Abstract
A method for solving numerically the mathematical model system of equations describing the process of replacing methane with carbon dioxide in CH\({}_{4}\) hydrate during the development of a gas hydrate deposit is presented. This model is considered in a one-dimensional linear approximation for the case of negative temperatures and injection of carbon dioxide in gaseous state. The process of CO\({}_{2}\)–CH\({}_{4}\) replacement is assumed to be equilibrium. Partial differential equations are solved using an implicit scheme and tridiagonal matrix algorithm. To solve the system of equations, the method of simple iterations is used. The phase transitions ‘‘methane+ice – methane hydrate’’ and ‘‘carbon dioxide+ice – carbon dioxide hydrate’’ are calculated using an original algorithm suggested by the authors.
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REFERENCES
BP Statistical Review of World Energy, 2019. https://www.bp.com/content/dam/bp/business-sites/en/global/corporate/pdfs/energy-economics/statistical-review/bp-stats-review-2019-full-report.pdf. Accessed 2020.
Resources to Reserves 2013 – Oil, Gas and Coal Technologies for the Energy Markets of the Future (International Energy Agency, 2013).
S. L. Borodin and D. S. Belskikh, ‘‘The current state of researches related to the extraction of methane from a porous medium containing hydrate,’’ Vestn. Tyumen. Univ., Fiz. Mat. Model. Neft’ Gaz Energet. 4, 131–147 (2018).
S. Y. Misyura and I. G. Donskoy, ‘‘Dissociation kinetics of methane hydrate and CO2 hydrate for different granular composition,’’ Fuel 262, 116614 (2020).
S. L. Borodin and D. S. Belskikh, ‘‘Mathematical modeling of the equilibrium complete replacement of methane by carbon dioxide in a gas hydrate reservoir at negative temperatures,’’ Vestn. Tyumen. Univ., Fiz. Mat. Model. Neft’ Gaz Energet. 2 (22), 63–80 (2020).
M. K. Khasanov, G. R. Rafikova, and N. G. Musakaev, ‘‘Mathematical model of carbon dioxide injection into a porous reservoir saturated with methane and its gas hydrate,’’ Energies 13, 440 (2020).
V. Sh. Shagapov, M. K. Khasanov, N. G. Musakaev, and N. H. Duong, ‘‘Theoretical research of the gas hydrate deposits development using the injection of carbon dioxide,’’ Int. J. Heat Mass Transfer 107, 347–357 (2017).
G. G. Tsypkin, ‘‘Formation of hydrate in injection of liquid carbon dioxide into a reservoir saturated with methane and water,’’ Fluid Dyn. 51, 672–679 (2016).
V. Sh. Shagapov, M. K. Khasanov, and N. G. Musakaev, ‘‘Injection of liquid carbon dioxide into a reservoir partially saturated with methane hydrate,’’ J. Appl. Mech. Tech. Phys. 6, 1083–1092 (2016).
Sh. Pandey and N. Solms, ‘‘Hydrate stability and methane recovery from gas hydrate through CH4–CO2 replacement in different mass transfer scenarios,’’ Energies 12, 2309 (2019).
M. K. Khasanov, N. G. Musakaev, M. V. Stolpovsky, and S. R. Kildibaeva, ‘‘Mathematical model of decomposition of methane hydrate during the injection of liquid carbon dioxide into a reservoir saturated with methane and its hydrate,’’ Mathematics 8, 1482 (2020).
A. N. Salamatin, A. Falenty, and W. F. Kuhs, ‘‘Diffusion model for gas replacement in an isostructural CH4-CO2 Hydrate System,’’ J. Phys. Chem. C 121, 17603–17616 (2017).
N. G. Musakaev, S. L. Borodin, and A. A. Gubaidullin, ‘‘Methodology for the numerical study of the methane hydrate formation during gas injection into a porous medium,’’ Lobachevskii J. Math. 41 (7), 1272–1277 (2020).
N. G. Musakaev and M. K. Khasanov, ‘‘Solution of the problem of natural gas storages creating in gas hydrate state in porous reservoirs,’’ Mathematics 8, 36 (2020).
V. Sh. Shagapov, N. G. Musakaev, and R. R. Urazov, ‘‘Mathematical model of natural gas flow in pipelines with allowance for the dissociation of gas hydrates,’’ J. Eng. Phys. Thermophys. 81, 287–296 (2008).
N. G. Musakaev and S. L. Borodin, ‘‘To the question of the interpolation of the phase equilibrium curves for the hydrates of methane and carbon dioxide,’’ MATEC Web of Conf. 115, 05002 (2017).
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The research was supported by the Russian Science Foundation (project no. 17-79-20001).
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(Submitted by D. A. Gubaidullin)
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Borodin, S.L., Khasanov, M.K. Methodology for Calculating the Parameters of the CO\({}_{\mathbf{2}}\)–CH\({}_{\mathbf{4}}\) Replacement Process in Methane Hydrate During the Gas Hydrate Deposits Development. Lobachevskii J Math 42, 1961–1968 (2021). https://doi.org/10.1134/S1995080221080084
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DOI: https://doi.org/10.1134/S1995080221080084