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A new leak location method based on leakage acoustic waves for oil and gas pipelines
Journal of Loss Prevention in the Process Industries 35 (2015) 236e246
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Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
A new leak location method based on leakage acoustic waves for oil and gas pipelines Cui-wei Liu a, c, d, Yu-xing Li a, c, d, *, Yu-kun Yan a, c, d, Jun-tao Fu b, Yu-qian Zhang a, c, d a
College of Pipeline and Civil Engineering in China University of Petroleum (East China), Qingdao 266580, China Sinopec Qingdao LNG Co.,Ltd, Qingdao 266400, China c Key Laboratory of Qingdao Oil and Gas Storage and Transportation Technologies, China d Key Laboratory of CNPC Heavy Gas Transportation and LNG Technologies, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 November 2014 Received in revised form 15 April 2015 Accepted 2 May 2015 Available online 4 May 2015
In order to study a new leak detection and location method for oil and natural gas pipelines based on acoustic waves, the propagation model is established and modified. Firstly, the propagation law in theory is obtained by analyzing the damping impact factors which cause the attenuation. Then, the dominantenergy frequency bands of leakage acoustic waves are obtained through experiments by wavelet transform analysis. Thirdly, the actual propagation model is modified by the correction factor based on the dominant-energy frequency bands. Then a new leak detection and location method is proposed based on the propagation law which is validated by the experiments for oil pipelines. Finally, the conclusions and the method are applied to the gas pipelines in experiments. The results indicate: the modified propagation model can be established by the experimental method; the new leak location method is effective and can be applied to both oil and gas pipelines and it has advantages over the traditional location method based on the velocity and the time difference. Conclusions can be drawn that the new leak detection and location method can effectively and accurately detect and locate the leakages in oil and natural gas pipelines. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Oil and gas pipelines Leakage acoustic wave Propagation model Experimental study Leak location
1. Introduction Nowadays, many leak detection and location methods (Murvay et al., 2012; Lay-Ekuakille et al., 2009; Kajiro et al., 1986; Sun, 2012) have been developed for oil and gas pipeline, such as methods based on mass/volume balance, negative pressure wave, transient model, distributed optical fiber and acoustic waves, etc. Among them the acoustic method is superior to the traditional ones: higher sensitivity, higher location accuracy, lower false alarm rate, shorter testing time and greater adaptability. The fundamental of the traditional acoustic leak detection and location method is: when leakage occurs, the acoustic waves are generated. They propagate to upstream and downstream which are captured by the acoustic sensors. And the arriving time at the upstream sensor is different from the one at the downstream sensor. Then based on the velocity and the time difference, the leakages are detected and located. The acoustic method has so many advantages, and it has been researched a lot. * Corresponding author. College of Pipeline and Civil Engineering in China University of Petroleum (East China), Qingdao 266580, China. E-mail addresses: [email protected] (C.-w. Liu), [email protected] (Y.-x. Li). http://dx.doi.org/10.1016/j.jlp.2015.05.006 0950-4230/© 2015 Elsevier Ltd. All rights reserved.
Gao et al. (2004) developed an analytical model to predict the cross correlation function of leak signals in plastic water pipes, which can be used to calculate the time difference and improve leak location accuracy. Brennan et al. (2007) presented a new interpretation of the process of cross-correlation for time delay estimation. Results showed that the time delay estimations and their variances calculation using time and frequency domain methods are almost identical. Meng et al. (2012) established a formula for gas pipelines leak location, which is modified with consideration of the influences of temperature and pressure. As a result, the location accuracy can be significantly improved with relative errors between 0.01% and 1.37%. Jin et al. (2014) proposed an integrated leakage detection and localization model for gas pipelines. Given that the spread velocity of acoustic waves in pipelines is related to the properties of the medium, such as pressure, density, specific heat, and so on, the paper proposed a modified acoustic velocity and location formula. At present, most of the acoustic method researches are carried out to improve the calculation accuracy of the acoustic velocity and the time difference, especially for long distance pipelines, while the velocity are difficult to confirm, especially for gas pipelines. And if the method is applied to field or long distance pipelines, the time
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difference calculation needs GPS (Global Position System) clock to label data to keep the time simultaneity of the measured signals. The accuracy of the velocity and the time difference restricts the application of the acoustic leak detection and location method. Meanwhile, a group of scholars conducted researches on the propagation characteristics of acoustic waves. Hunaidi and Chu (1999) carried out experiments in plastic water pipes, of which the results show that the amplitude of signals attenuates with the propagation distance at the speed of 0.25 dB/m, and the propagation velocity of signals whose frequency is lower than 50 Hz is independent of frequency, and that acoustic signals propagate faster by 7% in winter than in summer. Muggleton et al. (2002) analyzed the mechanism of propagation behavior of sound and vibration waves caused by leakages of fluid-filled round pipeline. They established the propagation model of signals and also analyzed the change and the attenuation characteristics of the acoustic signals. Liu et al. (2003) studied the attenuation characteristics of the wave of fluid-filled pipeline and the results show that longitudinal wave attenuates slower in pipeline. They also compared the propagation characteristics of waves in different pipe wall materials and came to a conclusion that waves in steel tube attenuate slower than them in PVC pipe. Domestic and international scholars have carried out researches on the propagation characteristics of acoustic waves for leak detection and location. Then the location method is proposed which is based on the propagation model and takes no account of the velocity and the time difference. Therefore, a new leak location method is necessary to study based on the propagation characteristics of leakage acoustic waves for oil and gas pipelines. 2. Preparation for the experiments
sensors, m; c is the propagation velocity of acoustic waves in the fluid, m/s; Dt is the time difference, s. Therefore, the exact arrival time of the acoustic signals at each monitor and the propagation velocity are critical for locating the leakages accurately. Especially the simultaneity of the two measured signals must be ensured for long distance pipelines. When the acoustic leak detection and location method is applied to field, firstly the measured signals should be time-granted by GPS clocks; and then the two signals are processed by the crosscorrelation analysis to obtain the time difference. The time difference is related to the peaks of the two signals. The cross-correlation analysis is defined as follows:
1 r12 ðtÞ ¼ M
M=2 Z
q1 ðtÞq2 ðt þ tÞdt
When leakage occurs, acoustic sensors installed at both ends of the pipeline measure the acoustic waves to determine whether a leak happens or not. This can be seen clearly in Fig. 1. Meanwhile, the system can locate the leakage based on the acoustic propagation velocity and the arrival time of acoustic signals at two adjacent acoustic sensors. The algorithm for the acoustic leak location is shown as follows:
(1)
where, x is the distance between leakage point and upstream sensor, m; L is the distance between upstream and downstream
where, M is the period that acoustic wave spreads between the two adjacent sensors, M ¼ L=c, t2ðM=2; M=2Þ. Theoretically, once leakage occurs, when t ¼ t0 , r12 ðtÞ will reach the maximum value which is expressed as below:
r12 ðt0 Þ ¼ maxr12 ðtÞ
(3)
By calculating the maximum value of r12 ðtÞ, the time difference t0 is calculated. The propagation velocity of acoustic waves along the oil pipeline can be expressed as:
(4)
d E0
where, D is the inside diameter, mm; d is the thickness of pipe wall, mm; E is the bulk modulus, Pa; E0 is the Young's modulus, Pa; r is the density, kg/m3. In gas pipelines, it can be assumed that the propagation process of acoustic waves is thermal isolation and E can be defined as E ¼ kv p. So combined with gas state equation, Equation (4) can be expressed as:
sffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi kv p 1 1 $qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ kv zRT $qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c¼ r kv p D 1þ 1 þ D kv p d E0
Fig. 1. Schematic diagram of acoustic leak detection system.
(2)
M=2
sffiffiffi E 1 $qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c¼ r 1þD E
2.1. Traditional leak detection and location method
x ¼ ðL þ cDtÞ=2
237
(5)
d E0
where, kv is the isentropic volume change exponent; p is the pressure of natural gas, Pa; R is the gas constant, kJ=ðkg,KÞ; T is the temperature, K; z is the compressibility factor. From analyses above, it can be known that the traditional method needs accurate calculations of the velocity and the time difference. The method to calculate the time difference costs much and wastes time, such as GPS clock and cross-correlation analysis. For oil and gas pipelines, the velocity equations are different, which means the traditional method should be adjusted to different conditions. The new proposed method based on the propagation model cares little about the velocity and the time difference, which cares only about the amplitude of the acoustic waves. In traditional method, the amplitude of the acoustic waves is used to calculate the time difference by the cross-correlation analysis, while it is used directly to locate the leakages in the new proposed method.
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2.2. New leak detection and location method based on propagation model of acoustic waves 2.2.1. Theoretical propagation model of acoustic waves in the pipeline Firstly, the basic equations of acoustic waves can be established based on some assumptions. Then the equations can be modified according to the actual working conditions. Assumptions are described as follows (He et al., 2006): (1) The media is the ideal fluid. Therefore the effect of heat conduction and the viscosity on the propagation can be ignored. (2) During the propagation process, acoustic waves can lead to condensation and expansion of the media, which is considered to be an adiabatic process. Therefore, the heat exchange between neighboring sections can also be ignored. (3) Acoustic waves propagate through the media with small amplitude and each acoustics-quantity is the first-order trace. Based on the assumptions above, according to the difference of wave front of acoustic waves in the pipelines, the leakage acoustic waves in the cylindrical pipe are the plane waves and the equation of the plane wave is one-dimensional, which can be illustrated as follows (Xu, 2003):
pðx; tÞ ¼ pa ejðutkxÞ
(6)
Where, pa is the amplitude of the acoustic waves, Pa; u is angular frequency, u ¼ 2pf , f is the frequency of acoustic wave, Hz; x is the propagation distance, m; k ¼ u=c0 is the wave number of undamped waves. So, the propagation model of acoustic waves in the fluid pipelines can be described as Equation (6). 2.2.2. Actual propagation model of acoustic waves in the pipeline When acoustic waves propagate in non-ideal medium, a dissipative process turning acoustic energy into heat energy will occur, which leads to the attenuation of acoustic waves. In actual oil and gas pipelines, damping effect should be taken into account as the pipeline is long. So the propagation equation of acoustic waves in the damping medium (Ma, 2004; Sun et al., 1994) can be derived from the basic equations of acoustic waves as damping effects (including viscous absorption and heat conduction) are considered. In the first instance, the heat conduction is neglected and the viscous absorption is considered, the wave equation is described as:
r0
v2 p v2 p v3 p ¼ Ks 2 þ h 2 vt 2 vx vx vt
(7)
00
where, h ¼ 4=3h0 þ h , Ks ¼ a20 r0 , and Ks is called adiabatic bulk modulus of elasticity. For one-dimensional plane wave, the solution to the Equation (7) is:
pðx; tÞ ¼ p0 ðx; tÞejut
(8)
Substituting (8) in (7), yields
r0 u2
v2 p0 v2 p ¼ ðKs þ juhÞ 20 2 vt vx
(9)
Then substituting K ¼ Ks þ juh in (9), yields
r0 u2
v2 p0 v2 p0 v2 p v2 p0 ¼K or k02 20 ¼ vt 2 vx2 vt vx2
(10)
pffiffiffiffiffiffiffiffiffiffiffi where, k0 ¼ u r0 =K , and because K is the complex number, k0 is also the complex number. It is assumed that k0 ¼ u=c0 jah . Thus the solution to the Equation (7) becomes: 0
pðx; tÞ ¼ p0 ejðutk xÞ
(11)
and
pðx; tÞ ¼ p0 e
ah x
ju txc
e
¼ p0 eah x ejðutkxÞ
(12)
In the Equation (12), Reðk0 Þ ¼ u=c0 , which is called the wave number; Imðk0 Þ ¼ ah , which is called viscous absorption coefficient and it represents the amplitude attenuation speed. Comparing Equation (12) with Equation (6), it can be concluded that the two equations have the same form. Then the heat conduction effect is taken into account, the equation with the viscothermal absorption coefficient can be obtained:
p ¼ p0 eax ejðutk0 xÞ
(13)
In Equation (13), a is the damping absorption coefficient of medium which describes the attenuation speed of the amplitude with the distance, a ¼ u2 b=2r0 c30 ; r0 is the density of medium, kg/ m3; c0 is the propagation speed of acoustic wave, m/s; x is the propagation distance, m; k0 ¼ u=c0 is the wave number of undamped waves. Equation (13) describes an acoustic wave which transmits to the positive direction of x with speed of c0 and angular frequency of u, and its amplitude is pa ¼ p0 eax . Therefore, comparing the Equation (13) with (6), the amplitude attenuation of acoustic waves with the distance can be described by Equation (14):
p ¼ p0 eax
(14)
In this equation, p0 is the amplitude of acoustic waves, Pa, which can be seen clearly in Fig. 2. It can be seen that the amplitude attenuation law follows the exponential curve with propagation distance. Considering the viscous absorption and heat conduction (Zhou et al., 2009) of the medium, the equation of damping absorption coefficient a can be obtained:
a ¼ ah0 þ ah00
1 þ ac ¼ rc0
sffiffiffiffiffiffiffiffi 00 h0 u u2 u2 1 1 ,h þ ,c þ 2r0 2r0 c30 Cv Cp 2r0 c30 (15)
As a result, the amplitude and the longest propagation distance of acoustic waves after attenuating can be calculated if all the following parameters of the pipelines are known: u is angular frequency, u ¼ 2pf , f is the frequency of acoustic wave, Hz; r is the inner radius of pipeline, m; r0 is the density of medium, kg/m3; c0 is the speed of acoustic wave in the pipeline, m/s; h0 is the shear 00 viscous coefficient of medium, Pa,s; h is the volume-change viscous coefficient of medium, Pa,s; c is the heat transfer coefficient, W=ðm,KÞ; Cv is the constant-volume specific heat and Cp is the constant-pressure specific heat, kJ=ðkg,KÞ. These can be verified by experiments.
2.2.3. New leak detection and location method based on propagation model of acoustic waves The high-frequency component of acoustic signal attenuates quickly, while the low-frequency component can propagate for a long distance. Therefore, the wavelet transform method is applied to extract the dominant-energy low-frequency band from the original measured signals, which can be seen in section 4.1. The
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Fig. 2. Amplitude of the acoustic waves.
damping absorption coefficient can be calculated by the Equation (15), of which the parameters need accurate values. Because the parameters are assigned by the mean values which will lead to errors, the theoretical damping absorption coefficient should be corrected by the fitted damping absorption coefficient in experimental results. In order to solve the problem, the Equation (15) can be modified as:
pA ¼ pA0 esax
(16)
In Equation (16), s is the correction coefficient and it can be 3e4 for water pipelines and 0.5e1.5 for gas pipelines after comparative analyses between the theoretical damping absorption coefficients and the fitted ones, which can be seen in section 4.1.1 and 4.2. Then a new method based on the Equation (16) is proposed. To make the method based on the propagation method clear, when a pipeline section is chosen to be monitored by the method, the steps of the method are shown as follows: (1) All the parameters about the monitored pipeline should be made clear and a is calculated by Equation (15); (2) The smallest detection capacity of leakage rate or orifice should be confirmed; (3) The test experiment with the smallest leakage orifice is carried out and the leakage occurs at one end of the pipeline, the acoustic waves are measured in the same end and the other end; (4) The sub-band amplitude of the two measured signals is obtained by the wavelet transform which equals to pA0 and pA , s is obtained and the ratio of the smaller amplitude to the lager one (pA =pA0 ) is set as the threshold value of the leak detection, and the sub-band amplitude measured in the same end which means the larger one, pA0 is regarded as the reference pressure which can be fixed to make leak detection; if the smallest leakage orifice is changed, the reference pressure should be altered; (5) When the sub-band amplitude of the two measured signals are p1 , p2 , if p1 =pA0 pA =pA0 or p2 =pA0 pA =pA0 is satisfied, the leak is detected; (6) And the leak is located through the following equations:
p1 ¼ p0 esax ; p2 ¼ p0 esaðLxÞ ;
p1 L lnðp1 =p2 Þ ¼ esaðL2xÞ ; x ¼ 2 2sa p2 (17)
In Equation (17), p0 is the sub-band amplitude of the leakage acoustic waves at the leakage point which is not necessary to measure; the distance between the leakage point and the upstream sensor is x; the total length of the chosen pipeline is L; the condition keeps the same, s,a can be regarded as fixed. In the calculation procedure of a, because the parameters in Equation (15) are not constant, the mean value of each parameter of the pipeline is applied, which will lead to errors. But the calculation of s through experiments can minimize the errors to confirm to the results of actual situations. And once the pipeline is chosen, the values of a and s can be calculated, and they can be fixed. Compared with the location method based on the time difference, the proposed method is simpler and more accurate. Though the calculation of a leads to the errors, the errors can be minimized by the calculation of s and their errors are so small. During the research, it was found that the calculations of a and s are not even necessary. The steps are shown as follows: (1) A pipeline section is chosen and the smallest detection capacity of leakage rate or orifice should be confirmed; (2) The test experiment with the smallest leakage orifice is carried out and the leakage occurs at one end of the pipeline, the acoustic waves are measured in the same end and the other end; the sub-band amplitude of the two measured signals is obtained by the wavelet transform which equals to pA0 and pA , the ratio of the smaller amplitude to the lager one ðpA =pA0 Þ is set as the threshold value of the leak detection, and the sub-band amplitude measured in the same end which means the larger one, pA0 is regarded as the reference pressure; (3) The test experiment with the smallest leakage orifice is carried out and the leakage occurs at one point in the pipeline; the distance between the chosen point and the starting end is known as x0 ; the acoustic waves are measured in two ends; the subband amplitude of the two measured signals is obtained by the wavelet transform which equals to p10 and p20 ; (4) If p1n =pA0 pA =pA0 or p2n =pA0 pA =pA0 is satisfied, the leak is detected; (5) According to Equation (17), lnðp10 =p20 Þ=ð2saÞ ¼ L=2 x0 is obtained, then the following equation is obtained:
Ln =2 xn lnðp1n =p2n Þ ¼ L0 =2 x0 lnðp10 =p20 Þ and the leakage point xn can be calculated.
(18)
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It can be seen the proposed leak detection and location method without the calculations of a and s can still be used effectively, which can be the second choice after the method with the calculations of a and s. Therefore, the proposed leak detection and location method has advantages over the traditional one based on the velocity and the time difference. The propagation law can help accomplish leak detection and location under different leakage orifices and the errors are small. In order to verify the leak detection and location method based on the propagation model, the experiments are carried out. To ensure the new method can be applied to both oil pipelines and gas pipelines, experiments of oil are firstly accomplished and then the experiments of gas pipelines are carried out.
compressor is the gas source. Water and oil droplets in the gas are removed. From a high-pressure surge tank, the gas enters into the test section, goes into the terminal surge tank and finally is discharged into the environment. For water pipelines, the spherical valve 1 and 4 should be closed and the spherical valve 2 and 3 should be opened. The water in the tank is forced by the pump and transported in the pipeline. Then the water goes back to the tank. The flow is controlled around 10 m3/h by the cutoff valve. The length of the test section is 205.0 m. There are some leakage points in the pipeline test section. Data acquisition programs have been written to measure and process the acoustic signals. The measurement range of the dynamic pressure sensor is 0e57.3 kPa, the sensitivity is 43.5 mV/kPa and the low frequency response is 0.5 Hz.
3. Experimental
3.1. Experiments for water pipelines
A pipeline loop (Li et al., 2010;Liu et al., 2014) for leak detection and location is designed and established after its similarity analysis with field transportation pipelines as shown in Fig. 3 and Fig. 4, of which the fluid can be gas or oil. In experiments, the natural gas can be replaced by the air and the oil can be replaced by the water. The leak flow rate is controlled by valve and orifice. The dynamic pressure sensors are installed 10 cm away from the leakage points. For gas pipelines, the highest permitted pressure is 2.5 MPa. The length of the test section is 203.0 m. The compressed air from the
To calculate a and s in the modified model, the experiments are carried out by two parts. Firstly, when the flow meter is 10.5 m3/h, the leakages occur with the orifices of 2 mm and 3 mm. The distance between the leakage point and the sensors are 0.1 m, 66.4 m, 136.3 m and 202.5 m. Then when the flow meter is 9.5 m3/h, the leakages occur with the orifices of 2 mm and 3 mm. The distance between the leakage point and the sensors are 0.1 m, 25.4 m, 91.6 m and 160.3 m. The sampling rate is 1000 Hz. For the verification of the new proposed method, the
Fig. 3. Structure chart of experimental pipe facility.
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241
Fig. 4. Pipeline leak detection test loop.
experiments are carried out by three parts, and each part is repeated twice which can be seen in Table 1. The flow meter is controlled around 10 m3/h and the sampling rate is 1000 Hz.
3.2. Experiments for gas pipelines To calculate a and s in the modified model, data are obtained when leakage point 1 leaks. The distances between the leakage point and the acoustic sensors are 0.1 m, 66.4 m, 136.3 m and 202.5 m. The operating pressure is 0.4 MPa, 0.8 MPa and 1.2 MPa. The leakage orifice is 0.10 mm, 0.50 mm, 0.70 mm and 1.00 mm. The sampling rate is 3000 Hz. For the verification of the new proposed method, the location experiments are carried out. The distance between the two sensors is 136.2 m, the leakage points are 40.24 m, 88.23 m and 128.25 m from the starting end sensor. The operating pressure is 0.45 MPa, 0.85 MPa and 1.25 MPa. The leakage orifice is 0.10 mm, 0.50 mm, 0.70 mm and 1.00 mm. The sampling rate is 3000 Hz.
Table 1 The leak location experiments for water pipelines. Number
Leakage orifice/mm
Test number
Distance between the two end sensors/m
Distance between the leakage point and the starting end sensor/m
1
2
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
140.95
116.8
74.45
50.3
3 4 2 3 4 2
2
3
2
201.2 139.3
110 47.7
4. Results and discussions 4.1. Research on the leak detection and location for oil pipelines After the experiments, the results of the leak location for oil pipelines are firstly accomplished, and then the location errors for gas pipelines are calculated. The theoretical damping absorption coefficient can be calculated by Equation (15). After the correction coefficient is concluded, the leak location errors can be obtained by Equation (17). Finally, the leak location errors without consideration of damping absorption coefficient and correction coefficient can be obtained by Equation (18).
4.1.1. Characteristics extracted by wavelet transform method for oil pipelines After the frequency-domain analyses, it can be found that the energy of the acoustic waves generated by leakages in oil pipelines concentrates on the frequency band of 0e20 Hz. In order to extract characteristics which can propagate for a long distance and to establish the propagation model for long distance oil pipelines, the leakage acoustic signals at sampling rate of 1000 Hz are processed by the improved wavelet algorithm. With the scale of 5, the sym8 of wavelet basis is applied to extract the information in frequency band of 0e20 Hz, which attenuates little. The subband frequency range is shown in Table 2. From Table 2, A5 is incorporated in the frequency band of 0e20 Hz. So A5 subband can be applied to conclude the damping absorption coefficient. And when the sampling rate is 3000 Hz, A7 (0e11.71875 Hz) subband is applied. The amplitude of the dominant frequency bands extracted from acoustic signals can be applied to calculate the damping absorption coefficient. The A5 amplitude attenuation law can be drawn as Fig. 5 when the leakage orifice is 2.0 mm. From Fig. 5, it can be known that as the propagation distance gets longer, the amplitude of A5 frequency band decreases. It can be concluded that the fitted curve follows the exponential law. And the damping absorption coefficient is calculated by the fitted curve. After analyses, the fitted damping absorption coefficients are concluded. And the Equations (15) and (16) are applied to calculate
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Table 2 Frequency range of all sub-bands for wavelet analysis for A5. Sequence number of subbands
A5
D5
D4
D3
D2
D1
Frequency range/Hz
0e15.625
15.625e31.25
31.25e62.5
62.5e125
125e250
250e500
values. The mean value of the pressure in the 160.3 m pipeline is larger than the one in the 202.5 m pipeline. In order to reduce the errors, the more pressure and temperature sensors are necessary. (2) When the theoretical damping absorption coefficients are calculated, the velocity of the fluid is neglected. And the interaction between the damping absorption coefficients and the fluid is the main research object in the future. (3) When the damping absorption coefficients are fitted, the amplitude is the one in the frequency band of A5, while when the theoretical ones are calculated, the amplitude is the one of the center frequency of the A5 band. The subband and the amplitude of A5 are determined by the signalprocessing method. And the amplitude is also influenced by the sampling rate. Because when the sampling rate is higher, the leakage time is preciser and the amplitude of the leakage time is preciser. These facts cause errors. To solve the problem, the improved signal-processing method is necessary, which can obtain the narrower sub-band. (4) The theoretical damping absorption coefficients are calculated through straight pipeline, while the fitted ones are obtained by experiments which have elbow pipes, reducing pipes, branch pipes and other obstacles such as metering instrumentations. All these contribute to the damping of acoustic waves. So the theoretical damping absorption coefficients must be amended to reduce errors.
Fig. 5. The fitted curve of experimental data when the leakage orifice is 2.0 mm of Number 1 test.
the coefficients. The temperature is 293.15 K and the fluid flowing in the pipeline is the water. The theoretical damping absorption coefficients can be obtained which can be seen clearly in Table 3 with the fitted ones. From Table 3, it can be known that the percentage of A5 amplitude is more than 80%, which can represent the original signal. And there exist errors between the fitted damping absorption coefficients and the theoretical ones. When the damping absorption coefficients are calculated by the Equation (15), of which the parameters are obtained by experiments. Among them, f equals to the center frequency of the extracted subband which is 7.8125 Hz here; r0 is the one under the average pressure in the pipeline, which equals to the average pressure of the measured ones by the upstream and down stream pressure sensors; c0 can be calculated by Equation (4); 00 h0 ; h ; c; Cv and Cp can be obtained under the average pressure and average temperature which is calculated by the upstream and down stream temperature sensors. When the damping absorption coefficients are fitted by the extracted amplitude from the measured signals, the sampling rate and the signal-processing method decide the results. The reasons for errors are given as follows:
In order to reduce the errors of absorption coefficients, the correction coefficient is proposed in Equation (16) and it can be 3e4 after comparative analyses between the theoretical damping absorption coefficients and the fitted ones for water pipelines in experiments. When it comes to the field, the value is based on the physical truth. 4.1.2. Leak detection and location results for oil pipelines After the calculations of the absorption coefficients and the correction coefficients, the Equation (17) can be used for leak detection and location. The test of number 1 with the leakage
(1) In the calculation procedure of the theoretical damping absorption coefficients, the parameters are set as the mean
Table 3 Theoretical and fitted absorption coefficients under different conditions for water pipelines. Number
1
Leakage orifice/mm
3
2
2
3
2
Distance/m
0.1 66.6 136.8 202.5 0.1 66.6 136.8 202.5 0.1 25.4 91.6 160.3 0.1 25.4 91.6 160.3
Amplitude/kPa
Percentage
Original signal
A5
39.324 38.265 33.058 30.970 21.619 18.310 16.360 14.173 37.265 35.899 31.571 28.925 22.220 19.231 18.025 15.625
36.077 35.429 29.792 27.896 17.120 15.607 14.635 12.940 34.514 33.193 29.062 26.700 19.183 17.502 16.260 14.412
0.917 0.926 0.901 0.901 0.792 0.852 0.895 0.913 0.926 0.925 0.921 0.923 0.863 0.910 0.902 0.922
Absorption coefficients Fitted value
Theoretical value
Errors/%
0.00140
0.000313
346.93
0.00133
0.000313
325.72
0.00164
0.000368
346.45
0.00166
0.000368
349.94
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orifice of 2 mm is regarded as the reference test, which means the A5 amplitude 17.120 kPa is the reference pressure, the ratio 12.940/ 17.120 (equals to 0.756) is the threshold value of the leak detection. Then, the leak location results are analyzed by Equation (17). Meanwhile, in order to minimize the influence of the absorption coefficients and the correction coefficients, the leak location results are analyzed by Equation (18). And when Equation (18) is used, the experiment of Number 1, leakage orifice 2 mm, the test number 1 is chosen as the one in which x0 ¼ 116:8 m, L0 ¼ 140:95 m, p10 =p20 ¼ 0:884. Because the pipeline keeps the same and in the same conditions, though the total distance between the two sensors is changed, the absorption coefficients and the correction coefficients can be regarded as the same. The results can be seen clearly in Table 4. And if the sampling rate is changed, the absorption coefficients and the correction coefficients should be calculated again because the energy dominant frequency band is changed. For example, if the sampling rate is 3000 Hz, the A7 is applied. These may waste time and cause calculation amount. But, the problem can be solved by the method based on the Equation (18) and the test experiment is carried out at 3000 Hz. The results of the leak location experiments at 3000 Hz can be seen clearly in Table 5 when the number 1 experiment is regarded as the test experiment. In Table 4, the errors equals to the ratio of the calculated distance between the leakage point and the starting end sensor minus the actual distance to the total distance between two sensors. It can be known that the leak detection and location method based on the propagation model is effective. The leakages are all detected. The
243
location errors generated by Equation (17) are 0.026%~2.580% and the ones generated by Equation (18) are 0.464%~2.559%. In Table 5, the number 1 experiment is set as the test experiment. The errors get larger when the total distance between two sensors gets longer. So in order to reduce the errors, when the distance between two sensors is changed, the test experiment of the changed distance should be carried out again. This means when the distance of the pipeline between two sensors keeps fixed, the errors are small. And comparing the errors in Table 4 with Table 5, it can be concluded that generally the ones are smaller at 3000 Hz than the ones at 1000 Hz. For the method based on the Equation (17), the errors result from the measurement of the distance between the two sensors, the extraction of the amplitude in some frequency band, and the calculation of the absorption coefficients and the correction coefficients. The reasons mainly come from the following aspects: (1) The precision of the distance lead to the errors. Because there are the elbows in the test section, the precise actual distance and total distance can not be measured. Then the errors of the measured distance also contribute to the errors of L in Equation (17). In a word, the actual distance, total distance and the calculated distance using L result in the errors. (2) Then the remaining reasons come from the calculated distance. 1) The measurement of the original signals a) The acoustic sensors which are used to measure the acoustic waves have inaccuracy.
Table 4 Leak detection and location results calculated by Equations (17) and (18) for water pipelines at 1000 Hz. Number Leakage Test Sampling p1 /kPa p1 =pA0 p2 /kPa p2 =pA0 Leak p1 =p2 Distance orifice/mm number Rate/Hz or no between the two end sensors/m
Distance between the leakage point and the starting end sensor/m
Distance calculated by Equation (17)/m
Errors generated by Equation (17)/%
Distance calculated by Equation (18)/m
Errors generated by Equation (18)/%
1
116.8
116.837 113.667 115.191 120.275 116.506 120.436 49.647 51.477 49.139 49.121 52.000 49.916 111.768 109.072 46.926 48.497
0.026 2.223 1.142 2.465 0.209 2.580 0.877 1.582 1.560 1.584 2.284 0.515 0.879 0.461 0.555 0.572
116.809 113.641 115.164 120.245 116.478 120.407 49.640 51.469 49.132 49.114 51.991 49.909 111.762 109.067 46.940 48.510
0.006 2.241 1.161 2.444 0.228 2.559 0.887 1.570 1.569 1.593 2.272 0.525 0.876 0.464 0.546 0.581
2
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
3 4 2 3 4 2
2
3
2
1000
14.954 14.673 25.337 27.562 40.866 38.163 13.416 16.194 28.537 31.465 45.370 43.587 16.101 14.785 15.824 16.433
0.873 0.857 1.480 1.610 2.387 2.229 0.784 0.946 1.667 1.838 2.650 2.546 0.940 0.864 0.924 0.960
16.916 16.460 28.537 31.465 46.189 43.587 13.867 16.820 29.456 32.477 47.189 45.083 16.587 15.121 14.895 15.533
0.988 0.961 1.667 1.838 2.698 2.546 0.810 0.982 1.721 1.897 2.756 2.633 0.969 0.883 0.870 0.907
yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes
0.884 140.95 0.891 0.888 0.876 0.885 0.876 0.967 74.45 0.963 0.969 0.969 0.961 0.967 0.971 201.2 0.978 1.062 139.3 1.058
50.3
110 47.7
Table 5 Leak location results calculated by Equation (18) for water pipelines at 3000 Hz. Number
Leakage orifice/mm
p1 /kPa
p2 /kPa
p1 =p2
Distance between the two end sensors/m
1 2 3 4 5 6 7 8 9 10
2
10.773 7.859 6.593 8.461 6.852 5.398 5.075 6.213 5.985 5.467
1.988 1.584 1.273 1.662 1.260 8.292 8.841 9.112 9.022 8.885
5.419 4.961 5.180 5.090 5.439 0.651 0.574 0.682 0.663 0.615
139.3
201.2
Distance between the leakage point and the starting end sensor/m 47.7
110
Distance calculated by Equation (18)/m
Errors generated by Equation (18)/%
47.696 48.842 48.283 48.509 47.649 106.176 107.809 105.574 105.931 106.908
0.003 0.820 0.419 0.581 0.037 1.901 1.089 2.200 2.022 1.537
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b) The operations of the experiments, especially the leakage occurring operations may cause the fluctuations of the data. Because the actual leakages occur abruptly, the leakage occurring operation may have minor differences, which lead to the minor differences in the waveform and amplitude. Though the operations are accomplished as well as possible, there exist errors. c) The sampling rate is related to the precision of the amplitude of the measured signals. When the sampling rate is larger, the amplitude of the original acoustic waves measured by the sensors are more accurate, which can contribute to the more accurate amplitude of the one in the energy dominant frequency band. The higher the sampling rate is, the preciser the amplitude is. But because there is limitation to the computer storage room, the sampling rate should be set appropriately. 2) The extraction of the amplitude from the measured signals by the applied wavelet transform method leads to the errors. a) The scale of the wavelet transform method decides the frequency band and the amplitude in the subband. In fact, when the larger scale is applied, the frequency band is smaller and the amplitude in the band is smaller, which means when the distance of the two sensors are long enough, the larger scale can be applied. b) The scale influences the waveform, especially the leakage occurring time judgment. The amplitude actually is the one at the leakage occurring time, which is the largest one of the signal. When the scale gets too large, the waveform of the signal gets smooth, which contribute to the inaccuracy of the leakage occurring time and the corresponding amplitude. Therefore, the scale should not be set too high. Generally, the scale should be set to make the frequency band locate in 0e20 Hz. To solve the problem, the signal-processing method should be improved. 3) The calculation of the absorption coefficients a) The parameters which are used to calculate the absorption coefficients are assigned as the mean value of the total length of the pipeline. In order to reduce the errors, the more pressure and temperature sensors are necessary. b) When the total distance between the two sensors is changed, the absorption coefficients and the correction coefficients are changed more or less while in table they are regarded as the same. c) When the theoretical damping absorption coefficients are calculated, the velocity of the fluid is neglected. And the interaction between the damping absorption coefficients and the fluid is the main research object in the future. 4) The fitting of correction coefficients a) As analyses above, it can be known that the theoretical calculation of the absorption coefficients has errors itself. And the experimental data have fluctuations which lead to errors in experiments also. So the calculation of correction coefficients may generate errors. b) Not only the errors are generated in the experiments, but also in the fitting procedure of the experimental data using curve-fitting method. c) The fitting of correction coefficients can minimize the errors generated by the absorption coefficients. To reduce the errors, the method based on the Equation (18) is applied to minimize the influences of calculations of the absorption coefficients and the correction coefficients. But the consequences show that it is not obvious that the errors are getting smaller. This is because the correction coefficients minimize the influence of the absorption coefficients to a certain
degree. And the errors come from other aspects as shown above. Therefore, in order to reduce the errors, the operations should be controlled under the same conditions as possible; then the acoustic sensors and the wavelet method should be improved; and the sampling rate should be set as high as possible, but the higher sampling rate may lead to more data, so the sampling rate can be set to some appropriate value. Though the errors exist, the method based on the Equations (17) and (18) can be able to detect and locate the leakages without the consideration of the velocity and the time difference of the acoustic waves. In a word, the leak detection and location method based on the propagation model can be applied to the water pipelines effectively. 4.2. Research on the leak detection and location for gas pipelines Due to the density of the fluid, the attenuation is more severe in the gas than in the water. According to the facts in section 4.1, the information in frequency band of 0e3 Hz is extracted from the data measured in the gas pipelines, which attenuates little. The leakage acoustic signals at sampling rate of 3000 Hz are processed by the improved wavelet algorithm. With the scale of 9, the sym8 of wavelet basis is applied. The subband frequency range is shown in Table 6. From Table 6, A9 is incorporated in the frequency band of 0e3 Hz. So A9 subband can be applied to conclude the damping absorption coefficients. And when the sampling rate is 1000 Hz, A8 (0e1.95313 Hz) subband is applied. The Equations (15) and (16) are applied to calculate the damping absorption coefficients. And the damping absorption coefficients are calculated by the fitted curves when the sampling rate is 3000 Hz. The theoretical and fitted damping absorption coefficients can be seen clearly in Table 7. From Table 7, it can be known that the fitted and the theoretical values of the absorption coefficients get less as the pressure levels get higher. A9 can be extracted from the leakage acoustic signals and it can propagate for a long distance; there are errors between the fitted damping absorption coefficients and the theoretical ones; the errors of A9 are lower than 20%. In order to reduce errors of leak location, the threshold value and the reference pressure are changed with the pressure: the threshold value is set as 0.0782/ 0.1136 (equals to 0.688) and pA0 is set as 0.1136 kPa at 0.40 MPa; the rest are 0.1855/0.2421 (equals to 0.766) and 0.2421 kPa at 0.80 MPa, and 0.3149/0.4275 (equals to 0.737) and 0.4275 kPa at 1.20 MPa. For Equation (18), the experiment of test number 1 of which the errors are 0.000 in Table 8 is always the one that the leakage point is known at different pressure levels. Then the location errors can be obtained by comparative analyses between the other experiments and the chosen test number 1. All leak location results can be seen clearly in Table 8. From Table 8, it can be known that most of the errors are small while some are large, which result from the reasons as discussed in the oil pipeline, especially the inaccuracy of the extracted amplitude. The inaccuracy of the amplitude comes from the inaccuracy of original signals measured by sensors and the limitations of the signal-processing method based on the wavelet transform. And the errors obtained by the Equation (17) are generally larger than the ones obtained by the Equation (18). This is because the method based on Equation (18) minimize the errors which come from the calculation of a and s. To reduce the errors, the better method to extract information in the low frequency band is important. Because the amplitude is very important, the acoustic sensor and the signal-processing method are to study in the future, which are also the key points for the traditional method based on the velocity and the time difference.
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245
Table 6 Frequency range of all sub-bands for wavelet analysis for A9. Sequence number of subbands
A9
D9
D8
D7
D6
D1
Frequency range/Hz
0e2.92969
2.92969e5.85938
5.85938e11.71876
11.71876e23.43752
23.43752e46.87504
750e1500
Table 7 Theoretical and fitted absorption coefficients under different conditions for gas pipelines. Pressure Level/MPa
Distance/m
Amplitude of A9/kPa 0.7 mm
1 mm
Fitted value
Theoretical value
Errors
0.4
0.1 66.4 136.3 202.5 0.1 66.4 136.3 202.5 0.1 66.4 136.3 202.5
0.1136 0.1008 0.0885 0.0782 0.2421 0.2164 0.2027 0.1855 0.4275 0.3851 0.362 0.3149
0.2173 0.2063 0.1951 0.1856 0.3372 0.3183 0.2916 0.2647 0.551 0.5103 0.4699 0.4125
0.00299
0.00353
0.15297
0.00203
0.00249
0.18376
0.00175
0.00202
0.13323
0.8
1.2
Absorption coefficients
Table 8 Leak location results under different conditions of gas pipelines. Pressure/ Leakage Test Distance between p1 /kPa p2 /kPa pA0 /kPa p1 =pA0 p2 =pA0 Threshold yes p1 =p2 MPa orifice/mm number the leakage point value or no and the starting end sensor/m
Distance calculated by Equation (17)/m
Errors generated by Equation (17)/%
Distance calculated by Equation (18)/m
Errors generated by Equation (18)/%
0.45
42.080 88.144 126.558 41.358 87.422 125.836 40.867 86.021 124.889 42.511 87.417 124.829 41.354 86.756 124.504 40.718 87.885 127.219
1.351 0.063 1.243 0.821 0.593 1.772 0.461 1.622 2.468 1.668 0.597 2.512 0.818 1.082 2.750 0.351 0.253 0.757
40.240 89.561 130.691 39.467 88.788 129.919 40.240 88.742 130.936 38.625 90.351 130.869 40.240 87.533 126.854 39.577 88.709 129.682
0.000 0.977 1.792 0.567 0.410 1.225 0.000 0.376 1.972 1.186 1.557 1.923 0.000 0.512 1.025 0.487 0.352 1.051
0.70
1.00
0.85
0.70
1.00
1.25
0.70
1.00
1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6
40.24 88.23 128.25 40.24 88.23 128.25 40.24 88.23 128.25 40.24 88.23 128.25 40.24 88.23 128.25 40.24 88.23 128.25
0.103 0.090 0.080 0.195 0.170 0.152 0.224 0.205 0.190 0.313 0.285 0.263 0.400 0.369 0.345 0.514 0.473 0.442
0.088 0.101 0.113 0.167 0.191 0.214 0.201 0.220 0.236 0.282 0.308 0.329 0.364 0.393 0.420 0.467 0.507 0.544
0.114
0.242
0.428
0.907 0.790 0.704 1.720 1.499 1.336 0.926 0.845 0.783 1.294 1.178 1.088 0.935 0.862 0.806 1.203 1.107 1.034
For application in field, when the operation pressure level is fixed which means the average value keeps constant, the method can be used well; when the operation pressure level is changed because of the relation between supply and demand of gas flow, the method can be adjusted to that pressure level. And as the test data base is enlarged by the operation signals, the method can be more and more accurate. So the proposed leak detection and location method without the calculations of a and s can still be used effectively, which can be combined with the method with the calculations of a and s. Therefore, the proposed leak detection and location method has advantages over the traditional one based on the velocity and the time difference, as nowadays acoustic sensors and signal processing method are both used for the two methods. The propagation law can help accomplish leak detection and location under different leakage orifices and the errors are small.
0.776 0.891 0.999 1.466 1.682 1.887 0.829 0.909 0.977 1.167 1.274 1.358 0.851 0.920 0.982 1.093 1.187 1.271
0.688
0.766
0.737
yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes
1.168 0.887 0.705 1.173 0.891 0.708 1.117 0.930 0.801 1.109 0.925 0.802 1.098 0.937 0.821 1.101 0.933 0.813
5. Conclusions The following conclusions can be drawn by researches on the new leak detection and location method based on the propagation law of leakage acoustic waves in oil and gas pipeline. (1) The information can be extracted by wavelet transform analysis from the leakage acoustic signals. Even after propagating for a long distance, acoustic characteristics can be obtained. (2) The propagation law of amplitude is obtained in the chosen frequency band with distance in actual pipeline. And the fitted absorption coefficient can be obtained based on experimental data. The theoretical absorption coefficient can be calculated.
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(3) The new leak location method based on the propagation model is proposed and then improved. The fundamental, steps and equations for both two new methods are concluded. (4) Though the errors exist, the two methods based on the propagation model including the Equations (17) and (18) can be able to detect and locate the leakages for the water pipelines effectively without the consideration of the velocity and the time difference of the acoustic waves. (5) The two methods based on the propagation model which means the Equations (17) and (18) can detect and locate the leakages in gas pipeline. The merits of the methods are concluded. Acknowledgments This paper was funded by the National Science Foundation of China (51104175), the Fundamental Research Funds for the Central Universities (14CX06135A) and (15CX06069A) and the Graduate Innovation Foundation of China University of Petroleum (YCX2014062). Thanks for the permission to publish this paper. References Brennan, M.J., Gao, Y., Joseph, P.F., 2007. On the relationship between time and frequency domain methods in time delay estimation for leak detection in water distribution pipes. J. Sound Vib. 304, 213e223. Gao, Y., Brennan, M.J., Joseph, P.F., et al., 2004. A model of the correlation function of leak noise in buried plastic pipes. J. Sound Vib. 277, 133e148.
He, L., Zhu, H.C., Qiu, X.J., et al., 2006. The Acoustics Theory and Engineering Application Books. Science Press, Beijing. Hunaidi, O., Chu, W.T., 1999. Acoustical characteristics of leak signals in plastic water distribution pipes. Appl. Acoust. 58 (3), 235e254. Jin, H., Zhang, L.B., Liang, W., et al., 2014. Integrated leakage detection and localization model for gas pipelines based on the acoustic wave method. J. Loss Prev. Process Ind. 27, 74e88. Kajiro, Watanabe, Shun, Matsukawa, Hitoshi, Yukawa, et al., 1986. Detection and location of a leak in a gas-transport pipeline by a new acoustic method. AIChE J. 32 (10), 1690e1702. , Vendramin, Giuseppe, Trotta, Amerigo, 2009. Spectral analysis Lay-Ekuakille, Aime of leak detection in a zigzag pipeline: a filter diagonalization method-based algorithm application. Measurement 42, 358e367. Li, Y.X., Tang, J.F., Wang, W.C., et al., 2010. Design and construction of an experimental device for acoustic leak detection in gas pipelines. Exp. Technol. Manage. 27 (8), 63e67. Liu, J.X., Li, T.Y., Liu, T.G., et al., 2003. The attenuation characteristics of waves in fluid-filled pipes surrounded by elastic media. J. Huazhong Univ. Sci. Technol. Nat. Sci. Ed. 31 (10), 90e92. Liu, C.W., Li, Y.X., Meng, L.Y., et al., 2014. Study on leak-acoustics generation mechanism for natural gas pipelines. J. Loss Prev. Process Ind. 32, 174e181. Ma, D.Y., 2004. Theoretical Basis of Modern Acoustics Books. Science Press, Beijing. Meng, L.Y., Li, Y.X., Wang, W.C., et al., 2012. Experimental study on leak detection and location for gas pipeline based on acoustic method. J. Loss Prev. Process Ind. 25, 90e102. Muggleton, J.M., Brennan, M.J., Pinnington, R.J., 2002. Wave number prediction of waves in buried pipes for water leak detection. J. Sound Vib. 249 (5), 939e954. Murvay, Pal-Stefan, Silea, Ioan, 2012. A survey on gas leak detection and localization techniques. J. Loss Prev. Process Ind. 25 (6), 966e973. Sun, L., 2012. Mathematical modeling of the flow in a pipeline with a leak. Math. Comput. Simul. 82, 2253e2267. Sun, X.F., Zhou, S., 1994. Aero-acoustics Books. National Defense Industry Press, Beijing. Xu, X.M., 2003. Acoustic Foundation Books. Science Press, Beijing. Zhou, A.G., Ruan, J.Y., Liu, K., 2009. Analysis and strategy for impacts on ultrasonic flow meters. Chin. J. Constr. Mach. 7 (4), 469e473.
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Journal of Loss Prevention in the Process Industries journal homepage: www.elsevier.com/locate/jlp
A new leak location method based on leakage acoustic waves for oil and gas pipelines Cui-wei Liu a, c, d, Yu-xing Li a, c, d, *, Yu-kun Yan a, c, d, Jun-tao Fu b, Yu-qian Zhang a, c, d a
College of Pipeline and Civil Engineering in China University of Petroleum (East China), Qingdao 266580, China Sinopec Qingdao LNG Co.,Ltd, Qingdao 266400, China c Key Laboratory of Qingdao Oil and Gas Storage and Transportation Technologies, China d Key Laboratory of CNPC Heavy Gas Transportation and LNG Technologies, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 November 2014 Received in revised form 15 April 2015 Accepted 2 May 2015 Available online 4 May 2015
In order to study a new leak detection and location method for oil and natural gas pipelines based on acoustic waves, the propagation model is established and modified. Firstly, the propagation law in theory is obtained by analyzing the damping impact factors which cause the attenuation. Then, the dominantenergy frequency bands of leakage acoustic waves are obtained through experiments by wavelet transform analysis. Thirdly, the actual propagation model is modified by the correction factor based on the dominant-energy frequency bands. Then a new leak detection and location method is proposed based on the propagation law which is validated by the experiments for oil pipelines. Finally, the conclusions and the method are applied to the gas pipelines in experiments. The results indicate: the modified propagation model can be established by the experimental method; the new leak location method is effective and can be applied to both oil and gas pipelines and it has advantages over the traditional location method based on the velocity and the time difference. Conclusions can be drawn that the new leak detection and location method can effectively and accurately detect and locate the leakages in oil and natural gas pipelines. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Oil and gas pipelines Leakage acoustic wave Propagation model Experimental study Leak location
1. Introduction Nowadays, many leak detection and location methods (Murvay et al., 2012; Lay-Ekuakille et al., 2009; Kajiro et al., 1986; Sun, 2012) have been developed for oil and gas pipeline, such as methods based on mass/volume balance, negative pressure wave, transient model, distributed optical fiber and acoustic waves, etc. Among them the acoustic method is superior to the traditional ones: higher sensitivity, higher location accuracy, lower false alarm rate, shorter testing time and greater adaptability. The fundamental of the traditional acoustic leak detection and location method is: when leakage occurs, the acoustic waves are generated. They propagate to upstream and downstream which are captured by the acoustic sensors. And the arriving time at the upstream sensor is different from the one at the downstream sensor. Then based on the velocity and the time difference, the leakages are detected and located. The acoustic method has so many advantages, and it has been researched a lot. * Corresponding author. College of Pipeline and Civil Engineering in China University of Petroleum (East China), Qingdao 266580, China. E-mail addresses: [email protected] (C.-w. Liu), [email protected] (Y.-x. Li). http://dx.doi.org/10.1016/j.jlp.2015.05.006 0950-4230/© 2015 Elsevier Ltd. All rights reserved.
Gao et al. (2004) developed an analytical model to predict the cross correlation function of leak signals in plastic water pipes, which can be used to calculate the time difference and improve leak location accuracy. Brennan et al. (2007) presented a new interpretation of the process of cross-correlation for time delay estimation. Results showed that the time delay estimations and their variances calculation using time and frequency domain methods are almost identical. Meng et al. (2012) established a formula for gas pipelines leak location, which is modified with consideration of the influences of temperature and pressure. As a result, the location accuracy can be significantly improved with relative errors between 0.01% and 1.37%. Jin et al. (2014) proposed an integrated leakage detection and localization model for gas pipelines. Given that the spread velocity of acoustic waves in pipelines is related to the properties of the medium, such as pressure, density, specific heat, and so on, the paper proposed a modified acoustic velocity and location formula. At present, most of the acoustic method researches are carried out to improve the calculation accuracy of the acoustic velocity and the time difference, especially for long distance pipelines, while the velocity are difficult to confirm, especially for gas pipelines. And if the method is applied to field or long distance pipelines, the time
C.-w. Liu et al. / Journal of Loss Prevention in the Process Industries 35 (2015) 236e246
difference calculation needs GPS (Global Position System) clock to label data to keep the time simultaneity of the measured signals. The accuracy of the velocity and the time difference restricts the application of the acoustic leak detection and location method. Meanwhile, a group of scholars conducted researches on the propagation characteristics of acoustic waves. Hunaidi and Chu (1999) carried out experiments in plastic water pipes, of which the results show that the amplitude of signals attenuates with the propagation distance at the speed of 0.25 dB/m, and the propagation velocity of signals whose frequency is lower than 50 Hz is independent of frequency, and that acoustic signals propagate faster by 7% in winter than in summer. Muggleton et al. (2002) analyzed the mechanism of propagation behavior of sound and vibration waves caused by leakages of fluid-filled round pipeline. They established the propagation model of signals and also analyzed the change and the attenuation characteristics of the acoustic signals. Liu et al. (2003) studied the attenuation characteristics of the wave of fluid-filled pipeline and the results show that longitudinal wave attenuates slower in pipeline. They also compared the propagation characteristics of waves in different pipe wall materials and came to a conclusion that waves in steel tube attenuate slower than them in PVC pipe. Domestic and international scholars have carried out researches on the propagation characteristics of acoustic waves for leak detection and location. Then the location method is proposed which is based on the propagation model and takes no account of the velocity and the time difference. Therefore, a new leak location method is necessary to study based on the propagation characteristics of leakage acoustic waves for oil and gas pipelines. 2. Preparation for the experiments
sensors, m; c is the propagation velocity of acoustic waves in the fluid, m/s; Dt is the time difference, s. Therefore, the exact arrival time of the acoustic signals at each monitor and the propagation velocity are critical for locating the leakages accurately. Especially the simultaneity of the two measured signals must be ensured for long distance pipelines. When the acoustic leak detection and location method is applied to field, firstly the measured signals should be time-granted by GPS clocks; and then the two signals are processed by the crosscorrelation analysis to obtain the time difference. The time difference is related to the peaks of the two signals. The cross-correlation analysis is defined as follows:
1 r12 ðtÞ ¼ M
M=2 Z
q1 ðtÞq2 ðt þ tÞdt
When leakage occurs, acoustic sensors installed at both ends of the pipeline measure the acoustic waves to determine whether a leak happens or not. This can be seen clearly in Fig. 1. Meanwhile, the system can locate the leakage based on the acoustic propagation velocity and the arrival time of acoustic signals at two adjacent acoustic sensors. The algorithm for the acoustic leak location is shown as follows:
(1)
where, x is the distance between leakage point and upstream sensor, m; L is the distance between upstream and downstream
where, M is the period that acoustic wave spreads between the two adjacent sensors, M ¼ L=c, t2ðM=2; M=2Þ. Theoretically, once leakage occurs, when t ¼ t0 , r12 ðtÞ will reach the maximum value which is expressed as below:
r12 ðt0 Þ ¼ maxr12 ðtÞ
(3)
By calculating the maximum value of r12 ðtÞ, the time difference t0 is calculated. The propagation velocity of acoustic waves along the oil pipeline can be expressed as:
(4)
d E0
where, D is the inside diameter, mm; d is the thickness of pipe wall, mm; E is the bulk modulus, Pa; E0 is the Young's modulus, Pa; r is the density, kg/m3. In gas pipelines, it can be assumed that the propagation process of acoustic waves is thermal isolation and E can be defined as E ¼ kv p. So combined with gas state equation, Equation (4) can be expressed as:
sffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi kv p 1 1 $qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ kv zRT $qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c¼ r kv p D 1þ 1 þ D kv p d E0
Fig. 1. Schematic diagram of acoustic leak detection system.
(2)
M=2
sffiffiffi E 1 $qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c¼ r 1þD E
2.1. Traditional leak detection and location method
x ¼ ðL þ cDtÞ=2
237
(5)
d E0
where, kv is the isentropic volume change exponent; p is the pressure of natural gas, Pa; R is the gas constant, kJ=ðkg,KÞ; T is the temperature, K; z is the compressibility factor. From analyses above, it can be known that the traditional method needs accurate calculations of the velocity and the time difference. The method to calculate the time difference costs much and wastes time, such as GPS clock and cross-correlation analysis. For oil and gas pipelines, the velocity equations are different, which means the traditional method should be adjusted to different conditions. The new proposed method based on the propagation model cares little about the velocity and the time difference, which cares only about the amplitude of the acoustic waves. In traditional method, the amplitude of the acoustic waves is used to calculate the time difference by the cross-correlation analysis, while it is used directly to locate the leakages in the new proposed method.
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2.2. New leak detection and location method based on propagation model of acoustic waves 2.2.1. Theoretical propagation model of acoustic waves in the pipeline Firstly, the basic equations of acoustic waves can be established based on some assumptions. Then the equations can be modified according to the actual working conditions. Assumptions are described as follows (He et al., 2006): (1) The media is the ideal fluid. Therefore the effect of heat conduction and the viscosity on the propagation can be ignored. (2) During the propagation process, acoustic waves can lead to condensation and expansion of the media, which is considered to be an adiabatic process. Therefore, the heat exchange between neighboring sections can also be ignored. (3) Acoustic waves propagate through the media with small amplitude and each acoustics-quantity is the first-order trace. Based on the assumptions above, according to the difference of wave front of acoustic waves in the pipelines, the leakage acoustic waves in the cylindrical pipe are the plane waves and the equation of the plane wave is one-dimensional, which can be illustrated as follows (Xu, 2003):
pðx; tÞ ¼ pa ejðutkxÞ
(6)
Where, pa is the amplitude of the acoustic waves, Pa; u is angular frequency, u ¼ 2pf , f is the frequency of acoustic wave, Hz; x is the propagation distance, m; k ¼ u=c0 is the wave number of undamped waves. So, the propagation model of acoustic waves in the fluid pipelines can be described as Equation (6). 2.2.2. Actual propagation model of acoustic waves in the pipeline When acoustic waves propagate in non-ideal medium, a dissipative process turning acoustic energy into heat energy will occur, which leads to the attenuation of acoustic waves. In actual oil and gas pipelines, damping effect should be taken into account as the pipeline is long. So the propagation equation of acoustic waves in the damping medium (Ma, 2004; Sun et al., 1994) can be derived from the basic equations of acoustic waves as damping effects (including viscous absorption and heat conduction) are considered. In the first instance, the heat conduction is neglected and the viscous absorption is considered, the wave equation is described as:
r0
v2 p v2 p v3 p ¼ Ks 2 þ h 2 vt 2 vx vx vt
(7)
00
where, h ¼ 4=3h0 þ h , Ks ¼ a20 r0 , and Ks is called adiabatic bulk modulus of elasticity. For one-dimensional plane wave, the solution to the Equation (7) is:
pðx; tÞ ¼ p0 ðx; tÞejut
(8)
Substituting (8) in (7), yields
r0 u2
v2 p0 v2 p ¼ ðKs þ juhÞ 20 2 vt vx
(9)
Then substituting K ¼ Ks þ juh in (9), yields
r0 u2
v2 p0 v2 p0 v2 p v2 p0 ¼K or k02 20 ¼ vt 2 vx2 vt vx2
(10)
pffiffiffiffiffiffiffiffiffiffiffi where, k0 ¼ u r0 =K , and because K is the complex number, k0 is also the complex number. It is assumed that k0 ¼ u=c0 jah . Thus the solution to the Equation (7) becomes: 0
pðx; tÞ ¼ p0 ejðutk xÞ
(11)
and
pðx; tÞ ¼ p0 e
ah x
ju txc
e
¼ p0 eah x ejðutkxÞ
(12)
In the Equation (12), Reðk0 Þ ¼ u=c0 , which is called the wave number; Imðk0 Þ ¼ ah , which is called viscous absorption coefficient and it represents the amplitude attenuation speed. Comparing Equation (12) with Equation (6), it can be concluded that the two equations have the same form. Then the heat conduction effect is taken into account, the equation with the viscothermal absorption coefficient can be obtained:
p ¼ p0 eax ejðutk0 xÞ
(13)
In Equation (13), a is the damping absorption coefficient of medium which describes the attenuation speed of the amplitude with the distance, a ¼ u2 b=2r0 c30 ; r0 is the density of medium, kg/ m3; c0 is the propagation speed of acoustic wave, m/s; x is the propagation distance, m; k0 ¼ u=c0 is the wave number of undamped waves. Equation (13) describes an acoustic wave which transmits to the positive direction of x with speed of c0 and angular frequency of u, and its amplitude is pa ¼ p0 eax . Therefore, comparing the Equation (13) with (6), the amplitude attenuation of acoustic waves with the distance can be described by Equation (14):
p ¼ p0 eax
(14)
In this equation, p0 is the amplitude of acoustic waves, Pa, which can be seen clearly in Fig. 2. It can be seen that the amplitude attenuation law follows the exponential curve with propagation distance. Considering the viscous absorption and heat conduction (Zhou et al., 2009) of the medium, the equation of damping absorption coefficient a can be obtained:
a ¼ ah0 þ ah00
1 þ ac ¼ rc0
sffiffiffiffiffiffiffiffi 00 h0 u u2 u2 1 1 ,h þ ,c þ 2r0 2r0 c30 Cv Cp 2r0 c30 (15)
As a result, the amplitude and the longest propagation distance of acoustic waves after attenuating can be calculated if all the following parameters of the pipelines are known: u is angular frequency, u ¼ 2pf , f is the frequency of acoustic wave, Hz; r is the inner radius of pipeline, m; r0 is the density of medium, kg/m3; c0 is the speed of acoustic wave in the pipeline, m/s; h0 is the shear 00 viscous coefficient of medium, Pa,s; h is the volume-change viscous coefficient of medium, Pa,s; c is the heat transfer coefficient, W=ðm,KÞ; Cv is the constant-volume specific heat and Cp is the constant-pressure specific heat, kJ=ðkg,KÞ. These can be verified by experiments.
2.2.3. New leak detection and location method based on propagation model of acoustic waves The high-frequency component of acoustic signal attenuates quickly, while the low-frequency component can propagate for a long distance. Therefore, the wavelet transform method is applied to extract the dominant-energy low-frequency band from the original measured signals, which can be seen in section 4.1. The
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Fig. 2. Amplitude of the acoustic waves.
damping absorption coefficient can be calculated by the Equation (15), of which the parameters need accurate values. Because the parameters are assigned by the mean values which will lead to errors, the theoretical damping absorption coefficient should be corrected by the fitted damping absorption coefficient in experimental results. In order to solve the problem, the Equation (15) can be modified as:
pA ¼ pA0 esax
(16)
In Equation (16), s is the correction coefficient and it can be 3e4 for water pipelines and 0.5e1.5 for gas pipelines after comparative analyses between the theoretical damping absorption coefficients and the fitted ones, which can be seen in section 4.1.1 and 4.2. Then a new method based on the Equation (16) is proposed. To make the method based on the propagation method clear, when a pipeline section is chosen to be monitored by the method, the steps of the method are shown as follows: (1) All the parameters about the monitored pipeline should be made clear and a is calculated by Equation (15); (2) The smallest detection capacity of leakage rate or orifice should be confirmed; (3) The test experiment with the smallest leakage orifice is carried out and the leakage occurs at one end of the pipeline, the acoustic waves are measured in the same end and the other end; (4) The sub-band amplitude of the two measured signals is obtained by the wavelet transform which equals to pA0 and pA , s is obtained and the ratio of the smaller amplitude to the lager one (pA =pA0 ) is set as the threshold value of the leak detection, and the sub-band amplitude measured in the same end which means the larger one, pA0 is regarded as the reference pressure which can be fixed to make leak detection; if the smallest leakage orifice is changed, the reference pressure should be altered; (5) When the sub-band amplitude of the two measured signals are p1 , p2 , if p1 =pA0 pA =pA0 or p2 =pA0 pA =pA0 is satisfied, the leak is detected; (6) And the leak is located through the following equations:
p1 ¼ p0 esax ; p2 ¼ p0 esaðLxÞ ;
p1 L lnðp1 =p2 Þ ¼ esaðL2xÞ ; x ¼ 2 2sa p2 (17)
In Equation (17), p0 is the sub-band amplitude of the leakage acoustic waves at the leakage point which is not necessary to measure; the distance between the leakage point and the upstream sensor is x; the total length of the chosen pipeline is L; the condition keeps the same, s,a can be regarded as fixed. In the calculation procedure of a, because the parameters in Equation (15) are not constant, the mean value of each parameter of the pipeline is applied, which will lead to errors. But the calculation of s through experiments can minimize the errors to confirm to the results of actual situations. And once the pipeline is chosen, the values of a and s can be calculated, and they can be fixed. Compared with the location method based on the time difference, the proposed method is simpler and more accurate. Though the calculation of a leads to the errors, the errors can be minimized by the calculation of s and their errors are so small. During the research, it was found that the calculations of a and s are not even necessary. The steps are shown as follows: (1) A pipeline section is chosen and the smallest detection capacity of leakage rate or orifice should be confirmed; (2) The test experiment with the smallest leakage orifice is carried out and the leakage occurs at one end of the pipeline, the acoustic waves are measured in the same end and the other end; the sub-band amplitude of the two measured signals is obtained by the wavelet transform which equals to pA0 and pA , the ratio of the smaller amplitude to the lager one ðpA =pA0 Þ is set as the threshold value of the leak detection, and the sub-band amplitude measured in the same end which means the larger one, pA0 is regarded as the reference pressure; (3) The test experiment with the smallest leakage orifice is carried out and the leakage occurs at one point in the pipeline; the distance between the chosen point and the starting end is known as x0 ; the acoustic waves are measured in two ends; the subband amplitude of the two measured signals is obtained by the wavelet transform which equals to p10 and p20 ; (4) If p1n =pA0 pA =pA0 or p2n =pA0 pA =pA0 is satisfied, the leak is detected; (5) According to Equation (17), lnðp10 =p20 Þ=ð2saÞ ¼ L=2 x0 is obtained, then the following equation is obtained:
Ln =2 xn lnðp1n =p2n Þ ¼ L0 =2 x0 lnðp10 =p20 Þ and the leakage point xn can be calculated.
(18)
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It can be seen the proposed leak detection and location method without the calculations of a and s can still be used effectively, which can be the second choice after the method with the calculations of a and s. Therefore, the proposed leak detection and location method has advantages over the traditional one based on the velocity and the time difference. The propagation law can help accomplish leak detection and location under different leakage orifices and the errors are small. In order to verify the leak detection and location method based on the propagation model, the experiments are carried out. To ensure the new method can be applied to both oil pipelines and gas pipelines, experiments of oil are firstly accomplished and then the experiments of gas pipelines are carried out.
compressor is the gas source. Water and oil droplets in the gas are removed. From a high-pressure surge tank, the gas enters into the test section, goes into the terminal surge tank and finally is discharged into the environment. For water pipelines, the spherical valve 1 and 4 should be closed and the spherical valve 2 and 3 should be opened. The water in the tank is forced by the pump and transported in the pipeline. Then the water goes back to the tank. The flow is controlled around 10 m3/h by the cutoff valve. The length of the test section is 205.0 m. There are some leakage points in the pipeline test section. Data acquisition programs have been written to measure and process the acoustic signals. The measurement range of the dynamic pressure sensor is 0e57.3 kPa, the sensitivity is 43.5 mV/kPa and the low frequency response is 0.5 Hz.
3. Experimental
3.1. Experiments for water pipelines
A pipeline loop (Li et al., 2010;Liu et al., 2014) for leak detection and location is designed and established after its similarity analysis with field transportation pipelines as shown in Fig. 3 and Fig. 4, of which the fluid can be gas or oil. In experiments, the natural gas can be replaced by the air and the oil can be replaced by the water. The leak flow rate is controlled by valve and orifice. The dynamic pressure sensors are installed 10 cm away from the leakage points. For gas pipelines, the highest permitted pressure is 2.5 MPa. The length of the test section is 203.0 m. The compressed air from the
To calculate a and s in the modified model, the experiments are carried out by two parts. Firstly, when the flow meter is 10.5 m3/h, the leakages occur with the orifices of 2 mm and 3 mm. The distance between the leakage point and the sensors are 0.1 m, 66.4 m, 136.3 m and 202.5 m. Then when the flow meter is 9.5 m3/h, the leakages occur with the orifices of 2 mm and 3 mm. The distance between the leakage point and the sensors are 0.1 m, 25.4 m, 91.6 m and 160.3 m. The sampling rate is 1000 Hz. For the verification of the new proposed method, the
Fig. 3. Structure chart of experimental pipe facility.
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241
Fig. 4. Pipeline leak detection test loop.
experiments are carried out by three parts, and each part is repeated twice which can be seen in Table 1. The flow meter is controlled around 10 m3/h and the sampling rate is 1000 Hz.
3.2. Experiments for gas pipelines To calculate a and s in the modified model, data are obtained when leakage point 1 leaks. The distances between the leakage point and the acoustic sensors are 0.1 m, 66.4 m, 136.3 m and 202.5 m. The operating pressure is 0.4 MPa, 0.8 MPa and 1.2 MPa. The leakage orifice is 0.10 mm, 0.50 mm, 0.70 mm and 1.00 mm. The sampling rate is 3000 Hz. For the verification of the new proposed method, the location experiments are carried out. The distance between the two sensors is 136.2 m, the leakage points are 40.24 m, 88.23 m and 128.25 m from the starting end sensor. The operating pressure is 0.45 MPa, 0.85 MPa and 1.25 MPa. The leakage orifice is 0.10 mm, 0.50 mm, 0.70 mm and 1.00 mm. The sampling rate is 3000 Hz.
Table 1 The leak location experiments for water pipelines. Number
Leakage orifice/mm
Test number
Distance between the two end sensors/m
Distance between the leakage point and the starting end sensor/m
1
2
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
140.95
116.8
74.45
50.3
3 4 2 3 4 2
2
3
2
201.2 139.3
110 47.7
4. Results and discussions 4.1. Research on the leak detection and location for oil pipelines After the experiments, the results of the leak location for oil pipelines are firstly accomplished, and then the location errors for gas pipelines are calculated. The theoretical damping absorption coefficient can be calculated by Equation (15). After the correction coefficient is concluded, the leak location errors can be obtained by Equation (17). Finally, the leak location errors without consideration of damping absorption coefficient and correction coefficient can be obtained by Equation (18).
4.1.1. Characteristics extracted by wavelet transform method for oil pipelines After the frequency-domain analyses, it can be found that the energy of the acoustic waves generated by leakages in oil pipelines concentrates on the frequency band of 0e20 Hz. In order to extract characteristics which can propagate for a long distance and to establish the propagation model for long distance oil pipelines, the leakage acoustic signals at sampling rate of 1000 Hz are processed by the improved wavelet algorithm. With the scale of 5, the sym8 of wavelet basis is applied to extract the information in frequency band of 0e20 Hz, which attenuates little. The subband frequency range is shown in Table 2. From Table 2, A5 is incorporated in the frequency band of 0e20 Hz. So A5 subband can be applied to conclude the damping absorption coefficient. And when the sampling rate is 3000 Hz, A7 (0e11.71875 Hz) subband is applied. The amplitude of the dominant frequency bands extracted from acoustic signals can be applied to calculate the damping absorption coefficient. The A5 amplitude attenuation law can be drawn as Fig. 5 when the leakage orifice is 2.0 mm. From Fig. 5, it can be known that as the propagation distance gets longer, the amplitude of A5 frequency band decreases. It can be concluded that the fitted curve follows the exponential law. And the damping absorption coefficient is calculated by the fitted curve. After analyses, the fitted damping absorption coefficients are concluded. And the Equations (15) and (16) are applied to calculate
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Table 2 Frequency range of all sub-bands for wavelet analysis for A5. Sequence number of subbands
A5
D5
D4
D3
D2
D1
Frequency range/Hz
0e15.625
15.625e31.25
31.25e62.5
62.5e125
125e250
250e500
values. The mean value of the pressure in the 160.3 m pipeline is larger than the one in the 202.5 m pipeline. In order to reduce the errors, the more pressure and temperature sensors are necessary. (2) When the theoretical damping absorption coefficients are calculated, the velocity of the fluid is neglected. And the interaction between the damping absorption coefficients and the fluid is the main research object in the future. (3) When the damping absorption coefficients are fitted, the amplitude is the one in the frequency band of A5, while when the theoretical ones are calculated, the amplitude is the one of the center frequency of the A5 band. The subband and the amplitude of A5 are determined by the signalprocessing method. And the amplitude is also influenced by the sampling rate. Because when the sampling rate is higher, the leakage time is preciser and the amplitude of the leakage time is preciser. These facts cause errors. To solve the problem, the improved signal-processing method is necessary, which can obtain the narrower sub-band. (4) The theoretical damping absorption coefficients are calculated through straight pipeline, while the fitted ones are obtained by experiments which have elbow pipes, reducing pipes, branch pipes and other obstacles such as metering instrumentations. All these contribute to the damping of acoustic waves. So the theoretical damping absorption coefficients must be amended to reduce errors.
Fig. 5. The fitted curve of experimental data when the leakage orifice is 2.0 mm of Number 1 test.
the coefficients. The temperature is 293.15 K and the fluid flowing in the pipeline is the water. The theoretical damping absorption coefficients can be obtained which can be seen clearly in Table 3 with the fitted ones. From Table 3, it can be known that the percentage of A5 amplitude is more than 80%, which can represent the original signal. And there exist errors between the fitted damping absorption coefficients and the theoretical ones. When the damping absorption coefficients are calculated by the Equation (15), of which the parameters are obtained by experiments. Among them, f equals to the center frequency of the extracted subband which is 7.8125 Hz here; r0 is the one under the average pressure in the pipeline, which equals to the average pressure of the measured ones by the upstream and down stream pressure sensors; c0 can be calculated by Equation (4); 00 h0 ; h ; c; Cv and Cp can be obtained under the average pressure and average temperature which is calculated by the upstream and down stream temperature sensors. When the damping absorption coefficients are fitted by the extracted amplitude from the measured signals, the sampling rate and the signal-processing method decide the results. The reasons for errors are given as follows:
In order to reduce the errors of absorption coefficients, the correction coefficient is proposed in Equation (16) and it can be 3e4 after comparative analyses between the theoretical damping absorption coefficients and the fitted ones for water pipelines in experiments. When it comes to the field, the value is based on the physical truth. 4.1.2. Leak detection and location results for oil pipelines After the calculations of the absorption coefficients and the correction coefficients, the Equation (17) can be used for leak detection and location. The test of number 1 with the leakage
(1) In the calculation procedure of the theoretical damping absorption coefficients, the parameters are set as the mean
Table 3 Theoretical and fitted absorption coefficients under different conditions for water pipelines. Number
1
Leakage orifice/mm
3
2
2
3
2
Distance/m
0.1 66.6 136.8 202.5 0.1 66.6 136.8 202.5 0.1 25.4 91.6 160.3 0.1 25.4 91.6 160.3
Amplitude/kPa
Percentage
Original signal
A5
39.324 38.265 33.058 30.970 21.619 18.310 16.360 14.173 37.265 35.899 31.571 28.925 22.220 19.231 18.025 15.625
36.077 35.429 29.792 27.896 17.120 15.607 14.635 12.940 34.514 33.193 29.062 26.700 19.183 17.502 16.260 14.412
0.917 0.926 0.901 0.901 0.792 0.852 0.895 0.913 0.926 0.925 0.921 0.923 0.863 0.910 0.902 0.922
Absorption coefficients Fitted value
Theoretical value
Errors/%
0.00140
0.000313
346.93
0.00133
0.000313
325.72
0.00164
0.000368
346.45
0.00166
0.000368
349.94
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orifice of 2 mm is regarded as the reference test, which means the A5 amplitude 17.120 kPa is the reference pressure, the ratio 12.940/ 17.120 (equals to 0.756) is the threshold value of the leak detection. Then, the leak location results are analyzed by Equation (17). Meanwhile, in order to minimize the influence of the absorption coefficients and the correction coefficients, the leak location results are analyzed by Equation (18). And when Equation (18) is used, the experiment of Number 1, leakage orifice 2 mm, the test number 1 is chosen as the one in which x0 ¼ 116:8 m, L0 ¼ 140:95 m, p10 =p20 ¼ 0:884. Because the pipeline keeps the same and in the same conditions, though the total distance between the two sensors is changed, the absorption coefficients and the correction coefficients can be regarded as the same. The results can be seen clearly in Table 4. And if the sampling rate is changed, the absorption coefficients and the correction coefficients should be calculated again because the energy dominant frequency band is changed. For example, if the sampling rate is 3000 Hz, the A7 is applied. These may waste time and cause calculation amount. But, the problem can be solved by the method based on the Equation (18) and the test experiment is carried out at 3000 Hz. The results of the leak location experiments at 3000 Hz can be seen clearly in Table 5 when the number 1 experiment is regarded as the test experiment. In Table 4, the errors equals to the ratio of the calculated distance between the leakage point and the starting end sensor minus the actual distance to the total distance between two sensors. It can be known that the leak detection and location method based on the propagation model is effective. The leakages are all detected. The
243
location errors generated by Equation (17) are 0.026%~2.580% and the ones generated by Equation (18) are 0.464%~2.559%. In Table 5, the number 1 experiment is set as the test experiment. The errors get larger when the total distance between two sensors gets longer. So in order to reduce the errors, when the distance between two sensors is changed, the test experiment of the changed distance should be carried out again. This means when the distance of the pipeline between two sensors keeps fixed, the errors are small. And comparing the errors in Table 4 with Table 5, it can be concluded that generally the ones are smaller at 3000 Hz than the ones at 1000 Hz. For the method based on the Equation (17), the errors result from the measurement of the distance between the two sensors, the extraction of the amplitude in some frequency band, and the calculation of the absorption coefficients and the correction coefficients. The reasons mainly come from the following aspects: (1) The precision of the distance lead to the errors. Because there are the elbows in the test section, the precise actual distance and total distance can not be measured. Then the errors of the measured distance also contribute to the errors of L in Equation (17). In a word, the actual distance, total distance and the calculated distance using L result in the errors. (2) Then the remaining reasons come from the calculated distance. 1) The measurement of the original signals a) The acoustic sensors which are used to measure the acoustic waves have inaccuracy.
Table 4 Leak detection and location results calculated by Equations (17) and (18) for water pipelines at 1000 Hz. Number Leakage Test Sampling p1 /kPa p1 =pA0 p2 /kPa p2 =pA0 Leak p1 =p2 Distance orifice/mm number Rate/Hz or no between the two end sensors/m
Distance between the leakage point and the starting end sensor/m
Distance calculated by Equation (17)/m
Errors generated by Equation (17)/%
Distance calculated by Equation (18)/m
Errors generated by Equation (18)/%
1
116.8
116.837 113.667 115.191 120.275 116.506 120.436 49.647 51.477 49.139 49.121 52.000 49.916 111.768 109.072 46.926 48.497
0.026 2.223 1.142 2.465 0.209 2.580 0.877 1.582 1.560 1.584 2.284 0.515 0.879 0.461 0.555 0.572
116.809 113.641 115.164 120.245 116.478 120.407 49.640 51.469 49.132 49.114 51.991 49.909 111.762 109.067 46.940 48.510
0.006 2.241 1.161 2.444 0.228 2.559 0.887 1.570 1.569 1.593 2.272 0.525 0.876 0.464 0.546 0.581
2
1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
3 4 2 3 4 2
2
3
2
1000
14.954 14.673 25.337 27.562 40.866 38.163 13.416 16.194 28.537 31.465 45.370 43.587 16.101 14.785 15.824 16.433
0.873 0.857 1.480 1.610 2.387 2.229 0.784 0.946 1.667 1.838 2.650 2.546 0.940 0.864 0.924 0.960
16.916 16.460 28.537 31.465 46.189 43.587 13.867 16.820 29.456 32.477 47.189 45.083 16.587 15.121 14.895 15.533
0.988 0.961 1.667 1.838 2.698 2.546 0.810 0.982 1.721 1.897 2.756 2.633 0.969 0.883 0.870 0.907
yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes
0.884 140.95 0.891 0.888 0.876 0.885 0.876 0.967 74.45 0.963 0.969 0.969 0.961 0.967 0.971 201.2 0.978 1.062 139.3 1.058
50.3
110 47.7
Table 5 Leak location results calculated by Equation (18) for water pipelines at 3000 Hz. Number
Leakage orifice/mm
p1 /kPa
p2 /kPa
p1 =p2
Distance between the two end sensors/m
1 2 3 4 5 6 7 8 9 10
2
10.773 7.859 6.593 8.461 6.852 5.398 5.075 6.213 5.985 5.467
1.988 1.584 1.273 1.662 1.260 8.292 8.841 9.112 9.022 8.885
5.419 4.961 5.180 5.090 5.439 0.651 0.574 0.682 0.663 0.615
139.3
201.2
Distance between the leakage point and the starting end sensor/m 47.7
110
Distance calculated by Equation (18)/m
Errors generated by Equation (18)/%
47.696 48.842 48.283 48.509 47.649 106.176 107.809 105.574 105.931 106.908
0.003 0.820 0.419 0.581 0.037 1.901 1.089 2.200 2.022 1.537
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b) The operations of the experiments, especially the leakage occurring operations may cause the fluctuations of the data. Because the actual leakages occur abruptly, the leakage occurring operation may have minor differences, which lead to the minor differences in the waveform and amplitude. Though the operations are accomplished as well as possible, there exist errors. c) The sampling rate is related to the precision of the amplitude of the measured signals. When the sampling rate is larger, the amplitude of the original acoustic waves measured by the sensors are more accurate, which can contribute to the more accurate amplitude of the one in the energy dominant frequency band. The higher the sampling rate is, the preciser the amplitude is. But because there is limitation to the computer storage room, the sampling rate should be set appropriately. 2) The extraction of the amplitude from the measured signals by the applied wavelet transform method leads to the errors. a) The scale of the wavelet transform method decides the frequency band and the amplitude in the subband. In fact, when the larger scale is applied, the frequency band is smaller and the amplitude in the band is smaller, which means when the distance of the two sensors are long enough, the larger scale can be applied. b) The scale influences the waveform, especially the leakage occurring time judgment. The amplitude actually is the one at the leakage occurring time, which is the largest one of the signal. When the scale gets too large, the waveform of the signal gets smooth, which contribute to the inaccuracy of the leakage occurring time and the corresponding amplitude. Therefore, the scale should not be set too high. Generally, the scale should be set to make the frequency band locate in 0e20 Hz. To solve the problem, the signal-processing method should be improved. 3) The calculation of the absorption coefficients a) The parameters which are used to calculate the absorption coefficients are assigned as the mean value of the total length of the pipeline. In order to reduce the errors, the more pressure and temperature sensors are necessary. b) When the total distance between the two sensors is changed, the absorption coefficients and the correction coefficients are changed more or less while in table they are regarded as the same. c) When the theoretical damping absorption coefficients are calculated, the velocity of the fluid is neglected. And the interaction between the damping absorption coefficients and the fluid is the main research object in the future. 4) The fitting of correction coefficients a) As analyses above, it can be known that the theoretical calculation of the absorption coefficients has errors itself. And the experimental data have fluctuations which lead to errors in experiments also. So the calculation of correction coefficients may generate errors. b) Not only the errors are generated in the experiments, but also in the fitting procedure of the experimental data using curve-fitting method. c) The fitting of correction coefficients can minimize the errors generated by the absorption coefficients. To reduce the errors, the method based on the Equation (18) is applied to minimize the influences of calculations of the absorption coefficients and the correction coefficients. But the consequences show that it is not obvious that the errors are getting smaller. This is because the correction coefficients minimize the influence of the absorption coefficients to a certain
degree. And the errors come from other aspects as shown above. Therefore, in order to reduce the errors, the operations should be controlled under the same conditions as possible; then the acoustic sensors and the wavelet method should be improved; and the sampling rate should be set as high as possible, but the higher sampling rate may lead to more data, so the sampling rate can be set to some appropriate value. Though the errors exist, the method based on the Equations (17) and (18) can be able to detect and locate the leakages without the consideration of the velocity and the time difference of the acoustic waves. In a word, the leak detection and location method based on the propagation model can be applied to the water pipelines effectively. 4.2. Research on the leak detection and location for gas pipelines Due to the density of the fluid, the attenuation is more severe in the gas than in the water. According to the facts in section 4.1, the information in frequency band of 0e3 Hz is extracted from the data measured in the gas pipelines, which attenuates little. The leakage acoustic signals at sampling rate of 3000 Hz are processed by the improved wavelet algorithm. With the scale of 9, the sym8 of wavelet basis is applied. The subband frequency range is shown in Table 6. From Table 6, A9 is incorporated in the frequency band of 0e3 Hz. So A9 subband can be applied to conclude the damping absorption coefficients. And when the sampling rate is 1000 Hz, A8 (0e1.95313 Hz) subband is applied. The Equations (15) and (16) are applied to calculate the damping absorption coefficients. And the damping absorption coefficients are calculated by the fitted curves when the sampling rate is 3000 Hz. The theoretical and fitted damping absorption coefficients can be seen clearly in Table 7. From Table 7, it can be known that the fitted and the theoretical values of the absorption coefficients get less as the pressure levels get higher. A9 can be extracted from the leakage acoustic signals and it can propagate for a long distance; there are errors between the fitted damping absorption coefficients and the theoretical ones; the errors of A9 are lower than 20%. In order to reduce errors of leak location, the threshold value and the reference pressure are changed with the pressure: the threshold value is set as 0.0782/ 0.1136 (equals to 0.688) and pA0 is set as 0.1136 kPa at 0.40 MPa; the rest are 0.1855/0.2421 (equals to 0.766) and 0.2421 kPa at 0.80 MPa, and 0.3149/0.4275 (equals to 0.737) and 0.4275 kPa at 1.20 MPa. For Equation (18), the experiment of test number 1 of which the errors are 0.000 in Table 8 is always the one that the leakage point is known at different pressure levels. Then the location errors can be obtained by comparative analyses between the other experiments and the chosen test number 1. All leak location results can be seen clearly in Table 8. From Table 8, it can be known that most of the errors are small while some are large, which result from the reasons as discussed in the oil pipeline, especially the inaccuracy of the extracted amplitude. The inaccuracy of the amplitude comes from the inaccuracy of original signals measured by sensors and the limitations of the signal-processing method based on the wavelet transform. And the errors obtained by the Equation (17) are generally larger than the ones obtained by the Equation (18). This is because the method based on Equation (18) minimize the errors which come from the calculation of a and s. To reduce the errors, the better method to extract information in the low frequency band is important. Because the amplitude is very important, the acoustic sensor and the signal-processing method are to study in the future, which are also the key points for the traditional method based on the velocity and the time difference.
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Table 6 Frequency range of all sub-bands for wavelet analysis for A9. Sequence number of subbands
A9
D9
D8
D7
D6
D1
Frequency range/Hz
0e2.92969
2.92969e5.85938
5.85938e11.71876
11.71876e23.43752
23.43752e46.87504
750e1500
Table 7 Theoretical and fitted absorption coefficients under different conditions for gas pipelines. Pressure Level/MPa
Distance/m
Amplitude of A9/kPa 0.7 mm
1 mm
Fitted value
Theoretical value
Errors
0.4
0.1 66.4 136.3 202.5 0.1 66.4 136.3 202.5 0.1 66.4 136.3 202.5
0.1136 0.1008 0.0885 0.0782 0.2421 0.2164 0.2027 0.1855 0.4275 0.3851 0.362 0.3149
0.2173 0.2063 0.1951 0.1856 0.3372 0.3183 0.2916 0.2647 0.551 0.5103 0.4699 0.4125
0.00299
0.00353
0.15297
0.00203
0.00249
0.18376
0.00175
0.00202
0.13323
0.8
1.2
Absorption coefficients
Table 8 Leak location results under different conditions of gas pipelines. Pressure/ Leakage Test Distance between p1 /kPa p2 /kPa pA0 /kPa p1 =pA0 p2 =pA0 Threshold yes p1 =p2 MPa orifice/mm number the leakage point value or no and the starting end sensor/m
Distance calculated by Equation (17)/m
Errors generated by Equation (17)/%
Distance calculated by Equation (18)/m
Errors generated by Equation (18)/%
0.45
42.080 88.144 126.558 41.358 87.422 125.836 40.867 86.021 124.889 42.511 87.417 124.829 41.354 86.756 124.504 40.718 87.885 127.219
1.351 0.063 1.243 0.821 0.593 1.772 0.461 1.622 2.468 1.668 0.597 2.512 0.818 1.082 2.750 0.351 0.253 0.757
40.240 89.561 130.691 39.467 88.788 129.919 40.240 88.742 130.936 38.625 90.351 130.869 40.240 87.533 126.854 39.577 88.709 129.682
0.000 0.977 1.792 0.567 0.410 1.225 0.000 0.376 1.972 1.186 1.557 1.923 0.000 0.512 1.025 0.487 0.352 1.051
0.70
1.00
0.85
0.70
1.00
1.25
0.70
1.00
1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6
40.24 88.23 128.25 40.24 88.23 128.25 40.24 88.23 128.25 40.24 88.23 128.25 40.24 88.23 128.25 40.24 88.23 128.25
0.103 0.090 0.080 0.195 0.170 0.152 0.224 0.205 0.190 0.313 0.285 0.263 0.400 0.369 0.345 0.514 0.473 0.442
0.088 0.101 0.113 0.167 0.191 0.214 0.201 0.220 0.236 0.282 0.308 0.329 0.364 0.393 0.420 0.467 0.507 0.544
0.114
0.242
0.428
0.907 0.790 0.704 1.720 1.499 1.336 0.926 0.845 0.783 1.294 1.178 1.088 0.935 0.862 0.806 1.203 1.107 1.034
For application in field, when the operation pressure level is fixed which means the average value keeps constant, the method can be used well; when the operation pressure level is changed because of the relation between supply and demand of gas flow, the method can be adjusted to that pressure level. And as the test data base is enlarged by the operation signals, the method can be more and more accurate. So the proposed leak detection and location method without the calculations of a and s can still be used effectively, which can be combined with the method with the calculations of a and s. Therefore, the proposed leak detection and location method has advantages over the traditional one based on the velocity and the time difference, as nowadays acoustic sensors and signal processing method are both used for the two methods. The propagation law can help accomplish leak detection and location under different leakage orifices and the errors are small.
0.776 0.891 0.999 1.466 1.682 1.887 0.829 0.909 0.977 1.167 1.274 1.358 0.851 0.920 0.982 1.093 1.187 1.271
0.688
0.766
0.737
yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes yes
1.168 0.887 0.705 1.173 0.891 0.708 1.117 0.930 0.801 1.109 0.925 0.802 1.098 0.937 0.821 1.101 0.933 0.813
5. Conclusions The following conclusions can be drawn by researches on the new leak detection and location method based on the propagation law of leakage acoustic waves in oil and gas pipeline. (1) The information can be extracted by wavelet transform analysis from the leakage acoustic signals. Even after propagating for a long distance, acoustic characteristics can be obtained. (2) The propagation law of amplitude is obtained in the chosen frequency band with distance in actual pipeline. And the fitted absorption coefficient can be obtained based on experimental data. The theoretical absorption coefficient can be calculated.
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(3) The new leak location method based on the propagation model is proposed and then improved. The fundamental, steps and equations for both two new methods are concluded. (4) Though the errors exist, the two methods based on the propagation model including the Equations (17) and (18) can be able to detect and locate the leakages for the water pipelines effectively without the consideration of the velocity and the time difference of the acoustic waves. (5) The two methods based on the propagation model which means the Equations (17) and (18) can detect and locate the leakages in gas pipeline. The merits of the methods are concluded. Acknowledgments This paper was funded by the National Science Foundation of China (51104175), the Fundamental Research Funds for the Central Universities (14CX06135A) and (15CX06069A) and the Graduate Innovation Foundation of China University of Petroleum (YCX2014062). Thanks for the permission to publish this paper. References Brennan, M.J., Gao, Y., Joseph, P.F., 2007. On the relationship between time and frequency domain methods in time delay estimation for leak detection in water distribution pipes. J. Sound Vib. 304, 213e223. Gao, Y., Brennan, M.J., Joseph, P.F., et al., 2004. A model of the correlation function of leak noise in buried plastic pipes. J. Sound Vib. 277, 133e148.
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