Filtration of two immiscible liquids in a viscoelastic porous medium

Margarita A. Tokareva ; Alexander A. Papin

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 18 (2025) no. 2, pp. 253-261.

Résumé

Governing equations for the motion of two immiscible fluids in a poroelastic skeleton are obtained within the framework of the theory of interacting continua. The stability of the steady-state solution of the system is investigated.

Détail

Keywords: poroelasticity, two-phase filtration, Darcy's law, stability, viscoelasticity.

Bibliographie

[1] Niemi, Bear and Bensabat (eds.), Geological Storage of CO2 in Deep Saline Formations, Springer, 2016

[2] M.Ferronato, G.Gambolati, C.Janna, P.Teatini, “Geomechanical issues of anthropogenic CO2 sequestration in exploited gas fields”, Energy Conversion and Management, 51 (2010), 1918–1928 | DOI

[3] A.Fabbri, N.Jacquemet, D.M.Seyedi, “A chemo-poromechanical model of oilwell cement carbonation under CO2 geological storage conditions”, Cement and Concrete Research, 42 (2012), 8–19 | DOI

[4] L.F.Athy, “Density, porosity, and compaction of sedimentary rocks”, Amer. Ass. Petrol. Geol. Bull., 14 (1930), 1–24

[5] K.Terzaghi, Theoretical Soil Mechanics, Wiley J., New York, 1943

[6] M.A.Biot, “General theory of three-dimensional consolidation”, J. Appl. Phys., 12:2 (1941), 155–164 | DOI

[7] O.B.Bocharov, “On the filtration of two immiscible liquids in a compressible formation”, Coll. scientific papers, Dynamics of continuous media, 50, USSR Academy of Sciences. Siberian Branch. Institute of Hydrodynamics, 1981, 15–36 (in Russian) | MR

[8] V.V.Vedernikov, V.N.Nikolaevskii, “Mechanics equations for porous medium saturated by a twophase liquid”, Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, 5 (1978), 769–773

[9] O.B.Bocharov, V.Ya.Rudyak, A.V.Seryakov, “The simplest models of deformation of a poroelastic medium saturated with fluids”, Physical and technical problems of mineral development, 2 (2014), 54–68 (in Russian) | MR

[10] V.Ya.Rudyak, O.B.Bocharov, A.V.Seryakov, “Hierarchical sequence of models and deformation peculiarities of porous media saturated with fluids”, Proceedings of the XLI Summer School-Conference Advanced Problems in Mechanics, APM-2013 (1-6 July , St-Petersburg), 2013, 183–190

[11] A.A.Papin, M.A.Tokareva, “On local solvability of the system of the equations of one dimensional motion of magma”, Journal of Siberian Federal Universit. Mathematics and Physics, 10:3 (2017), 385–395 | DOI | MR

[12] M.A.Tokareva, A.A.Papin, “Global solvability of a system of equations of one-dimensional motion of a viscous fluid in a deformable viscous porous medium”, Journal of Applied and Industrial Mathematics, 13:2 (2019), 350–362 | DOI | MR

[13] M.A.Tokareva, A.A.Papin, “On the existence of global solution of the system of equations of one-dimensional motion of a viscous liquid in a deformable viscous porous medium”, Siberian Electronic Mathematical Reports, 18:2 (2021), 1397–1422 | MR

[14] P.V.Gilev, A.A.Papin, “Filtration of two immiscible incompressible fluids in a thin poroelastic layer”, Journal of Applied and Industrial Mathematics, 18 (2024), 234–245 | DOI | MR

[15] R.I.Nigmatulin, Fundamentals of the Mechanics of Heterogeneous Media, Izdatel'stvo Nauka, M., 1978 (in Russian) | MR

[16] J.Bear, A.H.D.Cheng, Modeling Groundwater Flow and Contaminant Transport, Springer Science $\$ Business Media, Berlin, 2010

[17] F.Schneider, J.L.Potdevin, S.Wolf, I.Faille, “Vechanical and chemical compaction model for sedimentary bsasin simulation”, Tectonophysics, 263 (1996), 307–317 | DOI

[18] S.N.Antontsev, A.V.Kazhikhov, V.N.Monakhov, Boundary Value Problems in Mechanics of Nonhomogeneous Fluids, North-Holland, 1989 | MR

[19] J.JE.Lee, Modelling and Simulation of Compacting Sedimentary Basins, University of Oxford, 2019

[20] P.A.Waldner, M.Schneebeli, U.Schultze-Zimmermann, H.Fluhler, “Effect of snow structure on water flow and solute transport”, Hydrological Processes, 18:7 (2008), 1271–1290 | DOI

[21] R.R.Khasanov, A.R.Smirnova, “Experimental research of physical characteristics of preliminary compressed clay soil at moistening”, International Research Journal, 12:66 (2017), 178–182 | DOI

[22] A. Fowler, Mathematical Geoscience, Springer-Verlag London Limited, 2011 | MR

[23] C.Morency et al., “A numerical model for coupled fluid flow and matrix deformation with applications to disequilibrium compaction and delta stability”, Journal of Geophysical Research: Solid Earth, 112:B10 (2007)

[24] J.A.D.Connolly, Y.Y.Podladchikov, “Compaction-driven fluid flow in viscoelastic rock”, Geodin. Acta, 11 (1998), 55–84 | DOI

[25] O.Coussy, Poromechanics, John Wiley Sons, 2004

[26] M.A.Tokareva, A.A.Papin, A.A.Beregovykh, “Two-phase filtration in a thin poroelastic layer”, AIP Conference Proceedings, 2528 (2022), 020008 | DOI

[27] V.V.Shelukhin, “A poroelastic medium saturated by a two-phase capillary fluid”, Contin. Mech. Thermodyn., 26:5 (2014), 619–638 | DOI | MR

[28] A.Jardani, A.Revil, “Seismoelectric couplings in a poroelastic material containing two immiscible fluid phases”, Geophys. J. Int., 202:2 (2015), 850–870 | DOI

[29] A.A.Glushkova, A.A.Papin, “Stability of two-phase flows in a poroelastic medium”, Proceedings of the Seminar on Geometry and Mathematical Modeling, 5 (2019), 55–59 (in Russian)

[30] S.K.Garg, J.W.Pritchett, “Dynamics of gasfluidized beds”, Journal of Applied Physics, 46 (1975), 4493 | DOI