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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     title = {Construction of an analytical solution of the problem on the formation of gas hydrate in a porous mine},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     volume = {172},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2019_172_a5/}
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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/