CONTROLO 2016 pp 285-295 | Cite as

PDE Model for Leakage Detection in High Pressure Gas Networks

  • T.-P. Azevedo PerdicoúlisEmail author
  • R. Almeida
  • P. Lopes dos Santos
  • G. Jank
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 402)


In this paper we design a model based method to locate a leakage and estimate its size in a gas network, using a linearised version of an hyperbolic PDE. To do this, the problem is reduced to two identical ODEs, allowing in this way for a representation of the pressure as well as the mass flow in terms of its system of fundamental solutions. Then using the available measurements at the grid boundary points, the correspondent coefficients can be determined. Assuming pressure continuity, we check for consistency of the coefficients in order to find faulty pipelines. Thence, the location of the leakage can be found either graphically or using a numerical method for a specific pipe. Next, its size can also be estimated.


Leakage detection Leakage location Gas networks PDE linearisation 



The first author is financed by FCT (Project ref. UID/EEA/00048/2013). The second author is financed by Portuguese Funds through FCT, within the Project UID/MAT/00013/2013.


  1. 1.
    Bagajewicz, M., Valtinson, G.: Leak detection in gas pipelines using accurate hydraulic models. Ind. Eng. Chem. Res. 53(44), 16964–16972 (2014)CrossRefGoogle Scholar
  2. 2.
    Baltazar, S.T., Azevedo Perdicoúlis, T.-P., Lopes dos Santos, P.: Quadripole models for simulation and leak detection on gas pipelines. Presented at the 47th PSIG Annual Meeting, Vancouver, Canada, 11–13 de Maio 2016Google Scholar
  3. 3.
    Baptista, H., Wagner, G., Bernhard, W.: Hydraulic model based gas leak detection and location. Presented at the 7th Global Congress on Information and Communication Technology in Energy, Busan, Korea (2005)Google Scholar
  4. 4.
    Bilman, L., Isermann, R.: Leak detection methods for pipelines. Automatica 23(3), 381–385 (1987)CrossRefzbMATHGoogle Scholar
  5. 5.
    Dymkou, S., Jank, G., Azevedo Perdicoúlis, T.-P.: Graph and 2-D systems approach in gas transport network modelling. Int. J. Tomogr. Stat. Special Issue Control Appl. Optim. Appl. Optim. Control Rob. Control Stabil. Appl. Ind. 6, 21–27 (2007)Google Scholar
  6. 6.
    Geiger, G.: State-of-the-art in leak detection and localisation. In: Pipeline Technology 2006 Conference, Hannover, Germany, 25 Apr 2006Google Scholar
  7. 7.
    Lopes dos Santos, P., Azevedo Perdicoúlis, T.-P., Ramos, J.A., Jank, G., Martins de Carvalho, J.L.: Leakage detection and location in gas pipelines through an LPV identification approach. Baleanu, D., Tenreiro Machado, J.A. (eds.) Commun. Nonlinear Sci. Numer. Simul. 16(12), 4657–4665 (2011)Google Scholar
  8. 8.
    Niepłocha, J.: Discrete-time quadratic optimal control of gas network systems. Found. Control Eng. 13(4), 175–186 (1988)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Osiadacz, A.J.: Simulation and Analysis of Gas Networks. E. & F.N. Spon, London (1987)zbMATHGoogle Scholar
  10. 10.
    Zerz, E.: Topics in Multidimensional Linear Systems Theory. Lecture Notes in Control and Information Sciences, vol. 256. Springer, London (2000)Google Scholar
  11. 11.
    Turkowski, M., Bratek, A., Słowikowski, M.: Methods and systems of leak detection in long range pipelines. J. Autom. Mob. Rob. Intell. Syst. 1(3), 39–46 (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • T.-P. Azevedo Perdicoúlis
    • 1
    Email author
  • R. Almeida
    • 2
  • P. Lopes dos Santos
    • 3
  • G. Jank
    • 4
  1. 1.UTAD and ISR CoimbraCoimbraPortugal
  2. 2.UTAD and Mathematics Centre CMATPole CMAT-UTADBragaPortugal
  3. 3.Faculdade de Engenharia da Universidade do PortoPortoPortugal
  4. 4.Aachen UniversityAachenGermany

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