Pressure Waves in Porous Medium Saturated with Liquid Containing Gas Bubbles
Publication: Journal of Engineering Mechanics
Volume 131, Issue 9
Abstract
Theoretical analyses on nonlinear pressure waves evolution in porous medium saturated with a liquid containing gas bubbles is carried out. The evolution equations for fast and slow longitudinal modes are derived for slightly nonlinear, disperse, and dissipation processes. The pressure wave distribution in gas bubble liquid-saturated porous media was investigated experimentally. It was revealed that both modes might have oscillating structure induced by bubble oscillation in the wave. It is shown that the wave damping is determined by a combined impact of heat losses due to gas cooling in the bubbles and dissipation due to longitudinal displacement of liquid and porous skeleton, both influenced by the wave. Experimental data on the velocity and structure of fast and slow modes are compared with results of theoretical modeling.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The funding for this work was provided by the Russian Fund for Basic Research under Grant No. UNSPECIFIED03-01-00211, State Support of Lead Research Schools provided by the President of the Russian Federation under Grant No. UNSPECIFIED523.2003.1, and Integration Project of the Siberian Branch of the Russian Academy of Sciences under Grant No. RAS22.
References
Auriault, J.-L., Boutin, C., Royer, P., and Schmitt, D. (2002). “Acoustics of a porous medium saturated by a bubbly fluid undergoing phase change.” Transp. Porous Media, 46, 43–76.
Bedford, A. and Stern, M. (1983). “A model for propagation in gassy sediments.” J. Acoust. Soc. Am., 73(2), 409–417.
Biot, M. A. (1956a). “Theory of propagation of elastic waves in a fluid- saturated porous solid. 1. Low-frequency range.” J. Acoust. Soc. Am., 28(2), 168–178.
Biot, M. A. (1956b). “Theory of propagation of elastic waves in a fluid-saturated porous solid. 2. Higher frequency range.” J. Acoust. Soc. Am., 28(2), 189–191.
Deresiewicz, H., and Skalak, R. (1963). “On uniqueness in dynamic poroelasticity.” Bull. Seismol. Soc. Am., 53(4), 783–788.
Dontsov, V. E. (1992). “Structure and dynamics of pressure disturbances of final amplitude in a porous medium, saturated by a liquid with gas bubbles.” Izv. Akad. Nauk, Mekh. Zhidk. Gaza, 1, 80–85.
Dontsov, V. E., Kuznetsov, V. V., and Nakoryakov, V. E. (1987). “The pressure waves in a porous medium saturated by liquid with gas bubbles.” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, 4, 85–92.
Dontsov, V. E., and Maslov, V. A. (1994). “Structure and dynamics of the slow pressure wave in a porous medium saturated with a liquid containing gas bubbles.” J. Appl. Mech. Tech. Phys., 35(1), 97–99.
Dunin, S., Mikhailov, D., and Nikolaevsky, V. (2002). “P-waves in realistic formations: Gas bubbles effect.” Poromechanics 2, Proc., 2nd Biot Conf. on Poromechanics, Grenoble, France, 715–721.
Gorbachev, P. Yu., Gurevich, B. Ya., and Lopatnikov, S. L. (1990). “The propagation elastic waves in a porous medium with stochastic inhomogeneous gas distribution.” Izv. Akad. Nauk. SSSR, Fiz. Zemli, 6, 28–32.
Herskowitz, M., Lewitsky, S., and Shreiber, I. (2000). “Attenuation of ultrasound in porous media with dispersed micro bubbles.” Ultrasonics, 38, 767–769.
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.
Nakoryakov, V. E., Pokusaev, B. G., and Schreiber, I. R. (1983). Propagation of waves in gas- and vapor-liquid media, Institute of Thermophysics, Novosibirsk, Russia.
Nigmatulin, R. I. (1978). Fundamentals of mechanics of heterogeneous media, Nauka, Moscow.
Plona, T. J. (1980). ”Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies.” Appl. Phys. Lett., 36(4), 259–261.
Smeulders, D. M. J., de la Rosette, J. P. M., and van Dongen, M. E. N. (1992). “Waves in partially saturated porous media.” Transp. Porous Media, 9, 25–37.
Smeulders, D. M. J., and van Dongen, M. E. N. (1997). “Wave propagation in porous media containing a dilute gas–liquid mixture: Theory and experiment.” J. Fluid Mech., 343, 351–373.
Van der Grinten, J. G. M., van Dongen, M. E. N., and van der Kogel, H. (1987). “Strain and pore pressure propagation in a water-saturated porous media.” J. Appl. Phys., 62(12), 4682–4687.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 131 • Issue 9 • September 2005
Pages: 966 - 973
Copyright
© 2005 ASCE.
History
Received: Jan 14, 2004
Accepted: Dec 1, 2004
Published online: Sep 1, 2005
Published in print: Sep 2005
Notes
Note. Associate Editor: Alexander H.-D. Cheng
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.