Lennart
Jönsson
Dep Water Resources Engineering, Univ of Lund, P.O.Box 118,
S-221 00 Lund, Sweden
Tel +46-46-2228101, E-mail: Lennart.Jonsson@tvrl.lth.se
Abstract:
Hydraulic transients in pipelines are normally
looked upon as a problem but could also be considered as a kind of a probe
propagating through the pipeline. Measurement and careful analysis of
a pressure transient could reveal some valuable properties of the
pipeline. Thus a leak in a single pipeline should affect the appearance of the
measured transient making it possible to indicate the existence of a leak as
well as pointing at the location of the leak. This paper will give some
theoretical and experimental evidence for this beneficial use of hydraulic
transients. In the first place theoretical computations of the effect of a leak
on the transient are discussed concerning the case with a single pipeline at
pump stop. It is shown that the transient wave interacts with the leak
generating a small pressure rise at the measurement point at the pumping
station. The elapsed time between pump stop and the recorded pressure rise can
be used for assessing the location of the leak. Secondly, results from transient
measurements on an experimental pipeline set-up with simulated leaks are
presented. Transients were generated through valve closure at the end of a 135 m
long pipeline. Leak flow rates of about 5 – 14 % of the pipe flow were
investigated and it was shown that the leak in most cases could be qualitatively
traced on the transient measurement and that the leak could be located with an
accuracy of a few meters on the basis of a good knowledge of the initial wave
propagation velocity.
Keywords: hydraulic transient, leak detection, experimental set-up
The phenomenon of waterhammer, i.e. hydraulic transients, occurs in water filled pipelines when the flow is rapidly changed, for instance due to pump stop or valve closure, and is normally considered to be a problem. At the location of the flow change a corresponding pressure change is generated and such a pressure variation will propagate through the pipeline as a wave with a certain wave speed depending on the elastic properties of the pipe and the liquid, typically in the range 300 – 1200 m/s. As the hydraulic transient could be characterized by strong pressure peaks, low pressure and/or cyclic pressure variations such transients might be physically dangerous to the pipeline.
However, hydraulic transients could also be looked upon as a valuable tool for extracting information on some hydraulic properties. The idea is based on the fact that a hydraulic transient is a kind of a “probe” propagating through the pipeline and being affected by some properties (irregularities) of the pipeline. An analysis of a registered transient will thus have the potential of providing some information on the hydraulic status of the pipeline. Thus, it has been demonstrated (Jönsson1997), (Jönsson 1999) that the existence of an air pocket, a leak, a malfunctioning check valve can be deduced from a pressure transient recording. This paper will focus on the use of hydraulic transients to detect a leak with an emphasis on results from an experimental set-up with simulated leaks.
The basic idea of using a hydraulic transient for leak detection in a single pipeline is sketched in Fig 1. A pipeline, length L m, connects a pumping station with a downstream reservoir. Pump stop will cause the pressure to drop instantaneously at the pump. The pressure drop will propagate through the pipeline with a certain wave speed a. As the negative pressure wave reaches a leak located at a distance L’ from the pumping station, a small part of the wave is reflected as a positive wave back towards the pumping station whereas the major part of the wave continues its propagation towards the downstream reservoir being reflected there. A measurement of the hydraulic transient at the pumping station will essentially appear as shown in Fig 1. Thus, the pressure drops instantaneously to an approximately atmospheric level and remains at this level until a small pressure rise after the time Δt is observed. This latter phenomenon is due to the reflected pressure wave from the leak. Subsequently, the check valve closes and the normal, oscillatory pressure, cycle period T, is obtained. In the first place the pressure trace indicates the existence of a small leak and secondly it is possible to deduce the approximate location by measuring the time period Δt and evaluating the wave speed a:
Fig. 1 Sketch of the basic idea for leak detection and the resulting hydraulic transient due to pump stop, a leak and the closure of a check valve
The wave speed a might be deduced theoretically using well established relations (Wylie & Streeter 1978) based on pipe data. Another possibility could be to use the measured pressure transient and the cycle time period T:
provided that the leak does not affect the wave speed significantly.
A number of simulations based on St
Venant’s 1-d equations of the effect of a leak in a single pipeline with a
pump and a shut-off valve were performed. Pipeline length L=1000 m, diameter
D=100 mm, wave speed a=1000 m/s, geometric
height Dz=20
m, frictional head=10 m. Pump data 
=30 m, 
=0.008 
, negligable inertia. The shut-off
valve was closed in 21 s and the pump was stopped after 8.5 s. Different
locations of the simulated leak were studied for two different leakage rates –
2% and 6% respectively of the steady state pipe flow. Fig 2 shows an example of
the calculated hydraulic transient just downstream of the valve for a 6% leak
located 300 m downstream of the pump. One could distinguish, Fig 2 bottom, the
slight pressure rise after 0.6 s due to the leak which is in complete agreement
with Eq(1). Moreover, one could also notice a distortion of the oscillating
pressure after valve closure, Fig 2 top.
Fig. 2 Computed hydraulic transient due to pump stop in a 1000 m pipeline with a 6% leak located 300 m downstream the pump. Top: the overall transient including oscillating pressures. Bottom: detail of the initial pressure drop with the small pressure rise due to the leak
In order to study the effect of a simulated leak on a transient an experimental set-up according to Fig 3 was used. A galvanized steel pipeline consisting of a 98.35 m, D=50 mm conduit and a 34.9 m, D=40 mm conduit was attached to a main (working essentially as a reservoir) with a pressure of about 5 bar. In some cases the D=50 mm part was exchanged for a similar pipe, D=40mm. The discharge end (to the atmosphere) or the pipeline was equipped with a ball valve which could be manually closed very fast. A mechanical flow meter was incorporated in the pipeline which was also equipped with three simulated leakage points, each consisting of a T-junction, a shut-off valve and a flow meter, at the distances 15.15m, 42.85 m, 79.65 m upstream from the ball valve respectively. The hydraulic transient was measured with a sample frequency of 640 Hz at the ball valve by means of a dynamic pressure transducer and a PC with an A/D-converter for data collection. A number of measurements was performed at rapid valve closure, thus producing a strong positive pressure wave propagating upstream in the pipeline and interacting with the leaks. At each run only one of the leakage points was active. The steady state flows in the pipeline and through the active leak were measured before the ball valve closure.
Fig. 3 Experimental set-up for transient measurements in a pipeline with simulated leaks. Transients generated through rapid ball valve closure at the downstream end
Fig 4 shows the measured transient
without any simulated leak with a pipeline flow of 1.43 l/s (0.73 m/s). An
initial rapid pressure rise, Fig 4 top, is obtained according to
Kutta-Joukowski’s law. After that the pressure rises much more gradually due
to friction in the pipeline (the line-packing effect). A pressure drop at time
t=3.22 s is obtained, most probably due to a reflection from the 
pipe bend (or possibly the flow
meter). At time t=3.3 s the reflected wave from the main has reached he
transient measurement point. The pressure wave velocity a could be calculated in
three different ways from the measurement:
Fig.
4 Measured transient without any leak, 
=1.43 l/s (0.73 m/s). Top: the overall transient including the pressure
oscillations. Bottom: detail of the initial pressure wave including the
reflected wave from the upstream main (reservoir)
(1) On the basis of the initial
pressure rise 139-55.9=83.1 m, the
steady state flow velocity v=0.73 m/s and Kutta-Joukowski’s law giving 
(2) On the basis of the reflection
time 0.2250 s for the initial pressure rise propagating 2.135 m giving 
(3) On the basis of the oscillating
period T for the oscillating pressure after valve closure giving
.
The method according to point 2 has been used for evaluating wave velocitiess for leak locations as the leak detection is based on an analysis of the initial pressure wave. The low velocity of a according to point 3 might be explained by the attenuating effect of small bubbles released during low pressure phases of the transient
Fig 5 shows an example of the measured transient for the case with a pipeline flow of 1.05 l/s (0.53 m/s), leakage flow of 0.13 l/s corresponding to a flow ratio of 12% and with the leakage point located 42.85 m upstream of the ball valve. The initial pressure rise, Fig 5 bottom, is the same as shown in Fig 4 bottom. However, after a certain period of time, Δt=3.020312-2.953125=0.0672 s, the slow pressure rise is changed to a pressure drop because of the wave reflection at the simulated leak. The initial wave velocity is evaluated to a=1234 m/s. A simple calculation of the location L’ of the leak gives:
Fig.
5 Measured transient with a leak at location 42.85 m, 
=1.05 l/s (0.53 m/s), 
=0.13 l/s. Top: the overall transient including the pressure oscillations.
Bottom: detail of the initial pressure wave. Notice the pressure drop at time
t=3.020 s due to the reflected wave from the leak
i.e.
L’=41.46 m to be compared with the real location 
.
Moreover, one could notice a difference as to the oscillatory behvaiour of the pressure oscillations between the leakage and the no-leakage cases, Fig 4 top and Fig 5 top respectively. The leakage case shows a more rapid attenuation of the pressure oscillations. They have also got a less smooth appearance.
The results of the analysis of a number of tests
are shown in Table 1:
Table 1 Analysis of leak
location on the basis of measured transients at valve closure. Wave velocities
determined according to the three methods described earlier
Qpipe Qleak Leak a1 a2 a3 Leak Leak
(l/s) (l/s) rate (m/s) (m/s) (m/s) location location
% real (m) determied(m)
0.80 0.04 5 1113 1243 940 42.85 45.5
1.67 0.08 5 1000 1160 983 42.85 50.75
0.80 0.05 6.2 1186 1280 943 42.85 48
0.83 0.09 10.8 1088 1208 918 42.85 42.5
1.67 0.20 12 968 1160 893 42.85 39.9
1.67 0.20 12 1009 1129 926 42.85 48.5
1.67 0.20 12 1032 1183 925 42.85 43.4
1.05 0.13 12.4 1152 1234 923 42.85 41.5
1.18 0.17 14.4 1209 1192 960 42.85 41
0.24 0.04 16.7 1164 1309 979 42.85 41.9
1.14 0.05 4.4 1209 1217 971 79.65 72.6
1.67 0.10 6 1004 1160 929 79.65 80.6
1.67 0.21 12.6 825 1094 938 79.65 78.6
On the basis of theoretical computations and measurements on an experimental set-up it has been shown that an analysis of a measured hydraulic transient can provide information on a possible leak in a single pipeline both qualitatively, i.e. indicating the existence of a leak, and quantitatively, i.e. indicating the location of the leak. The latter aspect can be addressed due to the reflection at the leak of a small part of an incoming hydraulic transient generated elsewhere through valve closure or pump stop. The leak will produce a more or less abrupt change in the recorded hydraulic transient and the temporal location of this change together with an appropriate wave propagation velocity makes it possible to calculate the leakage point. The former aspect is, besides the abrupt change, also illustrated through the more rapid attenuation of the ensuing pressure oscillations and the more or less distorted harmonic oscillations.
Leakage rates from 5-14 % were investigated and the general observation was that the influence of the leak increased with increasing leakage rates. Another important factor is related to the size and rapidness of the initial pressure change due to the flow change. The general observation was that the stronger and the more rapid this pressure change is the more discernable is the effect on the hydraulic transient. Small leaks, of the order of 1-2%, seem to be difficult to trace experimentally.
An accurate location of a leak is crucially dependent on the appropriate value of the wave velocity. Different methods for deducing the wave velocity from the measured transients showed significant differences. Thus, the initial wave velocity, based on the reflection time through the whole pipeline length was of the order of 1200 m/s whereas the calculated wave velocity based on the oscillating pressures was approximately 20% lower, i.e. of the order of 950 m/s. As the leak detection method was based on the initial wave properties the former, higher value was used. One important future research topic should focus on real wave velocities in different situations.
Comparisons between the deduced and real leakage points for the cases described in Table 1 show that the leak could be located with an accuracy of about 0-7 m for the simulated leaks at the real locations 42.85 and 79.65 m from the transient measurement point. Tests with the simulated leakage point at 15.15 m were difficult or impossible to evaluate, most probably due to the very short reflection time compared to the closure time of the valve. In some cases there were difficulties in detecting the leakage point at 79.65 m as there could be an interference with the effect of the pipe bend.
Interpretation of a measured hydraulic transient
in terms of properties of a pipeline should be carried out with due respect to
existing knowledge about the pipeline – pipe material, diameter(s), possible
branching, profile etc. A computation of the expected hydraulic transient in
normal conditions and in the case with an assumed leak will also be valuable for
the analysis of a measured transient.
Acknowledgements
This research has been supported by the VA-FORSK foundation and Ångpanneföreningens Forskningsstiftelse (Å-F Research foundation), both Stockholm, Sweden which is gratefully acknowledged. Moreover, the cooperation with Anders Svensson, VAI VA-PROJEKT AB, Växjö and the city of Malmö concerning measurements is appreciated.