Abstract
Water injection in a closed pipe at one end causes force deformation of the pipe. The expansion changes of the pipeline under different liquid injection pressures are studied combined with theoretical and experimental results. A new relationship between liquid injection pressure and water injection volume of the pipeline is proposed based on elastic mechanics, which is analyzed and verified. The experimental results show that at the early stage, the variation of water injection amount and pipeline deformation show nonlinear change, and the change rate liquid injection volume is constantly decreasing after the liquid injection pressure is increased to some value. Subsequently, there is a linear relationship between water injection and water injection pressure. The inner diameter and length of pipeline have significance influences on the deformation of the pipeline. With the increase of inner diameter and length of the pipeline, the rising rate of water injection volume is accelerated. The proposed equation can well express the relationship between the water injection change volume and the pipeline deformation under water injection pressures. The theory could provide useful theoretical reference for the study of pipeline blockage in the future.
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References
Barber, and James, R., Elasticity (Kluwer academic publishers, Dordrecht, 2002)
A.P. Boresi, K. Chong, J.D. Lee, Elasticity in engineering mechanics (John Wiley and Sons, 2010)
K.H. Cho, S.J. Ahn, J.H. Cho, C. Jung, M.K. Han, S.J. Park, S.J. Woo, The characteristics of retinal emboli and its association with vascular reperfusion in retinal artery occlusion. Invest Ophth. Vis. Sci. 57(11), 4589–4598 (2016)
Duan, H.F., Lee, P.J., Ghidaoui, M.S., Tung, Y.K., 2011. Extended blockage detection in pipelines by using the system frequency response analysis. J. Water Res.. Plan. Man. 55–62.
H.F. Duan, P.J. Lee, A. Kashima, J. Lu, M.S. Ghidaoui, Y.K. Tung, Extended blockage detection in pipes using the system frequency response: analytical analysis and experimental verification. J. Hydraul. Eng. 139(7), 763–771 (2013)
W. Duan, R. Kirby, J. Prisutova, K.V. Horoshenkov, On the use of power reflection ratio and phase change to determine the geometry of a blockage in a pipe. Appl. Acoust. 87, 190–197 (2015)
Hanmaiahgari, P.R., M. Elkholy, C.K. Riahi-Nezhad., 2017. Identification of partial blockages in pipelines using genetic algo-rithms. Sadhana-acad. P. Eng. Sci. 42 (9), 1543–1556.
K.D. Langdon, C.A. Cordova, S. Granter-Button, J.D. Boyd, J. Peeling, T.H. Murphy, D. Corbett, Executive dysfunction and blockage of brain microvessels in a rat model of vascular cognitive impairment. J. Cerebr. Blood F. Met. 38(10), 1727–2174 (2018)
P.J. Lee, J.P. Vitkovsky, M.F. Lambert, A.R. Simpson, J.A. Liggett, Frequency domain analysis for detecting pipeline leaks. J. Hydraul. Eng. 131(7), 596–604 (2005)
J.F. Lei, H.A. Will, Thin-film thermocouples and strain-gauge technologies for engine applications. Sensor. Actuat. A-Phys. 65(2–3), 187–193 (1998)
M. Louati, M.S. Ghidaoui, Eigenfrequency shift mechanism due to an interior blockage in a pipe. J. Hydraul. Eng. 144(1), 04017055 (2018)
S.M. Melle, K. Liu, Practical fiber-optic Bragg grating strain gauge system. Appl. Optics 32(19), 3601–3609 (1993)
P.K. Mohapatra, M.H. Chaudhry, A.A. Kassem, J. Moloo, Detection of partial blockage in single pipelines. J. Hydraul. Eng. 132(2), 200–206 (2006)
V. Pratap, S. Rajendran, R.K. Agrawal, S.S. Indimath, B.P. Reddy, S. Balamurugan, Blockage detection in gas pipelines to prevent failure of transmission line. J. Pipeline Syst. Eng. 12(3), 04021031 (2021)
W. Qunli, F. Fricke, Estimation of blockage dimensions in a duct using measured Eigen frequency shifts. J. Sound Vib. 133(2), 289–301 (1989)
M.P. Roth, A. Verdecchia, R.M. Harrington, Y. Liu, High-resolution imaging of hydraulic-fracturing-induced earthquake clusters in the Dawson-Septimus area, Northeast British Columbia. Canada. Seismol. Res. Lett. 91(5), 2744–2756 (2020)
A.M. Sattar, M.H. Chaudhry, A.A. Kassem, Partial blockage detection in pipelines by frequency response method. J. Hydraul. Eng. 134(1), 76–89 (2008)
R. Schultz, G. Atkinson, D.W. Eaton, Y.J. Gu, H. Kao, Hydraulic fracturing volume is associated with induced earthquake productivity in the Duvernay play. Science 359(6373), 304–308 (2018)
W. Wan, W. Huang, C. Li, Sensitivity analysis for the resistance on the performance of a pressure vessel for water hammer protection. J. Press. Vess-T-ASME 136(1), 011303 (2014)
B. Wang, R.M. Harrington, Y. Liu, H. Kao, H. Yu, A study on the largest hydraulic-fracturing-induced earthquake in Canada: Observations and static stress-drop estimation. B. Seismol. Soc. Am. 110(5), 2283–2294 (2020)
R. Wang, Y.J. Gu, R. Schultz, A. Kim, G. Atkinson, Source analysis of a potential hydraulic-fracturing-induced earthquake near Fox Creek. Alberta. Geophys. Res. Lett. 43(2), 564–573 (2016)
N. Watanabe, M. Egawa, K. Sakaguchi, T. Ishibashi, N. Tsuchiya, Hydraulic fracturing and permeability enhancement in granite from subcritical/brittle to supercritical/ductile conditions. Hydraulic fracturing and permeability enhancement in granite from subcritical/brittle to supercritical/ductile conditions. Geophys. Res. Lett. 44(11), 5468–5475 (2017)
I. Yamaguchi, A laser-speckle strain gauge. Eur. Phys. J. E 14(11), 1270 (1981)
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This work was supported by the National Natural Science Foundation of China (Grant Nos. 41831289, 41772250, and 42072276).
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Ma, H., Feng, P. & Qian, J. Relationship between water injection volume and liquid injection pressure under the condition of pipeline deformation. Eur. Phys. J. Spec. Top. (2022). https://doi.org/10.1140/epjs/s11734-022-00666-8
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DOI: https://doi.org/10.1140/epjs/s11734-022-00666-8