Features of mathematical modeling of natural gas production and transport systems in the Russia’s arctic zone
- 1 — Ph.D., Dr.Sci. Chief Researcher Institute of Oil and Gas Problems, Siberian Division RAS
- 2 — Ph.D., Dr.Sci. Leading Researcher Institute of Oil and Gas Problems, Siberian Division RAS
- 3 — Ph.D. Senior Researcher Institute of Oil and Gas Problems, Siberian Division RAS
Abstract
The necessity of accounting for real gas properties, thermal interaction with permafrost rocks and the possibility of formation (dissociation) of gas hydrates in these objects for adequate description of the operation of gas wells and main gas pipelines in the regions of the Far North by appropriate mathematical models is shown. Mathematical models that take into account the non-isothermal gas flow within the framework of pipe hydraulics, the change of the area of tube cross-section due to the formation of hydrates and the dependence of the heat transfer coefficient between gas and hydrate layer on the varying flow area over time are proposed. The corresponding conjugate problem of heat exchange between the imperfect gas in the well and the environment (rocks) is reduced to solving differential equations describing the non-isothermal flow of gas in the pipes and the heat transfer equations in rocks with the corresponding conjugation conditions. In the quasi-stationary mathematical model of hydrate formation (dissociation), the dependence of the gas-hydrate transition temperature on the pressure of gas is taken into account. Established that the formation of hydrates in wells, even at low reservoir temperatures and a thick layer of permafrost, takes a fairly long period of time, which allows to quickly prevent the creation of emergency situations in gas supply systems. Some decisions taken in the design of the first section of the main gas pipeline «Power of Siberia» have been analyzed by methods of mathematical modeling. In particular, it is shown that if the gas is not dried sufficiently, the outlet pressure may drop below the allowable limit in about 6-7 hours. At the same time, for completely dry gas, it is possible to reduce the cost of thermal insulation of the pipeline at least two fold.
References
- Argunova K.K., Bondarev E.A., Rozhin I.I. Mathematical models of hydrate formation in gas wells. Kriosfera Zemli. 2011. Vol.15. N2, p.65-69 (in Russian).
- Argunova K.K., Bondarev E.A., Rozhin I.I. Properties of real gas and their analytical representation. Gazokhimiya. 2010. N6 (16), p.52-54 (in Russian).
- Argunova K.K. Numerical study of nonlinear effects in models of natural gas production. The author ... Candidate of Physics and Mathematics. Yakutskii gosudarstvennyi universitet im. M.K.Ammosova. Yakutsk, 2005, p.18 (in Russian).
- Bondarev E.A., Argunova K.K. Mathematical models of hydrate formation in gas wells. Informatsionnye i matematicheskie tekhnologii v nauke i upravlenii: Trudy XIV Baikal'skoi vserossiiskoi konferentsii. Irkutsk: ISEM SO RAN, 2009. Iss.3, p.41-51 (in Russian).
- Budak B.M., Solov'eva E.N., Uspenskii A.B. A difference method with smoothing of the coefficients for the solution of the Stefan problem. Zhurnal vychisl. matematiki i mat. fiziki. 1965. Vol.5. N5, p.828-840 (in Russian).
- Vukalovich M.P., Novikov I.I. Equation of state of real gas. Мoscow– Leningrad: Gosenergoizdat, 1948, p.340 (in Russian).
- Latonov V.V., Gurevich G.R. Calculation of the compressibility of natural gases. Gazovaya promyshlennost'. 1969. N2, p.7-9 (in Russian).
- Argunova K.K., Bondarev E.A., Nikolaev V.E., Rozhin I.I. Determination of the interval of hydrate formation in wells drilled in permafrost rocks. Elektronnyi nauchnyi zhurnal «Neftegazovoe delo». 2008. URL: www.ogbus.ru/authors/Argunova/ Argunova_2.pdf, p.11 (in Russian). (data obrashcheniya 2.10.2017).
- Perepelichenko V.F. Prospects for developing a unique oil and gas condensate field of Yakutia. Elektronnyi nauchnyi zhurnal «Georesursy. Geoenergetika. Geopolitika». 2012. Iss.1(5). URL: oilgasjournal.ru/vol_5/perepelich.pdf, p.8 (in Russian). (data obrashcheniya 4.09.2017).
- Samarskii A.A., Moiseenko B.D. Economical scheme of end-to-end calculations for multidimensional Stefan problems. Zhurnal vychisl. matematiki i mat. fiziki. 1965. Vol.5. N5, p.816-827 (in Russian).
- Isaev S.I., Kozhinov I.A., Kofanov V.I., Leont'ev A.I., Mironov B.M., Nikitin V.M., Petrazhitskii G.B., Samoilov M.S., Khvostov V.I., Shishov E.V. Theory of heat and mass transfer. Мoscow: Vysshaya shkola, 1979, p.495 (in Russian).
- Bondarev E.A., Vasil'ev V.I., Voevodin A.F., Pavlov N.N., Shadrina A.P. Thermohydrodynamics of gas production and transport systems. Novosibirsk: Nauka. Sibirskoe otdelenie, 1988, p.272 (in Russian).
- Tikhonov A.N., Samarskii A.A. Equations of mathematical physics. Мoscow: Nauka, 1977, p.736 (in Russian)
- Bondarev E.A. Modeling the formation of hydrates in gas wells in their thermal interaction with rocks / E.A.Bondarev, I.I.Rozhin, K.K.Argunova // Journal of Engineering Physics and Thermophysics. 2014. Vol. 87. N 4. Р. 900-907. DOI: 10.1007/s10891-014-1087-0.
- Kay W.B. Density of hydrocarbon gases and vapors at high temperature and pressures // Industrial & Engineering Chemistry Research. 1936. Vol. 28. P. 1014-1019.
- Sloan E.D. Clathrate hydrates of natural gases / E.D.Sloan, C.A.Koh. Boca Raton: Taylor & Francis Group/CRC Press, 2008. 720 p.