Abstract
The features of propagation of longitudinal and transverse waves (LW and TW) in fractured porous medium (FPM) saturated with liquid are investigated by methods of multiphase mechanics. The mathematical model of FPM accounting for inequality of velocities and pressures of liquid in pores and fractures, liquid mass exchange and nonstationary interaction forces is developed. Processes of monochromatic wave propagation are studied. The dispersion relation is obtained and the effect of model parameters on wave propagation is analysed. It is established that one transverse and three longitudinal waves propagate in FPM saturated with liquid. The fastest LW is a deformational wave and the two others are filtrational. Filtrational waves attenuate much stronger than deformational and transverse waves. Distinction of velocities and pressures in liquid in various pore systems provides an explanation for the existence of the two filtrational waves in porous medium with two different characteristic sizes of pores.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Auriault, J.-L. and Boutin, C.: 1992, Deformable porous media with double porosity. Quasi-static. 1: Coupling effects, Transport in Porous Media 7(1), 63–82.
Auriault, J.-L. and Royer, P.: 1993, Ecoulement déun gaz dans un milieu poreux a double porosite, C. R. Acad. Sci., Ser. 2, 317(4), 431–436.
Bai, M., Ma, Q. and Roegiers, J.-C: 1994, Dual-porosity behaviour of naturally fractured reservoirs, Int. J. Numer. Anal Meth. Geomech. 18(6), 359–376.
Barenblatt, G. I., Zheltov, Yu. P. and Kochina, I. N.: 1960, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, PMM 24(5), 1286–1303.
Barenblatt, G. I., Entov, V. M. and Ryzhik, V. M.: 1984, Flow of Liquids and Gases in Natural Seams, Nedra, Moscow (in Russian).
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), 169–178.
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), 179–191.
Biot, M. A.: 1962, Mechanics of deformation and acoustic propagation in porous media, J. Appl. Soc. Phys. 33(4), 1482–1498.
Buyevich, Yu. A.: 1984, Structural and mechanical properties and filtration in elastic fractured porous material, IFZh 46(4), 593–600.
Chen Zhangxin: 1994, Large-scale averaging analysis of single phase flow in fractured reservoirs, SIAM J. Appl. Math. 54(3), 541–659.
Dinariyev, O. Yu.: 1990, Filtration in fractured medium with fractal geometry of fractures, Doklady AN, MZhG (5), 66–70.
Dinariyev, O. Yu.: 1992, Flow of liquid and gases in porous media with fractal geometry, Doklady AN, MZhG (5), 101–109.
Dinariyev, O. Yu.: 1994, Curve of pressure restore for fractal fractured porous medium, PMM 58(4), 172–175.
Egorov, A. G., Kosterin, A. V. and Skvortsov, E. V.: 1990, Consolidation and Acoustical Waves in Saturated Porous Media, Izdatel’stvo Kazanskogo universiteta, Kazan (in Russian).
Isakovich, M. A.: 1973, General Acoustics, Nauka, Moscow (in Russian).
Nigmatulin, R. I.: 1978, Fundamentals of Mechanics of Heterogeneous Media, Nauka, Moscow (in Russian).
Nigmatulin, R. I.: 1990, Dynamics of Multiphase Media, Hemisphere, New York.
Nikolayevskii, V. N., Basniyev, K. S., Gorbunov, A. T. and Zotov, G. A.: 1970, Mechanics of Saturated Porous Media, Nedra, Moscow (in Russian).
Nikolayevskii, V. N.: 1984, Mechanics of Porous and Fractured Media, Nedra, Moscow (in Russian).
Royer, P. and Auriault J.-L.: 1994, Transient quasi-static gas flow through a rigid porous medium with double porosity, Transport in Porous Media 17(1), 33–57.
Saucier Antoine: 1992, Effective permeability of multifractal porous media, Physica. A 183(4), 381–397.
Tuncay, K. and Corapcioglu, M. Y.: 1996a, Wave propagation in fractured porous media, Transport in Porous Media 23, 237–258.
Tuncay, K. and Corapcioglu, M. Y.: 1996b, Body waves in fractured porous media saturated by two immiscible Newtonian fluids, Transport in Porous Media 23, 259–273.
Wilson, R. K., and Aifantis, E. C.: 1982, On the theory of consolidation with double porosity, Int. J. Engng. Sci. 20(9), 1009–1035.
Wilson, R. K. and Aifantis, E. C: 1984, A double porosity model for acoustic wave propagation in fractured-porous rock, Int. J. Engng. Sci. 22(8), 1209–1217.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Gubaidullin, A.A., Kuchugurina, O.Y. (1999). The Peculiarities of Linear Wave Propagation in Double Porous Media. In: De Boer, R. (eds) Porous Media: Theory and Experiments. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4579-4_3
Download citation
DOI: https://doi.org/10.1007/978-94-011-4579-4_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5939-8
Online ISBN: 978-94-011-4579-4
eBook Packages: Springer Book Archive