Water Resour Manage DOI 10.1007/s11269-014-0752-6
Leak Size, Detectability and Test Conditions in Pressurized Pipe Systems How Leak Size and System Conditions Affect the Effectiveness of Leak Detection Techniques Marco Ferrante · Bruno Brunone · Silvia Meniconi · Bryan W. Karney · Christian Massari
Received: 10 December 2013 / Accepted: 8 July 2014 © Springer Science+Business Media Dordrecht 2014
Abstract The relationships between leak geometry and detectability are explored with a distinction between steady- and unsteady-state based techniques. Various criteria to evaluate the size and detectability of a leak are first discussed. These criteria can be useful for the benchmarking and the comparison of different techniques. Since the test conditions play a crucial rule in leak detectability, the proposed criteria take this effect into account. Furthermore, they show that while in steady-state conditions increases in system pressure enhance leak detectability, in transient state, by contrast, higher pressures tend to decrease detectability. This effect is also confirmed by experimental tests carried out at the Water Engineering Laboratory of the University of Perugia. Keywords Leakage · Pipe systems · Leak detection
1 Introduction Leakage is considered as a growing and main concern in water resources management because of the increasing water demand and energy cost of non-revenue water (e.g., Colombo and Karney 2002). As a result, leak control and detection techniques in pipe
M. Ferrante () · B. Brunone · S. Meniconi Dipartimento di Ingegneria Civile ed Ambientale, University of Perugia, Via G. Duranti 93, 06125 Perugia, Italy e-mail:
[email protected] B. W. Karney Department of Civil Engineering, University of Toronto, Toronto, Canada C. Massari Research Institute for Geo-Hydrological Protection, National Research Council CNR, Via Madonna Alta, 126-06128 Perugia, Italy
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systems (Araujo et al. 2006) are receiving an increasing interest from the managers and scientific community. Leak control is a symptomatic treatment which reduces both leakage and customer head dependent demands. Leak detection, by contrast, seeks to understand why leaks and systems failures occur in order to treat their cause directly. Several leak detection techniques have been proposed and implemented in the last decades (e.g., Colombo et al. 2009; Puust et al. 2010) based on a variety of strategies ranging from acoustic detection to simple mass balance techniques, utilizing both steady and unsteady flow conditions. A complete comparison of different techniques requires the examination of several of their features such as cost and duration of tests, disruption to normal system operation, complexity of the instrumentation, efficiency in leak location and sizing. This paper is focused on the comparison between different leak detection techniques with respect to leak detectability, particularly their effectiveness in detecting small leaks. First, the definition of benchmark criteria to properly estimate the size of a leak is given. This leads to unexpected interconnections between leak size, detectability and optimal test conditions. In fact, associating just the physical size of a leak – i.e. its area – to the measure of its detectability, may be greatly misleading and gives rise to errors in the comparison: the same leak, of given area, can be detected or not by the same leak detection technique depending on the functioning conditions of the system during the tests. In terms of detectability, the same leak effectively acts as though it has different sizes. As a consequence, the evaluation of the smallest detectable leak by means of a given technique is not a trivial matter since it depends not only on the leak area and on the type of the tests (e.g., in steady or unsteady-state conditions) but also on the discharge and pressure regime (test conditions). This explains also why, as a side effect, the benchmarking leads us to necessarily consider a very relevant issue: the best test conditions for leak detection. When steady-state data are used, the dependence of the effectiveness of a given leak detection technique on the test conditions is widely accepted. The minimum night flow consumption measurement is a direct consequence of this fact: the higher the pressure regime – as it happens during the night – the more evident a leak of a given area (and, of course, at night the more the leak flow dominates the total flow). In this case, the detectability of a leak – its effective size – increases with the values of the pressure inside the pipe and discharge through it. On the contrary, the role played by the system conditions during transient tests has not been clearly explored in the existing literature and is analyzed in this paper. To this end, available criteria to evaluate the size of a leak are first discussed according to the physical principles on which the different leak detection techniques are based. These criteria can be used to benchmark the leak detection techniques but also, and more importantly, to find the optimal functioning conditions to enhance the efficiency of each leak detection technique. To conclude, the repercussions on the diagnosis of real pipe systems are discussed and it is shown that test conditions that favour the performance of a given technique may be the worst environment when a different approach is followed.
2 The Sizing Criteria 2.1 The Geometric Criterion Perhaps the most obvious way to measure a leak is through its area, AL : very large leaks and bursts are clearly readily detected.
Leak Size, Detectability and Test Conditions in Pressurized Pipe Systems
A dimensionless quantity can be obtained by considering the ratio of AL to the pipe cross-sectional area, A AL (1) lg = A The geometric parameter, lg , points out the scale effect of a leak: as an example, a circular leak of 1 mm diameter in a pipe of 1 m diameter can be considered as a small leak but the same leak is one hundred times larger in a 0.1 m diameter pipe. The scale parameter AE (2) = CL lg lk = A can be considered a further improvement with respect to lg since the leak discharge coefficient, CL , transforms AL into the effective area AE = CL AL . The effective area defines the hydraulic behavior of the leak completely and it is relevant for the practical applications. In fact, AE can be directly estimated by a leak detection technique and it is commonly used in the pressurized pipe system models within the steady and unsteady-state approach (e.g., Colombo et al. 2009; Ferrante 2012; Gong et al. 2013; Liggett and Chen 1994; Massari et al. 2012, 2013; Pudar and Liggett 1992; Shamloo and Haghighi 2009; Soares et al. 2011; V´ıtkovsk´y et al. 2000). The parameter lk has been also used to distinguish between leaks whose behavior is not affected by the shape (Brunone and Ferrante 2001) – defined as small leaks (lk ≤ 1/10) – and the others. It is noteworthy that, when the leak area varies with the pressure (e.g., Ferrante et al. 2011; Ferrante 2012; Greyvenstein and van Zyl 2007; Massari et al. 2012; Walski et al. 2006) a reference value in terms of pressure should be used in Eqs. 1 and 2, such as the leak area corresponding to a zero pressure inside the pipe (AL0 and AE0 , respectively). Although lg and lk give a rough estimate of the relevance of the leak with respect to the pipe size, the geometric criterion mostly neglects the effects of the test conditions on the detectability. In fact, it is well-known that the same leak in the same pipe can produce a small leakage when the pressures are small and a large leakage for high pressures. As an example, system managers sometimes note that during the night some small leaks can produce wet zones on the road above, disappearing in the late morning. Then it can be affirmed that, in terms of detectability, the same leak may have a different effect and behavior depending on the system functioning conditions. 2.2 The Steady-State Criterion If outflow is relevant for leak sizing, as when mass balance is used, the flow parameter lq =
QL QD
(3)
represents an improvement since it introduces the steady-state functioning conditions; in Eq. 3, QD and QL are the steady-state flow in the pipe downstream of the leak and through the leak, respectively. Assuming that the leak is supplied by only one side of the pipe, it is 0 ≤ lq < ∞ with lq = 0 being the leak-free limit case; on the contrary, lq = ∞ indicates the other limit case in which a complete or 100 % leakage happens. The improvement due to the definition of the flow parameter, lq , with respect to lg and lk is clear considering that the same leak in the same pipe produces the same constant values of lg and lk regardless the functioning conditions, while lq takes into account the
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actual leakage due to the pressure regime and provide a helpful measure of leak size and detectability. Assuming the orifice (or Torricelli’s) equation with a constant leak effective area, (4) QL = AE VT = AE 2gHL it is
√ AE 2gHL VT = lk = lk lvs (5) A VD VD where HL = total head drop at the leak, VD = QD /A is the mean velocity in the pipe downstream of the leak, VT = mean velocity at the vena contracta (or Torricelli’s velocity), and g = gravitational acceleration. Equation 5 shows that the functioning conditions embedded in lvs (= VT /VD ) transform lk into lq . The importance of lvs is evident considering the group of the techniques – frequently used in practice – based on the mass balance. In this case, the measurement of the system inflow and outflow allows to estimate the leakage level of the system or of some parts of it. To limit the uncertainty related to the outflow measurements and to have a better estimate of the real losses (Lambert and Hirner 2000), tests are carried out during the night, in order to increase pressure and then leakage as well as reduce pipe discharges due to the customer demands. In this sense, lq defines properly the effective size of a leak with respect to the system operating conditions since, according to Eq. 5, a pressure increase enhances leak detectability when steady-state tests are executed. This corresponds to an increase in lvs , and hence in lq , for the same leak of a given scale parameter lk . Furthermore, when pressure and discharge are measured at some selected sections of the pipe system and leaks are the unknowns in the momentum and continuity set of equations (inverse analysis), the larger lq the better conditioned the equations (Pudar and Liggett 1992). lq =
2.3 The Unsteady-State Criterion The definition of lq by Eq. 3 clearly reflects the steady-state conditions. Interestingly, as is shown below, the same criterion can be misleading when tests are carried out in unsteadystate conditions. In the last decades, within leak detection transient test-based techniques (TTBTs), two basic approaches are followed (Brunone and Ferrante 2004). In the first approach, within a classic Inverse Transient Analysis (Liggett and Chen 1994), the governing equations can be integrated in the time domain (Covas and Ramos 2010; Kapelan et al. 2003, 2004; V´ıtkovsk´y et al. 2000; Vitkovsky et al. 2007). Alternatively, they can be converted into the frequency domain after having linearized the perturbed friction term and the nonlinear boundary conditions (e.g., the ones at the operating valve and at the leak) to reduce the needed amount of computational time (Duan et al. 2010, 2011; Ghazali et al. 2012; Kim 2005; Lee et al. 2005, 2006, 2007b; Liou 1998; Mpesha et al. 2001, 2002; Wang et al. 2002). In the second approach, the characteristics of the possible leaks are inferred directly from pressure signals by measuring the arrival time and the entity of the pressure waves reflected by the leak at the measurement sections (Brunone 1989, 1999; Brunone et al. 2008; Jonsson and Larson 1992; Jonsson 1994, 1999, 2001; Lee et al. 2007a; Liou and Tian 1995; Silva et al. 1996). A reliable detection of pressure wave arrival times can be obtained by means of the wavelet analysis (Ferrante and Brunone 2003b; Ferrante et al. 2007, 2009a; Stoianov et al. 2001). Since this tool has interesting applications in the leakage detection techniques and
Leak Size, Detectability and Test Conditions in Pressurized Pipe Systems
it has been borrowed from the edge detection techniques, this specific use can be defined as leak-edge detection (Ferrante et al. 2009b). When the pressure signals are analyzed in the time domain, the leak reflection coefficient lr =
HR HI
(6)
plays a crucial role, with HR and HI being the amplitude of the pressure wave reflected and incoming at the leak, respectively. In fact, for a given HI , the higher HR – which carries the information about the leak – the higher lr and so the leak detectability. Under the assumptions of the Allievi-Joukovsky theory and using Eq. 4, the following simplified equation can be derived (Liou 1998) √ −1 A 2gHL (7) lr = − 1 + 2 AE a with a = pressure wave speed, that is valid if HR + HI < HL
(8)
If such a condition is not met, lr depends also on HI , and then QD . Even if Eq. 7 has been proposed more than a decade ago, its reliability as well as its effects on the modality of transient test execution have never been checked extensively. When the pressure signals are analyzed in the frequency domain, the amplitude of the waves in Eq. 6 is substituted by the impedances of the leak, ZL , and of the pipe, ZC , defining the impedance ratio (Ferrante and Brunone 2003a) li =
ZC ZL
(9)
where ZC = a/gA. Under the same assumptions of Eq. 7, it is ZL = 2HL /QL and Eq. 9 becomes a QL (10) li = gA 2HL It has been demonstrated that the frequencies corresponding to the maxima of the experimental pressure spectrum change when li changes (Ferrante and Brunone 2003a). It has also been suggested that a criterion to discriminate between small and large leaks can be based on the value of li . Since both lr and li come from the integration of the same differential equations, it is not surprising that they are linked by the relationship − lr−1 = 2li−1 + 1
(11)
which shows that an increase in lr corresponds to an increase in li and vice versa. Then, when transient tests are executed for pipe diagnosis, both li and lr could be used to measure the entity of a leak. By Eqs. 2 and 5 it can be written: 2 −1 (12) lr = − 1 + lk lvt where lvt (= VaT ) transforms a steady-state criterion in an unsteady-state criterion. Comparing the parameter lvs of Eq. 5 and lvt of Eq. 12, it arises that, for a given leak, while an increase in the steady-state leakage QL increases VT , and then it causes an increase in lvs , it has an opposite effect on lvt . As a consequence, in steady-state conditions the larger VT the more evident the leak, whereas the opposite happens during transient tests. In other
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words, the higher the pressure at the leak, HL , the more detectable the leak only if steadystate tests are carried out. On the contrary, high pressures decrease leak detectability within TTBTs according to Eq. 6 which shows that parameter lr clearly reflects the circumstances under which the lower the mean pressure in the system, the more evident a leak of a given size. This makes quite unreliable any criterion about leak detectability within TTBTs just in terms of a “reasonable” size or discharge.
3 Comparison of the Proposed Criteria The above criteria are compared in Fig. 1. In this figure HL varies with the functioning conditions while we assume that the parameter lk does not vary with the functioning conditions (i.e., AE = AE0 = const.). Assuming a value of VD = 1 m/s, by means of Eq. 5, lq is plotted as a function of lk and HL . Solid lines correspond to a constant value of lq . Similarly, assuming a = 1000 m/s, by means of Eq. 12 on the same figure it is possible to plot li as a function of lk and HL . Dashed lines correspond to a constant value of li . Although given values of VD and a have been used, lq and li depend linearly on 1/VD and a, respectively. Hence, the plot can be generalised considering that the solid lines correspond to a constant lq VD value while the dashed lines also correspond to a constant 1000 li /a value. Due to the inverted dependence of lq and li on VT and hence on HL , solid lines, corresponding to a constant lq , decrease with HL while dashed lines, corresponding to constant li , increase with HL . The same functions of Fig. 1 are reported on separate plots in Fig. 2: while lq increases with lk and HL (Fig. 2a), li increases with lk but decreases with HL (Fig. 2b).
0
10
lq = 20
li = 50
lq = 10 li = 20 −1
10
lq = 5
li = 10
lq = 2
li = 5
lk
lq = 1 li = 2 −2
10
lq = 0.5
li = 1 lq = 0.2 li = 0.5
lq = 0.1
li = 0.2 −3
10
5
li = 0.1 10
15
20
25
30
35 40 45 50
HL (m) Fig. 1 Dependence of lq (= QL /QD ) (solid lines) and li (= ZC /ZL ) (dashed lines) on lk (= AE /A) and HL , for a=1000 m/s and VD =1 m/s
Leak Size, Detectability and Test Conditions in Pressurized Pipe Systems
(a)
(b) 2
10
2
10
li
lq
10 0
0
10 −2
10 0 10
0
2
10
−1
10
1
10
lk
−2
10
0
10
HL (m)
10
2
10
−1
10
1
10
lk
−2
10
0
10
HL (m)
Fig. 2 Variation with HL and lk of lq (a) and li (b)
Assuming that lq and li measure leak detectability in steady-state and transient conditions, respectively, it implies that an increase in HL increases the detectability of a leak of a given geometry (i.e. lk ) only in steady-state conditions while it acts in the opposite direction if a leak detection technique based on transient tests is used. This comparison also confirms that while in steady-state conditions an increase of the pressures in the pipe system increases the effects in terms of leakage and enhance the leak detectability, in transient tests it acts on the opposite. This particular aspect is analyzed in the following by means of an ad hoc experimental investigation since it has never been pointed out in literature.
4 Experimental Assessment 4.1 Experimental Setup Experimental tests have been carried out at the Water Engineering Laboratory (WEL) of the University of Perugia, Italy. The experimental setup (Fig. 3a) comprises a high density polyethylene (HDPE) pipe with L = 166.28 m, internal diameter D = 93.3 mm, nominal diameter DN110, and wall thickness e = 8.1 mm. This pipe connects the upstream tank to the downstream maneuver valve – ball valve DN50 – that discharges in the air. At the pipe inlet a control valve – butterfly valve DN100 – is installed. To simulate a leak discharging into the atmosphere, a device (Fig. 3b) with an orifice at its wall is installed at a distance L = 105.44 m from the maneuver valve. With respect to the previous laboratory arrangement (Brunone and Ferrante 2001; Ferrante and Brunone 2003a; Ferrante et al. 2009a, b) this device allows to simulate leaks of different size by changing the steel plate with the rectangular hole (Table 1). By means of tests performed on another experimental set-up (Ferrante 2012; Ferrante et al. 2011; Massari et al. 2012) it has been verified that Eq. 4 holds for both the used plates. The values of AE have been also evaluated by fitting Eq. 4 to the test data (Fig. 4 and Table 1). During tests, pressure signal is measured with a frequency acquisition of 1024 Hz at section M, immediately upstream of the maneuver valve V and at the supply tank T (Fig. 3a). Piezoresistive transducers with a full scale of 3.5, 7 or 10 bar, depending on the pressure maximum value during the transient test, are used. The steady-state discharge, QI , both upstream (I = U ) and downstream (I = D) of the leak is measured by means of magnetic flow meters.
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(a)
(b) Fig. 3 Sketch of the experimental setup (T = supply tank, C = control valve, M = measurement section, V = maneuver valve) (a) and device simulating a leak of length l and width b (b)
4.2 Laboratory Tests Two series of transient tests have been executed — series 1 and 2 — differing for the leak plate, as summarized in Tables 1 and 2. All transients are generated by the fast and complete closure of the maneuver valve. Within each test series, different flow conditions have been considered by varying the initial opening degree of both the control and maneuver valve. Within each of the two series, two types of tests have been carried out:
Table 1 Geometry of the leaks for Test series 1 and 2 Leak area, AL mm2
Leak effective area, AE mm2
1
52.52
33.59
2
116.64
82.56
Series
Steel plate
Leak Size, Detectability and Test Conditions in Pressurized Pipe Systems −3
3
x 10
Series 1 Series 2 A =3.359 10−5 m2 E
2.5
−5
2
A =8.256 10
m
5
15
E
QL (m3/s)
2
1.5
1
0.5
0 0
10
20
25
30
35
40
45
50
55
HL (m)
Fig. 4 The relationship between HL and QL for the two used plates (experimental data and fitting)
– –
a-tests with a local head loss at the inlet (i.e., with the control valve partially closed), and b-tests with no local head loss at the inlet (i.e., with the control valve completely opened).
Table 2 Summary of the carried out tests. Type a denotes tests with completely opened control valve C whereas during type b tests control valve C is partially closed test series-no.
type
QD
HL
lq
lr
li
1-01
a
2.43
4.17
0.125
0.067
-
1-02
a
2.90
6.99
0.136
0.057
-
1-03
a
1.86
12.89
0.287
0.049
-
1-04
b
1.05
20.36
0.639
0.042
0.088
1-05
b
2.90
19.17
0.225
0.040
0.084
1-06
b
4.87
17.97
0.130
0.039
0.080
1-07
b
2.90
43.81
0.339
0.029
0.059
1-08
b
4.85
36.96
0.187
0.030
0.061
2-01
a
2.98
3.62
0.233
0.153
-
2-02
b
1.90
18.18
0.821
0.099
0.220
2-03
b
2.98
18.79
0.532
0.094
0.207
2-04
b
4.05
18.71
0.391
0.091
0.201
2-05
b
2.98
33.39
0.709
0.076
0.164
2-06
b
4.88
31.92
0.424
0.074
0.160
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As an example, in Fig. 5 the pressure signals at section M, H t , for two tests from Series 1 a and b with a given QD (= 2.90 l/s) are reported, with the superscript t denoting the instantaneous value. The main difference between these two types of pressure signals concerns the pressure oscillations after the first characteristic time of the pipe, which are practically missing for the a-type test. In other words, for a given QD , the b-tests allow to explore transient behavior due to the variation in HL in the long term while the a-tests allow to reach very low values of HL . Both types are reliable for evaluating lr but only b-type tests are useful to calculate li . Figure 6 shows the pressure signals at section M for three tests of Series 2 for a given QD (= 2.98 l/s) and different values of HL . It can be observed that the smaller HL , the larger the pressure wave reflected by the leak for a given HI . In fact (Table 2) for HL = 3.62 m, lr is equal to 0.153 whereas it decreases to 0.094 for HL = 18.79 m and to 0.076 for HL = 33.39 m. To compare properly transient tests with different initial conditions in terms of QD , and then HI , the pressure signals are normalized by means of the following relationship: ht =
(H t − H ) HAJ
(13)
with HAJ = aVD /g being the Allievi-Joukowsky overpressure. Figure 7 shows the dimensionless pressure signal, ht , for all tests of Series 1 during the first characteristic time; in the inset the pressure wave reflected by the leak is magnified. The pressure signals for Series 2 are reported in Fig. 8. As an example of the analysis of pressure signals in the frequency domain, the impulse response functions, Y (f ), derived by the b-type signals of Fig. 8 are shown in Fig. 9 (Ferrante and Brunone 2003a). It can be observed that the larger the impedance ratio li (i.e. the smaller HL ), the more different the impulse response function with respect to the case of the leak-free pipe. 20 a−type test (no. 1−02) b−type test (no. 1−05) 15
pressure signal, Ht(m)
10
5
0
−5
−10
−15 0
1
2
3
4
5
6
7
8
time, t(s)
Fig. 5 Pressure signals for a-type and b-type tests of Series 1 with a given discharge, QD (= 2.90 l/s)
Leak Size, Detectability and Test Conditions in Pressurized Pipe Systems
16
14
pressure signal, Ht(m)
12
10 16
8
15 6
14 13
4
12 2
2−01 (HL = 3.62 m)
11
0.55
0.6
2−03 (HL = 18.79 m)
0.65
2−05 (H = 33.79 m) L
0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
time, t(s)
Fig. 6 The pressure signals for tests of Series 2 for a given discharge, QD (= 2.98 l/s), and different values of HL
To check quantitatively the effect of HL on the detectability of a leak during a transient test, as well as the reliability of Eq. 7, the effect of HL on lr has been evaluated. According to Eq. 6, to obtain the experimental value of lr , the incident and reflected pressure waves at the leak have been determined by a 1-D numerical model based on the Method of Characte-
1
dimensionless pressure signal, ht
0.8 0.6 0.4 0.2 0.95 0 0.9 −0.2
1−01 1−02 1−03 1−04 1−05 1−06 1−07 1−08
0.85 −0.4 0.8 −0.6 −0.8 0
0.58 0.6 0.62 0.64 0.66 0.1
0.2
0.3
0.4
0.5
time, t(s)
Fig. 7 The dimensionless pressure signals for tests of Series 1
0.6
0.7
0.8
0.9
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1
dimensionless pressure signal, ht
0.8 0.6 0.4 0.2 0
0.9 0.85
−0.2
0.8
−0.4
0.75
−0.6
0.65
2−01 2−02 2−03 2−04 2−05 2−06
0.7
−0.8 0
0.55 0.1
0.6 0.2
0.65 0.3
0.4
0.5
0.6
0.7
0.8
0.9
time, t(s)
Fig. 8 The dimensionless pressure signals for tests of Series 2
1200
2−02(li=0.220)
1100
2−03(li=0.207) 2−04 (l =0.201) i
1000
2−05 (li=0.164) 900
2−06 (li=0.160)
800
leak free pipe
|Y(f)|
700 600 500 400 300 200 100 0
0.5
1
1.5
frequency (Hz)
Fig. 9 The impulse response function for b-type tests of Series 2
2
2.5
3
Leak Size, Detectability and Test Conditions in Pressurized Pipe Systems
ristics. Such a model has been calibrated by means of the data acquired at the measurement section immediately upstream of the valve to simulate the transients in the laboratory pressurized pipe considering the viscoelastic effects (Meniconi et al. 2012a, b, 2013). In this way the amplitudes of the incident and reflected waves at the leak have been evaluated, which are slightly different from the amplitude of the same waves at the measurement section, that is placed at a distance L from the leak. The comparison between such values of lr and those given by Eq. 7 reported in Fig. 10 confirms that the smaller HL , the less reliable Eq. 7, because condition (8) is not fulfilled. The general behavior of the dependence of lr on HL provided by Eq. 7, i.e. the smaller HL the more detectable the leak (i.e., the larger lr ) is also confirmed. In other words, the decrease of the leak detectability with HL in transient tests is analytically and experimentally confirmed. As a consequence, the usual steady-state derived common sense, i.e. the higher the pressure the more evident the leak, leads to a complete misunderstanding when applied to the measure of the TTBTs effectiveness. The decrease of the pressure in the system before the transient test can transform a leak with a small area into an easy-to-detect – or large – leak. This is the opposite of what happens to small leaks which disappear with low pressure steady-state conditions. In Fig. 11 the steady- and the unsteady-state criteria are compared on the basis of the carried out tests. The experimental data for Series 1 and 2 of lq VD and li are plotted against the measured values of HL . Furthermore, the curves of the relationships between the same quantities, defined by Eqs. 5 (dotted lines) and 7 (dashed lines), are also plotted. Once again the experimental values confirm the analytical results.
0.35 Series 1: 1−D numerical model Series 1: Eq. (7) Series 2: 1−D numerical model Series 2: Eq. (7)
0.3
0.25
lr
0.2
0.15
0.1
0.05
0
1
10
HL (m)
Fig. 10 The behavior of lr vs. HL : comparison between 1-D numerical model and Eq. 7
M. Ferrante et al. 0.4 Series 2: li
0.35 0.3
lqVD , li
0.25
Series 1: li Series 2: lqVD
0.2 0.15 0.1 0.05 0
Series 1: lqVD 1
10
HL (m)
Fig. 11 b-type tests of Series 1 and 2: variation of lq and li
5 Conclusions Based both on the results of the metrics and on the experimental evidence, it is clear that when different leak detection techniques are compared in terms of leak detectability, test conditions should be taken into account. While it is clear that a burst should be easy to detect by any technique, the dimensions of the leak cannot be considered as a reliable way to determine the leak detectability. The test conditions can be used to improve the leak detectability, transforming the same small leak in a large one. For the leak detection techniques based on steady-state measurements, it is well-known that an increase in the pressures and hence in the leakage, improves the technique performance in terms of capacity to detect leaks. Combining this effect with low system demands, as at night, increases the ratio between leakages and demands. On the contrary, for the unsteady-state leak detection techniques, it is shown that an increase in the pressure system decreases the leak detectability. A given “small” leak can be transformed in a “large” leak by considering proper low pressure initial conditions. This result, based on some theoretical considerations, is also experimentally confirmed.
Acknowledgments This research has been supported by the Italian Ministry of Education, University and Research (MIUR), under the Projects of Relevant National Interest “Advanced analysis tools for the management of water losses in urban aqueducts”, “Tools and procedures for an advanced and sustainable management of water distribution systems”, and Fondazione Cassa Risparmio Perugia under the project “Hydraulic characterization of innovative pipe materials” (no. 2013.0050.021).
Leak Size, Detectability and Test Conditions in Pressurized Pipe Systems
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