Arabian Journal for Science and Engineering

, Volume 43, Issue 11, pp 6509–6522 | Cite as

Study of Pulse Wave Propagation and Attenuation Mechanism in Shale Reservoirs During Pulse Hydraulic Fracturing

  • Pei HeEmail author
  • Jiyou Xiong
  • Zhaohui Lu
  • Linhua Pan
  • Dawei Qin
Research Article - Petroleum Engineering


Hydraulic fracturing (HF) is indispensable in shale gas, but there are also problems existed in high ratio of energy consumption and low ratio of energy utilization. Based on hydraulic fracturing and pulsating jet, pulse hydraulic fracturing (PHF) has been widely used and achieved good results in the coal-bed methane. This paper attempts to study the mechanism of pulse wave propagation and attenuation during PHF in shale reservoirs, which provides theoretical support for application. On the basis of the motion equation and continuity equation, the two-dimensional propagation and attenuation equation with damping and fissure width during PHF is established and fracture network is simulated based on DFN discrete random model. The mathematical and physical model is verified by laboratory experiment The study of PHF superiority, PHF waveform effect, PHF propagation and attenuation characters are also performed. Results indicate that PHF propagation has two stages: The first is the pressure fluctuation is sharp in the process of the initial fracturing. The second is a stable state is appeared after a period of time. Compared with HF, PHF can pressurize obviously the pressure gradient of pulse waveform, which is an important parameter of affecting pulse pressure: the greater pressure gradient, the more obvious water hammer and supercharging effect. In the process of PHF propagation, pressure distribution complicates under the supercharging. Pressure wave has different attenuation characteristics in two steps. These research results will provide guidance for optimizing technical parameters for using PHF technology in shale reservoirs.


Pulse hydraulic fracturing Pulse wave Propagation and attenuation Rectangular pulse Pressurize 



Hydraulic fracturing


Pulse hydraulic fracturing

List of symbols

\(\vec {u}\)

Velocity vector of PHF fluid

\(\rho \)

Fluid density

\(\vec {f}\)

Mass force and frictional resistance

\(\nabla \)

Differential operator



\(\tau \)

Integral parameter

\(\alpha \)

Speed of fluid pressure wave in the water


Volume elastic coefficient of fluid

\(\delta \)

Fissure width

\(\lambda \)

Comprehensive damping coefficient





\(R_1 \)

Solved inradius

\(R_2 \)

Solved exradius

\(\upphi \left( {{x},{y}} \right) \)

Initial condition of solved domain

\({\uppsi }\left( {{x},{y}} \right) \)

First-order partial differential initial condition of solved domain

\({\upvarphi }\left( {t} \right) \)

Boundary condition of inner circle

\(\upphi \left( {t} \right) \)

Boundary condition of excircle


Function of x, y and t

\(\xi ,\eta ,\zeta \)

Variables of integration

\(\Omega \)

Integral area


Elasticity modulus of rock


Equivalent diameter of fissure


Reynolds number

\(\nu \)

Average flow velocity of fissure section

\(d_\mathrm{e} \)

Equivalent diameter

\(\mu \)

Liquid viscosity

\(k_s \)

Roughness of fissure


Energy of unit mass

\(W_\mathrm{k} \)

Kinetic energy of unit mass

\(\Delta m\)

Unit mass

\(W_\mathrm{p} \)

Elastic potential energy of unit mass


Maximum pressure amplitude

\(\omega \)





Energy density


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The study was financially supported by the National Natural Science Foundation of China (Grant Nos. 51304258, 51604050), the Natural Science Foundation of Chong Qing city (Grant Nos. cstc2016shmszx9003, cstc2017jcyjBX0076).


  1. 1.
    Dong, D.; Wang, Y.; Li, X.; Zou, C.; Guan, Q.; Zhang, C.; Bai, W.: Breakthrough and prospect of shale gas exploration and development in China. Nat. Gas Ind. B 3(1), 12–26 (2016)CrossRefGoogle Scholar
  2. 2.
    Al Rbeawi, S.; Tiab, D.: Pressure behaviours and flow regimes of a horizontal well with multiple inclined hydraulic fractures. Int. J. Oil Gas Coal Technol. 6(1–2), 207–241 (2013)CrossRefGoogle Scholar
  3. 3.
    Gregory, K.B.; Vidic, R.D.; Dzombak, D.A.: Water management challenges associated with the production of shale gas by hydraulic fracturing. Elements 7(3), 181–186 (2011)CrossRefGoogle Scholar
  4. 4.
    Li, B.; Zhang, J.S.; Yao, H.Z.; Wei, L.J.; Dong, Q.; Gao, F.: Study of high pressure pulsation hydraulic hammer on coal seam affusion. Min. Saf. Environ. Prot. 38(2), 14–16 (2011)Google Scholar
  5. 5.
    Di, C.; Li, X.Z.; Li, Q.G.: Research and application of coal seam pulse hydraulic fracturing technology. J. China Coal Soc. 36(12), 1996–2001 (2012)Google Scholar
  6. 6.
    Wang, W.; Li, X.; Lin, B.; Zhai, C.: Pulsating hydraulic fracturing technology in low permeability coal seams. Int. J. Min. Sci. Technol. 25(4), 681–685 (2015)CrossRefGoogle Scholar
  7. 7.
    Li, X.Z.; Lin, B.Q.; Di, C.; Li, Q.G.; Ni, G.H.: The mechanism of breaking coal and rock by pulsating pressure wave in single low permeability seam. Meitan Xuebao J. China Coal Soc. 38(6), 918–923 (2013)Google Scholar
  8. 8.
    Zhai, C.; Yu, X.; Xiang, X.; Li, Q.; Wu, S.; Xu, J.: Experimental study of pulsating water pressure propagation in CBM reservoirs during pulse hydraulic fracturing. J. Nat. Gas Sci. Eng. 25, 15–22 (2015)CrossRefGoogle Scholar
  9. 9.
    Lu, P.; Li, G.; Huang, Z.; He, Z.; Li, X.; Zhang, H.: Modeling and parameters analysis on a pulsating hydro-fracturing stress disturbance in a coal seam. J. Nat. Gas Sci. Eng. 26, 253–263 (2015)CrossRefGoogle Scholar
  10. 10.
    Zhu, H.Q.; Zhang, M.B.; Shen, J.; Hu, R.L.: Permeability enhancing mechanism and numerical analysis on pulsating water injection in low permeability coal seams. J. China Coal Soc. 38(S2), 343–347 (2013)Google Scholar
  11. 11.
    Pei-Qing, L.; Ai-Hua, L.: Model discussion of pressure fluctuations propagation within lining slab joints in stilling basins. J. Hydraul. Eng. 133(6), 618–624 (2007)CrossRefGoogle Scholar
  12. 12.
    Li, A.; Liu, P.: Mechanism of rock-bed scour due to impinging jet. J. Hydraul. Res. 48(1), 14–22 (2010)CrossRefGoogle Scholar
  13. 13.
    Fiorotto, V.; Rinaldo, A.: Discussion of “Karnafuli Project, Model Studies of Spillway Damage” by C. Edward Bowers and Joel Toso (May, 1988, Vol. 114, No. 5). J. Hydraul. Eng. 116(6), 850–852 (1990)CrossRefGoogle Scholar
  14. 14.
    Smith, C.D.: Discussion of “Karnafuli Project, Model Studies of Spillway Damage” by C. Edward Bowers and Joel Toso (May, 1988, Vol. 114, No. 5). J. Hydraul. Eng. 116(6), 852–853 (1990)CrossRefGoogle Scholar
  15. 15.
    Fiorotto, V.; Rinaldo, A.: Fluctuating uplift and lining design in spillway stilling basins. J. Hydraul. Eng. 118(4), 578–596 (1992)CrossRefGoogle Scholar
  16. 16.
    Fiorotto, V.; Rinaldo, A.: Turbulent pressure fluctuations under hydraulic jumps. J. Hydraul. Res. 30(4), 499–520 (1992)CrossRefGoogle Scholar
  17. 17.
    Saad, M.A.: Compressible Fluid Flow, p. 570. Prentice-Hall Inc, Englewood Cliffs, NJ (1985)Google Scholar
  18. 18.
    Huang, L.-B.: Study on the Method for Calculation and the Theory of Water Hammer (Doctoral dissertation, Zhengzhou university) (2012)Google Scholar
  19. 19.
    Nikuradse, J.: Gesetzmäßigkeiten der turbulenten Strömung in glatten Rohren (Nachtrag). Forsch. Ingenieurwes. 4(1), 44–44 (1933)CrossRefGoogle Scholar
  20. 20.
    Huang, B.X.: Research on theory and application of hydraulic fracture weakening for coal-rock mass. J. China Coal Soc. 35(10), 1765–1766 (2010)Google Scholar
  21. 21.
    Li, G.; Liu, L.; Huang, Z.; Niu, J.: Study of effect of hydraulic perforating on formation fracturing pressure. J. China Univ. Petrol. (Edn. Nat. Sci.) 30(5), 42–45 (2006)Google Scholar
  22. 22.
    Sears, F.W.; Zemansky, M.W.; Young, H.D.: University Physics: Part 2, p. 262 (1963)Google Scholar
  23. 23.
    Alonso, M.; Finn, E.J.: Fundamental University Physics, vol. 2. Addison-Wesley, Reading, MA (1967)Google Scholar
  24. 24.
    Ghidaoui, M.S.; Zhao, M.; McInnis, D.A.; Axworthy, D.H.: A review of water hammer theory and practice. Appl. Mech. Rev. 58(1/6), 49 (2005)CrossRefGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  • Pei He
    • 1
    • 2
    • 3
    • 4
    Email author
  • Jiyou Xiong
    • 1
  • Zhaohui Lu
    • 2
    • 3
    • 4
  • Linhua Pan
    • 2
    • 3
    • 4
  • Dawei Qin
    • 1
  1. 1.State Key Laboratory Oil and Gas Reservoir Geology and ExploitationSouthwest Petroleum UniversityChengduChina
  2. 2.National and Local Joint Engineering Research Center of Shale Gas Exploration and DevelopmentChongqing Institute of Geology and Mineral ResourcesChongqingChina
  3. 3.Key Laboratory of Shale Gas Exploration, Ministry of Land and ResourcesChongqing Institute of Geology and Mineral ResourcesChongqingChina
  4. 4.Chongqing Engineering Research Center for Shale Gas Resource and ExplorationChongqing Institute of Geology and Mineral ResourcesChongqingChina

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