Numerical simulation in problems with dissociation of gas hydrates in a porous medium in one-dimensional formulation

Yu.A. Poveshchenkoab*, V.O. Podrygaa,c**, I.V. Popova,b*** , S.B. Popova****, P.I. Rahimlya*****, G.I. Kazakevichd******
aKeldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia
bNational Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, 115409 Russia
cMoscow Automobile and Road Construction State Technical University, Moscow, 125319 Russia
d P.P. Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, 117997 Russia
E-mail: *hecon@mail.ru, **pvictoria@list.ru, ***piv2964@mail.ru,
****popovsb@yandex.ru, *****pervin@rehimli.info, ******gkazakevich@yandex.ru
Received May 10, 2019

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DOI: 10.26907/2541-7746.2019.2.205-229

For citation: Poveshchenko Yu.A., Podryga V.O., Popov I.V., Popov S.B., Rahimly P.I., Kazakevich G.I. Numerical simulation in problems with dissociation of gas hydrates in a porous medium in one-dimensional formulation. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2019, vol. 161, no. 2, pp. 205–229. doi: 10.26907/2541-7746.2019.2.205-229. (In Russian)

Abstract

The paper deals with some typical problems of gas hydrates dissociation in a porous medium, which in the flrst approximation can be reduced to one-dimensional. The research aims to study the mutual efiects 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 difierence 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 simplifles 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 flelds 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, flltering, numerical simulation
Acknowledgments. The work was supported by the Russian Foundation for Basic Research (projects no. 16-29-15081-ofl m, 18-07-00841-a, and 18-51-18004-Bolg a).

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