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
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).
References
1. Istomin V.A., Yakushev V.S. Gazovye gidraty v prirodnykh usloviyakh [Gas Hydrates in Natural Conditions]. Moscow, Nedra, 1992. 236 p. (In Russian)
2. Ginsburg G.D., Solov'ev V.A. Submarinnye gazovye gidraty [Submarine Gas Hydrates]. St. Petersburg, VNIIOkeanol., 1994. 200 p. (In Russian)
3. Englezos P. Clathrate hydrates. Ind. Eng. Chem. Res. J., 1993, vol. 32, no. 7, pp. 1251-1274. doi: 10.1021/ie00019a001.
4. Gudzenko V.T., Varenichev A.A., Gromova M.P. Gas hydrates. Informational and analytical review. Geol., Geoflz., Razrab. Neft. Gazov. Mestorozhd., 2016, no. 5, pp. 39-68. (In Russian)
5. Byk S.Sh., Makogon Yu.F., Fomina V.I. Gazovyye gidraty [Gas Hydrates]. Moscow, Khimiya, 1980. 296 p. (In Russian)
6. Perlstein G.Z., Sergeev D.O., Tipenko G.S., Tumskoi V.E., Khimenkov A.N., Vlasov A.N., Merzlyakov V.P., Stanilovskaya Yu.V. Hydrocarbon gases and cryolithozone of the Arctic shelf. Arkt.: Ekol. Ekon., 2015, no. 2, pp. 35-44. (In Russian)
7. Bondarev E.A., Rozhin I.I., Popov V.V., Argunova K.K. Assessment of possibility of natural gas hydrates underground storage in permafrost regions. Earth's Cryos., 2015, vol. 19, no. 4, pp. 58{67.
8. Maksimov A.M., Yakushev V.S., Chuvilin E.M. Assessment of possible gas outburst during decomposition of gas hydrates in reservoirs. Dokl. Ross. Akad. Nauk, 1997, vol. 352, no. 4, pp. 532-534. (In Russian)
9. Vasil'eva Z.A., Eflmov S.I., Yakushev V.S. Prediction of thermal interaction between oil/gas wells and intra-permafrost metastable gas hydrates. Earth's Cryos., 2016, vol. 20, no. 1, pp. 60-63.
10. Sergienko V.I., Lobkovskii L.I., Semiletov I.P., Dudarev O.V., Dmitrevskii N.N., Shakhova N.E., Romanovskii N.N., Kosmach D.A., Nikol'skii D.N., Nikiforov S.L., Salomatin A.S., Anan'ev R.A., Roslyakov A.G., Salyuk A.N., Karnaukh V.V., Chernykh D.B., Tumskoi V.E., Yusupov V.I., Kurilenko A.V., Chuvilin E.M., Bukhanov B.A. The degradation of submarine permafrost and the destruction of hydrates on the shelf of east arctic seas as a potential cause of the \Methane Catastrophe": Some results of integrated studies in 2011. Dokl. Earth Sci., 2012, vol. 446, no. 1, pp. 1132-1137. doi: 10.1134/S1028334X12080144.
11. Tsypkin G.G. Formation of the impermeable layer in the process of methane hydrate dissociation in porous media. Fluid Dyn., 2017, vol. 52, no. 5, pp. 657-665. doi: 10.1134/S0015462817050076.
12. Kim H.C., Bishnoi P.R., Heidemann R.A., Rizvi S.S.H. Kinetics of methane hydrate decomposition. Chem. Eng. Sci., 1987, vol. 42, no. 7, pp. 1645-1653.
13. Yousif M.H., Abass H.H., Selim M.S., Sloan E.D. Experimental and theoretical investigation of methane-gas-hydrate dissociation in porous media. SPE Reservoir Eng., 1991, vol. 6, no. 1, pp. 69-76. doi: 10.2118/18320-PA.
14. Aziz K., Settari A. Petroleum Reservoir Simulation. London, New York, Elsevier, 1979. 476 p.
15. Goel N., Wiggins M., Shah S. Analytical modeling of gas recovery from in situ hydrates dissociation. J. Pet. Sci. Eng., 2001, vol. 29, no. 2, pp. 115-127. doi: 10.1016/S0920-4105(01)00094-8.
16. Khataniar S., Kamath V.A., Omenihu S.D., Patil S.L., Dandekar A.Y. Modeling and economic analysis of gas production from hydrates by depressurization method. Can. J. Chem. Eng., 2002, vol. 80, no. 1, pp. 135-143.
17. Jeannin L., Bayi A., Renard G., Bonnefoy O., Herri J.M. Formation and dissociation of methane hydrates in sediments. Part II: Numerical modeling. Proc. 4th Int. Conf. on Gas Hydrates, Yokohama, Japan, May 19-23, 2002, 2002, vol. 2, pp. 802-806.
18. Basniev K.S., Kochina I.N., Maksimov V.M. Podzemnaya gidromekhanika [Underground Fluid Mechanics]. Moscow, Nedra, 1993. 416 p. (In Russian)
19. Istomin V.A., Kwon V.G. Preduprezhdenie i likvidatsiya gazovykh gidratov v sistemakh dobychi gaza [Prevention and Elimination of Gas Hydrates in Gas Production Systems]. Moscow, IRTs Gazprom, 2004. 504 p.(In Russian)
20. Istomin V.A., Yakushev V.S., Kwon V.G., Chuvilin E.M. The efiect of self-preservation of gas hydrates. Gazov. Prom-st., 2006, spec. issue, pp. 36-46. (In Russian)
21. Yakushev V.S. Prirodnyi gaz i gazovye gidraty v kriolitozone [Natural Gas and Gas Hydrates in the Cryolithozone]. Moscow, VNIIGAZ, 2009. 192 p. (In Russian)
22. Chuvilin E.M., Bukhanov B.A. Change of thermal conductivity of gas-saturated rocks during hydrate formation and freeze-thawing. Part 2. Research results. Krios. Zemli, 2014, no. 2, pp. 57-65. (In Russian)
23. Wilder J.W., Moridis G.J., Wilson S.J., Kurihara M., White M.D., Masuda Y., Anderson B.J., Collett T.S., Hunter R.B., Narita H., Pooladi-Darvish M., Rose K., Boswell R. An international efiort to compare gas hydrate reservoir simulators. Proc. 6th Int. Conf. on Gas Hydrates (ICGH 2008), Vancouver, Canada, July 6-10, 2008, 2008. 12 p.
24. Pinero E., Hensen C., Haeckel M., Rottke W., Fuchs T., Wallmann K. 3-D numerical modelling of methane hydrate accumulations using PetroMod. Mar. Pet. Geol., 2016, vol. 71, pp. 288-295. doi: 10.1016/j.marpetgeo.2015.12.019.
25. Qorbani K., Kvamme B. Non-equilibrium simulation of CH4 production from gas hydrate reservoirs through the depressurization method. J. Nat. Gas Sci. Eng., 2016, vol. 35, pt. B, pp. 1544-1554. doi: 10.1016/j.jngse.2016.03.102.
26. Dmitrievskii A.N., Lobkovskii L.I., Kazakevich G.I., Poveshchenko Yu.A., Balanyuk I.E., Ilyukhin L.N. Numerical modeling of fluid movement in the process of formation of hydrocarbon deposits based on the Predverhoyanskiy deflection. Geol., Geoflz., Razrab. Neft. Mestorozhd., 1995, no. 7, pp. 2-6. (In Russian)
27. Rahimly P.I., Poveshchenko Yu.A., Podryga V.O., Rahimli O.R., Popov S.B. Modeling the processes of joint flltration in melted zone and piezocunductive medium with gas hydrate inclusions. Prepr. IPM im. M.V. Keldysha, 2018, no. 40. 32 p. (In Russian)
28. Tsypkin G.G. Techeniya s fazovymi perekhodami v poristykh sredakh [Flows with Phase Transitions in Porous Media]. Moscow, Fizmatlit, 2009. 230 p. (In Russian)
29. Lobkovsky L.I., Ramazanov M.M. Frontal mode of heat and mass transfer in a gas hydrate reservoir at negative temperatures. Izv. Ross. Akad.Nauk. Mekh. Zhidk. Gaza, 2018, no. 4, pp. 75-89. (In Russian)
30. Chersky N.V., Bondarev E.A. On the thermal method of development of gas hydrate deposits. Dokl. Akad. Nauk SSSR, 1972, vol. 203, no. 3, pp. 550-552. (In Russian)
31. Verigin N.N., Khabibullin I.L., Khalikov G.A. Linear problem of the decomposition of gas hydrates in a porous medium. Izv. Akad. Nauk SSSR. Mekh. Zhidk. Gaza, 1980, no. 1, pp. 174-177. (In Russian)
32. Verigin N.N., Khabibullin I.L., Khalikov G.A. Axisymmetric problem of heat and mass transfer in saturated porous medium. J. Eng. Phys., 1980, vol. 38, no. 5, pp. 581-585. doi: 10.1007/BF00861276.
33. Bondarev E.A., Maksimov A.M., Tsypkin G.G. Mathematical modeling of gas hydrate dissociation. Dokl. Akad. Nauk SSSR, 1989, vol. 308, no. 3, pp. 575-578. (In Russian)
34. Nigmatulin R.I., Shagapov V.Sh., Syrtlanov V.R. Self-similar problem of decomposition of gas hydrates in a porous medium upon depression and heating. J. Appl. Mech. Tech. Phys., 1998, vol. 39, no. 3, pp. 421-427. (In Russian)
35. Shchebetov A.V. Creating methods for predicting the e–ciency of development of gas hydrate deposits. Cand. Tekh. Sci. Diss. Moscow, 2007. 126 p. (In Russian)
36. Khasanov M.K., Musakaev N.G. Gas hydrate formation in porous ice rich methane reservoirs upon injection of carbon dioxide: Forward modeling. Earth's Cryos., 2016, vol. 20, no. 3, pp. 59-65.
37. Shagapov V.Sh., Chiglintseva A.S., Rusinov A.A. Mathematical modeling of the formation of hydrate in the reservoir saturated with snow during the injection of cold gas. Vychisl. Mekh. Sploshnykh Sred, 2016, vol. 9, no. 2, pp. 173-181. (In Russian)
38. Shagapov V.Sh., Musakaev N.G. Dinamika obrazovaniya i razlozheniya gidratov v sistemakh dobychi, transportirovki i khraneniya gaza [Dynamics of Hydrate Formation and Decomposition in Gas Production, Transportation, and Storage Systems]. Moscow, Nauka, 2016. 238 p. (In Russian)
39. Dzhafarov D.S. Mathematical modeling of the dissociation of gas hydrates in the application to the interpretation of studies of gas hydrate wells in non-stationary flltration modes. Cand. Tekh. Sci. Diss. Moscow, 2015. 120 p. (In Russian)
40. Ahmadi G., Ji C., Smith D.H. A simple model for natural gas production from hydrate decomposition. Ann. N. Y. Acad. Sci., 2000, vol. 912, no. 1, pp. 420-427. doi: 10.1111/j.1749-6632.2000.tb06796.x.
41. Kamath V.A., Godbole S.P. An analytic model for analyzing the efiects of dissociation of hydrates on the thermal recovery of heavy oils. SPE Reservoir Eng., 1988, vol. 3, no. 2, art. 14224-PA. doi: 10.2118/14224-PA.
42. Kamath V.A., Mutalik P.N., Sira J.H. Experimental study of brine injection and depressurization methods for dissociation of gas hydrates. SPE Form. Eval., 1991, vol. 6, no. 4, pp. 477-484.
43. Vasil'ev V.I., Popov V.V., Tsypkin G.G. Numerical investigation of the decomposition of gas hydrates coexisting with gas in natural reservoirs. Fluid Dyn., 2006, vol. 41, no. 4, pp. 599-605.
44. Kazakevich G., Minervina E., Poveshchenko Y. Hydrocarbon migration in the process of pool formation: Numerical modeling of nonlinear efiects. Dokl. Ross. Akad. Nauk, 2002, vol. 383, no. 1, pp. 103-105. (In Russian)
45. Dmitriyevskii A., Karakin A., Poveshchenko Y., Kazakevich G. The self-oscillatory nature of the fluid-dynamic regime of the sedimentary basin in the zone of the Caspian deposits. Geol., Geoflz., Razrab. Neft. Gazov. Mestorozhd., 2017, no. 1, pp. 45{49. (In Russian)
46. Shakirov R.B., Obzhirov A.I., Salomatin A.S., Makarov M.M. New data on lineament control of modern centers of methane degassing in east Asian seas. Dokl. Earth Sci., 2017, vol. 477, no. 1, pp. 1287-1290. (In Russian)
47. Poveshchenko O.Yu., Gasilova I.V., Galiguzova I.I., Dorofeeva E.Yu, Ol'khovskaya O.G., Kazakevich G.I. A fluid dynamics model for a porous media, containing gas hydrate deposits. Mat. Model., 2013, vol. 25, no. 10, pp. 32-42. (In Russian)
48. Kazakevich G.I., Klochkova L.V., Poveshchenko Yu.A., Tishkin V.F. A mathematical study of the system of equations of gas hydrate processes in a porous medium. Zh. Srednepovolzh. Mat. O-va., 2011, vol. 13, no. 1, pp. 7-11. (In Russian)
49. Gasilov V.A., Gasilova I.V., Klochkova L.V., Poveshchenko Yu.A., Tishkin V.F. Difierence schemes based on the support operator method for fluids dynamics problems in a collector containing gas hydrates. Comput. Math. Math. Phys., 2015, vol. 55, no. 8, pp. 1310-1323. doi: 10.1134/S0965542515080114.
50. Poveshchenko Yu.A., Kazakevich G.I. Mathematical modeling of gas hydrate processes. Mat. Mash. Sist., 2011, vol. 3, pp. 105-110. (In Russian)
51. Degtyarev B.V., Bukhgalter E.B. Bor'ba s gidratami pri ekspluatatsii gazovykh skvazhin v severnykh rayonakh [Fight against Hydrates in the Operation of Gas Wells in the NorthernAreas]. Moscow, Nedra, 1976. 195 p. (In Russian)
52. Rahimly P.I., Sharova Yu.S., Rahimly O.R., Podryga V.O., Gasilova I.V., Popov S.B., Poveshchenko Yu.A. Mathematical modeling of some problems of fluid dynamics in porous media with gas hydrates based on splitting by physical processes. Prepr. IPM im. M.V. Keldysha, 2018, no. 39. 27 p. (In Russian)
53. Karslow G., Eger D. Teploprovodnost' tverdykh tel [Thermal Conductivity of Solids]. Moscow, Nauka, 1964. 488 p. (In Russian)
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