Algorithm for solving the problem of methane hydrate decomposition in a closed hydrate-containing region of a porous medium

About the authors:

Nail G. Musakaev, Dr. Sci. (Phys.-Math.), Professor, Professor of the Department of Applied and Technical Physics, School of Natural Science, University of Tyumen, Tyumen, Russia; Chief Researcher, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences, Tyumen, Russia; musakaev68@yandex.ru, https://orcid.org/0000-0002-8589-9793

Stanislav L. Borodin, Cand. Sci. (Phys.-Math.), Senior Researcher, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; eLibrary AuthorID, ORCID, Web of Science ResearcherID, Scopus Author ID, s.l.borodin@yandex.ru; ORCID: 0000-0002-2850-5989

Denis S. Belskikh, Junior Researcher, Tyumen Branch of the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences; denisbelskikh@gmail.com; ORCID: 0000-0002-0813-5765

Abstract:

Russia has a law on limiting greenhouse gas emissions, signed by the President of the Russian Federation in July 2021. The list of greenhouse gasses includes methane, and its reserves in the form of gas hydrates largely prevail over the reserves of free methane. The formation of gas hydrates occurs at sufficiently low temperatures and high pressures. A significant part of the “sleeping giants”, as journalists dubbed the methane-containing deposits, are in the Arctic region, and they are very sensitive to warming. The release of this greenhouse potential would have very negative consequences for the Earth’s climate. Thus, it is necessary to study the process of gas hydrate decomposition under thermal impact on a hydrate-containing porous medium. It is worth noting the importance of theoretical research to solve this problem, which includes the construction of a mathematical model of the process under study, algorithmization, software implementation and computational experiments.

The paper presents a two-dimensional approximation of the formulated problem of heating at the upper boundary of the porous medium’s closed region containing methane and its hydrate initially. A mathematical model is presented, which is based on the mass conservation equations for methane, water and gas hydrate; Darcy’s law for the motion of the gas and liquid phases; the equation of a real gas state, the energy conservation equation considering thermal conductivity, convection, adiabatic cooling, the Joule-Thomson effect and absorption of latent heat during hydrate formation. An algorithm for the numerical implementation of the mathematical model is constructed and a computer code is developed to calculate main parameters of the process in the work, the computer program is updated to calculate the main parameters of the process researched in the article.

References:

1. Basniev K. S., Kochina I. N., Maksimov V. M. 1993. Underground fluid mechanics. Moscow: Nedra. 416 p. [In Russian]

2. Bondarev E. A., Rozhin I. I., Popov V. V., Argunova K. K. 2015. “Assessment of possibility of natural gas hydrates underground storage in permafrost regions”. Earth’s Cryosphere, vol. 19, no. 4, pp. 64-74. [In Russian]

3. Borodin S. L., Belskikh D. S. 2018. “The current state of researches related to the extraction of methane from a porous medium containing hydrate”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 4, no. 4, pp. 131-147. [In Russian]. DOI: 10.21684/2411-7978-2018-4-4-131-147

4. Vasilev A. А., Melnikov V. P., Semenov P. B., Oblogov G. E., Streletskaya I. D. 2019. “Methane concentration and emission in dominant landscapes of typical tundra of Western Yamal”. Reports of the Academy of Sciences, vol. 485, no 1, pp. 284-287. DOI: 10.1134/S1028334X19030085

5. Kiselev A. A. Reshetnikov A. I. 2013. “Methane in the Russian Arctic: Observation and calculation results”. Arctic and Antarctic Research, no. 2 (96), pp. 5-15. [In Russian]

6. Lobkovskii L. I., Ramazanov M. M. 2017. “Mathematical model of axisymmetric quasi-steady-state heat and mass transfer in a gas hydrate reservoir”. Fluid Dynamics, vol. 52, no. 4, pp. 536-546. DOI: 10.1134/S0015462817040081

7. Lobkovskiy L. I., Nikiforov S. L., Libina N. V., Ananiev R. A., Meluzov A. A., Roslyakov A. G., Dmitrevskiy N. N., Semiletov I. P. 2015. “Gas extraction and degradation of the submarine permafrost rocks on the Laptev Sea shelf”. Oceanology, vol. 55, no. 2, pp. 283-290. DOI: 10.1134/S0001437015010129

8. Musakaev N. G., Borodin S. L., Belskikh D. S. 2018. “Calculation of the parameters for the process of gas injection into a reservoir saturated with methane and its hydrate”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 4, no. 3, pp. 165-178. [In Russian]. DOI: 10.21684/2411-7978-2018-4-3-165-178

9. Musakaev N. G., Belskikh D. S. 2021. “Numerical study of the process of gas hydrate decomposition under the thermal impact on the hydrate-containing region of a porous formation”. Scientific notes of Kazan University. Series Physical and Mathematical Sciences, vol. 163, no. 2, pp. 153-166. [In Russian]. DOI: 10.26907/2541-7746.2021.2.153-166

10. Nigmatulin R. I. 1987. Dynamics of Multiphase Media: in 2 volumes. Volume 1. Moscow: Nauka. [In Russian]

11. Shagapov V. S., Musakaev N. G. 2016. Dynamics of Hydrate Formation and Decomposition in Gas Production, Transportation and Storage Systems. Moscow: Nauka. 238 p. [In Russian]

12. Shagapov V. S., Nasyrova L. A. 1999. “Heating of a porous medium partially filled with gas hydrate in the presence of impermeable boundaries”. High Temperature, vol. 37, no. 5, pp. 784-789. [In Russian]

13. Shagapov V. S., Khasanov M. K., Gimaltdinov I. K., Stolpovsky M. V. 2013. “The features of gas hydrate dissociation in porous media at warm gas injection”. Thermophysics and Aeromechanics, vol. 20, no. 3, pp. 339-346. DOI: 10.1134/S0869864313030104 [In Russian]

14. Shagapov V. S., Yumagulova Y. A. 2013. “An increase of liquid pressure in enclosure under thermal effect through walls”. Thermophysics and Aeromechanics, vol. 20, no. 4, pp. 495-502. DOI: 10.1134/S0869864313040124 [In Russian]

15. Shagapov V. S., Chiglintseva A. S., Rusinov A. A. 2016. “Theoretical modeling of gas extraction from a partially gas-saturated porous gas-hydrate reservoir with respect to thermal interactions with surrounding rocks”. Theoretical Foundations of Chemical Engineering, vol. 50, no. 4, pp. 449-458. DOI: 10.1134/S004057951604045X [In Russian]

16. Sharafutdinov R. F., Davletshin F. F. 2021. “An analytical model of a non-stationary temperature field in a reservoir with a hydraulic fracturing”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 7, no. 2 (26), pp. 75-94. [In Russian]. DOI: 10.21684/2411-7978-2021-7-2-75-94 [In Russian]

17. Sharafutdinov R. F., Davletshin F. F. 2021. “Numerical study of non-isothermal filtration of compressible fluid in a low-permeability reservoir with a hydraulic fracture”. Journal of Applied Mechanics and Technical Physics, vol. 62, no. 2, pp. 317-328. DOI: 10.1134/S0021894421020164

18. Ahmadi G., Ji C., Smith H. D. 2004. “Numerical solution for natural gas production from methane hydrate dissociation”. Journal of Petroleum Science and Engineering, vol. 41, no. 4, pp. 269-285. DOI: 10.1016/j.profnurs.2003.09.004

19. Archer D. 2007. “Methane hydrate stability and anthropogenic climate change”. Biogeosciences, vol. 4, pp. 521-544. DOI: 10.5194/BG-4-521-2007

20. Davletshina M. R., Stolpovskii M. V., Solovev D. B. 2019. “Decomposition of methane hydrate with heat exposure”. IOP Conference Series: Earth and Environmental Science, vol. 272, no. 3, art. 032239. DOI: 10.1088/1755-1315/272/3/032239

21. Euskirchen E. S., Bret-Harte M. S., Shaver G. R., Edgar C. W., Romanovsky V. E. 2017. “Long-term release of carbon dioxide from Arctic tundra ecosystems in Alaska”. Ecosystems, vol. 20, pp. 960-974. DOI: 10.1007/s10021-016-0085-9

22. Liu Y., Strumendo M., Arastoopour H. 2009. “Simulation of methane production from hydrates by depressurization and thermal stimulation”. Industrial and Engineering Chemistry Research, vol. 48, no. 5, pp. 2451-2464. DOI: 10.1021/ie8005275

23. Makogon Y. F., Holditch S. A., Makogon T. Y. 2007. “Natural gas-hydrates — A potential energy source for the 21^st Century”. Journal of Petroleum Science and Engineering, vol. 56, pp. 14-31. DOI: 10.1016/j.petrol.2005.10.009

24. Misyura S. Y., Donskoy I. G., Manakov A. Y., Morozova V. S., Strizhak P. A., Skiba S. S., Sagidullin A. K. 2021. “Studying the influence of key parameters on the methane hydrate dissociation in order to improve the storage efficiency”. Journal of Energy Storage, vol. 44, art. 103288. DOI: 10.1016/j.est.2021.103288

25. Musakaev N. G., Belskikh D. S., Borodin S. L. 2021. “Mathematical model and method for solving the problem of non-isothermal gas and liquid filtration flow during dissociation of gas hydrates”. Lobachevskii Journal of Mathematics, vol. 42, no. 9, pp. 2198-2204. DOI: 10.1134/S1995080221090225

26. Musakaev N. G., Khasanov M. K. 2019. “On the issue of the solutions existence of the problem of gas hydrate dissociation in a porous medium with the formation of an extended region of phase transitions”. Journal of Physics: Conference Series, vol. 1404, art. 012034. DOI: 10.1088/1742-6596/1404/1/012034

27. Musakaev N. G., Borodin S. L. 2017. “To the question of the interpolation of the phase equilibrium curves for the hydrates of methane and carbon dioxide”. MATEC Web of Conferences, vol. 115, art. 05002. DOI: 10.1051/matecconf/201711505002

28. Neumann R. B., Moorberg C. J., Lundquist J. D., Turner J. C., Waldrop M. P., McFarland J. W., Euskirchen E. S., Edgar C. W., Turetsky M. R. 2019. “Warming effects of spring rainfall increase methane emissions from thawing permafrost”. Geophysical Research Letters, vol. 46, no. 3, pp. 1393-1401. DOI: 10.1029/2018GL081274

29. Xu W., Ruppel C. 1999. “Predicting the occurrence, distribution, and evolution of methane gas hydrate in porous marine sediments”. Journal of Geophysical Research, vol. 104, no. B3, pp. 5081-5095. DOI: 10.1029/1998JB900092