«Automation and Informatization of the fuel and energy complex»

Features of applying the global gradient method for simulating stationary modes of gas transport systems in the "Volna" software computing complex

UDC: 681.5:622.279
DOI: 10.33285/2782-604X-2023-12(605)-53-64

Authors:

¹ E.I. Zababakhin RFNC-VNIITF, Snezhinsk, Russia

Keywords: modeling of gas transportation systems, stationary flow regime, natural gas, pipeline, global gradient method, "Volna" software package

Annotation:

To calculate stationary non-isothermal modes in complex long-length gas transportation systems (GTS) with a relief arbitrary topology, an effective iterative method is proposed, developed on the basis of the global gradient method (GGM) with the ability to simulate critical flows, both in the internal pipes and at the boundaries of the system. In the outer iterative cycle, a combination of two models is used: an approximate fast-running model with lumped parameters and an "exactly" running model with distributed parameters, based on solving a system of stationary gas dynamics equations. The outer iterative cycle consists of three main stages: isothermal, thermal, and the lumped parameter model identification stage. At the isothermal stage, the GTS structure is calculated by applying the global gradient method with the ability to simulate critical flows. At this stage, a fast running lumped parameter pipe model is used. At the thermal stage, an "accurate" model with distributed parameters is used to calculate the temperature along the gas pipeline and at the GTS nodes. Here the average gas temperature in the pipes (on the arcs) is determined, which is used in the pipe model at the thermal stage. At the identification stage, the empirical parameters of the lumped parameter model are adjusted so that this model completely coincides with the "accurate" model in the task of determining the flow rate on the arcs from the pressures at the ends of the arcs. The proposed method simultaneously uses the positive aspects of the two models. On the one hand, the speed and convergence of Newton iterations in the MGG are ensured due to the use of the model with lumped parameters. On the other hand, the accuracy of a model with distributed parameters is achieved, based on solving stationary equations of gas dynamics adopted in the "Volna" software and computing complex. The proposed method is implemented in the "Volna" software package. Production calculations of several main GTS were carried out.

Bibliography:

1. Todini E. Un metodo del gradiente per la verifica reti idrauliche // Bollttino degli Ingengneri della. – Toscana, 1979. – No. 11. – P. 11–14.
2. Todini E., Pilati S. A gradient algorithm for the analysis of pipe networks // Computer Applications in Water Supply. Vol. 1. System analysis and simulation. – London: John Wiley & Sons, 1988. – P. 1–20.
3. Korel'shneyn L.B., Pashenkova E.S. Opyt ispol'zovaniya metoda global'nogo gradienta pri raschete ustanovivshegosya izotermicheskogo techeniya zhidkostey i gazov v truboprovodakh // Truboprovodnye sistemy energetiki. Razvitie teorii i metodov mat. modelirovaniya i optimizatsii. – Novosibirsk: Nauka, 2008. – S. 80–89.
4. Korel'shneyn L.B., Pashenkova E.S. Opyt ispol'zovaniya metodov global'nogo gradienta i dekompozitsii pri raschete ustanovivshegosya neizotermicheskogo techeniya zhidkostey i gazov v truboprovodakh // Truboprovodnye sistemy energetiki. – Novosibirsk: Nauka, 2010. – S. 103–114.
5. Popov R.V. Primenenie metoda global'nogo gradienta dlya modelirovaniya gazotransportnykh sistem // Mat. modeli i metody analiza i optimal'nogo sinteza razvivayushchikhsya truboprovodnykh i gidravlicheskikh sistem: tr. XIV Vseros. nauch. seminara, Belokurikha, Altayskiy kray, 8–13 sent. 2014 g. – Irkutsk: ISEM SO RAN, 2014. – S. 83–92.
6. Sukharev M.G., Popov R.V. Novaya metodika modelirovaniya nestatsionarnykh techeniy gaza v sistemakh gazosnabzheniya // Izv. RAN. Energetika. – 2015. – № 2. – S. 150–159.
7. Metodiki, algoritmy i programmnyy kompleks "Volna" dlya modelirovaniya nestatsionarnykh rezhimov gazoprovodov / Maks.G. Anuchin, Mikh.G. Anuchin, A.N. Kuznetsov [i dr.] // Truboprovodnye sistemy energetiki. Razvitie teorii i metodov mat. modelirovaniya i optimizatsii. – Novosibirsk: Nauka, 2008. – S. 60–73.
8. Metodika rascheta techeniya prirodnogo gaza po trube v programmnom komplekse modelirovaniya gazotransportnykh sistem "Volna" / A.A. Vorob'ev, A.A. Kalinin, G.V. Kaspiev [i dr.] // Mat. modelirovanie. – 2014. – T. 26, № 7. – S. 87–96.
9. Anuchin Maks.G., Anuchin Mikh.G., Kuznetsov A.N. Ekonomichnyy metod rascheta statsionarnykh rezhimov gazotransportnykh sistem // Mat. modelirovanie. – 2016. – T. 28, № 4. – S. 64–76.
10. Merenkov A.P., Khasilev V.Ya. Teoriya gidravlicheskikh tsepey / otv. red. M.G. Sukharev. – M.: Nauka, 1985. – 278 s.
11. Sukharev M.G., Karasevich A.M. Tekhnologicheskiy raschet i obespechenie nadezhnosti gazo- i nefteprovodov. – M.: Neft' i gaz, 2000. – 271 s.
12. Charnyy I.A. Neustanovivsheesya dvizhenie real'noy zhidkosti v trubakh. – 2-e izd., pererab. i dop. – M.: Nedra, 1975. – 296 s.
13. Valderrama J.O. The State of the Cubic Equations of State // Industrial & Engineering Chemistry Research. – 2003. – Vol. 42, Issue 8. – P. 1603–1618. – DOI: 10.1021/ie020447b
14. Al'tshul' A.D., Kiselev P.G. Gidravlika i aerodinamika. – M.: Stroyizdat, 1965. – 274 s.
15. Raschety skorosti padeniya davleniya pri razryve magistral'nogo gazoprovoda / Maks.G. Anuchin, Mikh.G. Anuchin, A.N. Kuznetsov [i dr.] // Gazovaya prom-st'. – 2022. – № 3(830). – S. 62–69.
16. Novitskiy N.N., Mikhaylovskiy E.A. Chislennoe reshenie zadach potokoraspredeleniya v gidravlicheskikh tsepyakh s sosredotochennymi parametrami pri proizvol'nykh zamykayushchikh sootnosheniyakh // Truboprovodnye sistemy energetiki: Mat. i komp'yuternoe modelirovanie / otv. red. N.N. Novitskiy. – Novosibirsk: Nauka, 2014. – S. 34–45.
17. Novitskiy N.N., Mikhaylovskiy E.A. Modifitsirovannyy metod konturnykh raskhodov dlya rascheta potokoraspredeleniya v gidravlicheskikh tsepyakh s sosredotochennymi parametrami pri proizvol'nykh zamykayushchikh sootnosheniyakh // Truboprovodnye sistemy energetiki: mat. i komp'yuternye tekhnologii intellektualizatsii / pod red. N.N. Novitskogo. – Novosibirsk: Nauka, 2017. – S. 51–59.
18. Korel'shteyn L.B. Sushchestvovanie, edinstvennost' i monotonnost' resheniya zadachi potokoraspredeleniya v gidravlicheskikh tsepyakh s zavisyashchimi ot davleniya zamykayushchimi sootnosheniyami // Mat. modeli i metody analiza i optimal'nogo sinteza razvivayushchikhsya truboprovodnykh i gidravlicheskikh sistem: tr. XVI Vseros. nauch. seminara, Irkutsk, 26 iyunya – 02 iyulya 2018 g. – Irkutsk: ISEM SO RAN, 2018. – S. 55–83.
19. Novitskiy N.N. Matematicheskie modeli i metody analiza spektra potokov v gidravlicheskikh tsepyakh // Truboprovodnye sistemy energetiki. Mat. modelirovanie i optimizatsiya. – Novosibirsk: Nauka, 2010. – S. 89–103.