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  4. Mathematical modeling of a small pressure disturbance in gas flow of a long pipeline

Mathematical modeling of a small pressure disturbance in gas flow of a long pipeline

MMC.
2017;
Volume 4, Number 2
: pp. 126-138
https://doi.org/10.23939/mmc2017.02.126
Received: December 10, 2017

Math. Model. Comput. Vol.4, No.2, pp.126-138 (2017)

Authors:
  1. V. Chekurin
  2. O. Khymko
1
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine; Kuyawy and Pomorze University in Bydgoszcz
2
Lviv Polytechnic National University

A mathematical model for propagation of a small disturbance in the moving gas of a long pipeline has been built in the paper. The model contains two coupled equations, the coefficients of which are expressed via the parameters of the initial process --- mass density and mass flow rate.  In the frame of the model, the influence of parameters of the initial stationary gas flow on propagation of the pulses initiated by a local fluctuation, originated in the stream, was studied numerically.   The developed model can be used for quantitative analysis of oscillations of operational regimes of the long-distance pipeline, which are caused by random stream fluctuations and/or operational pulsation of the compressors.  The model can be also useful to study negative pressure waves emerging in the pipeline during its local depressurization.

nonlinear problems
non-stationary processes
gas dynamics
gas flow in long pipeline
wave in moving gas
small disturbance propagation
  1. Hamilton S., Charalambous H.  Leack Detection: Technologies and Implementation. London, IWA Publishing (2013).
  2. Murvay P.-S., Silea I.  A Survey on Gas Leak Detection and Localization Techniques.  Journal of Loss Prevention in the Process Industry. 25 (6), 966--973 (2012).
  3. Hou Q., Ren L., Jiao W., Zou P., Song G.  An Improved Negative Pressure Wave Method for. Natural Gas Pipeline Leak Location Using FBG Based Strain. Sensor and Wavelet.  Mathematical Problems in Engineering. 2013, Article ID 278794, 8 pages (2013).
  4. Geiger G., Werner T, Matko D.  Knowledge based Leak Monitoring for Pipelines.  4th IFAC Workshop on On-Line Fault Identification and Supervision in the Chemical Process Industries, June 7--8 2001, Jejudo Islands (Korea). 34 (27), 249--254 (2001).
  5. Kjell-Edvind Froysa, Per Lunde, Anfinn Paulsen and Endre Jacobsen. Density and Caloric Value Measurement in NATUREL gas Using Ultrasonic Flow Meters.  Results from Testing on Various North Sea Gas Field Data.     24th International North Sea Flow Measurement Workshop, 24th--27th October 2006.
  6. Shapiro A. H. The Dynamics and Thermodynamics of Compressible Fluid Flow. The Ronald Press Company, New York (1954).
  7. Starling K. E., Savidge J. L.  Compressibility factors of natural gas and other related hydrocarbon gases.  American Gas Association, Transmission Measurement Committee Report No. 8, Second Edition, Arlington, Virginia (1992), and Errata No. 1, (1994).
  8. Chekurin V. F., Khymko O. M.  Mathemetical model for propagation of long acoustic waves in the flow of a gas pipeline.  Proceedings of  XXII International Seminar.  Workshop on direct and inverse problems of electromagnetic and acoustic wave theory (DIPED).   Dnipro, Ukraine (September 25--28, 2017), 80--83 (2017).