Geodesic
The problem of the propagation of acoustic waves in a porous environment saturated with bubble liquid
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 13 (2021) no. 1, pp. 59-66

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In many cases, formation fluids contain gas. For example, a gas-liquid mixture in a porous medium is formed during acid treatment of low-permeability zones, during water-gas stimulation of reservoirs, etc. Therefore, it seems relevant to take into account the presence of gas bubbles when studying wave processes in porous media saturated with liquid. In this work, the propagation of acoustic waves in a porous medium saturated with a gas-liquid mixture is theoretically investigated taking into account the interfacial forces of interaction between the liquid and the matrix, and heat transfer between the gas and the liquid. A general system of equations and physical relations is written, which describes the propagation of waves in a porous medium filled with bubble liquid. A dispersion relation is obtained that describes the dependence of the complex wave vector on the frequency, on the basis of which the dependence of the phase velocity and attenuation coefficient on the frequency for “fast” and “slow” waves is investigated. The calculation results make it possible to evaluate the effect of gas bubbles on the propagation of sound waves in a porous medium saturated with bubble liquid. In addition, the results of the work can be used to interpret the data of acoustic sounding of porous media.
Keywords: porous medium, acoustic wave, bubble liquid, “fast” wave, “slow” wave. 
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     author = {L. F. Sitdikova and I. K. Gimaltdinov},
     title = {The problem of the propagation of acoustic waves in a porous environment saturated with bubble liquid},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {59--66},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2021_13_1_a6/}
}
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L. F. Sitdikova; I. K. Gimaltdinov. The problem of the propagation of acoustic waves in a porous environment saturated with bubble liquid. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 13 (2021) no. 1, pp. 59-66. http://geodesic.mathdoc.fr/item/VYURM_2021_13_1_a6/