Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Gas Network Benchmark Models

  • Chapter
  • First Online:
Applications of Differential-Algebraic Equations: Examples and Benchmarks

Part of the book series: Differential-Algebraic Equations Forum ((DAEF))

Abstract

The simulation of gas transportation networks becomes increasingly more important as its use-cases broaden to more complex applications. Classically, the purpose of the gas network was the transportation of predominantly natural gas from a supplier to the consumer for long-term scheduled volumes. With the rise of renewable energy sources, gas-fired power plants are often chosen to compensate for the fluctuating nature of the renewables, due to their on-demand power generation capability. Such an only short-term plannable supply and demand setting requires sophisticated simulations of the gas network prior to the dispatch to ensure the supply of all customers for a range of possible scenarios and to prevent damages to the gas network. In this work we describe the modeling of gas networks and present benchmark systems to test implementations and compare new or extended models.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Change history

  • 25 January 2019

    Correction to: Gas Network Benchmark Models

Notes

  1. 1.

    In [8] an approximation of γ = 1.296 is used.

References

  1. Azevedo-Perdicoúlis, T.-P., Jank, G.: Modelling aspects of describing a gas network through a DAE system. In: Proceedings of the 3rd IFAC Symposium on System Structure and Control, vol. 40(20), pp. 40–45 (2007). https://doi.org/10.3182/20071017-3-BR-2923.00007

    Article  Google Scholar 

  2. Chaczykowski, M.: Sensitivity of pipeline gas flow model to the selection of the equation of state. Chem. Eng. Res. Des. 87, 1596–1603 (2009). https://doi.org/10.1016/j.cherd.2009.06.008

    Article  Google Scholar 

  3. Chodanovich, I.J., Odischarija, G.E.: Analiž žavisimosti dlja koeffizienta gidravličeskogo soprotivlenija (analysis of the dependency of the pipe friction factor). Gažovaja Promyshlennost 9(11), 38–42 (1964)

    Google Scholar 

  4. Colebrook, C.F.: Turbulent flows in pipes, with particular reference to the transition region between smooth and rough pipe laws. J. Inst. Civ. Eng. 11, 133–156 (1939)

    Article  Google Scholar 

  5. Domschke, P., Geißler, B., Kolb, O., Lang, J., Martin, A., Morsi, A.: Combination of nonlinear and linear optimization of transient gas networks. INFORMS J. Comput. 23(4), 605–617 (2011). https://doi.org/10.1287/ijoc.1100.0429

    Article  MathSciNet  Google Scholar 

  6. Dymkou, S., Leugering, G., Jank, G.: Repetitive processes modelling of gas transport networks. In: 2007 International Workshop on Multidimensional (nD) Systems, pp. 101–108 (2007). https://doi.org/10.1109/NDS.2007.4509556

  7. Ehrhardt, K., Steinbach, M.C.: Nonlinear optimization in gas networks. In: Bock, H.G., Phu, H.X., Kostina, E., Rannacher, R. (eds.) Modeling, Simulation and Optimization of Complex Processes. Proceedings of the International Conference on High Performance Scientific Computing, pp. 139–148. Springer, Berlin (2005). https://doi.org/10.1007/3-540-27170-8_11

    Chapter  Google Scholar 

  8. Fügenschuh, A., Geißler, B., Gollmer, R., Morsi, A., Pfetsch, M.E., Rövekamp, J., Schmidt, M., Spreckelsen, K., Steinbach, M.C.: Chapter 2: physical and technical fundamentals of gas networks. In: Koch, T., Hiller, B., Pfetsch, M.E., Schewe, L. (eds.) Evaluating Gas Network Capacities. MOS-SIAM Series on Optimization, pp. 17–43. SIAM, Philadelphia (2015). https://doi.org/10.1137/1.9781611973693.ch2

    Chapter  Google Scholar 

  9. Grundel, S., Jansen, L.: Efficient simulation of transient gas networks using IMEX integration schemes and MOR methods. In: 54th IEEE Conference on Decision and Control (CDC), pp. 4579–4584 (2015). https://doi.org/10.1109/CDC.2015.7402934

  10. Grundel, S., Hornung, N., Klaassen, B., Benner, P., Clees, T.: Computing surrogates for gas network simulation using model order reduction. In: Surrogate-Based Modeling and Optimization. Applications in Engineering, pp. 189–212. Springer, New York (2013). https://doi.org/10.1007/978-1-4614-7551-4_9

    Chapter  Google Scholar 

  11. Grundel, S., Jansen, L., Hornung, N., Clees, T., Tischendorf, C., Benner, P.: Model order reduction of differential algebraic equations arising from the simulation of gas transport networks. In: Progress in Differential-Algebraic Equations. Differential-Algebraic Equations Forum, pp. 183–205. Springer, Berlin (2014). https://doi.org/10.1007/978-3-662-44926-4_9

    MATH  Google Scholar 

  12. Grundel, S., Hornung, N., Roggendorf, S.: Numerical aspects of model order reduction for gas transportation networks. In: Simulation-Driven Modeling and Optimization. Proceedings in Mathematics & Statistics, vol. 153, pp. 1–28. Springer, Basel (2016). https://doi.org/10.1007/978-3-319-27517-8_1

    Google Scholar 

  13. Herty, M.: Modeling, simulation and optimization of gas networks with compressors. Netw. Heterog. Media 2(1), 81–97 (2007). https://doi.org/10.3934/nhm.2007.2.81

    Article  MathSciNet  Google Scholar 

  14. Herty, M., Mohring, J., Sachers, V.: A new model for gas flow in pipe networks. Math. Methods Appl. Sci. 33, 845–855 (2010). https://doi.org/10.1002/mma.1197

    MathSciNet  MATH  Google Scholar 

  15. Hofer, P.: Beurteilung von Fehlern in Rohrnetzberechnungen (error evaluation in calculation of pipelines). GWF–Gas/Erdgas 114(3), 113–119 (1973)

    Google Scholar 

  16. Huck, C., Tischendorf, C.: Topology motivated discretization of hyperbolic PDAEs describing flow networks. Technical report, Humboldt-Universität zu Berlin (2017). Available from: https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/137

  17. Humpola, J., Joormann, I., Kanelakis, N., Oucherif, D., Pfetsch, M.E., Schewe, L., Schmidt, M., Schwarz, R., Sirvent, M. GasLib – a library of gas network instances. Technical report, Mathematical Optimization Society (2017). Available from: http://www.optimization-online.org/DB_HTML/2015/11/5216.html

  18. Králik, J., Stiegler, P., Vostrý, Z., Záworka, J.: Dynamic Modeling of Large-Scale Networks with Application to Gas Distribution. Automation and Control, vol. 6. Elsevier, New York (1988)

    Google Scholar 

  19. LeVeque, R.J.: Nonlinear conservation laws and finite volume methods. In: Steiner, O., Gautschy, A. (eds.) Computational Methods for Astrophysical Fluid Flow. Saas-Fee Advanced Courses, vol. 27, pp. 1–159. Springer, Berlin (1997). https://doi.org/10.1007/3-540-31632-9_1

    Google Scholar 

  20. LIWACOM Informationstechnik GmbH and SIMONE research group s. r. o., Essen. SIMONE Software. Gleichungen und Methoden (2004). Available from: https://www.liwacom.de

  21. Mischner, J., Fasold, H.G., Heymer, J. (eds.): gas2energy.net. Edition gas for energy. DIV (2016). Available from: https://www.di-verlag.de/de/gas2energy.net2

  22. Moritz, S.: A mixed integer approach for the transient case of gas network optimization. Ph.D. thesis, Technische Universität, Darmstadt (2007). Available from: http://tuprints.ulb.tu-darmstadt.de/785/

  23. Nekrasov, B.: Hydraulics for Aeronautical Engineers. Peace Publishers, Moscow (1969). Available from: https://archive.org/details/in.ernet.dli.2015.85993

    Google Scholar 

  24. Nikuradse, J.: Gesetzmäßigkeiten der turbulenten Strömung in glatten Rohren. VDI-Forschungsheft 356, 1–36 (1932)

    MATH  Google Scholar 

  25. Osiadacz, A.: Simulation of transient gas flows in networks. Int. J. Numer. Methods Fluids 4, 13–24 (1984). https://doi.org/10.1002/fld.1650040103

    Article  Google Scholar 

  26. Osiadacz, A.J., Chaczykowski, M.: Verification of transient gas flow simulation model. In: PSIG Annual Meeting, pp. 1–10 (2010). Available from: https://www.onepetro.org/conference-paper/PSIG-1010

  27. Papay, J.: A Termelestechnologiai Parameterek Valtozasa a Gazlelepk Muvelese Soran, pp. 267–273. Tud. Kuzl., Budapest (1968)

    Google Scholar 

  28. Pfetsch, M.E., Fügenschuh, A., Geißler, B., Geißler, N., Gollmer, R., Hiller, B., Humpola, J., Koch, T., Lehmann, T., Martin, A., Morsi, A., Rövekamp, J., Schewe, L., Schmidt, M., Schultz, R., Schwarz, R., Schweiger, J., Stangl, C., Steinbach, M.C., Vigerske, S., Willert, B.M.: Validation of nominations in gas network optimization: models, methods, and solutions. Optim. Methods Softw. (2014). https://doi.org/10.1080/10556788.2014.888426

    Article  MathSciNet  Google Scholar 

  29. van der Hoeven, T.: Math in gas and the art of linearization. Ph.D. thesis, University of Groningen (2004). Available from: http://hdl.handle.net/11370/0bbb8138-6d96-4d79-aac3-e46983d1fd33

  30. Zigrang, D.J., Sylvester, N.D.: A review of explicit friction factor equations. J. Energy Resour. Technol. 107(2), 280–283 (1985). https://doi.org/10.1115/1.3231190

    Article  Google Scholar 

Download references

Acknowledgements

Supported by the German Federal Ministry for Economic Affairs and Energy, in the joint project: “MathEnergy – Mathematical Key Technologies for Evolving Energy Grids”, sub-project: Model Order Reduction (Grant number: 0324019B).

The work for the article has been conducted within the Research Campus MODAL funded by the German Federal Ministry of Education and Research (BMBF) (fund number 05M14ZAM).

We also acknowledge funding through the DFG CRC/Transregio 154 “Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks”, Subproject C02.

Author information

Authors and Affiliations

  1. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

    Peter Benner, Sara Grundel & Christian Himpe

  2. Department of Mathematics, Humboldt-Universität zu Berlin, Berlin, Germany

    Christoph Huck, Tom Streubel & Caren Tischendorf

  3. Department of Optimization at Zuse Institute Berlin, Berlin, Germany

    Tom Streubel

Authors
  1. Peter Benner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sara Grundel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christian Himpe
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Christoph Huck
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Tom Streubel
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Caren Tischendorf
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sara Grundel .

Editor information

Editors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Stephen Campbell

  2. Institut für Mathematik, Technische Universität Ilmenau, Ilmenau, Germany

    Achim Ilchmann

  3. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Volker Mehrmann

  4. Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany

    Timo Reis

1 Electronic Supplementary Material

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Benner, P., Grundel, S., Himpe, C., Huck, C., Streubel, T., Tischendorf, C. (2018). Gas Network Benchmark Models. In: Campbell, S., Ilchmann, A., Mehrmann, V., Reis, T. (eds) Applications of Differential-Algebraic Equations: Examples and Benchmarks. Differential-Algebraic Equations Forum. Springer, Cham. https://doi.org/10.1007/11221_2018_5

Download citation

Publish with us

Policies and ethics

Search

Navigation