WS2
LEAK ANALYSIS IN PIPES USING TRANSIENTS
B. Brunone and M. Ferrante
Department of Civil and Environmental Engineering, University of Perugia
L. Ubertini
Department of Hydraulics and Transportation, University of Rome “La Sapienza”
1. INTRODUCTION
Many problems face engineers in the design and maintenance of water distribution
networks. These problems can be grouped into two types: network characteristic definition
problems, and problems associated with computer hydraulic modeling.
The network
characteristic definition problems involve physical parameters such as unknown pipe and valve
layouts, unauthorized users of water, and pipes deteriorating and forming leaks. Computer
hydraulic modeling can pose uncertainty, not necessarily with the accuracy of the software
package, but rather with the confidence in parameters used in the models. Some of the largest
issues in water distribution are calibration of models and detecting leaks.
It has been estimated that, as an example, within the Asia-Pacific region, as well as in
most European countries, at least 25 % of the water supply is being lost from water distribution
networks. This is very costly for both the water utility who directly loses money and the
consumer who is indirectly penalized through increases in water rates. There is no completely
satisfactory method for finding leaks or unauthorized use of water at present without costly meter
reading and exact quantification of flows. Although there have been methods in the past that can
quantify and locate leaks, they have only really been for single long pipelines rather than
networked systems.
The aim of the present paper is to show that leak detection and evaluation in pipe
systems can be reached by means of unsteady-state tests that minimize both time consuming and
costs for Water Supply Companies as well as minimize the risks for the integrity of conduits.
In the paper, first the traditional techniques for leak detection are described; second,
principles on which the proposed technique is based are analyzed; third numerical and
experimental evidence of the effects of leaks on pressure transient are shown.
2. “TRADITIONAL” TECHNIQUES FOR LEAK DETECTION
The detection of leaks in pipe networks is an important issue. The presence of leaks in a
network will lower the hydraulic efficiency of that network. In most countries water is a finite
resource and leaks deplete that store. This usually results in a higher cost of water to the
population. The detection of leaks can also find unauthorized use of water whereby people are
stealing this valuable resource. In pipe networks that transport potentially hazardous fluids, the
detection of leaks can stop or minimize any contamination of the environment. Leaks can be a
precursor to failure of pipes if they are subjected to extra pressure events. There are many
different techniques to prove the existence and location of leaks, with most coming from the field
of oil and gas where the consequences of leaks are the most severe.
2.1
Hydrostatic Method
The traditional method of determining and locating leaks is to test each length of pipe line
as it is layed. This involves pressurizing the pipe with a low-cost liquid, usually water. Pressure
sensors are then positioned in the pipe to see if there is any reduction of pressure that could mean
the presence of a leak. This is a good technique because leaks can be found when the pipe has
just been placed and the leaking pipe can be easily replaced with a non-faulty member. The only
problem with this method is that it cannot easily be done with existing pipe networks, due to the
fact that part of the network has to be shut down. Another traditional technique is just to measure
the inflow and compare it with the outflow. If there are any differences there must be leaks. It
should be said that this is a very cost efficient way to show the existence of leaks. A drawback
with this is that the number and location of leaks are unknown, thus tracking them down can be a
problem.
2.2 Acoustical Method
This procedure uses the correlation between acoustic velocity and pressure in a liquid
filled pipeline to detect leaks. This method has been used to test the integrity of pipelines in the
oil and gas field. The manner in which this technique is set up is to have at one end of the
pipeline a pressure gauge and a few meters apart from it a sound transmitter. The sound
transmitter generates signals in the range of 2 to 1,000 Hz with an amplitude of about 1 kPa. The
signal travels down the pipe then the transducer detects and records the echo. Using the time
difference between the outgoing and incoming signals, the acoustic velocity can be calculated.
Readings of both pressure and acoustic velocity are then taken at about half hour intervals so a
graph can be drawn up. If there are no leaks the acoustic velocity curve will mimic the pressure
curve, if there is a leak the acoustic velocity curve will link, and not correlate after the leak
occurs. The leakage rate can also be estimated based on the difference between the acoustic
velocity and the pressure and the measured pressure change/volume change.
The advantage in using this technique is that there are no temperature measurements
needed, not like other hydrostatic methods (especially for gas pipelines) where multiple
temperature readings are needed to check if the pressure drops can be attributed to temperature
drops. Also the equipment can be set up at just one end of the pipe meaning, that data telemetry
is not needed for very long pipes and other pipes do not need to be excavated to install sensors.
Disadvantages of this technique are few, but some are very important. One of the most important
is the presence of air in a pipeline. This reduces the bulk modulus and density of the liquid and
can cause large reductions in the acoustic velocity. Another is the amount of suspended solids in
the liquid. Suspended solids will increase the density of the liquid and cause a decrease in the
acoustic velocity. These decreases in the acoustic velocity can be initially interpreted as leaks.
The last problem is noise that can be detected by the transducer which may come from the
environment or electrical equipment. While the method detects the presence of a leak, the
location cannot be determined. This is not a problem when testing the integrity of pipes or
connections, but is a drawback if the leak is to be repaired.
2.3
Inverse Steady-State Method
The use of inverse steady state analysis to find leaks was carried out by Pudar and Liggett
(1992). The data consisted of flows and pressures at various positions in the network. The
approach behind the analysis was to set up the steady state equations and include a leak area at
nodes. An orifice equation was applied to calculate flow due to pressure loss. An objective
function was then created which was the sum of the squares of the differences in measurable
properties such as pressures and flows. The transition then followed a minimization process to
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fit the leak areas to the measured values. Pudar and Liggett concluded that inverse steady state
leak detection would only be commercially possible if there was massive data for a system.
3. THE PROPOSED TECHNIQUE
The technique here proposed for leak detection is part of the class of the Transient
Analysis Methods which are based on the properties of transmission and reflection of pressure
waves (Brunone 1989, 1999; Brunone and Ferrante 1999; Jönsson 1994, 1995; Liggett and Chen,
1994).
When a pressure wave due to a change of the flow propagates in an intact pipe, it is
modified by friction forces which cause the progressive damping and smoothing of pressure
peaks (e.g. Brunone et al. 1995). Devices, changes in pipe characteristics, sediment or air
accumulation, and leaks all abruptly affect the characteristics of the pressure wave (Brunone
1989, 1999; Brunone and Ferrante 1999; Jönsson 1994, 1995). Specifically, a leak has three
effects on the resultant pressure graph. The first effect is when the initial pressure wave reaches
the leak. It will produce a reflection which can be seen when it arrives back at the section where
the pressure wave has been determined. The amplitude of the reflected wave increases with
increasing the dimension of the leak. The time difference between the initial transient wave and
the reflected wave can then be measured and the location down the pipe can be calculated by the
following equation:
s 
t  a
2
(1)
where: s = distance to the leak from the section where the pressure wave has been produced,
T = time difference between the initial transient wave and the reflected wave,
a = wave propagation velocity.
Moreover, by considering partial reflection of pressure waves which takes place at a leak,
the discharge behavior of the leak itself can be assessed.
The second effect is the distortion in the oscillatory peaks and troughs that occur after the
main pressure rise has occurred.
The third and last effect due to the leakage is a reduction in the amplitude of the
oscillatory pattern after the main pressure rise has occurred.
Thus, for a given change of the flow, the presence of a leak can be detected by analyzing
the pressure signal, that is the pressure time-history at a section of the pipe. Of course, the larger
and the faster the flow change which gives rise to transient, and then the larger and the steeper
the pressure wave, the better the leak detection. The measured pressure signal can be compared
with the predictions of a numerical model for the same transient assuming the pipe to be intact.
Alternatively, experimental values previously obtained, such as when the pipe was just built, can
be taken into account.
4. NUMERICAL AND EXPERIMENTAL EVIDENCE OF THE EFFECTS OF LEAKS
ON PRESSURE TRANSIENT
Numerical modeling
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Firstly, the possibility of locating a leak on the basis of transient tests is shown by
discussing the results of numerical simulations; details of the numerical model are given in
(Brunone 1989, 1999) as well as in Appendix I.
Example refers to an iron outfall pipe with diameter D = 300 mm, length L = 1000 m,
characteristic roughness  = 0.4 mm (Colebrook-White equation), a = 1250 m/s. Transients are
caused by an increase ho of the piezometric head in the initial section created, for example, by a
pressurized tank truck. The pressure signal, hm, is shown (Fig. 1) at the measurement section (s =
sm = 50 m) downstream of the controlled valve whose action gives rise to the transient ( ho = 5
m). In the graph, the bold line represents an intact pipe, whereas the thin lines refer to a damaged
pipe where, at the section s  = 400 m, a leak of different discharge behavior is located: C  A = 20,
80 and 180 mm2, respectively, with C  and A being the coefficient of discharge and the area of
the leak. Furthermore, the dimensionless time  = t/ is considered, with t being the time since
the beginning of the valve motion and  = 2L/a. Fig. 1 shows that for the intact pipe, hm is
practically constant and equal to ho in the time interval [1, 3], with 1 = sm/(2L), the time at
which the pressure wave approaches section m, and 3 = 1 - sm/L, the time when the pressure
wave, reflected back at the end diffuser, arrives at section m. For a damaged pipe, by contrast, at
2 = s /L - 1, a reduction y of hm occurs, an effect which increases with increasing C  A .
Laboratory Tests
With respect to the case of an intact pipe, numerical simulations confirm that, when a
pressure wave arrives at the orifice node, a part of it is transmitted and the other part is reflected
back, with the reflection phenomenon depending on the characteristics of the leak. Therefore, as
already mentioned, the pressure signal conveys information about the state of the system: not
only the presence of a leakage, but also its location and size.
An experimental apparatus has been designed and constructed to investigate unsteadystate flow processes in pressurized pipes in the Laboratory of Hydraulics of the Department of
Water and Structural Engineering of the University of Perugia, Italy. The apparatus consists of
(Fig. 2):
(i)
upstream pressurized tank (air vessel) in which the pressure can be held nearly constant;
in fact, during tests the speed of two submerged pumps, drawing water from the recycling
reservoir, can be varied;
(ii)
polyethylene pipe, 352 m in length of internal diameter 93.8 mm and wall thickness of
8.1 mm; the pipe is arranged in concentric circles with bends having a minimum radius
equal to 1.5 m and is almost horizontal, except for the last short part;
(iii)
downstream hand operated quick-closure ball valve that discharges into a free surface
tank.
In order to simulate a leak, a device with a variable diameter orifice at its wall has been
used (Fig.2). Pressure has been measured at the upstream tank and at the downstream end section
of the pipe (the measurement section in Fig. 2). Pressure transducers are of the strain-gauge type,
with a recording range of 0 to 60 m of water, an accuracy of 0.5% of the full-range scale and a
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time response of 50 ms. Output signals from pressure transducers are read directly into a PC at a
rate of 130 Hz.
Transient events have been caused by quick closure of the end valve. The device
simulating the leak has been placed at a distance s = 128.12 m from the end section of the pipe.
In tests, different values of the orifice diameter have been considered in order to evaluate the
effects of the dimension of the leak on the characteristics of the pressure signal, for a given shape
of the leak. Furthermore, some tests have concerned an intact pipe with the orifice simulating the
leak closed by a disk. As a result of the pressure signal analysis extended to all tests, the mean
value of the velocity of the water hammer wave a = 359.9 m/s has been estimated; small
differences in the a value from test to test can be explained with the existence of small trapped
air volumes.
To allow detailed discussion, only four of the experimental results from the laboratory
apparatus are chosen as entirely typical of the remainder. The related traces of pressure signal,
hm, observed at the measurement section are shown in Figs. 3 to 6, where the reference datum for
hm is the floor of the laboratory and t is time since data acquisition.
Transient of Fig. 3 corresponds to the intact-pipe condition. Thus, it can be assumed as a
reference for no-leak conditions during transients.
Transients of Figs. 4 to 6 correspond to damaged-pipe conditions. In these plots it is
evident that the pressure wave reflected at the leak modifies the pressure signal giving rise to a
dent. Furthermore, the presence of the leak causes a faster damping of the pressure signal.
In Table I, the diameter d of the orifice simulating the leak along with the experimental
values of hm, y and t are given, where hm = maximum value of the overpressure due to the
closure of the valve; y = piezometric head reduction (dent) due to the leak; t = t1 – t0, with t0 =
time at which closure begins and t1 = time when the reflected wave arrives at the measurement
section. As can be seen from Table I, in order to make easier the evaluation of the effects of the
leak, the value of hm is almost the same for the chosen transients. As expected, for a given hm,
the larger d, the larger the dent y.
Table I. Characteristics of transients
Test
(no.)
1
2
d
(mm)
--4.9
hm
(m)
16.75
15.70
y
(m)
--1.04
t
(s)
--0.728
3
4
9.9
15.9
15.05
15.97
2.49
4.47
0.727
0.719
On the basis of the knowledge of t and a, the calculated value of leak location, s , can
be obtained through Eq. (1). In Table II, the values of
s along with those of the relevant
percentage error,  , in the leak location:
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 
s


 s
100
s
(2)
are shown.
Table II. Leak location on the basis of test results
Test

(no.)
s
(m)
(%)
1
2
3
4
--131.00
130.82
129.55
--2.25
2.11
1.12
Basing on Table II, it can be seen that for all considered cases the error in leak location is
acceptable. Moreover, for given hm and shape of the leak, the smaller d the greater  because of
uncertainty in determining the actual time at which the reflected wave reaches the measurement
section. In other words, the larger hm, and then y, the more evident the discontinuity in the
pressure signal due to the reflected wave.
On the basis of the value of y, the discharge behavior of the leak can be determined using
inverse transient calculations (Brunone 1999).
Results of both numerical simulation and laboratory tests carried out on a long pipe
confirm the reliability and validity of the proposed technique, at least when a simple pipe system
is considered. The transient tests proposed do not require complex equipment to be carried out, in
fact pressure measurement at only one section is needed, and do not give rise to dangerous overpressures (about 10 – 15 m of water column). The state of the pipe can then be determined
periodically by comparing the present pressure signal with the one recorded, as an example, just
after the construction corresponding to an intact pipe.
REFERENCES
Brunone, B. (1989). “A technique for leak detection in wastewater outfalls. Numerical
experiments”, Congress on ‘Wastewater Outfalls’, Ischia, Italy, Univ. of Naples, D.223-236 (in
Italian).
Brunone, B. (1999). “A transient test-based technique for leak detection in outfall pipes”, J. Water
Resour. Plng. and Mgmt., ASCE (in press).
Brunone, B., and Ferrante, M. (1999). “On leak detection in single pipes using unsteady-state tests”,
In M.H. Hamza (Editor): Modeling and Simulation, IASTED ACTA PRESS, Anaheim,
California, 268-272.
Brunone, B., Golia, U.M., and Greco, M. (1995). “Effects of two-dimensionality on pipe transients
modeling”, J. Hydr. Engrg., ASCE, 121(12), 906-912.
Jönsson, L. (1994). “Detection of leaks using pressure transients”, Report, Univ. of Lund, Sweden.
Jönsson, L. (1995). “Leak detection in pipelines using hydraulic transients. Laboratory
measurements”, Report, Univ. of Lund, Sweden.
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Liggett, J. A., and Chen, L. (1994). “Inverse transient analysis in pipe networks”, J. Hydr. Engrg,
ASCE, 120(8), 934 -955.
Pudar, R.S., and Liggett, J.A. (1992). “Leaks in pipe networks”, J. Hydr. Engrg, ASCE, 118(7),
1031-1046.
Wylie, E. B., and Streeter, V. L. (1993). “Fluid transients in systems”, Prentice Hall, Englewood
Cliffs, N.J.
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APPENDIX I – NUMERICAL SIMULATION OF TRANSIENTS IN DAMAGED PIPES
When numerically modeling unsteady-state flow in pressurized pipes (Wylie and Streeter
1993), the instantaneous value at time t of the discharge through a leak, Q t , can be visualized as
occurring through a lateral orifice. Thus Q t is assumed to be given by the traditional equation:
Qt  C A 2 g ht  z 
(A1)
in which C  and A are the coefficient of discharge and the area of the orifice, respectively; g is
the acceleration due to gravity; ht and z are the piezometric head and the elevation at the orifice
node, respectively.
To obtain the time-history of ht and Q t , the differential equations for transient flow can
be used. When the method of characteristics is considered, within a finite-difference
approximation, at the orifice node, along with at any interior computational node, the following
equations can be written:
ht = Cu  Bu Qut
(A2)
ht = C d  Bd Qdt
(A3)
for the reach length s upstream (along the C+ characteristic line) and downstream (along the Ccharacteristic line) the orifice node, respectively. In (A2) and (A3), the condition of a common
piezometric head, ht  hut  hdt , at the orifice node is assumed and Qut ( Q dt ) is the upstream
(downstream) discharge and s = axial co-ordinate, with s = 0 at the initial section of the pipe. In
(A2) and (A3), coefficients are defined as: Cu  ht 1t  BQ t 1t ; Bu  B  R Q t 1t ;
 t
 t
C d  ht 1t  BQ t 1t ; Bd  B  R Qt 1t ; where ht 1
and Q t 1
 t
 t
( ht 1
and Q t 1
) are the
piezometric head and the discharge at the node upstream (downstream) the orifice node at time
t  t , respectively; t = time step; B  a /gA is the pipe characteristic impedance; A = crosssectional area of the pipe; R   s / 2 gDA 2  is the pipe resistance coefficient;  = DarcyWeisbach friction factor and D = pipe internal diameter.
Furthermore, at any time t the continuity equation must be satisfied at the orifice node:
t
Qu  Qdt  Qt
(A4)
The boundary conditions to be satisfied both at the upstream and downstream end section
of the pipe depend on the characteristics of the induced action, which gives rise to he pressure
wave, along with on those of the pipe.
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