Geodesic
Numerical simulation in problems with dissociation of gas hydrates in a porous medium in one-dimensional formulation
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 161 (2019) no. 2, pp. 205-229

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The paper deals with some typical problems of gas hydrates dissociation in a porous medium, which in the first approximation can be reduced to one-dimensional. The research aims to study the mutual effects of underground gas hydrates and climate change, as well as some important technological and ecological problems of the flow in the well or fault area in the presence of hydrate-containing formations. New conservative difference schemes were developed for this class of problems. They are based on the splitting of gas-hydrodynamic processes. The advantage of these schemes is the phased solution of parabolic and hyperbolic equations. This approach greatly simplifies the solution procedure and at the same time increases its stability. Notably, within the framework of the approach, an algorithm was proposed to jointly solve the systems of equations describing the processes in various fields characterized by their own set of coexisting phases. The coordination of computational schemes for them is not a trivial and automatic process. Numerical calculations using mathematical modeling for the joint description of the gas hydrate zone and the zone with no gas hydrates were carried out. The results of calculations showed the applicability of the developed methods for solving the problems under study.
Keywords: gas hydrates, filtering, numerical simulation. 
@article{UZKU_2019_161_2_a3,
     author = {Yu. A. Poveshchenko and V. O. Podryga and I. V. Popov and S. B. Popov and P. I. Rahimly and G. I. Kazakevich},
     title = {Numerical simulation in problems with dissociation of gas hydrates in a porous medium in one-dimensional formulation},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {205--229},
     publisher = {mathdoc},
     volume = {161},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2019_161_2_a3/}
}
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Yu. A. Poveshchenko; V. O. Podryga; I. V. Popov; S. B. Popov; P. I. Rahimly; G. I. Kazakevich. Numerical simulation in problems with dissociation of gas hydrates in a porous medium in one-dimensional formulation. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 161 (2019) no. 2, pp. 205-229. http://geodesic.mathdoc.fr/item/UZKU_2019_161_2_a3/