Numerical algorithm for solving the problem of one-dimensional radial nonisothermic gas filtration

About the author:

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

Abstract:

When natural gas production, the formation of gas hydrate in the well bottom zone due to the reduction of temperature is possible, especially in the cases, when the reservoir thermobaric conditions initially close to the formation conditions of the hydrate of reservoir gas. For numerical experiments to assess this phenomenon the mathematical model of the one-dimensional radial nonisothermic gas filtration is constructed in this work. For the numerical implementation of the model an algorithm, which is based on an implicit difference scheme, sweep method and the method of simple iterations, is suggested. The computer code to calculate the distribution of different filtration flow parameters for gas production in different reservoir and operating conditions is written.  The time and accuracy of calculations depending on the time step are estimated.

References:

1.             Alishaev M. G., Rozenberg M. D., Tesljuk E. V. Neizotermicheskaja fil’tracija pri razrabotke neftjanyh mestorozhdenij [Non-isothermal Filtration during the Development of Oil Fields]. M.: Nedra, 1985. 271 p. (In Russian)

2.             Argunova K. K., Bondarev E. A., Popov V. V., Rozhin I. I. O matematicheskom modelirovanii razrabotki Messojahskogo mestorozhdenija [On Simulation of Case History of the Messoyakha Gas Field] // Neftegazovoe delo. [Oil and Gas Business]. 2008. No 1. http://ogbus.ru/. (In Russian)

3.             Basiiev K. S., Kochina I. N., Maksimov V. M. Podzemnaja gidromehanika: Uchebnik dlja vuzov [Subsurface Hydromechanics]. M.: Nedra, 1993. 416 p. (In Russian)

4.             Vargaftik N. B. Spravochnik po teplofizicheskim svojstvam gazov i zhidkostej [Thermophysical Properties of Gases and Liquids]: Handbook.  M.: Nauka [Science], 1972. 720 p. (In Russian)

5.             Vargaftik N. B., Filippov L. P., Tarzimanov A. A., Tockij E. E. Spravochnik po teploprovodnosti zhidkostej i gazov [Thermal Conductivity of Liquids and Gases]: Handbook. M.: Energoatomizdat, 1990. 352 p. (In Russian)

6.             Latonov V. V., Gurevich G. R. Raschet kojefficienta szhimaemosti prirodnogo gaza [Calculation of Compressibility Factor of Natural Gas] // Gazovaja promyshlennost’ [Gas Industry Journal]. 1969. No 2. Pp. 7-9. (In Russian)

7.             Leont’ev N. E. Osnovy teorii fil’tracii: Uchebnoe posobie [Foundations of the Filter Theory]: Textbook. M.: Izd-vo Centra prikladnyh issledovanij pri mehaniko-matematicheskom fakul’tete MGU [Publisher Center for Applied Studies of Moscow State University], 2009. 88 p. (In Russian)

8.             Musakaev N. G., Hasanov M. K. Matematicheskoe modelirovanie processa dobychi gaza iz gazogidratnoj zalezhi s uchetom obrazovanija l’da [Mathematical Modeling of Gas Extraction from a Gas-hydrate Reservoir with Account of the Ice Formation] // Vestnik Tjumenskogo gosudarstvennogo universiteta [Tyumen State University Herald]. 2014.
No 7. Pp. 43-50. (In Russian)

9.             Musakaev N. G., Borodin S. L., Romanjuk S. N. Chislennoe issledovanie processa protaivanija mnogoletnih merzlyh porod pri rabote dobyvajushhej skvazhiny s ustanovkoj jelektrocentrobezhnyh nasosov [Numerical Research of Frozen Rock Thawing when Operation of the Production well Equiped with an Installation of Electrical Centrifugal Pump] // Vestnik Novosibirskogo gosudarstvennogo universiteta. Matematika, mehanika, informatika [Novosibirsk State University Herald. Mathematics, Mechanics, Computer Science]. 2013. Vol. 13 (2). Pp. 15-20. (In Russian)

10.         Musakaev N. G., Borodin S. L., Romanjuk S. N. Metody reshenija odnomernoj radial’noj zadachi teploperedachi v okruzhajushhie skvazhinu merzlye porody [Solution Methods of One-dimensional Radial Problem of Heat Transfer in the Permafrost Formations Surrounding a Well] // Vestnik Tjumenskogo gosudarstvennogo universiteta [Tyumen State University Herald]. 2014. No 7. Pp. 19-26. (In Russian)

11.         Nikolaevskij V. N., Basniev K. S., Gorbunov A. T., Zotov G. A. Mehanika nasyshhennyh poristyh sred [Mechanics of Saturated Porous Media]. M.: Nedra, 1970. 335 p. (In Russian)

12.         Programma i tezisy dokladov konferencii “Gazovye gidraty v jekosisteme Zemli – 2014” [The Program and Abstracts of the Conference “Gas Hydrates in the Ecosystem of the Earth – 2014”]. Novosibirsk: INH SO RAN, 2014. 104 p. (In Russian)

13.         Proektirovanie razrabotki i jekspluatacija neftjanyh mestorozhdenij [Design of Oil Field Development and Exploitation]: Instruction Manual / Sh. K. Gimatudinova (Ed.). M.: Nedra, 1983. T. 2: Proektirovanie razrabotki [Vol. 2 Design of Oil Field Development]. 431 p. (In Russian)

14.         Charnyj I. A. Podzemnaja gidrogazodinamika [Subsurface Fluid Dynamics]. M.: Gostoptehizdat, 1963. 396 p. (In Russian)

15.         Chekaljuk Je. B. Termodinamika neftjanogo plasta [Thermodynamics of Oil Formations]. M.: Nedra, 1965. 238 p. (In Russian)

16.         Bruce E. Poling, John M. Prausnitz, John P. O’Connell. The properties of gases and liquids. 5th Ed. 2001. 803 p.

17.         Shagapov V. Sh., Musakaev N. G., Khasanov M. K. Formation of gas hydrates in a porous medium during an injection of cold gas // Int. J. of Heat and Mass Transfer. 2015. Vol. 84. Pp. 1030-1039.