2. Theoretical analysis of wave transmission characteristics in pipeline

Transcription

1 30th Euroean Conference on Acoustic Emission Testing & 7th International Conference on Acoustic Emission University of Granada, Setember Theoretical Analysis and Exerimental Study of Gas Pieline Acoustic Emission Signal Transmit Seed SHEN Gongtian 1, QIN Xianyong 1, HE Renyang 1, XIU ChangZheng 2 1 China Secial Equiment Insection and Research Institute, Beijing, China, Phone: , Fax: ; qinzetian123906@yahoo.com.cn; shen_gongtian@csei.org.cn; herenyang@163.com 2 General Administration of Quality Suervision, Insection and Quarantine of the P.R.China, Secial Equiment Safety Suervision Bureau, Beijing, China, Phone: , Fax: ; wtxiu@263.net Abstract Transmit seed of leak emission signal is a key factor for gas ieline leak location. The aer using the elastic wave transmission equation to study sound transmission characteristics of gas ieline wall, relationshi between and the grou velocity and hase velocity. The theoretical transmit seed is analyzed based on disersion and attenuation characteristics analysis. The transmit seed of leak signal are measured in exeriments, and the seed value for gas steel ieline leak emission signal is mainly about from 900m/s to 1200m/s. Keywords: Transmit seed, gas ieline, 1. Introduction leak emission signal Pieline leakage introduces high-frequency sound waves, which transmit along the ie wall with the form of elastic waves reflecting between the two surfaces of ie, and the tube wall surface limitation leads to guided waves in ie. This aer mainly studies the amlitude attenuation and frequency disersion characteristics of leakage wave in transmission rocess, analyzing the relationshi between hase velocity and grou velocity, and doing exerimental study to verify the theoretical analysis results. The liquid ieline leak velocity is analyzed in exerimental studies for two kinds of gas ieline to get higher leak location accuracy. 2. Theoretical analysis of wave transmission characteristics in ieline 2.1Grou velocity and hase velocity of elastic wave The grou velocity refers to the elastic wave velocity of energy roagation, which is about the family of the similar frequency waves; the hase velocity is at the fixed hase to the direction of roagation. Elastic waves roagate with grou velocity[1].as shown in Fig.1, waveform A is at a certain distance L, while waveform B is at L + l. Comarison of two shows B moved forward by time t 1, while the time difference of two oints at same hase is t 2. Grou velocity and hase velocity can be simly exressed as: c g = l t 2,c = l t 1 (1) The relationshi between the grou velocity and hase velocity for two harmonics with same amlitude but slightly different in frequency is u = Acos( k1 x ω1t) + Acos( k2 x ω2t) (2)

2 Fig.1 The relationshi between grou velocity and hase velocity Where, k1 = ω1 / c1, k2 = ω2 / c2.through the following substitution, 1 ω = ω 2 ω 1 ; k = k2 k1 ; ω = ( ω 2 + ω 1 ) 2 ; c ω 1 = = ; k ( k 2 + k 1 ) k 2 We get 1 1 u = 2Acos( kx ωt)cos( k x ω t) (3) 2 2 The grou velocity is defined as c g = dω / dk (4) Where ω is circular frequency,k is wave number. The hase velocity is defined as c = ω / k (5) Different harmonic has different hase velocities c, but the suerosed wave grou transmits with same transmission seed c g. Phase velocity and grou velocity has the following relations c g = c 2 c = dc ω c dω c 2 dc ( fd) d( fd) Where,f is guided wave frequency,d is waveguide thickness,f d is the frequency-thickness roducts. As for the late, d is its thickness and for the circular tube, d is tube wall thickness. 2.2Multi-modal and disersion characteristics analysis of guided wave in ie Disersion refers to the henomenon of seed change with frequency due to structure and geometric size. Disersion henomenon makes the elastic wave signal in initial osition distorted with the transmission rocess. Guided waves in ies are divided into three categories [2]: (1) Axially symmetric longitudinal mode L(0,m), m=1,2,3, (6)

3 (2) Axially symmetric torsional mode T(0,m), m=1,2,3, (3) Non axially symmetric bending mode F(n,m), n=1,2,3, ; m=1,2,3, Above, m is mode in the above modal, reflecting the vibration shae of modal in the thickness direction; n reresents circumferential order number, reflecting the siral transmission form of modal around ie wall. When the wall is thinner, and the diameter is larger, the L (0, m) modes corresond to late or Lamb waves; and T (0, m) modes can corresond to the late SH wave [3]. Three modes of eriheral vibration diagrams [4]are shown in Fig. 2. From Fig.2, for L mode (n=0), the vibration of ieline article in the circumferential direction is erendicular to the tube wall thickness direction, symmetric article motion; vibration direction of T mode guided wave is always along the tube of the tangential direction; for the F mode, when n=1, article vibration direction is along a single radial. Guided wave of F(1, m) mode is a non-axis-symmetric in relation to circumferential angle with three direction dislacement comonents. According to ieline leakage oint of ie wall stress, we may consider that ieline leakage vibration mode for F (1, m) mode. Take steel ie for leak simulation exeriment, diameter D is 50mm, wall thickness is 3mm; density is 7800 kg/m 3, E is 206 GPa as the Young's elastic modulus; Poisson's ratio is 0.3;using the disersion curve equation and the grou velocity formula we can obtained the relationshi of grou velocity and frequency. In this aer, frequencies below 25 khz are analyzed, as shown in Fig.3. Fig.2 Periheral vibration modal sketch ma Pieline leakage vibration mode is mainly F(1, m) modes. For the mentioned test ieline, leakage wave grou velocity is about m/sin the F(1, 1) mode within the sectrum of1-25 khz. 2.3Elastic wave attenuation in ieline For elastic wave roagation in ies with the increase of roagation distance, the energy and the amlitude of vibration reduce gradually. It is the attenuation henomenon, and mainly contains disersion, scattering and absortion.

4 Scattering attenuation is comosed of elastic wave roagation in non-uniform medium; in fact, gas ieline is non-uniform. Scattering attenuation is one of the most imortant factors, as a large number of exeriments showed that scattering attenuation has exonential law [5]. Elastic wave roagation in metal ie, internal friction occurs within materials, and a art of the wave energy changes into heat, causing the absortion [6].The absortion attenuation also has exonential trend. F(1,2) Fig.3 Disersion curve of test ieline grou velocity 3Exerimental on gas ieline leak signal roagation characteristics 3.1Gas ieline leak signalwaveform characteristics Using the leak emission signal as sound sources, the simulation exeriments are carried out on three-dimensional susended ieline. The signal acquisition instruments are installed at 1 m, 10 m and 30 m distance from the sound source. emission signals in time domain collected at different ositions are shown in Fig.4. As can be seen from the grah, the curve of emission signal at1 m distance from the leak hole has more eaks. At 10-m distance from the leak hole, the signal has less eaks, while at 30-m distance from the leak hole, almost no obvious eaks are visible. This shows that leak signal frequency disersion haens in the roagation, with amlitude of high frequency signals reducing and the roortion of the low frequency signal energy increasing. 3.2 Gas ieline leak signal attenuation characteristics The leak signals are examined for energy attenuation characteristics in time domain and frequency domain.fig.5 (a), (b) and (c) resectively show the leak signal waveform in time domain and frequency domain at 1m 5m and 10m distance from the leak hole. The

5 emission signal energy attenuation curves from different distances are shown in Fig.6.The amlitude of signal at 10m distance is about 1/15 that at 1m distance, while the root mean square(rms) is about 1/20 over the same distance. Signal energy trends from different osition in figure 6 shows that energy attenuation is faster at small roagation distance, closer to leak source. Fig.4 emission signal waveform from different collection osition Fig. 5(a) emission signal waveform in time and frequency domain at 1m

6 Fig. 5(b) emission signal waveform in time and frequency domain at 5m Fig.5(c) emission signal waveform in time and frequency domain at 10m

7 Fig.6 emission signal energy attenuation curve in different distances (Note: RMS- Root Mean Square; PPV-Peak to eak value; MV-Mean value.) 4. Pieline leak signal roagation velocity 4.1 Exerience value analysis of leak signal roagation velocity Universal ieline leak detection instrument finder RT is suitable for leak ositioning on cast iron ies, steel ies and PVC ies. The inner liquid ieline leak signal roagation velocities in finder RT are shown in Table 1. Table 1 Pieline leak signal roagation velocities Diameter/mm Cast Iron Pie Steel Pie PVC Pie

8 From the above table, among the normal ie diameter range, the velocity on steel ieline is about m/s, and that of cast iron ieline is about m/s, while that of PVC ieline is about m/s. The velocity becomes smaller as the diameter increases. 4.2 emission signal roagationexeriment (1) Exeriment on CSEI test ie simulation test is made on the China Secial Equiment Insection and Research Institute (CSEI) test ieline to get roagation velocity. Data collecting and analysis system is Gas Pieline Detecting and Locating System, develoed by CSEI. It contains data collecting module, sensors, GPS Antenna, comuter and data collecting and Analysis software, which is shown as Fig.7. Fig.7 Gas Pieline Detecting and Locating System The test ieline length is 34m, diameter is 219mm, and ie wall is 6mm.The ieline test oint layout and testing icture is shown as Fig.8 (a)and (b). One sensor is fixed on R1 oint, the distance from R1 oint to leak oint A is 10m, and another sensor is laced on R2 oint. The distance from R2 oint to leak oint A was varied between 1 and 19m. Test results are shown in Table 2. Point Sensor R1 1.3m 10m A Point Sensor R2 8.2m Φ159 34m Φ219mm Fig.8 (a) Pieline test oint arrangement

9 Serial number Fig.8 (b)testing icture Table 2 signal roagation velocity on CSEI test ieline distance between R2 and A (m) age oints and the R1 and R2 itch difference(m) seed 1 seed 2 seed 3 seed According to the 40 tests of leak signal roagation velocity, given in table 2, the mean velocity on this ieline is 1010m / s. (2) Exeriment on CUP test ie simulation test on the China University of Petroleum (CUP)test ieline was done to get roagation velocity. The test ieline length is 160m, diameter is 50mm, and ie wall is

10 3mm.The ieline test oint layout is shown as Fig.9. The distance between A oint and B oint is 15m. One sensor is laced on R1 oint, the distance from R1 oint to leak oint A is 3m, and another sensor is laced on variable R2 oint. Test results are as shown in Table 3. Serial number Fig.9Pieline test oint layout Table 3 emission signal roagation seed on CUP test ieline distance between R2 and A (m) age oints and the R1 and R2 itch difference(m) seed 1 seed 2 seed 3 seed According to the 32tests of roagation velocity in table 3, the mean velocity on this test ieline is 1071m / s. 5. Conclusions From the above study, the leak wave roagates in ieline as guided wave with grou velocity. Pieline leak vibration modal is mainly F(1, m) mode. signal frequency disersion and energy attenuation haens in the roagation, with amlitude of high frequency signals reducing and the roortion of the low frequency signal energy increasing, and energy attenuation is different along with the roagation though with same roagation distance, the closer to leak source, the energy decays faster. The transmit

11 velocity of leak signal are measured in two tyical exerimental ies showing the gas steel ieline leak emission signal transmit velocity value is about 900m/s to 1200m/s. Acknowledgements The authors are grateful to suort rovided by the National Science and Technology lanning roject of China (2011BAK06B01) and China Secial Equiment Insection and Research Institute suort lanning (2010 Inner-12). References 1. Yang Yongbo. A Study on Guided Wave Theory of Hollow Circular Cylinders and Plate-like Concrete Structures. Institute of Rock &Soil Mechanics, The Chinese Academy of Sciences, Doctor Dissertation, Ai Chun-an, Li Jian. Numerical Calculation For Lamb Wave Frequency Equation. NDT, Vol 27, No 6, , Hou Yunxia. Study on Proagation Characteristics of Lamb Wave and Guided Wave in Pies. Dalian University of Technology, Master Dissertation, 2009, Qi Ruicai. Pressure Pieline NDT Method Using Ultrasonic Guided Wave Method. Dalian University of Technology, Master Dissertation, 2006, Li Chaning, Liu Xuewei, Wang Xiangchun, et al,. Seismic wave scattering theory, scattering characteristics and its alications. PROGRESS IN EXPLORATION GEOPHYSICS, Vol 28, No 2, 82-89, Qin Xianyong. Research on gas ieline leak emission detection key technology. Beihang University and China Secial Equiment Insection and Research Institute, Postdoctoral Dissertation, 2011,09.