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A novel location algorithm for pipeline leakage based on the attenuation of negative pressure wave
Process Safety and Environmental Protection 123 (2019) 309–316
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Process Safety and Environmental Protection journal homepage: www.elsevier.com/locate/psep
A novel location algorithm for pipeline leakage based on the attenuation of negative pressure wave Juan Li ∗ , Qiang Zheng, Zhihong Qian, Xiaoping Yang College of Communication Engineering, Jilin University, Chang Chun, China
a r t i c l e
i n f o
Article history: Received 13 March 2018 Received in revised form 9 January 2019 Accepted 14 January 2019 Available online 30 January 2019 Keywords: Pipeline leakage Negative pressure wave Leakage localization Pressure difference Time difference
a b s t r a c t Numerous types of liquid, such as water, oil, and so on, are transported via pipelines. Thus, leakage in the pipelines can cause severe hazards to liquid transportation and pose great risks to industries, environment and dwellers. For the purpose of an accurate identification of the leakage location, a novel location algorithm is proposed in this paper based on the attenuation of negative pressure wave (ANPW). As such, this paper presents some of the first efforts in the investigation of the relationship between the pressure difference and leakage location. This is in direct contrast with the traditional method, which relies on the use of the time difference and the velocity of NPW for leakage detection and location. Accordingly, the ANPW method avoids the potential problems of the traditional NPW method – the difficulty for pinpointing the time difference and the disturbance of the velocity of NPW by the liquid flow rate in the pipeline. To explore this new method, this paper firstly deduces the propagation equation of NPW along with the pipeline using the momentum equation and the continuity equation. This is followed by proposing that the ANPW method depends on the change of pressure in place of the time difference. Thirdly, a test of the method in the actual pipeline and comparison between the ANPW method and the time difference method are conducted. Yielding the largest error of 1.161% and the smallest error of 0.355%, the experiment leads to the conclusion that the new method can be applied to the location of pipeline leakage. © 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1. Introduction Pipelines provide one of the most convenient and economical means of transportation for large quantities of oil, water and gas in industries. While making great contributions to the economy, the rapid development of pipeline transportation in the last decades has also brought safety issues such as pipeline leakage to public concern. Caused by numerous problems such as corrosion, aging and third-party interference, pipeline leakage can lead to financial loss, environmental disruption and even harm to civil security. Therefore, there is pressing needs for feasible methods to detect leakage immediately and confirm leakage point accurately to minimize the detrimental effects of leakage (Murvay, 2012). Research on pipeline leakage mainly involves methods based on acoustic waves (Liu et al., 2015; Mendoza and Carrillo, 2004), vibration signal (Sepideh et al., 2017; Doorhy, 2011), fiber signal (Fu et al., 2010) and negative pressure wave (NPW) (Li et al., 2006;
∗ Corresponding author. E-mail addresses: [email protected] (J. Li), [email protected] (Q. Zheng), [email protected] (Z. Qian), [email protected] (X. Yang).
Liang et al., 2013a; Liu et al., 2017). Among all the methods, the NPW method stands out for its simplicity to deploy, economy, higher sensitivity, lower false alarm rate, and higher stability accuracy. Hence, the NPW method is widely used in pipeline leakage detection and location (Elaoud et al., 2010; Ni et al., 2014). The NPW method works like this: generated when leakage occurs, The NPWs spread to upstream and downstream stations, where they are captured by the pressure sensors. As the time of arrival is different between the upstream and downstream sensors, the leakages are detected and located based on the wave velocity and the time difference. Since its adoption, the NPW method has received much research attention and improvement. Specifically, Hou and Zhang, 2013 proposed the double sensors method to reduce the false alarm rate because leak detection system based on a single sensor often caused false alarm. Sun and Chang, 2014 adopted an integrated-signal method which combined the pressure and flow rate signals for liquid pipelines, thus yielding changes larger than pressure signals and unaffected by the end equipment. To reduce the noise in pipeline pressure signals, Lu et al. (2016) based their small noise reduction method on empirical mode decomposition, which used denoised pressure signals to identify the location of leakage by the time difference. Wang et al. (2017) sought to accurately detect pipeline
https://doi.org/10.1016/j.psep.2019.01.010 0957-5820/© 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
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Nomenclature A a D E e F f g K Lp l ll+ P Pl P P0 PLp Q Ql − Ql + Q Re s T t t1 t2 t V x
the cross-sectional area of the pipeline the velocity of NPW the inner diameter of the pipeline the pipeline modulus of elasticity the wall thickness of the pipeline sampling rate the friction factor determined by the Fanning equation gravity acceleration the water bulk modulus of elasticity the whole length of the pipeline the leakage site from the upstream station the coordinate distance before l the coordinate distance after l the pipeline pressure before leakage the pipeline pressure after leakage the pressure change at leakage point the pressure change at upstream station the pressure change at downstream station the mass flow rate before leakage the mass flow rate before l the mass flow rate after l the change of mass flow rate after leakage Reynolds number complex variables in the Laplace transform Temperature time parameter the arrival times at upstream station the arrival times at downstream station time difference the velocity of flow distance parameter
Greek symbol the density of the water the included angle between the pipeline and hori zontal ε absolute roughness
Fig. 1. Scheme of NPW for pipeline leakage localization.
leakage point and the pressure variation in the inlet and outlet is investigated while time difference is not factored in. The organization of the paper is as follows. The methodology of the ANPW method is deduced in Section 2. The validation of the ANPW method is given in Section 3. Section 4 is the results and discussion of the experiment. Finally, a conclusion is drawn in Section 6. 2. Methodology of ANPW 2.1. Traditional location method based on the time difference This section gives a brief introduction to the principle of the traditional location method. Fig. 1 shows how NPW works in leakage localization of the pipeline. As leakage occurs, the pressure suddenly decreases and propagates to upstream and downstream stations. These drops of pressure are detected by pressure sensors at different time in the two stations. Thus, the point of leakage can be determined by calculating the time difference between two stations. In Fig. 1, the length of the pipeline between the two stations is Lp . Pressure sensors capturing pressure signals are settled in the two stations. Leakage occurs at the point of l from the upstream station. The sensor in the upstream station picks up signals of pressure drops resulting from pipeline leakage at the moment of t1 and the sensor in the downstream station receives signals at t2 . Therefore, the equation can be obtained as follows: t1 =
l a−V
(1)
t2 =
Lp − l a+V
(2)
From the above equation, the distance between the upstream station and the leakage point can be calculated using Eq. (3): leakage by utilizing a system with FBG-Based sensors. By raising the number of sensors that can be multiplexed along a pipeline, the capability of the FBG-based system can be improved. Although much research has been conducted for the purpose of more accurate calculation of the time difference and the NPW velocity, especially in the case of long-distance pipeline transportation, the effect is limited. Keeping the time simultaneity of the signals being measured relies on confirming the data with the use of a Global Position System (GPS) clock. Also, the velocity of liquid changes with the statement of pipeline and disturb the velocity of NPW. These issues limit the applicability of the NPW method (Zhang et al., 2015). Researchers have made various efforts to overcome these limitations. Drago et al. (2000) derived a nonlinear distributed parameters model to use a lumped parameter system as a description of the pipeline. Ge et al. (2008) deduced the attenuation of NPW that travels along a pipeline by the nonlinear distributed parameters model. He et al. (2017) simulated the entire leaking process and established three models to calculate the flow rate and volume of the leakage. Inspired by aforementioned views, this paper proposes a novel location algorithm based on the attenuation of NPW named the ANPW method. For the first time, the relationship between the
l=
1 Lp + t (a − V ) 2
(3)
where t = t1 − t2 . From Eq. (3), the traditional method of leakage location depends on the time difference, the velocity of NPW and liquid flow rate. However, with the statement of pipeline change, liquid flow also varies. In addition, it is difficult to accurately measure the time difference. Thus, it is crucial to explore a new method that does not rely on the use of the time difference and liquid flow rate. Accordingly, a new pipeline location algorithm from the perspective of wave propagation characteristics is explored in this paper. 2.2. Theoretical propagation model of NPW The following assumptions can be made for deriving a mathematical model of the flow along pipelines (Drago et al., 2000): • • • • •
Fluid is compressible. Flow is viscous. Flow is adiabatic. The density of fluid is constant. Flow is one-dimensional.
J. Li et al. / Process Safety and Environmental Protection 123 (2019) 309–316
In order to describe the state of the pipeline, two equations named momentum equation and continuity equation are listed as follows: (Ben-Mansour et al., 2019)
fV V ∂V ∂V 1 ∂P V =0 + + + g sin + ∂x 2D ∂x ∂t V
∂P ∂P ∂V + + a2 =0 ∂x ∂t ∂x
(6)
Ignore the convective derivative of the pipeline and substitute Eq. (6) into Eq. (4) and Eq. (5), we can get:
fQ Q
∂P 1 ∂Q =0 + + g sin + 2DA2 ∂x A ∂t
(7)
∂P a2 ∂Q + =0 A ∂x ∂t
(8)
Ql− = A
P + a Q /A − Pl
Ql+ = A
Pl + a Q /A − P a
(9)
=Q+
A P a
(11)
Q = Q + Q
(12)
Substitute Eq. (11) and Eq. (12) into Eq. (7) and Eq. (8) and make linearization of the final equation, we can get L
∂Q ∂P + RQ = − ∂t ∂x
(13)
C
∂P ∂Q =− ∂t ∂x
(14)
where L = 1/A, R = f Q /A2 D, C = A/a2 are similar respectively with inductivity, resistance and capacitance. When we take Laplace transform of Eqs. (13) and (14), we can obtain: dP (x, s) dx
dQ (x, s) CsP (x, s) = − dx
(15) (16)
To solve the above two equations, we can differentiate Eqs. (15) and (16) with respect to x: (Ls + R)
dQ (x, s) =− dx
(x, s)
dx2
dP (x, s) d2 Q (x, s) =− Cs dx dx2
(Ls + R) C3 e−nx + C4 enx = nC1 e−nx − nC2 enx
C1 Ls + R = = C3 n
Ls + R = Zk Cs
(24)
when x tends to +∞ in Eq. (23), we can get:
Ls + R C2 =− =− C4 n
Ls + R = −Zk Cs
(26)
Q (0, s) = C3 + C4
(27)
C3 =
1 1 P (0, s) + Q (0, s) 2Zk 2
(17)
(28)
1 1 P (0, s) + Q (0, s) 2Zk 2
(29)
Similarly, C1 =
1 Z P (0, s) + k Q (0, s) 2 2
(30)
C2 =
1 Z P (0, s) − k Q (0, s) 2 2
(31)
Substitute these values into Eqs. (19) and (20):
P Lp , s = cosh nLp P (0, s)
(32)
− Zk sinh nLp Q (0, s)
Q Lp , s = −
1 sinh nLp P (0, s) Zk
Combine with the above two equations, we can get an equation as follows:
P Lp , s + Q Lp , s
= cosh nLp −
1 sinh nLp P (0, s) + Zk
cosh nLp − Zk sinh nLp
Q (0, s)
From Eq. (34), we can obtain:
(34)
P (0, s) = A1 P Lp , s + A1 Q Lp , s − A1 A2 Q (0, s)
P Lp , s = (18) where,
1 P (0, s) + A2 Q (0, s) − Q Lp , s A1
P (x, s) = C1 e−nx + C2 enx
(19)
A2 = cosh nLp − Zk sinh nLp
Q (x, s) = C3 e−nx + C4 enx
(20)
(Ls + R) Cs.
(33)
+ cosh nLp Q (0, s)
A1 = 1/ cosh nLp − 1/Zk sinh nLp
where n =
(25)
P (0, s) = Zk C3 − Zk C4
which are known as wave equations, and thus we can get the solution:
(23)
when x tends to −∞ in Eq. (23), we can get:
(10)
P = P + P
d2 P
Substitute Eq. (19) and Eq. (20) into Eq. (15), we can get:
C4 = −
There P and Q are described as follows:
(Ls + R) Q (x, s) = −
(22)
We can get the solution from the above two equations: A = Q − P a
The mass flow rate Ql+ after l is:
Q (0, s) = C3 + C4
a
(21)
So Eqs. (21) and (22) can be written as follows:
The mass flow rate Ql− before l is:
P (0, s) = C1 + C2
From the fluid dynamics we have: Q = VA
When x tends to zero in the above two equations, we can get:
(4) (5)
311
(35) (36)
When the water pipeline leaks at l from the inlet, separate the whole pipeline into two sections: one is x = 0 to, and another is
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x = l+ to x = Lp ; both of the sections abide by Eqs. (35) and (36). The relation between inlet and the leaking site can be expressed as follows:x = l−
P (0, s) = A3 P l− , s + A3 Q l− , s − A3 A4 Q (0, s)
P l− , s =
s→0
+
P l , s = A5 P Lp , s + A5 Q Lp , s − A5 A6 Q l , s
1 P l+ , s + A6 Q l+ , s − Q Lp , s A5
A4 = cosh n Lp − l
−
− 1/Zk sinh n Lp − l
− Zk sinh n Lp − l
+
P l , s = P l , s =
Q (0, s) = Q l− , s = −
+
Q Lp , s = Q l , s =
(42)
A/a P
(43)
s
A/a P
(44)
s
P Lp , s =
1 P l+ , s + (A6 − 1) Q Lp , s A5
(45)
(46)
Substitute Eq. (41)–(44) into Eq. (45) and Eq. (46), according to the Laplace final value theorem, we get the results: P0 = limsP (0, s) s→0
= lims A3 P l− , s + A3 (1 − A4 ) Q (0, s) s→0
= P 1 −
A RL a
(50)
K/ 1 + (K/E)(D/e)C1
(51)
It is convenient to adopt Fanning friction factor because it is better suited for transition flows (Chen, 1979). The equation is written as follows:
1
= −4 log +
7.149
5.0452 ε/D − log 3.7065 Re
0.8981
ε/D
1.1098
2.8257
(52)
Re
Therefore, the proposed ANPW method depends on the change of pressure instead of the time difference. It has advantages over the traditional one: it can locate pipe leakage under different leakage orifice with fewer errors. The following experiments are conducted to verify the new ANPW method. 3. Experimental steps
So Eqs. (37) and (40) can be written as follows: P (0, s) = A3 P l− , s + A3 (1 − A4 ) Q (0, s)
It can be seen from Eq. (50) that the leakage point is confirmed by some factors, such as inlet pressure variation, outlet pressure variation, the velocity of the NPW, the diameter of pipelines, the friction factor of pipelines, the velocity of the water in the pipeline before leak and the whole length of pipelines. The velocity of the NPW is expressed as follows:
f
P s
(49)
P0 + PLp
(41)
(48)
P0 Lp − aD/f V P0 − PLp
l= (40)
When the pipeline leaks at a moment, the pipeline has some boundary condition as follows:
Q (l+ , s) = Q Lp , s
A R Lp − l a
Thus, the relationship can be made clear between the leakage point l and the change of the pressure in inlet and outlet:
a=
Q (l− , s) = Q (0, s)
1 − Aa Rl P0 = PLp 1 − Aa R(Lp − l)
(39)
where, A5 = 1/ cosh n Lp − l
A5
Now the final mathematical expression of the attenuation of the NPW can be obtained. From Eqs. (47) and (48), it is concluded that the change of the pressure is only determined by the leaking point from inlet, so we can integrate the two formulas as follows:
And the relation between the leaking point and outlet can be expressed as follows:
P l+ , s + (A6 − 1) Q Lp , s
2.3. A novel leakage location method based on propagation model of NPW
A4 = cosh (nl) − Zk sinh (nl)
1
(38)
A3 = 1/ cosh (nl) − 1/Zk sinh (nl)
P Lp , s =
= lims
(37)
where,
s→0
= P 1 −
1 P (0, s) + A4 Q (0, s) − Q l− , s A3
+
PLp = limsP Lp , s
(47)
3.1. Experimental facility The water pipeline is still working in daily life, making it necessary to build the experiment facility. Thus, a laboratory scaled water pipeline loop is established after analysis of the actual water pipeline, as presented in Figs. 2 and 3,. The diameter of the pipeline is 50 mm and the length is 50 m. Stored in the tank, the water circulates along the pipeline with the pump working. There are three leakage points in the pipeline, with the leak flow rate controlled via a valve and the orifice. Data acquisition is achieved using two pressure sensors and the oscilloscope. Sensor1 is installed 4.8 m away from the inlet and Sensor2 is installed 3 m away from the outlet. Both of the sensors are the same type named MIK-P300, with the full scale (F.S) is from 0Mpa to 0.6Mpa and the precision of 0.1% F.S, which means changes can be detected once the pressure variation is more than 0.6Kpa. The sampling rate of the oscilloscope is 250 Hz.
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Fig. 2. Experimental pipeline loop.
Table 1 Experimental parameters. Length of the pipeline(L) Diameter of the pipeline(D) Density of the water() Pressure of the inlet(P) Velocity of the water(V) Thickness of pipeline(e) Bulk modulus of elasticity(K) Sampling rate(f) Temperature(T) Velocity of the NPW(a)
50 m * 50 mm * 3 998.203 kg/m * 0.36Mpa * 1 m/s * 0.006 m * ˆ 2.39 × 109Pa * 250 Hz * 293 K * 360.56 m/s *
experiments are conducted by three parts and repeated twice, as shown in Table 2 4. Results and discussion Fig. 3. Structure chart of experimental pipeline.
The temperature is 293 K. The operating pressure is 0.36Mpa. The leakage orifice is divided into 4 levels according to the diameters of the leakage points, which are 5 mm, 10 mm, 15 mm and 20 mm, respectively. The top right corner of Fig. 2 specifically shows the 4 levels of the leakage. Sensor1 is regarded as the starting sensor and Sensor2 the ending sensor. The distance between the two sensors is 42.2 m. The distance between leakage Point 1, 2, and 3 and Sensor1 is 7.5 m, 22 m, and 35.7 m, respectively. 3.2. Leak location experiments This part of the paper compares the ANPW method with the time difference method in different cases at the experimental pipeline loop. Some main parameters are listed in Table 1. The system raises the alarm and locates leakage positions with two methods once the mutation is over the threshold. In this paper, the threshold value for leak detection is set at 0.018Mpa, which is 5% initial operating pressure. To verify the ANPW method, the
4.1. Preprocessing of the pressure signal In the adoption of the NPW method to locate leakage point, it is important to consider the confounding factor of extraneous noise. To reduce the effect of noise and improve the accuracy of measurement, signals captured by the experiment are usually filtered using the wavelet transform method. This approach highlights key characteristics of the signals and minimizes the extraneous noise, thereby effectively improving the measurement. In the experiment, a db5 wavelet is used to reduce the impact of the noise and threshold value is set at 1.5. Fig. 4 shows the signal captured by the inlet pressure sensor and Fig. 5 the denoised signal obtained using wavelet transform. 4.2. Defining the time difference Eq. (3) confirms that the leakage point is depended on the time difference t, the velocity of NPW and flow. Fig. 6 shows the denoised pressure signals captured by the two sensors settled in the stations. Because the pressure curves are smooth, distinguishing the pressure drop becomes easier. As shown in Fig. 6, the features
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Table 2 Leakage location experiments. Number
Leakage orifice level
Test number
1
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
2 1
3 4 1 2
2
3 4 1 2
3
3 4
Distance between the leakage point and upstream station/m * * * * * * * * * * * * * * * * * * * * * * * *
7.5
22
35.7
Fig. 4. Original signal.
in the pressure signals at the starting and ending points of the pressure drop are clearly distinguishable. t is the mean of difference of sample points, which Eq. (53) is able to confirm:
n2 − n1 + n4 − n3 2
As shown in Fig. 6, t is 0.086 s. According to Eq. (3), the leakage can be located at 36.6 m from the upstream station and the error is 0.9 m, about 2.01% accuracy. 4.3. Leakage location results After the noise is minimized using the wavelet transform method, Eqs. (3) and (53) can be adopted for the traditional leakage location and Eq. (50) can be employed for the ANPW method. According to the leakage location results presented in Table 3, both methods are effective in detecting and locating the leakage. All the leakage points are detected. Error in location generated by Eq. (3) is 1.66%–3.08% and error generated by Eq. (50) is 0.355%–1.161%. It can be concluded that the errors using the ANPW method are smaller and more stable. As indicated in Table 3, in leakage Point 1, the maximum location error is 0.995% when the leakage orifice is at level 1 and the maximum location error is 0.379% when the leakage orifice is at level 4. The same applies to situations in leakage Point 2 and 3. This indicates that the error of location is gradually decreasing as the leakage orifice is gradually increasing. It also suggests that small pressure variation leads to large errors. In addition, the average error of leakage Point 1, 2 and 3 are 0.693%, 0.782% and 0.699%, respectively. Both of the two methods make some errors, which are the results of the following factors: • The presence of elbows, valves and so on in the pipeline makes the pressure variation different from the straight pipeline. However, as Eq. (50) is deduced based on the straight pipeline, errors are inevitable. Thus, to eliminate the errors generated by the complexity of the pipeline, various types of pipeline should be further studied. • When calculating the leakage location by Eq. (50), the parameters are only obtained by the valves and sensors, which is different from when the whole pipeline is under consideration. • Sensors used in this experiment do not represent the actual condition. Hence, errors reduction requires using more temperature and pressure sensors to calculate the mean values so that the true value can be approximated.
Fig. 5. Denoised signal.
t =
Fig. 6. Pressure drop of signal.
Even if the ANPW method also makes some errors, the errors are smaller than those obtained using the traditional method. It is thus concluded that the ANPW method has some advantages over the traditional method.
(53)
where n1 and n2 are the time points when NPW drops, whereas n3 and n4 are the time points when NPW reaches leakage stability.
4.4. Analysis of user operation In this part, we investigate the behavior of the ANPW method in situation that can potentially lead to false results. Fig. 7 is the valve
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Table 3 Leakage location results. Leakage point
Distance from inlet /m
Distance between the two sensors /m
Leakage orifice level
Test number
Distance calculated by the time difference/m
Error/%
Distance calculated by the ANPW/m
Error/%
1
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
8.50 6.58 8.40 8.45 8.32 6.77 8.28 8.20 23.12 23.04 22.94 22.88 22.75 22.72 21.28 22.76 37.10 34.45 36.98 37.00 36.90 34.76 36.55 36.48
2.37% 2.18% 2.13% 2.25% 1.94% 1.73% 1.85% 1.66% 2.65% 2.46% 2.23% 2.09% 1.80% 1.78% 1.71% 1.71% 3.32% 2.96% 3.03% 3.08% 2.84% 2.23% 2.01% 1.85%
7.09 7.08 7.16 7.80 7.79 7.73 7.66 7.69 21.51 22.46 21.68 22.34 21.69 22.30 22.22 22.20 36.14 36.17 35.41 36.01 35.45 35.43 35.88 35.55
0.972% 0.995% 0.806% 0.711% 0.687% 0.545% 0.379% 0.450% 1.161% 1.090% 0.758% 0.806% 0.735% 0.711% 0.521% 0.474% 1.043% 1.114% 0.687% 0.735% 0.592% 0.640% 0.427% 0.355%
2 1
7.5
3 4 1 2
2
22
42.2
3 4 1 2
3
35.7
3 4
Fig. 8. Pressure drop of signal.
Sensor2 when the leakage location calculated by ANPW method is close to 42.2 m. 5. Conclusions Based on the above research on the novel position algorithm method based on the attenuation of the NPW in water pipeline, the following conclusions can be drawn: Fig. 7. Valve downstream from Sensor2.
which is located at the end of pipeline and the distance between the Sensor2 and valve is 2.8 m. This valve operation can be regarded as opening an actual tap by user. If an actual tap opened downstream from Sensor2, the experiment figure is shown as Fig. 8. From the experimental figure, the red line is upstream station pressure and the pressure variation is 0.1659Mpa, meanwhile, the blue line is downstream station pressure and the pressure variation is 0.1984Mpa. We find that if the tap is opened, the leakage localization is 42.57 m away from the inlet and very close to 42.2 m which is the distance between the Sensor1 and Sensor2. Thus, it can be considered that there is a user operation occurring at downstream from
• The location algorithm is relative to the pressure variation in inlet and outlet, which depends on the attenuation of NPW, as deduced by the momentum equation and continuity equation. The ANPW method does not require the time difference, thus improving the applicability of the NPW method. • When the ANPW method is applied to the pipeline, noise may cause appreciable errors. Wavelet is highly capable of restraining the noise and making the valves in accordance with the true valves. • In the experiments, both the ANPW method and the time difference method perform well in the detection and location of water pipeline leakage. The ANPW method is superior to the time difference method in many cases.
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• When the location of leakage calculated by the ANPW method is at the ending sensor, a circumstance should be considered that user operation maybe occurs downstream, away from ending sensor. • The ANPW method can effectively detect and locate pipe leakage, with the largest location error of 1.161% and the smallest error of 0.355% in the actual water pipeline. Acknowledgments This paper is supported by Jilin Provincial Special Funding for Industrial Innovation (Grant No. 2017C031-1), the key Science Foundation of the Department of Science and Technology of Jilin Province (Grant No.20180201081SF) and Jilin University-Province Collaboration Funding (Grant No. SXGJQY2017-9). Thanks for the permission to publish this paper. References Ben-Mansour, R., Habib, M.A., Khalifa, A., Youcef-Toumi, K., Chatzigeorgious, D., 2012. Computational fluid dynamic simulation of small leaks in water pipelines for direct leak pressure transduction. Comput. Fluids 57, 110–123. Chen, N.H., 1979. An explicit equation for friction factor in pipe. Ind. Eng. Chem. Fund. 18 (296). Doorhy, J., 2011. Real-time pipeline leak detection and location using volume balancing. Pipeline Gas J. 238 (2), 65–66. Drago, M., Geiger, G., Gregoritza, W., 2000. Pipeline simulation technique. Math. Comput. Simul. 52, 211–230. Elaoud, S., Hadj-Tajeb, L., Hadj-Tajeb, E., 2010. Leak detection of hydrogen-natural gas mixtures in pipes using the characteristics method of specified time intervals. J. Loss Prev. Process Ind. 23 (5), 637–645. Ge, C., Wang, G., Ye, H., 2008. Analysis of the smallest detectable leakage flow rate of negative pressure wave-based leak detection systems for liquid pipelines. Comput. Chem. Eng. 32 (8), 1669–1680.
He, G., Liang, Y., Li, Y., 2017. A method for simulating the entire leaking process and calculating the liquid leakage volume of a damaged pressurized pipeline. J. Hazard. Mater. 332, 19–32. Hou, C.X., Zhang, E.H., 2013. Pipeline leak detection based on double sensor negative pressure wave. Appl. Mech. Mater. 313, 1225–1228. Li, Y., Sun, L., Jin, S., et al., 2006. Long range hot oil pipeline leak detection and location technique based on negative pressure wave. In: International Pipeline Conference., pp. 963–968. Liang, W., Kang, J., Zhang, L., 2013a. Leak detection for long transportation pipeline using a state coupling analysis of pump units. J. Loss Prev. Process Ind. 26 (4), 586–593. Liu, C., Li, Yan, Yan, Yu-kun, Fu, J., Zhang, Y., 2015. A new leak location method based on leakage acoustic waves for oil and gas pipelines. J. Loss Prev. Process Ind. 35, 236-146. Liu, C.W., Li, Y.X., Fang, L.P., et al., 2017. Leakage monitoring research and design for natural gas pipelines based on dynamic pressure waves. J. Process Control 50, 66–76. Lu, W., Zhang, L., Liang, W., et al., 2016. Research on a small-noise reduction method based on EMD and its application in pipeline leakage detection. J. Loss Prev. Process Ind. 41, 282–293. Mendoza, M., Carrillo, A., 2004. New distributed optical sensor for detection and localization of liquid hydrocarbons. Part II: optimization of the elastomer performance. Sens. Actuators A 111, 154–165. Murvay, Pal-Stefan, Silea, loan, 2012. A survey on gas leak detection and localization techniques. J. Loss Prev. Process Ind. 25 (6), 966–973. Ni, L., Jiang, J.C., Pan, Y., et al., 2014. Leak location of pipelines based on characteristic entropy. J. Loss Prev. Process Ind. 30, 24–36. Sepideh, Y., Kalyan, R.P., Sez, A., 2017. Novel vibration-based technique for detecting water pipeline leakage. Struct. Infrastruct. Eng. 13 (6), 731–742. Sun, L., Chang, N., 2014. Intergrated-signal-based leak location method for liquid pipelines. J. Loss Prev. Process Ind. 32, 311–318. Wang, J.P., Zhao, L., Liu, T.Y., 2017. Novel negative pressure wave-based pipeline leak detection system using Fiber bragg grating-based pressure sensors. J. Light. Technol. 35 (16), 3366–3373. Zhang, T.T., Tan, Y.F., Zhang, X.D., et al., 2015. A novel hybrid technique for leak detection and location in straight pipelines. J. Loss Prev. Process Ind. 35, 157–168.
Contents lists available at ScienceDirect
Process Safety and Environmental Protection journal homepage: www.elsevier.com/locate/psep
A novel location algorithm for pipeline leakage based on the attenuation of negative pressure wave Juan Li ∗ , Qiang Zheng, Zhihong Qian, Xiaoping Yang College of Communication Engineering, Jilin University, Chang Chun, China
a r t i c l e
i n f o
Article history: Received 13 March 2018 Received in revised form 9 January 2019 Accepted 14 January 2019 Available online 30 January 2019 Keywords: Pipeline leakage Negative pressure wave Leakage localization Pressure difference Time difference
a b s t r a c t Numerous types of liquid, such as water, oil, and so on, are transported via pipelines. Thus, leakage in the pipelines can cause severe hazards to liquid transportation and pose great risks to industries, environment and dwellers. For the purpose of an accurate identification of the leakage location, a novel location algorithm is proposed in this paper based on the attenuation of negative pressure wave (ANPW). As such, this paper presents some of the first efforts in the investigation of the relationship between the pressure difference and leakage location. This is in direct contrast with the traditional method, which relies on the use of the time difference and the velocity of NPW for leakage detection and location. Accordingly, the ANPW method avoids the potential problems of the traditional NPW method – the difficulty for pinpointing the time difference and the disturbance of the velocity of NPW by the liquid flow rate in the pipeline. To explore this new method, this paper firstly deduces the propagation equation of NPW along with the pipeline using the momentum equation and the continuity equation. This is followed by proposing that the ANPW method depends on the change of pressure in place of the time difference. Thirdly, a test of the method in the actual pipeline and comparison between the ANPW method and the time difference method are conducted. Yielding the largest error of 1.161% and the smallest error of 0.355%, the experiment leads to the conclusion that the new method can be applied to the location of pipeline leakage. © 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1. Introduction Pipelines provide one of the most convenient and economical means of transportation for large quantities of oil, water and gas in industries. While making great contributions to the economy, the rapid development of pipeline transportation in the last decades has also brought safety issues such as pipeline leakage to public concern. Caused by numerous problems such as corrosion, aging and third-party interference, pipeline leakage can lead to financial loss, environmental disruption and even harm to civil security. Therefore, there is pressing needs for feasible methods to detect leakage immediately and confirm leakage point accurately to minimize the detrimental effects of leakage (Murvay, 2012). Research on pipeline leakage mainly involves methods based on acoustic waves (Liu et al., 2015; Mendoza and Carrillo, 2004), vibration signal (Sepideh et al., 2017; Doorhy, 2011), fiber signal (Fu et al., 2010) and negative pressure wave (NPW) (Li et al., 2006;
∗ Corresponding author. E-mail addresses: [email protected] (J. Li), [email protected] (Q. Zheng), [email protected] (Z. Qian), [email protected] (X. Yang).
Liang et al., 2013a; Liu et al., 2017). Among all the methods, the NPW method stands out for its simplicity to deploy, economy, higher sensitivity, lower false alarm rate, and higher stability accuracy. Hence, the NPW method is widely used in pipeline leakage detection and location (Elaoud et al., 2010; Ni et al., 2014). The NPW method works like this: generated when leakage occurs, The NPWs spread to upstream and downstream stations, where they are captured by the pressure sensors. As the time of arrival is different between the upstream and downstream sensors, the leakages are detected and located based on the wave velocity and the time difference. Since its adoption, the NPW method has received much research attention and improvement. Specifically, Hou and Zhang, 2013 proposed the double sensors method to reduce the false alarm rate because leak detection system based on a single sensor often caused false alarm. Sun and Chang, 2014 adopted an integrated-signal method which combined the pressure and flow rate signals for liquid pipelines, thus yielding changes larger than pressure signals and unaffected by the end equipment. To reduce the noise in pipeline pressure signals, Lu et al. (2016) based their small noise reduction method on empirical mode decomposition, which used denoised pressure signals to identify the location of leakage by the time difference. Wang et al. (2017) sought to accurately detect pipeline
https://doi.org/10.1016/j.psep.2019.01.010 0957-5820/© 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
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Nomenclature A a D E e F f g K Lp l ll+ P Pl P P0 PLp Q Ql − Ql + Q Re s T t t1 t2 t V x
the cross-sectional area of the pipeline the velocity of NPW the inner diameter of the pipeline the pipeline modulus of elasticity the wall thickness of the pipeline sampling rate the friction factor determined by the Fanning equation gravity acceleration the water bulk modulus of elasticity the whole length of the pipeline the leakage site from the upstream station the coordinate distance before l the coordinate distance after l the pipeline pressure before leakage the pipeline pressure after leakage the pressure change at leakage point the pressure change at upstream station the pressure change at downstream station the mass flow rate before leakage the mass flow rate before l the mass flow rate after l the change of mass flow rate after leakage Reynolds number complex variables in the Laplace transform Temperature time parameter the arrival times at upstream station the arrival times at downstream station time difference the velocity of flow distance parameter
Greek symbol the density of the water the included angle between the pipeline and hori zontal ε absolute roughness
Fig. 1. Scheme of NPW for pipeline leakage localization.
leakage point and the pressure variation in the inlet and outlet is investigated while time difference is not factored in. The organization of the paper is as follows. The methodology of the ANPW method is deduced in Section 2. The validation of the ANPW method is given in Section 3. Section 4 is the results and discussion of the experiment. Finally, a conclusion is drawn in Section 6. 2. Methodology of ANPW 2.1. Traditional location method based on the time difference This section gives a brief introduction to the principle of the traditional location method. Fig. 1 shows how NPW works in leakage localization of the pipeline. As leakage occurs, the pressure suddenly decreases and propagates to upstream and downstream stations. These drops of pressure are detected by pressure sensors at different time in the two stations. Thus, the point of leakage can be determined by calculating the time difference between two stations. In Fig. 1, the length of the pipeline between the two stations is Lp . Pressure sensors capturing pressure signals are settled in the two stations. Leakage occurs at the point of l from the upstream station. The sensor in the upstream station picks up signals of pressure drops resulting from pipeline leakage at the moment of t1 and the sensor in the downstream station receives signals at t2 . Therefore, the equation can be obtained as follows: t1 =
l a−V
(1)
t2 =
Lp − l a+V
(2)
From the above equation, the distance between the upstream station and the leakage point can be calculated using Eq. (3): leakage by utilizing a system with FBG-Based sensors. By raising the number of sensors that can be multiplexed along a pipeline, the capability of the FBG-based system can be improved. Although much research has been conducted for the purpose of more accurate calculation of the time difference and the NPW velocity, especially in the case of long-distance pipeline transportation, the effect is limited. Keeping the time simultaneity of the signals being measured relies on confirming the data with the use of a Global Position System (GPS) clock. Also, the velocity of liquid changes with the statement of pipeline and disturb the velocity of NPW. These issues limit the applicability of the NPW method (Zhang et al., 2015). Researchers have made various efforts to overcome these limitations. Drago et al. (2000) derived a nonlinear distributed parameters model to use a lumped parameter system as a description of the pipeline. Ge et al. (2008) deduced the attenuation of NPW that travels along a pipeline by the nonlinear distributed parameters model. He et al. (2017) simulated the entire leaking process and established three models to calculate the flow rate and volume of the leakage. Inspired by aforementioned views, this paper proposes a novel location algorithm based on the attenuation of NPW named the ANPW method. For the first time, the relationship between the
l=
1 Lp + t (a − V ) 2
(3)
where t = t1 − t2 . From Eq. (3), the traditional method of leakage location depends on the time difference, the velocity of NPW and liquid flow rate. However, with the statement of pipeline change, liquid flow also varies. In addition, it is difficult to accurately measure the time difference. Thus, it is crucial to explore a new method that does not rely on the use of the time difference and liquid flow rate. Accordingly, a new pipeline location algorithm from the perspective of wave propagation characteristics is explored in this paper. 2.2. Theoretical propagation model of NPW The following assumptions can be made for deriving a mathematical model of the flow along pipelines (Drago et al., 2000): • • • • •
Fluid is compressible. Flow is viscous. Flow is adiabatic. The density of fluid is constant. Flow is one-dimensional.
J. Li et al. / Process Safety and Environmental Protection 123 (2019) 309–316
In order to describe the state of the pipeline, two equations named momentum equation and continuity equation are listed as follows: (Ben-Mansour et al., 2019)
fV V ∂V ∂V 1 ∂P V =0 + + + g sin + ∂x 2D ∂x ∂t V
∂P ∂P ∂V + + a2 =0 ∂x ∂t ∂x
(6)
Ignore the convective derivative of the pipeline and substitute Eq. (6) into Eq. (4) and Eq. (5), we can get:
fQ Q
∂P 1 ∂Q =0 + + g sin + 2DA2 ∂x A ∂t
(7)
∂P a2 ∂Q + =0 A ∂x ∂t
(8)
Ql− = A
P + a Q /A − Pl
Ql+ = A
Pl + a Q /A − P a
(9)
=Q+
A P a
(11)
Q = Q + Q
(12)
Substitute Eq. (11) and Eq. (12) into Eq. (7) and Eq. (8) and make linearization of the final equation, we can get L
∂Q ∂P + RQ = − ∂t ∂x
(13)
C
∂P ∂Q =− ∂t ∂x
(14)
where L = 1/A, R = f Q /A2 D, C = A/a2 are similar respectively with inductivity, resistance and capacitance. When we take Laplace transform of Eqs. (13) and (14), we can obtain: dP (x, s) dx
dQ (x, s) CsP (x, s) = − dx
(15) (16)
To solve the above two equations, we can differentiate Eqs. (15) and (16) with respect to x: (Ls + R)
dQ (x, s) =− dx
(x, s)
dx2
dP (x, s) d2 Q (x, s) =− Cs dx dx2
(Ls + R) C3 e−nx + C4 enx = nC1 e−nx − nC2 enx
C1 Ls + R = = C3 n
Ls + R = Zk Cs
(24)
when x tends to +∞ in Eq. (23), we can get:
Ls + R C2 =− =− C4 n
Ls + R = −Zk Cs
(26)
Q (0, s) = C3 + C4
(27)
C3 =
1 1 P (0, s) + Q (0, s) 2Zk 2
(17)
(28)
1 1 P (0, s) + Q (0, s) 2Zk 2
(29)
Similarly, C1 =
1 Z P (0, s) + k Q (0, s) 2 2
(30)
C2 =
1 Z P (0, s) − k Q (0, s) 2 2
(31)
Substitute these values into Eqs. (19) and (20):
P Lp , s = cosh nLp P (0, s)
(32)
− Zk sinh nLp Q (0, s)
Q Lp , s = −
1 sinh nLp P (0, s) Zk
Combine with the above two equations, we can get an equation as follows:
P Lp , s + Q Lp , s
= cosh nLp −
1 sinh nLp P (0, s) + Zk
cosh nLp − Zk sinh nLp
Q (0, s)
From Eq. (34), we can obtain:
(34)
P (0, s) = A1 P Lp , s + A1 Q Lp , s − A1 A2 Q (0, s)
P Lp , s = (18) where,
1 P (0, s) + A2 Q (0, s) − Q Lp , s A1
P (x, s) = C1 e−nx + C2 enx
(19)
A2 = cosh nLp − Zk sinh nLp
Q (x, s) = C3 e−nx + C4 enx
(20)
(Ls + R) Cs.
(33)
+ cosh nLp Q (0, s)
A1 = 1/ cosh nLp − 1/Zk sinh nLp
where n =
(25)
P (0, s) = Zk C3 − Zk C4
which are known as wave equations, and thus we can get the solution:
(23)
when x tends to −∞ in Eq. (23), we can get:
(10)
P = P + P
d2 P
Substitute Eq. (19) and Eq. (20) into Eq. (15), we can get:
C4 = −
There P and Q are described as follows:
(Ls + R) Q (x, s) = −
(22)
We can get the solution from the above two equations: A = Q − P a
The mass flow rate Ql+ after l is:
Q (0, s) = C3 + C4
a
(21)
So Eqs. (21) and (22) can be written as follows:
The mass flow rate Ql− before l is:
P (0, s) = C1 + C2
From the fluid dynamics we have: Q = VA
When x tends to zero in the above two equations, we can get:
(4) (5)
311
(35) (36)
When the water pipeline leaks at l from the inlet, separate the whole pipeline into two sections: one is x = 0 to, and another is
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x = l+ to x = Lp ; both of the sections abide by Eqs. (35) and (36). The relation between inlet and the leaking site can be expressed as follows:x = l−
P (0, s) = A3 P l− , s + A3 Q l− , s − A3 A4 Q (0, s)
P l− , s =
s→0
+
P l , s = A5 P Lp , s + A5 Q Lp , s − A5 A6 Q l , s
1 P l+ , s + A6 Q l+ , s − Q Lp , s A5
A4 = cosh n Lp − l
−
− 1/Zk sinh n Lp − l
− Zk sinh n Lp − l
+
P l , s = P l , s =
Q (0, s) = Q l− , s = −
+
Q Lp , s = Q l , s =
(42)
A/a P
(43)
s
A/a P
(44)
s
P Lp , s =
1 P l+ , s + (A6 − 1) Q Lp , s A5
(45)
(46)
Substitute Eq. (41)–(44) into Eq. (45) and Eq. (46), according to the Laplace final value theorem, we get the results: P0 = limsP (0, s) s→0
= lims A3 P l− , s + A3 (1 − A4 ) Q (0, s) s→0
= P 1 −
A RL a
(50)
K/ 1 + (K/E)(D/e)C1
(51)
It is convenient to adopt Fanning friction factor because it is better suited for transition flows (Chen, 1979). The equation is written as follows:
1
= −4 log +
7.149
5.0452 ε/D − log 3.7065 Re
0.8981
ε/D
1.1098
2.8257
(52)
Re
Therefore, the proposed ANPW method depends on the change of pressure instead of the time difference. It has advantages over the traditional one: it can locate pipe leakage under different leakage orifice with fewer errors. The following experiments are conducted to verify the new ANPW method. 3. Experimental steps
So Eqs. (37) and (40) can be written as follows: P (0, s) = A3 P l− , s + A3 (1 − A4 ) Q (0, s)
It can be seen from Eq. (50) that the leakage point is confirmed by some factors, such as inlet pressure variation, outlet pressure variation, the velocity of the NPW, the diameter of pipelines, the friction factor of pipelines, the velocity of the water in the pipeline before leak and the whole length of pipelines. The velocity of the NPW is expressed as follows:
f
P s
(49)
P0 + PLp
(41)
(48)
P0 Lp − aD/f V P0 − PLp
l= (40)
When the pipeline leaks at a moment, the pipeline has some boundary condition as follows:
Q (l+ , s) = Q Lp , s
A R Lp − l a
Thus, the relationship can be made clear between the leakage point l and the change of the pressure in inlet and outlet:
a=
Q (l− , s) = Q (0, s)
1 − Aa Rl P0 = PLp 1 − Aa R(Lp − l)
(39)
where, A5 = 1/ cosh n Lp − l
A5
Now the final mathematical expression of the attenuation of the NPW can be obtained. From Eqs. (47) and (48), it is concluded that the change of the pressure is only determined by the leaking point from inlet, so we can integrate the two formulas as follows:
And the relation between the leaking point and outlet can be expressed as follows:
P l+ , s + (A6 − 1) Q Lp , s
2.3. A novel leakage location method based on propagation model of NPW
A4 = cosh (nl) − Zk sinh (nl)
1
(38)
A3 = 1/ cosh (nl) − 1/Zk sinh (nl)
P Lp , s =
= lims
(37)
where,
s→0
= P 1 −
1 P (0, s) + A4 Q (0, s) − Q l− , s A3
+
PLp = limsP Lp , s
(47)
3.1. Experimental facility The water pipeline is still working in daily life, making it necessary to build the experiment facility. Thus, a laboratory scaled water pipeline loop is established after analysis of the actual water pipeline, as presented in Figs. 2 and 3,. The diameter of the pipeline is 50 mm and the length is 50 m. Stored in the tank, the water circulates along the pipeline with the pump working. There are three leakage points in the pipeline, with the leak flow rate controlled via a valve and the orifice. Data acquisition is achieved using two pressure sensors and the oscilloscope. Sensor1 is installed 4.8 m away from the inlet and Sensor2 is installed 3 m away from the outlet. Both of the sensors are the same type named MIK-P300, with the full scale (F.S) is from 0Mpa to 0.6Mpa and the precision of 0.1% F.S, which means changes can be detected once the pressure variation is more than 0.6Kpa. The sampling rate of the oscilloscope is 250 Hz.
J. Li et al. / Process Safety and Environmental Protection 123 (2019) 309–316
313
Fig. 2. Experimental pipeline loop.
Table 1 Experimental parameters. Length of the pipeline(L) Diameter of the pipeline(D) Density of the water() Pressure of the inlet(P) Velocity of the water(V) Thickness of pipeline(e) Bulk modulus of elasticity(K) Sampling rate(f) Temperature(T) Velocity of the NPW(a)
50 m * 50 mm * 3 998.203 kg/m * 0.36Mpa * 1 m/s * 0.006 m * ˆ 2.39 × 109Pa * 250 Hz * 293 K * 360.56 m/s *
experiments are conducted by three parts and repeated twice, as shown in Table 2 4. Results and discussion Fig. 3. Structure chart of experimental pipeline.
The temperature is 293 K. The operating pressure is 0.36Mpa. The leakage orifice is divided into 4 levels according to the diameters of the leakage points, which are 5 mm, 10 mm, 15 mm and 20 mm, respectively. The top right corner of Fig. 2 specifically shows the 4 levels of the leakage. Sensor1 is regarded as the starting sensor and Sensor2 the ending sensor. The distance between the two sensors is 42.2 m. The distance between leakage Point 1, 2, and 3 and Sensor1 is 7.5 m, 22 m, and 35.7 m, respectively. 3.2. Leak location experiments This part of the paper compares the ANPW method with the time difference method in different cases at the experimental pipeline loop. Some main parameters are listed in Table 1. The system raises the alarm and locates leakage positions with two methods once the mutation is over the threshold. In this paper, the threshold value for leak detection is set at 0.018Mpa, which is 5% initial operating pressure. To verify the ANPW method, the
4.1. Preprocessing of the pressure signal In the adoption of the NPW method to locate leakage point, it is important to consider the confounding factor of extraneous noise. To reduce the effect of noise and improve the accuracy of measurement, signals captured by the experiment are usually filtered using the wavelet transform method. This approach highlights key characteristics of the signals and minimizes the extraneous noise, thereby effectively improving the measurement. In the experiment, a db5 wavelet is used to reduce the impact of the noise and threshold value is set at 1.5. Fig. 4 shows the signal captured by the inlet pressure sensor and Fig. 5 the denoised signal obtained using wavelet transform. 4.2. Defining the time difference Eq. (3) confirms that the leakage point is depended on the time difference t, the velocity of NPW and flow. Fig. 6 shows the denoised pressure signals captured by the two sensors settled in the stations. Because the pressure curves are smooth, distinguishing the pressure drop becomes easier. As shown in Fig. 6, the features
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J. Li et al. / Process Safety and Environmental Protection 123 (2019) 309–316
Table 2 Leakage location experiments. Number
Leakage orifice level
Test number
1
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
2 1
3 4 1 2
2
3 4 1 2
3
3 4
Distance between the leakage point and upstream station/m * * * * * * * * * * * * * * * * * * * * * * * *
7.5
22
35.7
Fig. 4. Original signal.
in the pressure signals at the starting and ending points of the pressure drop are clearly distinguishable. t is the mean of difference of sample points, which Eq. (53) is able to confirm:
n2 − n1 + n4 − n3 2
As shown in Fig. 6, t is 0.086 s. According to Eq. (3), the leakage can be located at 36.6 m from the upstream station and the error is 0.9 m, about 2.01% accuracy. 4.3. Leakage location results After the noise is minimized using the wavelet transform method, Eqs. (3) and (53) can be adopted for the traditional leakage location and Eq. (50) can be employed for the ANPW method. According to the leakage location results presented in Table 3, both methods are effective in detecting and locating the leakage. All the leakage points are detected. Error in location generated by Eq. (3) is 1.66%–3.08% and error generated by Eq. (50) is 0.355%–1.161%. It can be concluded that the errors using the ANPW method are smaller and more stable. As indicated in Table 3, in leakage Point 1, the maximum location error is 0.995% when the leakage orifice is at level 1 and the maximum location error is 0.379% when the leakage orifice is at level 4. The same applies to situations in leakage Point 2 and 3. This indicates that the error of location is gradually decreasing as the leakage orifice is gradually increasing. It also suggests that small pressure variation leads to large errors. In addition, the average error of leakage Point 1, 2 and 3 are 0.693%, 0.782% and 0.699%, respectively. Both of the two methods make some errors, which are the results of the following factors: • The presence of elbows, valves and so on in the pipeline makes the pressure variation different from the straight pipeline. However, as Eq. (50) is deduced based on the straight pipeline, errors are inevitable. Thus, to eliminate the errors generated by the complexity of the pipeline, various types of pipeline should be further studied. • When calculating the leakage location by Eq. (50), the parameters are only obtained by the valves and sensors, which is different from when the whole pipeline is under consideration. • Sensors used in this experiment do not represent the actual condition. Hence, errors reduction requires using more temperature and pressure sensors to calculate the mean values so that the true value can be approximated.
Fig. 5. Denoised signal.
t =
Fig. 6. Pressure drop of signal.
Even if the ANPW method also makes some errors, the errors are smaller than those obtained using the traditional method. It is thus concluded that the ANPW method has some advantages over the traditional method.
(53)
where n1 and n2 are the time points when NPW drops, whereas n3 and n4 are the time points when NPW reaches leakage stability.
4.4. Analysis of user operation In this part, we investigate the behavior of the ANPW method in situation that can potentially lead to false results. Fig. 7 is the valve
J. Li et al. / Process Safety and Environmental Protection 123 (2019) 309–316
315
Table 3 Leakage location results. Leakage point
Distance from inlet /m
Distance between the two sensors /m
Leakage orifice level
Test number
Distance calculated by the time difference/m
Error/%
Distance calculated by the ANPW/m
Error/%
1
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
8.50 6.58 8.40 8.45 8.32 6.77 8.28 8.20 23.12 23.04 22.94 22.88 22.75 22.72 21.28 22.76 37.10 34.45 36.98 37.00 36.90 34.76 36.55 36.48
2.37% 2.18% 2.13% 2.25% 1.94% 1.73% 1.85% 1.66% 2.65% 2.46% 2.23% 2.09% 1.80% 1.78% 1.71% 1.71% 3.32% 2.96% 3.03% 3.08% 2.84% 2.23% 2.01% 1.85%
7.09 7.08 7.16 7.80 7.79 7.73 7.66 7.69 21.51 22.46 21.68 22.34 21.69 22.30 22.22 22.20 36.14 36.17 35.41 36.01 35.45 35.43 35.88 35.55
0.972% 0.995% 0.806% 0.711% 0.687% 0.545% 0.379% 0.450% 1.161% 1.090% 0.758% 0.806% 0.735% 0.711% 0.521% 0.474% 1.043% 1.114% 0.687% 0.735% 0.592% 0.640% 0.427% 0.355%
2 1
7.5
3 4 1 2
2
22
42.2
3 4 1 2
3
35.7
3 4
Fig. 8. Pressure drop of signal.
Sensor2 when the leakage location calculated by ANPW method is close to 42.2 m. 5. Conclusions Based on the above research on the novel position algorithm method based on the attenuation of the NPW in water pipeline, the following conclusions can be drawn: Fig. 7. Valve downstream from Sensor2.
which is located at the end of pipeline and the distance between the Sensor2 and valve is 2.8 m. This valve operation can be regarded as opening an actual tap by user. If an actual tap opened downstream from Sensor2, the experiment figure is shown as Fig. 8. From the experimental figure, the red line is upstream station pressure and the pressure variation is 0.1659Mpa, meanwhile, the blue line is downstream station pressure and the pressure variation is 0.1984Mpa. We find that if the tap is opened, the leakage localization is 42.57 m away from the inlet and very close to 42.2 m which is the distance between the Sensor1 and Sensor2. Thus, it can be considered that there is a user operation occurring at downstream from
• The location algorithm is relative to the pressure variation in inlet and outlet, which depends on the attenuation of NPW, as deduced by the momentum equation and continuity equation. The ANPW method does not require the time difference, thus improving the applicability of the NPW method. • When the ANPW method is applied to the pipeline, noise may cause appreciable errors. Wavelet is highly capable of restraining the noise and making the valves in accordance with the true valves. • In the experiments, both the ANPW method and the time difference method perform well in the detection and location of water pipeline leakage. The ANPW method is superior to the time difference method in many cases.
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• When the location of leakage calculated by the ANPW method is at the ending sensor, a circumstance should be considered that user operation maybe occurs downstream, away from ending sensor. • The ANPW method can effectively detect and locate pipe leakage, with the largest location error of 1.161% and the smallest error of 0.355% in the actual water pipeline. Acknowledgments This paper is supported by Jilin Provincial Special Funding for Industrial Innovation (Grant No. 2017C031-1), the key Science Foundation of the Department of Science and Technology of Jilin Province (Grant No.20180201081SF) and Jilin University-Province Collaboration Funding (Grant No. SXGJQY2017-9). Thanks for the permission to publish this paper. References Ben-Mansour, R., Habib, M.A., Khalifa, A., Youcef-Toumi, K., Chatzigeorgious, D., 2012. Computational fluid dynamic simulation of small leaks in water pipelines for direct leak pressure transduction. Comput. Fluids 57, 110–123. Chen, N.H., 1979. An explicit equation for friction factor in pipe. Ind. Eng. Chem. Fund. 18 (296). Doorhy, J., 2011. Real-time pipeline leak detection and location using volume balancing. Pipeline Gas J. 238 (2), 65–66. Drago, M., Geiger, G., Gregoritza, W., 2000. Pipeline simulation technique. Math. Comput. Simul. 52, 211–230. Elaoud, S., Hadj-Tajeb, L., Hadj-Tajeb, E., 2010. Leak detection of hydrogen-natural gas mixtures in pipes using the characteristics method of specified time intervals. J. Loss Prev. Process Ind. 23 (5), 637–645. Ge, C., Wang, G., Ye, H., 2008. Analysis of the smallest detectable leakage flow rate of negative pressure wave-based leak detection systems for liquid pipelines. Comput. Chem. Eng. 32 (8), 1669–1680.
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