ACCEPTED VERSION
Wang, Xiaojian; Lambert, Martin Francis; Simpson, Angus Ross; Liggett, James A.; Vitkovsky,
John Leak detection in pipelines using the damping of fluid transients Journal of Hydraulic
Engineering, 2002; 128 (7):697-711
© 2002 American Society of Civil Engineers
http://hdl.handle.net/2440/994
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28 March 2014
1
Leak Detection in Pipelines Using the
Damping of Fluid Transients
Xiao-Jian Wang
1
, Martin F. Lambert
2
, Angus R. Simpson
3
, James A. Liggett
4*
and John P. Vítkovský
5
Abstract: Leaks in pipelines contribute to damping of transient events. That
fact leads to a method to find location and magnitude of leaks. Because the
problem of transient flow in pipes is nearly linear, the solution of the
governing equations can be expressed in terms of a Fourier series. All Fourier
components are damped uniformly by steady pipe friction, but each
component is damped differently in the presence of a leak. Thus, overall leak-
induced damping can be divided into two parts. The magnitude of the
damping indicates size of a leak whereas different damping ratios of the
various Fourier components are used to find location of a leak. This method
does not require rigorous determination and modeling of boundary conditions
and transient behavior in the pipeline. The technique is successful in
detecting, locating and quantifying a 0.1% size leak with respect to the cross-
sectional area of a pipeline.
1
Postgraduate Student, Dept. of Civil & Environmental Engineering, Adelaide University, Adelaide, SA
5005, Australia. email: xwang@civeng.adelaide.edu.au.
2
Senior Lecturer, Dept. of Civil & Environmental Engineering, Adelaide University, Adelaide, SA 5005,
Australia. email: mlambert@civeng.adelaide.edu.au.
3
Associate Professor, Dept. of Civil & Environmental Engineering, Adelaide University, Adelaide, SA
5005, Australia. email: asimpson@civeng.adelaide.edu.au. Member, ASCE.
4
Professor Emeritus, School of Civil & Environmental Engineering, Cornell University, Ithaca, N.Y. 14853-
3501, USA. email: jal8@cornell.edu.
*
Corresponding author.
5
Research Associate, Dept. of Civil & Environmental Engineering, Adelaide University, Adelaide, SA
5005, Australia. email: jvitkovs@civeng.adelaide.edu.au.
2
Introduction
Leakage from pipelines has the potential to cause significant environmental damage and
economic loss. While pipelines are designed and constructed to maintain their integrity, it
is difficult to avoid the occurrence of leakage in a pipeline system during its lifetime
(Hovey and Farmer 1999). Often, accurate leak detection, enabling a quick response, is
necessary to minimize damage. Leak detection methods previously proposed are:
reflected wave or timing methods (Jönsson 1995, Covas and Romas 1999, Brunone 1999);
volume balance methods (Griebenow and Mears 1989, Liou 1994); pressure or flow
deviation methods (Griebenow and Mears 1989, Liou and Tian 1995); acoustic methods
(Fuchs and Riehle 1991); pig-based monitoring and on-line surveillance methods (Black
1992, Weil et al. 1994, Furness and Reet 1998); frequency analysis methods (Jönsson and
Larson 1992, Mpesha et al. 2001); inverse techniques (Pudar and Liggett 1992, Liggett
and Chen 1994, Vítkovský, 2001); and a genetic algorithm method (Vítkovský et al.
2000). However, no single method can always meet operational needs from an accuracy
and cost point of view (Furness and Reet 1998). Each of these leak detection techniques
has its advantages and disadvantages in different circumstances. Liou (1998) used a
pseudo-random binary signal (p.r.b.s) sequence as a transient tool and showed that change
of the spatial damping of the p.r.b.s sequence along the pipeline can be used to detect a
leak. A leak detection, location and quantification method that uses damping of a transient
event by a leak is presented in this paper.
Transient response of a pipeline with a distributed leak was investigated by Wiggett
(1968). They found that the transients in a pipeline were greatly affected by the magnitude
of the distributed lateral flow. To investigate the effects of the demands on the transients
in a field pipe network test, McInnis and Karney (1995) used a similar distributed leak
3
model based on the method of characteristics. Recent experimental and numerical work at
Adelaide University has demonstrated that attenuation of transients in a pipeline due to a
small leak is significant, as shown in Fig. 1. That observation has lead to this work, which
attempts to detect leak occurrence, not by trying to model a transient event, as is required
in inverse transient analysis (Liggett and Chen 1994), but by analyzing transient damping
or decay of a pressure signal, a much simpler process. The technique does not require
rigorous determination and modeling of boundary conditions and other transient behavior.
It follows the approach used in pressure measurement where the (often large) common-
mode pressure is removed through the use of differential rather than absolute pressure
measurement devices. Baseline studies of pipelines that appear to be leak free can be used
to increase the accuracy of the process, but are not necessary to apply the basic method.
Transient pressure waves are used for the attenuation study because measurement of
pressure in pipelines is more accurate (and considerably less expensive) than measurement
of flow.
In the following section, the governing equations for unsteady pipeline flow with a leak
are derived and non-dimensional parameters governing the behavior of pipeline transients
are established. Analytical solutions for friction damping and leak damping are then
obtained from the linearized equations. The leak detection method is developed in the
next section followed by two numerical examples. Finally, results of experimental tests
are presented.
Governing Equations
A control volume located between points 1 and 2 in Fig. 2 is used for the derivation of the
unsteady flow equations (continuity and momentum) with leakage. The pipe is considered
