Abstract
The features of propagation of one-dimensional monochromatic waves and dynamics of weak perturbations with axial and central symmetries in liquid-saturated porous medium are investigated. Non-stationary interaction forces and viscoelastic skeleton characteristics are taken into account. The research is carried out within the two-velocity, two-stress tensor model by applying methods of multiphase media mechanics. The system of equations is solved numerically by applying Fast Fourier Transform (FFT) algorithm. The influence of geometry of the process on wave propagation behavior is studied.
It is shown that the initial pressure perturbation splits into two waves: fast (deformational) wave and slow (filtrational) one. Each of them is followed by the balance wave: that is, rarefaction wave after compression wave and compression wave after rarefaction wave; at that slow wave and balance one following fast wave may interfere.
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References
Bedford, A., and Stern, M.: 1983, A model for wave propagation in gassy sediments,J. Acoust. Soc. Am. 73 (2), 409–417.
Berryman, J. G.: 1988, Elastic wave propagation in fluid-saturated porous media,J. Acoust. Soc. Am. 69 (2), 416–424.
Biot, M. A.: 1956, The theory of elastic waves in a fluid saturated porous rock—1. Low-frequency range,J Acoust. Soc. Am. 28, 168–178.
Domenico, S. N.: 1977, Elastic properties of unconsolidated porous sand reservoirs,Geophysics 42 (7), 1339–1368.
Frenkel, M. I.: 1944, On the theory of seismic and seismoelectric phenomena in saturated soils,Izvestiya Akademii Nauk SSSR, Ser. geogr. i geofiz. 8 (4), 133–150.
Geuze, E. C., and Kie, Tan Tjong: 1954,The Mechanical Behavior of Clays, Academic Press, New York.
Hamilton, E. L.: 1972, Compressional wave attenuation in marine sediments,Geophysics 37 (4), 620–646.
Hamilton, E. L., and Bachman, R. T.: 1982, Sound velocity and related properties of marine sediments,J. Acoust. Soc. Am. 72 (6), 1891–1904.
Hovem, J. M., and Ingrem, G. D.: 1979, Viscous attenuation of sound in saturated sand,J. Acoust. Soc. Am. 66 (6), 1807–1812.
Johnson, D. L., and Plona, T. J.: 1982, Acoustic slow waves and the consolidation transition,J. Acoust. Soc. Am. 72 (2) 556–565.
Lamb, H.: 1932,Hydrodynamics, Cambridge.
Landau, L. D., and Lifshitz, E. M.: 1959,Fluid Mechanics, Pergamon, New York.
McLeroy, E. C., and De Loach, A.: 1968, Sound speed and attenuation from 15 to 1500 kHz, measured in natural sea-floor sediments,J. Acoust. Soc. Am 44 (4), 1148–1150.
Nakoryakov, V. E., Kuznetsov, V. V., and Dontsov, V. E.: 1989, Pressure waves in saturated porous media,Int. J. Multiphase Flow 15 (6), 857–875.
Nigmatulin, R. I.: 1991,Dynamics of Multiphase Media, Hemisphere Publ. Corp., New York.
Nigmatulin, R. I., and Gubaidullin, A. A.: 1991, Fundamentals of mechanics of saturated porous media: Basic equations and waves, in S. Kakac (ed),Convective Heat and Mass Transfer in Porous Media, Kluwer, Dordrecht, pp. 600–607.
Nigmatulin, R. I., and Gubaidullin, A. A.: 1992, Linear waves in saturated porous media,Transport in Porous Media 9 (1,2), 135–142.
Nikolayevskii, V. N., Basniyev, K. S., Gorbunov, A. T., and Zotov, G. A.: 1970,Mechanics of Saturated Porous Media, Nedra, Moscow [in Russian].
Plona, T. J.: 1980, Observation of second bulk compressional wave in a porous medium at ultrasonic frequencies,Appl. Phys. Lett. 36, 259–261.
Sniekers, R. W. J. M., Smoulders, D. M. J., Van Dongen, M. E. H., and Van der Kogel, H.: 1989, Pressure wave propagation in a partially water-saturated porous medium,J. Appl. Phys. 66 (9), 4522–4524.
Stoll, R. D.: 1980, Theoretical aspect of sound transmission in sediments,J. Acoust. Soc. Am. 68 (5), 1341–1347.
Van der Grinten, J. G. M., Van Dongen, M. E. H., and Van der Kogel, H.: 1985, A shock tube technique for studying pore-pressure propagation in a dry and water-saturated porous medium,J. Appl. Phys. 58 (8), 2937–2942.
Van der Grinten, J. G. M., Van Dongen, M. E. H., and Van der Kogel, H.: 1987, Strain and pore pressure propagation in a water-saturated porous medium,J. Appl. Phys. 62 (12), 4682–4687.
Van der Grinten, J. G. M.: 1987,An Experimental Study of Shock-Induced Wave Propagation in Dry, Water-Saturated and Partially Saturated Porous Media, Tech. Univ. Eindhoven, The Netherlands.
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Gubaidullin, A.A., Kuchugurina, O.Y. One-dimensional linear waves with axial and central symmetries in saturated porous media. Transp Porous Med 22, 73–90 (1996). https://doi.org/10.1007/BF00974312
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DOI: https://doi.org/10.1007/BF00974312