Difference schemes based on the support operator method for fluids dynamics problems in a collector containing gas hydrates

详细信息    查看全文

• 作者：V. A. Gasilov ; I. V. Gasilova…
• 关键词：numerical experiment ; support operator method ; unstructured meshes ; fluid dynamics ; porous medium ; gas hydrates
• 刊名：Computational Mathematics and Mathematical Physics
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：55
• 期：8
• 页码：1310-1323
• 全文大小：1,865 KB
• 参考文献：1.A. A. Samarskii, V. F. Tishkin, A. P. Favorskii, and M. Yu. Shashkov, 鈥淯se of the support operator method for constructing difference analogues of operations of tensor analysis,鈥?Differ. Equations 18 (7), 881鈥?85 (1982).MathSciNet
  2.A. B. Khrulenko, A. P. Favorskii, and V. Ya. Karpov, Vector and Tensor Models: Handbook in Two Parts (MAKS, Moscow, 2009) [in Russian].
  3.P. Englezos, 鈥淐lathrate hydrates,鈥?Ind. Eng. Chem. Res. 32, 1251鈥?274 (1993).CrossRef
  4.S. Sh. Byk, Yu. F. Makogon, and V. I. Fomina, Gas Hydrates (Khimiya, Moscow, 1980) [in Russian].
  5.A. G. Groisman, Thermophysical Properties of Gas Hydrates (Nauka, Novosibirsk, 1985) [in Russian].
  6.V. A. Istomin and V. S. Yakushev, Gas Hydrates in Natural Conditions (Nedra, Moscow, 1992) [in Russian].
  7.Yu. F. Makogon, Natural Gas Hydrates (Nedra, Moscow, 1974) [in Russian].
  8.Yu. F. Makogon, Natural Gas Hydrates (PennWell, Tulsa, 1997).
  9.V. P. Mel鈥檔ikov, A. N. Nesterov, and A. M. Reshetnikov, 鈥淕as hydrate dissociation under atmospheric pressure,鈥?Gaz. Promyshl., special issue on gas hydrates, 55鈥?1 (2006).
  10.B. V. Degtyarev and E. B. Bukhgalter, Control of Hydrates on Gas Wells in Northern Regions (Nedra, Moscow, 1976) [in Russian].
  11.P. Gayet, C. Dicharry, C. Marion, et al., 鈥淢ethane hydrate equilibrium conditions in a porous medium: From experiment to theory,鈥?Proceedings of the 5th International Conference on Gas Hydrates, Trondheim, Norway (2005), pp. 1627鈥?635.
  12.S. M. Fedoseev and V. R. Larionov, 鈥淪tudy of hydrate formation in porous media,鈥?Gaz. Promyshl., special issue on gas hydrates, 28鈥?9 (2006).
  13.L. G. Tang, G. Li, Y. M. Hao, R. Xiao, C. Huang, S. S. Fan, and Z. P. Feng, 鈥淓ffects of salt on the formation of gas hydrate in porous media,鈥?Proceedings of the 5th International Conference on Gas Hydrates, Trondheim, Norway (2005), pp. 155鈥?60.
  14.G. L. Moridis, Y. Seol, and T. J. Kneafsey, 鈥淪tudies of reaction kinetics of methane hydrate dissociation in porous media,鈥?Proceedings of the 5th International Conference on Gas Hydrates, Trondheim, Norway (2005), pp. 21鈥?0.
  15.A. F. Beznosikov and V. N. Maslov, 鈥淓ffect of water, ice, and hydrates in a collector on its permeability,鈥?Tr. VNIIEGazprom, No. 8, 84鈥?9 (1975).
  16.Yu. P. Korotaev and A. S. Skhalyakho, 鈥淓ffect of a stationary water hydrate phase on porous medium gas flows,鈥?VNIIEGazprom Inf. Sb. Razrab. Ekspluat. Gaz. Gazokondens. Mestorozhd., No. 11, 19鈥?3 (1974).
  17.Yu. P. Korotaev and A. S. Skhalyakho, 鈥淓xperiment facility and technique for studying the hydrate effect on porous medium gas flows,鈥?VNIIEGazprom Inf. Sb. Razrab. Ekspluat. Gaz. Gazokondens. Mestorozhd., No. 10, 16鈥?9 (1974).
  18.V. A. Nenakhov, 鈥淔eatures of water flow through hydrate-bearing porous media,鈥?EI VNIIEGazprom, Ser. Geol. Buren. Razrab. Gas. Mestorozhd., No. 10, 9鈥?0 (1982).
  19.H. Minagawa, R. Ohmura, T. Takahashi, et al., 鈥淲ater permeability measurements of natural gas hydrate-bearing sediments obtained from Mallik 5L-38,鈥?Abstracts of Mallik International Symposium 鈥淔rom Mallik to the Future鈥?/em> (Technology Research Center Japan National Oil Corporation, 2003), p. 33.
  20.V. R. Syrtlanov and V. Sh. Shagapov, 鈥淒issociation of hydrates in a porous medium under depressive effects,鈥?J. Appl. Mech. Tech. Phys. 36 (4), 585鈥?93 (1995).CrossRef
  21.R. I. Nigmatulin, V. Sh. Shagapov, and V. R. Syrtlanov, 鈥淪elf-similar problem of decomposition of gas hydrates in a porous medium upon depression and heating,鈥?J. Appl. Mech. Tech. Phys. 39 (3), 421鈥?27 (1998).CrossRef
  22.Y. Masuda, Y. Konno, M. Kurihara, H. Ouchi, Y. Kamata, T. Ebinuma, and H. Narita, 鈥淰alidation study of numerical simulator predicting gas production performance from sediments containing methane hydrate,鈥?Proceedings of the 5th International Conference on Gas Hydrates, Trondheim, Norway (2005), Vol. 3, pp. 1076鈥?085.
  23.Y. Masuda, M. Kurihara, H. Ohuchi, and T. Sato, 鈥淎 field-scale simulation study on gas productivity of formations containing gas-hydrates,鈥?Proceedings of the 4th International Conference on Gas Hydrates, Yokohama, May 19鈥?3 (2002), pp. 40鈥?6.
  24.G. L. Moridis, 鈥淣umerical studies of gas production from methane hydrates,鈥?SPE Gas Technology Symposium, Calgary, Alberta, Canada Soc. Petrol. Eng., 2002), SPE-75691-MS.
  25.W. J. A. M. Swinkels, 鈥淭hermal reservoir simulation model of production from naturally occurring gas hydrate accumulations,鈥?SPE Annual Technical Conference and Exhibition, Houston, Texas (Soc. Petrol. Eng., 1999), SPE-56550-MS.
  26.H. C. Kim, P. R. Bishnoi, R. A. Heidemann, and S. S. Rizvi, 鈥淜inetics of methane hydrate decomposition,鈥?Chem. Eng. Sci. 42 (7), 1645鈥?653 (1987).CrossRef
  27.G. J. Moridis, J. Apps, K. Pruess, and L. Mayer, 鈥淓OSHYDR: A THOGH2 module for CH4-hydrate release and flow in the surface,鈥?Report LBNL-42386 (Lawrence Berkeley National Laboratory, Berkeley, CA, 1998).
  28.G. D. Ginsburg and V. A. Solov鈥檈v, Submarine Gas Hydrates (Vseross. Naucho-Issled. Inst. Okeanologiya, St. Petersburg, 1994) [in Russian].
  29.G. G. Tsypkin, Porous Medium Flows with Phase Transitions (Fizmatlit, Moscow, 2009) [in Russian].
  30.K. S. Basniev, I. N. Kochina, and V. M. Maksimov, Underground Hydrodynamics (Nedra, Moscow, 1993) [in Russian].
  31.K. S. Basniev and A. V. Nifantov, 鈥淭hree-dimensional mathematical model of methane hydrate decomposition in a porous medium under heating,鈥?Nauka Tekh. Gaz. Promyshl., No. 1鈥?, 61鈥?7 (2004).
  32.K. Aziz and A. Settari, Petroleum Reservoir Simulation (Applied Science, London, 1979; Nedra, Moscow, 1982).
  
• 作者单位：V. A. Gasilov (1)
  I. V. Gasilova (1)
  L. V. Klochkova (1)
  Yu. A. Poveshchenko (1) (2)
  V. F. Tishkin (1)
  
  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia
  2. National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1555-6662

文摘

Difference schemes based on the support operator method are considered as applied to fluid dynamics in underground collectors containing gas hydrate deposits. A system of mass and energy balances describing fluid dynamics in a porous medium containing gas hydrate deposits is given. A dissipative hydrate equation is derived that determines the thermodynamic evolution of the parameters of the system. It is shown that the jumps in specific volumes and internal energy occurring in phase transitions play a crucial role in the stability of the evolution of the system in the dissipation thermodynamic module of the system. A family of rotation-invariant difference schemes of the support operator method on unstructured meshes is constructed for numerical computations. The schemes are tested on a series of model problems. Their numerical solutions are presented. Keywords numerical experiment support operator method unstructured meshes fluid dynamics porous medium gas hydrates