Geodesic
Construction of an analytical solution of the problem on the formation of gas hydrate in a porous mine
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 3, Tome 172 (2019), pp. 91-95.

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In this paper, we propose the mathematical formulation of the problem on injection of a cold gas into a porous medium accompanied by the formation of gas hydrate. The mathematical formulation of the problem is an initial-boundary-value problem for a system of nonlinear partial differential equations expressing the laws of conservation of mass and energy supplemented by the conditions of mass and heat balance at the moving boundary of phase transitions. Within the framework of the rectilinear parallel approximation, we construct approximate analytical solutions with a temperature jump at the boundary where the gas hydrate appears. These solutions describe the relationship between the coordinate of the boundary of phase transition and the parameters of the injected gas and porous medium.
Keywords: differential equation, mathematical model, analytical solutions, gas hydrate
Mots-clés : filtration, phase transition. 
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N. G. Musakaev; M. K. Khasanov; S. L. Borodin. Construction of an analytical solution of the problem on the formation of gas hydrate in a porous mine. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 3, Tome 172 (2019), pp. 91-95. http://geodesic.mathdoc.fr/item/INTO_2019_172_a5/

[1] Bondarev E. A., Rozhin I. I., Popov V. V., Argunova K. K., “Otsenka vozmozhnosti podzemnogo khraneniya gidratov prirodnogo gaza v zone mnogoletnei merzloty”, Kriosfera Zemli., 19:4 (2015), 64–74

[2] Kuznetsov F. A., Istomin V. A., Rodionova T. V., “Gazovye gidraty: istoricheskii ekskurs, sovremennoe sostoyanie, perspektivy issledovanii”, Ros. khim. zh., 47:3 (2003), 5–18

[3] Nigmatulin R. I., Dinamika mnogofaznykh sred, Nauka, M., 1987

[4] Nurislamov O. R., Shagapov V. Sh., “Nagnetanie gaza vo vlazhnuyu poristuyu sredu s obrazovaniem gazogidrata”, Prikl. mat. mekh., 73:5 (2009), 809–823 | MR | Zbl

[5] Shagapov V. Sh., Musakaev N. G., Khasanov M. K., “Nagnetanie gaza v poristyi rezervuar, nasyschennyi gazom i vodoi”, Teplofiz. aeromekh., 12:4 (2005), 645–656 | MR

[6] Shagapov V. Sh., Khasanov M. K., Gimaltdinov I. K., Stolpovskii M. V., “Chislennoe modelirovanie obrazovaniya gazogidrata v poristom plaste konechnoi protyazhennosti pri produvke ego gazom”, Prikl. mekh. tekhn. fiz., 52:4 (2011), 116–126 | Zbl

[7] Shagapov V. Sh., Khasanov M. K., Musakaev N. G., “Obrazovanie gazogidrata v poristom rezervuare, chastichno nasyschennom vodoi, pri inzhektsii kholodnogo gaza”, Prikl. mekh. tekhn. fiz., 49:3 (2008), 137–150 | Zbl

[8] Chatti I., Delahaye A., Fournaison L., Petitet J. P., “Benefits and drawbacks of clathrate hydrates: a review of their areas of interest”, Energy Conv. Manag., 46:9–10 (2005), 1333–1343 | DOI

[9] Demirbas A., “Natural gas”, Methane Gas Hydrate, Springer, London, 2010, 57–76 | DOI

[10] Shagapov V. Sh., Musakaev N. G., Khasanov M. K., “Formation of gas hydrates in a porous medium during an injection of cold gas”, Int. J. Heat Mass Trans., 84 (2015), 1030–1039 | DOI

[11] Sloan E. D., Koh C. A., “Natural gas hydrates: Recent advances and challenges in energy and environmental applications”, AIChE J., 53:7 (2007), 1636–1643 | DOI

[12] Veluswamy H. P., Kumar A., Seo Y., Lee J. D., Linga P., “A review of solidified natural gas (SNG) technology for gas storage via clathrate hydrates”, Appl. Energy., 216 (2018), 262–285 | DOI