Geodesic
Modeling the variability of seismic properties of frozen multiphase media depending on temperature
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. B203-B231 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A three-phase model of a deformable porous medium saturated with a mixture of liquid and gas is presented. The derivation of the model is based on the theory of Hyperbolic Thermodynamically Compatible systems (HTC) applied to a mixture of solid, liquid and gas. The resulting governing equations are hyperbolic and satisfy the laws of thermodynamics (energy conservation and entropy growth). Based on the formulated nonlinear model, governing equations for modeling the propagation of small amplitude seismic waves are obtained. These equations have been used to study the variability of wave fields caused by temperature changes in geological media with porous structures saturated with a mixture of liquid and gas. Numerical examples are presented to illustrate the peculiarities of wave propagation in media of varying porosity and different ratios of liquid and gas fractions. The finite difference scheme on staggered grids has been used for the numerical solution.
Keywords: Poroelasticity, three-phase flow, hyperbolic thermodynamically compatible model
Mots-clés : wave propagation. 
@article{SEMR_2024_21_2_a79,
     author = {G. Reshetova and E. Romenski},
     title = {Modeling the variability of seismic properties of frozen multiphase media depending on temperature},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {B203--B231},
     year = {2024},
     volume = {21},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a79/}
}
TY  - JOUR
AU  - G. Reshetova
AU  - E. Romenski
TI  - Modeling the variability of seismic properties of frozen multiphase media depending on temperature
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2024
SP  - B203
EP  - B231
VL  - 21
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a79/
LA  - en
ID  - SEMR_2024_21_2_a79
ER  - 
%0 Journal Article
%A G. Reshetova
%A E. Romenski
%T Modeling the variability of seismic properties of frozen multiphase media depending on temperature
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2024
%P B203-B231
%V 21
%N 2
%U http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a79/
%G en
%F SEMR_2024_21_2_a79
G. Reshetova; E. Romenski. Modeling the variability of seismic properties of frozen multiphase media depending on temperature. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. B203-B231. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a79/

[1] M.A. Biot, “Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range”, J. Acoust. Soc. Amer., 28:2 (1956), 168–178 | DOI | MR

[2] M.A. Biot, “Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range”, J. Acoust. Soc. Amer., 28:2 (1956), 179–191 | DOI | MR

[3] J.M. Carcione, C. Morency, V. Santos, “Computational poroelasticity – A review”, Geophysics, 75:5 (2010), 75A229–75A243 | DOI

[4] F. Pesavento, B.A. Schrefler, G. Sciumè, “Multiphase flow in deforming porous media: a review”, Arch. Comput. Methods Eng., 24:2 (2017), 423–448 | DOI | MR | Zbl

[5] Zhiqi Shi, Xiao He, Dehua Chen, Xiuming Wang, “Seismic wave dispersion and attenuation resulting from multiscale wave-induced fluid flow in partially saturated porous media”, Geophys. J. Intern., 236:2 (2024), 1172–1182 | DOI

[6] S.K. Godunov, E.I. Romenskii, Elements of continuum mechanics and conservation laws, Kluwer, New York, 2003 | DOI | MR | Zbl

[7] E. Romenski, “Hyperbolic systems of thermodynamically compatible conservation laws in continuum mechanics”, Math. Comput. Modelling, 28:10 (1998), 115–130 | DOI | MR

[8] I. Peshkov, M. Pavelka, E. Romenski, M. Grmela, “Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations”, Contin. Mech. Thermodyn., 30:6 (2018), 1343–1378 | DOI | MR | Zbl

[9] E. Romenski, G. Reshetova, I. Peshkov, M. Dumbser, “Modeling wavefields in saturated elastic porous media based on thermodynamically compatible system theory for two-phase solid-fluid mixtures”, Comput. Fluids, 206 (2020), 104587 | DOI | MR | Zbl

[10] G. Reshetova, E. Romenski, “Diffuse interface approach to modeling wavefields in a saturated porous medium”, Appl. Math. Comput., 398 (2021), 125978 | DOI

[11] E. Romenski, G. Reshetova, I. Peshkov, “Two-phase hyperbolic model for porous media saturated with a viscous fluid and its application to wavefield simulation”, Appl. Math. Modelling, 106 (2022), 567–600 | DOI | MR | Zbl

[12] E. Romenski, G. Reshetova, I. Peshkov, “Computational model for compressible two-phase flow in a deformed porous medium”, Computational Science and Its Applications – ICCSA 2021, ICCSA 2021, Lecture Notes Computer Science, 12949, eds. Gervasi O., et al., Springer, Cham, 2021 | DOI

[13] E. Romenski, G. Reshetova, I. Peshkov, “Thermodynamically compatible hyperbolic model of a compressible multiphase flow in a deformable porous medium and its application to wavefields modeling”, AIP Conf. Proc., 2448:1 (2021), 020019 | DOI

[14] E. Romenski, A. Belozerov, I. Peshkov, “Conservative formulation for compressible multiphase flows”, Q. Appl. Math., 74:1 (2016), 113–136 | DOI | MR | Zbl

[15] J. Virieux, “P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method”, Geophysics, 51:4 (1986), 889–901 | DOI

[16] A.R. Levander, “Fourth-order finite-difference P-SV seismograms”, Geophysics, 53:11 (1988), 1379–1492 | DOI

[17] R.W. Graves, “Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences”, Bull. Seismolog. Soc. America, 86:4 (1996), 1091–1106 | DOI | MR

[18] T.N. Davis, Permafrost: a guide to frozen ground in transition, University of Alaska Press, Fairbanks, 2001 https://www.geobotany.org/library/pubs/DavisN2001_permafrost_ch4.pdf

[19] A.A. Samarskii, The theory of difference schemes, Marcel Dekker, New York, 2001 | DOI | MR | Zbl

[20] P. Moczo, J. Kristek, V. Vavrycuk, R. J. Archuleta, L. Halada, “3D heterogeneous staggered-grid finite-difference modeling of seismic motion with volume harmonic and arithmetic averaging of elastic moduli and densities”, Bull. Seismolog. Soc. America, 92:8 (2002), 3042–3066 | DOI