rocks. As a result, appearance of the radiation frequencies observed in the experiment is demonstrated. It is also shown that due to the nonlinear interaction between elementary sources of the acoustic radiation, its spectrum is enriched with combination frequencies. In the case where the ratios of the frequencies of the interacting oscillators are fractional, the acoustic interaction can lead to nonlinear synchronization of elementary radiation sources.
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References
R. M. McKinly, F. M. Bower, and R. C. Rumble, J. Petrol. Tech., 25, No. 3, SPE-3999-PA (1973). https://doi.org/10.2118/3999-PA.
E. F. Afanas’ev, K. L. Grdzelova, and D. V. Plyushchev, Dokl. Akad. Nauk SSSR, 3, 554–557 (1987).
S. A. Nikolaev and M. N. Ovchinnikov, Akust. Zh., 38, No. 1, 114–118 (1992).
A. I. Ipatov and M. I. Kremenetsky, Geophysical and Hydrodynamic Control of Hydrocarbon Field Development [in Russian], Reg. Khaot. Din. Publ., Moscow–Izhevsk (2010).
E. A. Marfin, Well Noise Logging and Vibroacoustic Treatment of Fluid-Saturated Formations [in Russian], Kazan (Volga Region) Federal Univ., Kazan (2012).
E. A. Marfin, I. S. Metelev, B. A. Garif’anov, and A. A. Abdrashitov, Uchen. Zap. Fiz. Fakult. Kazan Univ., 6, 146316 (2014).
G. B. Pykhachev and R. G. Isaev, Underground Hydraulics [in Russian], Nedra, Moscow (1973).
V. N. Shchelkachev and B. B. Lapuk, Underground Hydraulics, Reg. Khaot. Din. Publ., Moscow–Izhevsk (2001).
L. K. Zarembo and V. A. Krasil’nikov, Introduction to Nonlinear Acoustics [in Russian], Nauka, Moscow (1966).
L. D. Landau and E. M. Lifshitz, Fluid Mechanics [in Russian], Butterworth-Heinemann, Oxford (1987).
K. R. Fritz, C.-C. Hantschk, S. Heim, et al., in: G. Müller and M. Möser, eds., Handbook of Engineering Acoustics, Springer-Verlag, Berlin–Heidelberg (2013), p. 577-636.
G. Mavko, T. Mukeji and J. Dvorkin, The Rock Physics Handbook: Tools for Seismic Analysis in Porous Media, Cambridge Univ. Press, Cambridge (2009).
G. I. Barenblatt, V. M. Entov, and V. M. Ryzhik, Motion of Fluids and Gases in Natural Formations [in Russian], Nedra, Moscow (1984).
S. I. Sergeev, N. I. Ryzhikov, and D. N.Mikhailov, J. Petrol. Sci. Eng., 172, 654–661 (2019). https://doi.org/10.1016/j.petrol.2018.08.018.
Yu. M. Zaslavsky, Tekh. Akust., 5, 48–58 (2005).
A. Kh. Mirzadzhanzade, M. M. Khasanov, and R. N. Bakhtizin, Simulation of Oil and Gas Production. Nonlinearity, Nonequilibrium, and Uncertainty [in Russian], Computer Research Inst., Moscow–Izhevsk (2004).
M. I. Rabinovich and D. I. Trubetskov, Oscillations and Waves in Linear and Nonlinear Systems, Kluwer, Dordrecht (1989).
D. Mikhailov and S. Sergeev, Water Resources Res., 55, No. 5, 4220–4232 (2019). https://doi.org/10.1029/2018WR024168.
A. V. Lebedev, Radiophys. Quantum Electron., 61, No. 4, 305–317 (2018). https://doi.org/10.1007/s11141-018-9892-5.
A. A. Andronov, A. A. Vitt, and S. E. Khaikin, Theory of Oscillators, Pergamon Press, Oxford (1966).
M. A. Isakovich, General Acoustics [in Russian], Nauka, Moscow (1973).
M. Sahimi, Applications of Percolation Theory, Taylor and Francis, London (1994).
M. Klaman and O. D. Lavrentovich, Soft Matter: An Introduction (Partially Ordered Media), Springer-Verlag, New York (2003).
J. Dvorkin and A. Nur, Geophysics, 58, No. 4, 524–533 (1993). https://doi.org/10.1190/1.1443435.
J. Dvorkin, R. Nolen-Hoeksema, and A. Nur, Geophysics, 59, No. 3, 428–438 (1994). https://doi.org/10.1190/1.1443605.
A. V. Lebedev and L. A.Ostrovsky, Acoust. Phys., 60, No. 5, 555–561 (2014). https://doi.org/10.1134/S1063771014050066.
A. N. Kolmogorov, Dokl. Akad. Nauk SSSR, 31, No. 2, 99–101 (1941).
L. A. Ostrovsky and P. A. Johnson, Rivista Nuovo Cim., 24, Ser. 4, No. 7, 1–46 (2001).
R. A. Guyer and P. A. Johnson, Nonlinear Mesoscopic Elasticity: the Complex Behaviour of Rocks, Soil, Concrete, Wiley-VCH, Wenheim (2009).
E. Skudrzyk, Simple and Complex Vibratory Systems, The Pennsylvania State Univ. Press, University Park, Pa. (1968).
N. P. Chrotiros, Acoustics of the Seabed as a Poroelastic Medium, Springer, New York (2017).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 63, No. 2, pp. 155–171, February 2020.
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Lebedev, A.V. Numerical Simulation of Filtration Noise. Radiophys Quantum El 63, 142–156 (2020). https://doi.org/10.1007/s11141-020-10042-y
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DOI: https://doi.org/10.1007/s11141-020-10042-y