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The numerical models applied to the transmission pipelines may acquire plain and accurate real-time measurement data from SCADA systems, which enhances the overall modelling quality. Moreover, it is frequently possible to enclose the damaged section within a control volume contained between a few metring stations.
Modelling leakages in distribution networks encounters some specific problems. The first issue is the lack of sufficient information on exit points. The distribution networks have a vast number of exit points to the domestic sector, supplied with diaphragm gas metres which fail to provide the operator with any real-time data.
Ó 2012 Elsevier Ltd. All rights reserved.
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1. Introduction
Operators of natural gas networks relatively often have to deal with pipeline failures, leading to various-scale gas leakages. Once the pipeline integrity is restored, the network operator should also quantify the gas release, which is essential for economic, environmental and operational reasons. The quantity of the released gas may also be a subject of a controversy if the operator claims its compensation from a third party responsable for the failure. Moreover, in some cases it is required to estimate in advance gas releases from potential failures, as a part of quantitative risk assessment procedures [1]. However, the leakage quantification is generally a complex and frequently ill-defined task. In order to quantify the leakage, operators may choose various modelling approaches, depending on the type of network and on the availability of measurement data. As demonstrated in the paper, the choice of the flow model as well as the value of the discharge coefficient are of high relevance to these procedures and, eventually, to the leakage quantification result.
Furthermore, distribution networks have a complex, branched and/or looped structure without flow metering at splits and junctions. It is therefore generally not possible to limit the flow problem to a single pipeline and the network has to be modelled as a whole system.
* Corresponding author. Tel.: þ48 32 237 1661; fax: þ48 32 237 2872. E-mail address: wojciech.kostowski@polsl.pl (W.J. Kostowski).
0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2012.02.076
abstract
The paper discusses chosen issues concerning damaged gas pipelines. Attention is paid to modelling the steady-state flow of natural gas in distribution pipelines, and the most commonly applied models of isothermal and adiabatic flow are evaluated for both the ideal and the real gas properties. A method of accounting for a leakage by means of a reference flow equation with a discharge coefficient is presented, and the dependency of the discharge coefficient on pressure is demonstrated both with literature data and the authors’ experimental results. A relevant computational study of a pipeline failure is presented for a high- and a medium pressure pipeline. The importance of an appropriate choice of the flow model (isothermal or adiabatic flow of real or ideal gas) is demonstrated by the results of the study. It is shown that accounting for the variability of the discharge coefficient is required if medium pressure pipelines are analysed. However, it is eventually shown that the impact of the discharge coefficient on the predicted outflow rate is of lesser importance than that of the applied flow model.
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W.J. Kostowski, J. Skorek / Energy 45 (2012) 481e488
Nomenclature
A
cross-sectional area, m2
CD
coefficient of discharge
D
diameter, m
g
gravitational acceleration, m/s2
Wojciech J. Kostowski*, Janusz Skorek
Institute of Thermal Technology, Silesian University of Technology, Konarskiego 22, PL-44-100 Gliwice, Poland
article info
The leakage quantification problem is specific for the transmission and the distribution networks respectively. For transmission networks, flow measurement data are available at each
Article history: Received 29 August 2011 Received in revised form 2 January 2012 Accepted 29 February 2012 Available online 5 April 2012
Keywords: Flow simulation Real gas Pipeline failure Leakage Discharge coefficient Gas networks
entry and exit point, so that the modelled network area may be limited to a single section of the damaged pipeline. Numerical models applied for solving the flow problem in a damaged pipe may use linearization of the governing equations based on the method of characteristics (MOC, [2,3]) or other numerical schemes (the Runge-Kutta method, [1]). The cited papers focus on transient flow simulation in pipeline sections adjacent to the failure and pay little attention on modelling the flow through the side-wall opening, which is assumed to be isentropic flow with a mass flow rate reduced by a discharge coefficient of an arbitrarily chosen, constant value (e.g. 0.8 [2]; 0.61 for subsonic flow and 1.0 elsewhere [1]).