Preview

Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki

Advanced search

Pressure Wave Interaction with Fractured Porous Zone in Porous Medium

https://doi.org/10.26907/2541-7746.2024.3.331-342

Abstract

The propagation of a pressure wave in a porous medium with a fractured porous zone was numerically investigated. The study used a two-velocity model of a porous medium and a three-velocity model of a fractured porous medium. The problem was examined in a twodimensional formulation, considering cases when a porous medium has a free surface or is unbounded. The fractured porous zone was shown to have either an ellipseor rectangle-shaped boundary. The influence of such inhomogeneities on the propagation of pressure perturbations was analyzed.

About the Authors

A. A. Gubaidullin
Tyumen Branch of Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences
Russian Federation

Tyumen, 625026



O. Yu. Boldyreva
Tyumen Branch of Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences
Russian Federation

Tyumen, 625026



D. N. Dudko
Tyumen Branch of Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences
Russian Federation

Tyumen, 625026



References

1. Denneman A.I.M., Drijkoningen G.G., Smeulders D.M.J., Wapenaar K. Reflection and transmission of waves at a fluid/porous-medium interface. Geophysics, 2002, vol. 67, no. 1, pp. 282–291. https://doi.org/10.1190/1.1451800.

2. Fellah Z.E., Berger S., Lauriks W., Depollier C., Aristegui C., Chapelon J.-Y. Measuring the porosity and the tortuosity of porous materials via reflected waves at oblique incidence. J. Acoust. Soc. Am., 2003, vol. 113, no. 5, pp. 2424–2433. https://doi.org/10.1121/1.1567275.

3. Kumar R., Kumar S., Miglani A. Reflection and transmission of plane waves between two different fluid-saturated porous half-spaces. J. Appl. Mech. Tech. Phys., 2011, vol. 52, no. 5, pp. 773–782. https://doi.org/10.1134/S0021894411050129.

4. Gimaltdinov I.K., Sitdikova L.F. The dynamics of the sound waves at oblique incidence on the border “porous medium–gas”. Vestn. TyumGU. Ser.: Fiz.-Mat. Model. Neft’, Gaz, Energ., 2015, vol. 1, no. 2 (2), pp. 112–123. (In Russian)

5. Gimaltdinov I.K., Sitdikova L.F., Dmitriev V.L., Levina T.M., Khabeev N.S., Wanqing S. Reflection of acoustic waves from a porous material at oblique incidence. J. Eng. Phys. Thermophys., 2017, vol. 90, no. 5, pp. 1043–1052. https://doi.org/10.1007/s10891-017-1655-1.

6. Gubaidullin A.A., Boldyreva O.Yu., Dudko D.N. Compression pulse propagation in fractured porous medium. Lobachevskii J. Math., 2023, vol. 44, no. 11, pp. 4987–4993. https://doi.org/10.1134/S1995080223110161.

7. Dai Z.-J., Kuang Z.-B., Zhao S.-X. Reflection and transmission of elastic waves from the interface of a fluid-saturated porous solid and a double porosity solid. Transp. Porous Media, 2006, vol. 65, no. 2, pp. 237–264. https://doi.org/10.1007/s11242-005-6084-5.

8. Kumar M., Barak M.S., Kumari M. Reflection and refraction of plane waves at the boundary of an elastic solid and double-porosity dual-permeability materials. Pet. Sci., 2019, vol. 16, no. 2, pp. 298–317. https://doi.org/10.1007/s12182-018-0289-z.

9. Gubaidullin A.A., Boldyreva O.Yu., Dudko D.N. Wave interaction with fractured porous layer in porous medium. Lobachevskii. J. Math., 2024, vol. 45, no. 5, pp. 1971–1979. https://doi.org/10.1134/S1995080224602145.

10. Gubaidullin A.A., Kuchugurina O.Yu. Propagation of weak perturbations in cracked porous media. J. Appl. Math. Mech., 1999, vol. 63, no. 5, pp. 769–777. https://doi.org/10.1016/S0021-8928(99)00097-0.

11. Nigmatulin R.I. Dynamics of Multiphase Media. Vol. 1. CRC Press, 1990. 532 p. 342 А.А. ГУБАЙДУЛЛИН и др.

12. MacCormack R.W. The effect of viscosity in hypervelocity impact cratering. Proc. AIAA Hypervelocity Impact Conf. AIAA Paper 69-354, 1969.

13. Gubaidullin A.A., Boldyreva O.Yu., Dudko D.N. Numerical simulation of wave propagation in a fractured porous medium. Lobachevskii J. Math., 2022, vol. 43, no. 12, pp. 3471–3477. https://doi.org/10.1134/S1995080222150094.

14. Gubaidullin A.A., Boldyreva O.Yu., Dudko D.N. Approach to the numerical study of wave processes in a layered and fractured porous media in a two-dimensional formulation. Mathematics, 2023, vol. 11, no. 1, art. 227. https://doi.org/10.3390/math11010227.


Review

For citations:


Gubaidullin A.A., Boldyreva O.Yu., Dudko D.N. Pressure Wave Interaction with Fractured Porous Zone in Porous Medium. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2024;166(3):331-342. (In Russ.) https://doi.org/10.26907/2541-7746.2024.3.331-342

Views: 102


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2541-7746 (Print)
ISSN 2500-2198 (Online)