Modeling of flows in porous media related to underground carbon dioxide storage using high performance computing systems
DOI:
https://doi.org/10.7242/1999-6691/2013.6.4.46Keywords:
underground storage, numerical modelling, parallel simulations, flows in porous media, multiphase flowsAbstract
In this work, the problem of carbon dioxide injection into a water saturated permeable layer is investigated. Using direct numerical simulations, we evaluate the CO2plume extension in the layer for different parameters of injection. The simulation results obtained for the complete mathematical model are compared with the approximate self-similar solution of the problem. The conditions of applicability of the self-similar asymptotics are determined. The computational capability of the model and the parallel efficiency of numerical simulations are estimated.
Downloads
References
Michael K., Golab A., Shulakova V. et al. Geological storage of CO2 in saline aquifers – A review of the experience from existing storage operations // Int. J. Greenh. Gas Con. – 2010. – V. 4, N. 4. – P. 659-667. DOI
2. Würdemann H., Möller F., Kühn M. et al. CO2SINK – From site characterisation and risk assessment to monitoring and verification: One year of operational experience with the field laboratory for CO2 storage at Ketzin, Germany // Int. J. Greenh. Gas Con. – 2010. – V. 4, N. 6. – P. 938-951. DOI
3. Special report on carbon dioxide capture and storage // Technical report, Intergovernmental Panel on Climate Change (IPCC). – Cambridge: Cambridge Univ Press, 2005. – 443 p. (URL: http://www.ipcc-wg3.de/special-reports/.files-images/SRCCS-WholeReport.pdf).
4. Singh V., Cavanagh A., Hansen H. et al. Reservoir modeling of CO2 plume behavior calibrated against monitoring data from Sleipner, Norway // Society of Petroleum Engineers. – 2010. – paper SPE-134891-MS. – 18 p. DOI
5. Aziz K., Settari A. Petroleum reservoir simulation. – London–NY: Applied Science Publishers, 1979. – 476 p.
6. Баренблат Г.И., Ентов В.М., Рыжик В.М. Движение жидкостей и газов в природных пластах. – М.: Недра, 1984. – 208 с.
7. Pruess K., Spycher N. ECO2N – A fluid property module for the TOUGH2 code for studies of CO2 storage in saline aquifers // Energ. Convers. Manage. – 2007. – V. 48, N. 6. – P. 1761-1767. DOI
8. TOUGH2 User’s Guide, Version 2.1: Report (revised) / K. Pruess et al. – Berkeley, Calif., U.S.: Lawrence Berkeley National Laboratory, 2011. – 214 р. – LBNL-43134.
9. Lyle S., Huppert H.E., Hallworth M. et al. Axisymmetric gravity currents in porous medium // J. Fluid Mech. – 2005. – V. 543. – P. 293-302. DOI
10. Bickle M., Chadwick A., Huppert H.E. et al. Modelling carbon dioxide accumulation at Sleipner: Implications for underground carbon storage // Earth Planet. Sc. Lett. – 2007. – V. 255, N. 1-2. – P. 164-176. DOI
11. Афанасьев А.А., Мельник О.Э. Об одном методе расчёта теплофизических свойств при до- и закритических условиях // Физ.-хим. кин. в газ. динамике. – 2013. – Т. 14. (URL: http://istina.msu.ru/publications/article/4786108/).
12. Афанасьев А.А., Мельник О.Э. О построении конечно-разностной схемы расчёта фильтрации при околокритических термодинамических условиях // Вычисл. мех. сплош. сред. – 2013. – T. 6, № 2 – С. 246-255. DOI
13. Алтунин В.В. Теплофизические свойства двуокиси углерода. – М.: Издательство стандартов, 1975. – 546 с.
14. Афанасьев А.А., Бармин А.А. Нестационарные одномерные фильтрационные течения воды и пара с учётом фазовых переходов // МЖГ. – 2007. – № 4. – С. 134-143. (Afanas’ev A.A., Barmin A.A. Unsteady one-dimensional water and steam flows through a porous medium with allowance for phase transitions // Fluid Dyn. – V. 42, N. 4. – P. 627-636.) DOI
15. Ривкин С.Л., Александров А.А. Теплофизические свойства воды и водяного пара. – М.: Энергия, 1980. – 424 c.
16. Афанасьев А.А., Мельник О.Э. О математическом моделировании многофазной фильтрации при околокритических условиях // Вестн. Моск. ун-та. Сер. 1. Математика, механика. – 2013. – № 3. – С. 68-72. (Afanas’ev A.A., Mel’nik O.E. Mathematical modeling of multiphase seepage under near-critical conditions // Mosc. Univ. Math. Bull. – 2013. – V. 68, N. 3. – P. 76-79. ) DOI
17. Brooks R.H., Corey A.T. Hydraulic properties of porous media // Hydrol. Papers. – Fort Collins, Colorado: Colorado State University, 1964. – N. 3. – 37 p.
18. Самарский А.А., Попов Ю.П. Разностные методы решения задач газовой динамики. – М.: Едиториал УРСС, 2004. – 424 с.
19. Кудряшов И.Ю., Максимов Д.Ю. Моделирование задач многофазной многокомпонентной фильтрации на многопроцессорных вычислительных комплексах: Препр. / ИПМ им. М.В. Келдыша. – М., 2009. – № 68. – 25 с. (URL: http://www.keldysh.ru/papers/2009/prep68/prep2009_68.pdf).
20. Афанасьев А.А., Мельник О.Э. Численное моделирование трёхфазной фильтрации при закачке углекислого газа в водонасыщенный пласт // Физ.-хим. кин. в газ. динамике. – 2013. – Т. 14. (URL: http://istina.msu.ru/publications/article/4786125/).
21. Коновалов А.В., Толмачев А.В., Партин А.С. Параллельное решение упругопластической задачи с применением трехдиагонального алгоритма LU-разложения из библиотеки ScaLAPACK // Вычисл. мех. сплош. сред. – 2011. – Т. 4, № 4. – С. 34-41. DOI
22. Борисов В.Е., Савенков Е.Б. Численное исследование метода предобуславливания Generalized Nested Factorization для промышленных задач пластовой фильтрации: Препр. / ИПМ им. М.В. Келдыша. – М., 2013. – № 12. – 18 с. (URL: http://www.keldysh.ru/papers/2013/prep2013_12.pdf).
23. Official Aztec User’s Guide. Version 2.1: Report / Sandia National Laboratories: Tuminaro R.S., Heroux M., Hutchinson S.A., Shadid J.N. – Albuquerque, NM, U.S., 1999. – 63 p. – SAND99-8801J.
24. URL: http://www.cs.sandia.gov/CRF/aztec1.html (дата обращения: 21.10.2013).
25. URL: http://trilinos.sandia.gov/ (дата обращения: 21.10.2013).
26. Saad Y. Iterative methods for sparse linear systems. – SIAM, Philadelphia, PA, US, 2000.
27. Saad Y. ILUT: A dual threshold incomplete LU factorization // Numer. Linear Algebr. – 1994. – V. 1, N. 4. – P. 387-402. DOI
28. Amdahl G.M. Validity of the single processor approach to achieving large-scale computing capabilities // AFIPS’67 Conf. Proc. NY, USA, April 18-20, 1967. – P. 483-485. DOI
29. Karypis G., Kumar V. A fast and highly quality multilevel scheme for partitioning irregular graphs // SIAM J. Sci. Comput. – 1999. – V. 20, N. 1. – P. 359-392. DOI
###
Michael K., Golab A., Shulakova V. et al. Geological storage of CO2 in saline aquifers - A review of the experience from existing storage operations // Int. J. Greenh. Gas Con. - 2010. - V. 4, N. 4. - P. 659-667. DOI
2. Wurdemann H., Moller F., Kuhn M. et al. CO2SINK - From site characterisation and risk assessment to monitoring and verification: One year of operational experience with the field laboratory for CO2 storage at Ketzin, Germany // Int. J. Greenh. Gas Con. - 2010. - V. 4, N. 6. - P. 938-951. DOI
3. Special report on carbon dioxide capture and storage // Technical report, Intergovernmental Panel on Climate Change (IPCC). - Cambridge: Cambridge Univ Press, 2005. - 443 p. (URL: http://www.ipcc-wg3.de/special-reports/.files-images/SRCCS-WholeReport.pdf).
4. Singh V., Cavanagh A., Hansen H. et al. Reservoir modeling of CO2 plume behavior calibrated against monitoring data from Sleipner, Norway // Society of Petroleum Engineers. - 2010. - paper SPE-134891-MS. - 18 p. DOI
5. Aziz K., Settari A. Petroleum reservoir simulation. - London-NY: Applied Science Publishers, 1979. - 476 p.
6. Barenblat G.I., Entov V.M., Ryzik V.M. Dvizenie zidkostej i gazov v prirodnyh plastah. - M.: Nedra, 1984. - 208 s.
7. Pruess K., Spycher N. ECO2N - A fluid property module for the TOUGH2 code for studies of CO2 storage in saline aquifers // Energ. Convers. Manage. - 2007. - V. 48, N. 6. - P. 1761-1767. DOI
8. TOUGH2 User’s Guide, Version 2.1: Report (revised) / K. Pruess et al. - Berkeley, Calif., U.S.: Lawrence Berkeley National Laboratory, 2011. - 214 r. - LBNL-43134.
9. Lyle S., Huppert H.E., Hallworth M. et al. Axisymmetric gravity currents in porous medium // J. Fluid Mech. - 2005. - V. 543. - P. 293-302. DOI
10. Bickle M., Chadwick A., Huppert H.E. et al. Modelling carbon dioxide accumulation at Sleipner: Implications for underground carbon storage // Earth Planet. Sc. Lett. - 2007. - V. 255, N. 1-2. - P. 164-176. DOI
11. Afanas’ev A.A., Mel’nik O.E. Ob odnom metode rasceta teplofiziceskih svojstv pri do- i zakriticeskih usloviah // Fiz.-him. kin. v gaz. dinamike. - 2013. - T. 14. (URL: http://istina.msu.ru/publications/article/4786108/).
12. Afanas’ev A.A., Mel’nik O.E. O postroenii konecno-raznostnoj shemy rasceta fil’tracii pri okolokriticeskih termodinamiceskih usloviah // Vycisl. meh. splos. sred. - 2013. - T. 6, No 2 - S. 246-255. DOI
13. Altunin V.V. Teplofiziceskie svojstva dvuokisi ugleroda. - M.: Izdatel’stvo standartov, 1975. - 546 s.
14. Afanas’ev A.A., Barmin A.A. Nestacionarnye odnomernye fil’tracionnye tecenia vody i para s ucetom fazovyh perehodov // MZG. - 2007. - No 4. - S. 134-143. (Afanas’ev A.A., Barmin A.A. Unsteady one-dimensional water and steam flows through a porous medium with allowance for phase transitions // Fluid Dyn. - V. 42, N. 4. - P. 627-636.) DOI
15. Rivkin S.L., Aleksandrov A.A. Teplofiziceskie svojstva vody i vodanogo para. - M.: Energia, 1980. - 424 c.
16. Afanas’ev A.A., Mel’nik O.E. O matematiceskom modelirovanii mnogofaznoj fil’tracii pri okolokriticeskih usloviah // Vestn. Mosk. un-ta. Ser. 1. Matematika, mehanika. - 2013. - No 3. - S. 68-72. (Afanas’ev A.A., Mel’nik O.E. Mathematical modeling of multiphase seepage under near-critical conditions // Mosc. Univ. Math. Bull. - 2013. - V. 68, N. 3. - P. 76-79. ) DOI
17. Brooks R.H., Corey A.T. Hydraulic properties of porous media // Hydrol. Papers. - Fort Collins, Colorado: Colorado State University, 1964. - N. 3. - 37 p.
18. Samarskij A.A., Popov U.P. Raznostnye metody resenia zadac gazovoj dinamiki. - M.: Editorial URSS, 2004. - 424 s.
19. Kudrasov I.U., Maksimov D.U. Modelirovanie zadac mnogofaznoj mnogokomponentnoj fil’tracii na mnogoprocessornyh vycislitel’nyh kompleksah: Prepr. / IPM im. M.V. Keldysa. - M., 2009. - No 68. - 25 s. (URL: http://www.keldysh.ru/papers/2009/prep68/prep2009_68.pdf).
20. Afanas’ev A.A., Mel’nik O.E. Cislennoe modelirovanie trehfaznoj fil’tracii pri zakacke uglekislogo gaza v vodonasysennyj plast // Fiz.-him. kin. v gaz. dinamike. - 2013. - T. 14. (URL: http://istina.msu.ru/publications/article/4786125/).
21. Konovalov A.V., Tolmacev A.V., Partin A.S. Parallel’noe resenie uprugoplasticeskoj zadaci s primeneniem trehdiagonal’nogo algoritma LU-razlozenia iz biblioteki ScaLAPACK // Vycisl. meh. splos. sred. - 2011. - T. 4, No 4. - S. 34-41. DOI
22. Borisov V.E., Savenkov E.B. Cislennoe issledovanie metoda predobuslavlivania Generalized Nested Factorization dla promyslennyh zadac plastovoj fil’tracii: Prepr. / IPM im. M.V. Keldysa. - M., 2013. - No 12. - 18 s. (URL: http://www.keldysh.ru/papers/2013/prep2013_12.pdf).
23. Official Aztec User’s Guide. Version 2.1: Report / Sandia National Laboratories: Tuminaro R.S., Heroux M., Hutchinson S.A., Shadid J.N. - Albuquerque, NM, U.S., 1999. - 63 p. - SAND99-8801J.
24. URL: http://www.cs.sandia.gov/CRF/aztec1.html (data obrasenia: 21.10.2013).
25. URL: http://trilinos.sandia.gov/ (data obrasenia: 21.10.2013).
26. Saad Y. Iterative methods for sparse linear systems. - SIAM, Philadelphia, PA, US, 2000.
27. Saad Y. ILUT: A dual threshold incomplete LU factorization // Numer. Linear Algebr. - 1994. - V. 1, N. 4. - P. 387-402. DOI
28. Amdahl G.M. Validity of the single processor approach to achieving large-scale computing capabilities // AFIPS’67 Conf. Proc. NY, USA, April 18-20, 1967. - P. 483-485. DOI
29. Karypis G., Kumar V. A fast and highly quality multilevel scheme for partitioning irregular graphs // SIAM J. Sci. Comput. - 1999. - V. 20, N. 1. - P. 359-392. DOI
Downloads
Published
Issue
Section
License
Copyright (c) 2013 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
