Skip to main content
SpringerLink
Log in

DEM modeling of hydraulic fracturing in permeable rock: influence of viscosity, injection rate and in situ states

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

Hydraulic fracturing in permeable rock is a complicated process which might be influenced by various factors including the operational parameters (e.g., fluid viscosity, injection rate and borehole diameter) and the in situ conditions (e.g., in situ stress states and initial pore pressure level). To elucidate the effects of these variables, simulations are performed on hollow-squared samples at laboratory scale using fully coupled discrete element method. The model is first validated by comparing the stress around the borehole wall measured numerically with that calculated theoretically. Systematic parametric studies are then conducted. Modeling results reveal that the breakdown pressure and time to fracture stay constant when the viscosity is lower than 0.002 Pa s or higher than 0.2 Pa s but increases significantly when it is between 0.002 and 0.2 Pa s. Raising the injection rate can shorten the time to fracture but dramatically increase the breakdown pressure. Larger borehole diameter leads to the increase in the time to fracture and the reduction in the breakdown pressure. Higher in situ stress requires a longer injection time and higher breakdown pressure. The initial pore pressure, on the other hand, reduces the breakdown pressure as well as the time to fracture. The increase in breakdown pressure with viscosity or injection rate can be attributed to the size effect of greater tensile strength of samples with smaller infiltrated regions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Adachi J, Siebrits E, Peirce A, Desroches J (2007) Computer simulation of hydraulic fractures. Int J Rock Mech Min 44:739–757

    Article  Google Scholar 

  2. Al-Busaidi A, Hazzard J, Young R (2005) Distinct element modeling of hydraulically fractured Lac du Bonnet granite. J Geophys Res Solid Earth 1978–2012:110

    Google Scholar 

  3. Bohloli B, de Pater CJ (2006) Experimental study on hydraulic fracturing of soft rocks: influence of fluid rheology and confining stress. J Petrol Sci Eng 53:1–12

    Article  Google Scholar 

  4. Bonilla-Sierra V, Scholtès L, Donzé FV, Elmouttie MK (2015) Rock slope stability analysis using photogrammetric data and DFN–DEM modelling. Acta Geotech 10:497–511

    Article  Google Scholar 

  5. Cundall PA, Strack OD (1979) A discrete numerical model for granular assemblies. Geotechnique 29:47–65

    Article  Google Scholar 

  6. Damjanac B, Detournay C, Cundall PA (2016) Application of particle and lattice codes to simulation of hydraulic fracturing. Comput Part Mech 3:249–261

    Article  Google Scholar 

  7. Detournay E (2016) Mechanics of hydraulic fractures. Annu Rev Fluid Mech 48:311–339

    Article  MathSciNet  MATH  Google Scholar 

  8. Duan K, Kwok C (2016) Evolution of stress-induced borehole breakout in inherently anisotropic rock: insights from discrete element modeling. J Geophys Res Solid Earth 121:2361–2381

    Article  Google Scholar 

  9. Duan K, Kwok CY, Ma X (2017) DEM simulations of sandstone under true triaxial compressive tests. Acta Geotech 12:495–510

    Article  Google Scholar 

  10. Duan K, Kwok CY, Pierce M (2016) Discrete element method modeling of inherently anisotropic rocks under uniaxial compression loading. Int J Numer Anal Meth Geomech 40:1150–1183

    Article  Google Scholar 

  11. Fatahi H, Hossain MM, Fallahzadeh SH, Mostofi M (2016) Numerical simulation for the determination of hydraulic fracture initiation and breakdown pressure using distinct element method. J Nat Gas Sci Eng 33:1219–1232

    Article  Google Scholar 

  12. Gan Q, Elsworth D, Alpern JS, Marone C, Connolly P (2015) Breakdown pressures due to infiltration and exclusion in finite length boreholes. J Petrol Sci Eng 127:329–337

    Article  Google Scholar 

  13. Goodfellow SD, Nasseri MHB, Maxwell SC, Young RP (2015) Hydraulic fracture energy budget: insights from the laboratory. Geophys Res Lett 42:3179–3187

    Article  Google Scholar 

  14. Grassl P, Fahy C, Gallipoli D, Wheeler SJ (2015) On a 2D hydro-mechanical lattice approach for modelling hydraulic fracture. J Mech Phys Solids 75:104–118

    Article  MathSciNet  MATH  Google Scholar 

  15. Haimson B (1968) Hydraulic fracturing in porous and nonporous rock and its potential for determining in situ stresses at great depth. Minnesota University, Minneapolis

    Google Scholar 

  16. Haimson B (2007) Micromechanisms of borehole instability leading to breakouts in rocks. Int J Rock Mech Min 44:157–173

    Article  Google Scholar 

  17. Haimson B, Fairhurst C (1967) Initiation and extension of hydraulic fractures in rocks. Soc Petrol Eng J 7:310–318

    Article  Google Scholar 

  18. Haimson BC, Zhao Z (1991) Effect of borehole size and pressurization rate on hydraulic fracturing breakdown pressure. In: The 32nd US symposium on rock mechanics (USRMS). American Rock Mechanics Association

  19. Hazzard JF, Young RP, Maxwell SC (2000) Micromechanical modeling of cracking and failure in brittle rocks. J Geophys Res Solid Earth 105:16683–16697

    Article  Google Scholar 

  20. Hubbert MK, Willis DG (1957) Mechanics of hydraulic fracturing. US Geol Surv 210:153–168

    Google Scholar 

  21. Itasca (2008) PFC2D particle flow code in 2 dimensions, 4.0th edn. Itasca, Minneapolis

    Google Scholar 

  22. Labra C, Rojek J, Oñate E, Zarate F (2008) Advances in discrete element modelling of underground excavations. Acta Geotech 3:317–322

    Article  Google Scholar 

  23. Li L, Meng Q, Wang S, Li G, Tang C (2013) A numerical investigation of the hydraulic fracturing behaviour of conglomerate in Glutenite formation. Acta Geotech 8:597–618

    Article  Google Scholar 

  24. Newman Jr J (1971) An improved method of collocation for the stress analysis of cracked plates with various shaped boundaries. NASA Tech. Note D-6373. Langley Research Center, Hampton

  25. Potyondy DO (2015) The bonded-particle model as a tool for rock mechanics research and application: current trends and future directions. Geosyst Eng 18:1–28

    Article  Google Scholar 

  26. Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min 41:1329–1364

    Article  Google Scholar 

  27. Pruess K (2006) Enhanced geothermal systems (EGS) using CO2 as working fluid—a novel approach for generating renewable energy with simultaneous sequestration of carbon. Geothermics 35:351–367

    Article  Google Scholar 

  28. Shimizu H, Murata S, Ishida T (2011) The distinct element analysis for hydraulic fracturing in hard rock considering fluid viscosity and particle size distribution. Int J Rock Mech Min 48:712–727

    Article  Google Scholar 

  29. Tomac I, Gutierrez M (2015) Formulation and implementation of coupled forced heat convection and heat conduction in DEM. Acta Geotech 10:421–433

    Article  Google Scholar 

  30. Tomac I, Gutierrez M (2017) Coupled hydro-thermo-mechanical modeling of hydraulic fracturing in quasi-brittle rocks using BPM-DEM. J Rock Mech Geotech Eng 9:92–104

    Article  Google Scholar 

  31. Warpinski NR, Mayerhofer MJ, Vincent MC, Cipolla CL, Lolon E (2009) Stimulating unconventional reservoirs: maximizing network growth while optimizing fracture conductivity. J Can Pet Technol 48:39–51

    Article  Google Scholar 

  32. Wu W, Zoback MD, Kohli AH (2017) The impacts of effective stress and CO2 sorption on the matrix permeability of shale reservoir rocks. Fuel 203:179–186

    Article  Google Scholar 

  33. Zhang X, Jeffrey RG, Thiercelin M (2009) Mechanics of fluid-driven fracture growth in naturally fractured reservoirs with simple network geometries. J Geophys Res Solid Earth 114:B12406

    Article  Google Scholar 

  34. Zhang X, Lu Y, Tang J, Zhou Z, Liao Y (2017) Experimental study on fracture initiation and propagation in shale using supercritical carbon dioxide fracturing. Fuel 190:370–378

    Article  Google Scholar 

  35. Zhao X, Young P (2011) Numerical modeling of seismicity induced by fluid injection in naturally fractured reservoirs. Geophysics 76:WC167–WC180

    Article  Google Scholar 

  36. Zhou J, Jin Y, Chen M (2010) Experimental investigation of hydraulic fracturing in random naturally fractured blocks. Int J Rock Mech Min 47:1193–1199

    Article  Google Scholar 

  37. Zoback MD, Moos D, Mastin L, Anderson RN (1985) Well bore breakouts and in situ stress. J Geophys Res Solid Earth 1978–2012(90):5523–5530

    Article  Google Scholar 

  38. Zoback MD, Rummel F, Jung R, Raleigh CB (1977) Laboratory hydraulic fracturing experiments in intact and pre-fractured rock. Int J Rock Mech Min Sci Geomech Abstr 14:49–58

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to appreciate the two anonymous reviewers for their constructive comments.

Author information

Authors and Affiliations

  1. School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, Singapore

    Kang Duan & Wei Wu

  2. Department of Civil Engineering, The University of Hong Kong, Hong Kong, Hong Kong

    Kang Duan, Chung Yee Kwok & Lu Jing

Authors
  1. Kang Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chung Yee Kwok
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lu Jing
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Chung Yee Kwok or Wei Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Duan, K., Kwok, C., Wu, W. et al. DEM modeling of hydraulic fracturing in permeable rock: influence of viscosity, injection rate and in situ states. Acta Geotech. 13, 1187–1202 (2018). https://doi.org/10.1007/s11440-018-0627-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-018-0627-8

Keywords

Search

Navigation