We propose a model that explains the microscopic origin of the nonstationarity and related filtering noise generation in porous media. The noise is not determined by hydrodynamic sources, and the transition to a turbulent flow regime in pores is not required for its occurrence. The physical mechanism of a nonstationary flow is connected with the development of instability at contacts inside cracks or grains, as well as with the presence of relaxation phenomena in voids and channels always available in rocks. It has been shown that the structural elements in rocks provide a self-excited oscillation regime. The proposed model is in good agreement with known experimental data.
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S. A. Nikolaev and M. N. Ovchinnikov, Akust. Zh., 38, No. 1, 114 (1992).
A. I. Ipatov, A.V. Gorodnov, L.P. Petrov, et al., AIS Karotazhnik, No. 122, 51 (2004).
A. I. Ipatov, A.V. Gorodnov, S. I. Ipatov, et al., Geofizika, 2, 25 (2004).
V.N. Shchelkachev and B.B. Lapuk, Underground Hydraulics [in Russian], State Scientific and Technical Publishing of Oil and Rock–Fuel Literature, Moscow (1949).
G. I. Barenblatt, V. M. Entov, and V.M. Ryzhik, Motion of Liquids and Gases in Natural Layers [in Russian], Nedra, Moscow (1984).
G. Mavko, T. Mukeji, and J. Dvorkin, The Rock Physics Handbook. Tools For Seismic Analysis in Porous Media, Cambridge University Press, Boston, MA (2009).
A. I. Ipatov and N. I. Kremenetsky, Geophysical and Hydrodynamic Control of the Hydrocarbon Fields Development [in Russian], I. M.Gubkin Russian State University of Oil and Gas, Research Center “Regular and Chaotic Dynamics,” Moscow (2010).
L.D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. VI. Fluid Mechanics, Pergamon, New York (1987).
M.N. Ovchinnikov, “Rheological models and evolution of physical fields in the underwater hydrosphere” [in Russian], D. Sc. thesis (phys. & math.), Kazan University (2004).
E. A. Marfin, I. S. Metelev, B. A. Garif’yanov, and A.A. Abdrashitov, Uchenye Zapiski Fiz. Fakult. Mosk. Univ ., No. 6, 146316 (2014).
Yu.M. Zaslavsky, Electronic journal “Tech. Acoustics,” http://www.ejta.org, 5 (2005).
A. Kh. Mirzadzhanzade, M.M. Khasanov, and R.N. Bakhtizin, Modeling of Iol Exploration Processes: Nonlinearity, Non-equilibrium, and Uncertainty [in Russian], Computer Research Institute of Izhevsk, Moscow (2004).
M. I. Rabinovich and D. I. Trubetskov, Introduction to the Theory of Oscillations and Waves [in Russian], Nauka, Moscow (2001).
K. L. Johnson, Contact Mechanics, Cambridge Univ. Press (1985).
R.A. Guyer and R.A. Johnson, Nonlinear Mesoscopic Elasticity: The Complex Behaviour of Rocks, Soil, Concrete, Wiley-VCH, Weinheim (2009).
W. F. Brace, E. Silver, K. Hadley, and C. Goetze, Science, 178, No. 4057, 162 (1972).
R. L. Kranz, Tectonophys., 100, Nos. 1–3, 449 (1983).
A. V. Lebedev and L. A. Ostrovsky, Acoust. Phys., 60, No. 5, 555 (2014).
J. Dvorkin and A. Nur, Geophys., 58, No. 4, 524 (1993).
J. Dvorkin, R. Nolen-Hoeksema, and A. Nur, Geophys., 59, No. 3, 428 (1994).
M. A. Biot, J. Acoust. Soc. Am., 28, No. 2, 168 (1956).
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).
A. A. Androvov, A.A. Vitt, and S.E. Khaikin, Theory of Oscillations, Pergamon Press, Oxford (1966).
A. D. Polyanin and A.V. Manzhirov, Handbook of Integral Equations, CRC Press, Boca Raton (1998).
M. A. Isakovich, General Acoustics [in Russian], Nauka, Mosocw (1973).
D. Maugis and M. Barquins, J. Phys. D: Appl. Phys., 11, No. 14, 1989 (1978).
B. V. Deryagin, N. V. Churaev, and V.M. Muller, Surface Forces [in Russian], Nauka, Moscow (1985).
K. Kendall, in: D.A. Dillard and A.V. Pocius (eds.), Energy Analysis of Adhesion, Vol. 1, The Mechanics of Adhesion, Elsevier, Amsterdam (2002), p. 77.
E. Bonnet, O. Bour, N.E. Odling, et al., Rev. Geophys., 39, No. 3, 347 (2001).
I. K. Kikoin, Reference Book of Physical Quantities [in Russian], Atomizdat, Moscow (1976).
J. J. Zhang and L.R. Bentley, CREWES Res. Report, 15, 1 (2003).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 61, No. 4, pp. 343–357, April 2018.
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Lebedev, A.V. A Nonlinear Relaxation Mechanism of the Filtering Noise Generation in Porous Media. Radiophys Quantum El 61, 305–317 (2018). https://doi.org/10.1007/s11141-018-9892-5
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DOI: https://doi.org/10.1007/s11141-018-9892-5