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Micromechanics of hydraulic fracturing and damage in rock based on DEM modeling

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Abstract

This paper presents a study of the micromechanics of the coupled hydro-mechanical (H-M) behavior of brittle rock during hydraulic fracturing. The study is conducted using the discrete element method (DEM), which spatially discretizes a rock mass into discrete disc particles, coupled with a solver for modeling fluid flow through a network of connected pores. In the coupled H-M DEM modeling, fluid flows through newly formed hydraulic fractures due to pore pressure increase from fluid injection in a wellbore and is coupled with rock mechanical response across a wide range of flow rates. The micromechanical insights from the DEM modeling provide better understanding of coupled H-M processes which precede rock breakdown during hydraulic fracturing, and the transition in deformation in brittle rock from a single hydraulic fracture to branched hydraulic fractures and a diffused damage zone. The effects of the properties of the fracturing fluid and the rock matrix as well as the effects of loading flow rate on the development of pressure-induced deformation and fracturing in crystalline brittle rocks fracturing are investigated. The DEM models used properties that were obtained by calibrating flow-rate-dependent stress–strain response against previously published experimental data on brittle rocks (granite in particular). DEM results are compared with experimental results from a true-triaxial scale model testing on hydraulic fracturing in an analogue rock. The presented results are expected to enable better understanding of conditions which lead to successful fracture propagation versus damage and fracture arrest in geo-reservoirs.

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References

  1. Economides, M.J., Nolte, K.G., Ahmed, U.: Reservoir Stimulation. Wiley, New York (2000)

    Google Scholar 

  2. Valkó, P., Economides, M.J.: Hydraulic Fracture Mechanics. Wiley, New York (1995)

    Google Scholar 

  3. Clark, J.B.: A hydraulic process for increasing the productivity of wells. Trans. AIME 186, 1–8 (1949)

    Article  Google Scholar 

  4. Yew, C.H.: Mechanics of Hydraulic Fracturing. Gulf Professional Publishing, Houston (1997)

    Google Scholar 

  5. Khristianovic, S., Zheltov, Y.: Formation of vertical fractures by means of highly viscous fluids. Presented at the (1955)

  6. Perkins, T.K., Kern, L.R.: Widths of hydraulic fractures. J. Pet. Technol. 13, 937–949 (1961)

    Article  Google Scholar 

  7. Clifton, R., Abou-Sayed, A.: A variational approach to the prediction of the three-dimensional geometry of hydraulic fractures. In: SPE/DOE Low Permeability Gas Reservoirs Symposium. Society of Petroleum Engineers, Denver, Colorado (1981)

  8. Economides, M.J., Boney, C.: Reservoir stimulation. Reserv. Stimul. (2000). https://doi.org/10.1017/CBO9781107415324.004

    Article  Google Scholar 

  9. Damjanac, B., Gil, I., Pierce, M., Sanchez, M., Van As, A., McLennan, J.: A new approach to hydraulic fracturing modeling in naturally fractured reservoirs. In: 44th U.S. Rock Mechanics Symposium and 5th U.S.-Canada Rock Mechanics Symposium, 27–30 June, Salt Lake City, Utah (2010)

  10. Kresse, O., Weng, X., Gu, H., Wu, R.: Numerical modeling of hydraulic fractures interaction in complex naturally fractured formations. Rock Mech. Rock Eng. 46, 555–568 (2013). https://doi.org/10.1007/s00603-012-0359-2

    Article  ADS  Google Scholar 

  11. Meyer, B.R., Bazan, L.W.: A discrete fracture network model for hydraulically induced fractures: theory, parametric and case studies. In: SPE hydraulic fracturing technology conference. Society of Petroleum Engineers (2011)

  12. Yang, Y., Tang, X., Zheng, H., Liu, Q., Liu, Z.: Hydraulic fracturing modeling using the enriched numerical manifold method. Appl. Math. Model. 53, 462–486 (2018). https://doi.org/10.1016/j.apm.2017.09.024

    Article  MATH  Google Scholar 

  13. Wu, Z., Sun, H., Wong, L.N.Y.: A cohesive element-based numerical manifold method for hydraulic fracturing modelling with Voronoi grains. Rock Mech. Rock Eng. (2019). https://doi.org/10.1007/s00603-018-1717-5

    Article  Google Scholar 

  14. Yang, Y., Tang, X., Zheng, H., Liu, Q., He, L.: Three-dimensional fracture propagation with numerical manifold method. Eng. Anal. Bound. Elem. 72, 65–77 (2016). https://doi.org/10.1016/J.ENGANABOUND.2016.08.008

    Article  MathSciNet  MATH  Google Scholar 

  15. Wu, Z., Fan, L., Liu, Q.: Micro-mechanical modeling of the macro-mechanical response and fracture behavior of rock using the numerical manifold method. Eng. Geol. 225, 49–60 (2017). https://doi.org/10.1016/J.ENGGEO.2016.08.018

    Article  Google Scholar 

  16. Ha, Y.D., Lee, J., Hong, J.-W.: Fracturing patterns of rock-like materials in compression captured with peridynamics. Eng. Fract. Mech. 144, 176–193 (2015). https://doi.org/10.1016/J.ENGFRACMECH.2015.06.064

    Article  Google Scholar 

  17. Nadimi, S., Miscovic, I., McLennan, J.: A 3D peridynamic simulation of hydraulic fracture process in a heterogeneous medium. J. Pet. Sci. Eng. 145, 444–452 (2016). https://doi.org/10.1016/J.PETROL.2016.05.032

    Article  Google Scholar 

  18. Wang, Y., Zhou, X., Xu, X.: Numerical simulation of propagation and coalescence of flaws in rock materials under compressive loads using the extended non-ordinary state-based peridynamics. Eng. Fract. Mech. 163, 248–273 (2016). https://doi.org/10.1016/J.ENGFRACMECH.2016.06.013

    Article  Google Scholar 

  19. Zhou, X.-P., Wang, Y.-T.: Numerical simulation of crack propagation and coalescence in pre-cracked rock-like Brazilian disks using the non-ordinary state-based peridynamics. Int. J. Rock Mech. Min. Sci. 89, 235–249 (2016). https://doi.org/10.1016/J.IJRMMS.2016.09.010

    Article  Google Scholar 

  20. Zhou, X.P., Shou, Y.D.: Numerical simulation of failure of rock-like material subjected to compressive loads using improved peridynamic method. Int. J. Geomech. 17, 04016086 (2017). https://doi.org/10.1061/(ASCE)GM.1943-5622.0000778

    Article  Google Scholar 

  21. Rabczuk, T., Ren, H.: A peridynamics formulation for quasi-static fracture and contact in rock. Eng. Geol. 225, 42–48 (2017). https://doi.org/10.1016/J.ENGGEO.2017.05.001

    Article  Google Scholar 

  22. Vorobiev, O.Y., Morris, J.P.: Modeling dynamic fracture in granite under in situ conditions at high temperatures and pressures. Int. J. Rock Mech. Min. Sci. 113, 241–254 (2019). https://doi.org/10.1016/j.ijrmms.2018.11.007

    Article  Google Scholar 

  23. Xie, L.X., Yang, S.Q., Gu, J.C., Zhang, Q.B., Lu, W.B., Jing, H.W., Wang, Z.L.: JHR constitutive model for rock under dynamic loads. Comput. Geotech. 108, 161–172 (2019). https://doi.org/10.1016/J.COMPGEO.2018.12.024

    Article  Google Scholar 

  24. Qin, R.S., Bhadeshia, H.K.: Phase field method. Mater. Sci. Technol. 26, 803–811 (2010). https://doi.org/10.1179/174328409X453190

    Article  Google Scholar 

  25. Mikelić, A., Wheeler, M.F., Wick, T.: A phase-field method for propagating fluid-filled fractures coupled to a surrounding porous medium. Multiscale Model. Simul. 13, 367–398 (2015). https://doi.org/10.1137/140967118

    Article  MathSciNet  MATH  Google Scholar 

  26. Heider, Y., Markert, B.: A phase-field modeling approach of hydraulic fracture in saturated porous media. Mech. Res. Commun. 80, 38–46 (2017). https://doi.org/10.1016/J.MECHRESCOM.2016.07.002

    Article  Google Scholar 

  27. Wang, J., Ma, F.: Method to address brittle rock strength scatter through fracture density. Rock Mech. Rock Eng. 52, 3485–3491 (2019). https://doi.org/10.1007/s00603-019-1736-x

    Article  ADS  Google Scholar 

  28. Liu, J., Wang, J.G., Gao, F., Leung, C.F., Ma, Z.: A fully coupled fracture equivalent continuum-dual porosity model for hydro-mechanical process in fractured shale gas reservoirs. Comput. Geotech. 106, 143–160 (2019). https://doi.org/10.1016/J.COMPGEO.2018.10.017

    Article  Google Scholar 

  29. Rayudu, N.M., Tang, X., Singh, G.: Simulating three dimensional hydraulic fracture propagation using displacement correlation method. Tunn. Undergr. Space Technol. 85, 84–91 (2019). https://doi.org/10.1016/J.TUST.2018.11.010

    Article  Google Scholar 

  30. Chen, Z.: An ABAQUS Implementation of the XFEM for Hydraulic Fracture Problems. In: Effective and Sustainable Hydraulic Fracturing. InTech (2013)

  31. Gordeliy, E., Peirce, A.: Coupling schemes for modeling hydraulic fracture propagation using the XFEM. Comput. Methods Appl. Mech. Eng. 253, 305–322 (2013). https://doi.org/10.1016/J.CMA.2012.08.017

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Lecampion, B.: An extended finite element method for hydraulic fracture problems. Commun. Numer. Methods Eng. 25, 121–133 (2009). https://doi.org/10.1002/cnm.1111

    Article  MathSciNet  MATH  Google Scholar 

  33. Qingwen, R., Yuwen, D., Tiantang, Y.: Numerical modeling of concrete hydraulic fracturing with extended finite element method. Sci. China Ser. E Technol. Sci. 52, 559–565 (2009). https://doi.org/10.1007/s11431-009-0058-8

    Article  MATH  Google Scholar 

  34. Carrier, B., Granet, S.: Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model. Eng. Fract. Mech. 79, 312–328 (2012). https://doi.org/10.1016/J.ENGFRACMECH.2011.11.012

    Article  Google Scholar 

  35. Liu, D., Lecampion, B., Benedetti, L.: Modeling of the propagation of hydraulic fracture using cohesive zone models. In: 15th Swiss Geoscience Meeting, Davos, Switzerland, November 17–18, 2017 (2017)

  36. Vahab, M., Khalili, N.: X-FEM modeling of multizone hydraulic fracturing treatments within saturated porous media. Rock Mech. Rock Eng. 10, 1–21 (2018). https://doi.org/10.1007/s00603-018-1419-z

    Article  Google Scholar 

  37. Wang, H.: Numerical modeling of non-planar hydraulic fracture propagation in brittle and ductile rocks using XFEM with cohesive zone method. J. Pet. Sci. Eng. 135, 127–140 (2015). https://doi.org/10.1016/J.PETROL.2015.08.010

    Article  Google Scholar 

  38. Duan, K., Kwok, C.Y., Wu, W., Jing, L.: 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

    Article  Google Scholar 

  39. Farkas, M.P., Yoon, J.S., Zang, A., Zimmermann, G., Stephansson, O., Lemon, M., Dankó, G.: Effect of foliation and fluid viscosity on hydraulic fracturing tests in mica schists investigated using distinct element modeling and field data. Rock Mech. Rock Eng. 52, 555–574 (2019). https://doi.org/10.1007/s00603-018-1598-7

    Article  ADS  Google Scholar 

  40. Tomac, I., Gutierrez, M.: Micromechanics of hydro-thermo-mechanical processes in rock accounting for thermal convection. J. Eng. Mech. 145, 04019055 (2019). https://doi.org/10.1061/(ASCE)EM.1943-7889.0001619

    Article  Google Scholar 

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

    Article  Google Scholar 

  42. Irwin, G.R.: Analysis of stresses and strains near the end of a crack traversing a plate. J. appl, Mech (1957)

    Google Scholar 

  43. Shlyapobersky, J.: Energy analysis of hydraulic fracturing. In: The 26th U.S. Symposium on Rock Mechanics (USRMS), 26–28 June, Rapid City, South Dakota (1985)

  44. Warpinski, N., Branagan, P., Wilmer, R.: In-Situ Stress Measurements at US DOE’s Multiwell Experiment Site, Mesaverde Group, Rifle, Colorado. J. Pet. Technol. 37, 527–536 (1985)

    Article  Google Scholar 

  45. Potyondy, D., Cundall, P.: A bonded-particle model for rock. Int. J. Rock Mech. 41, 1329–1364 (2004)

    Article  Google Scholar 

  46. Potyondy, D.O.: Simulating stress corrosion with a bonded-particle model for rock. Int. J. Rock Mech. Min. Sci. 44, 677–691 (2007)

    Article  Google Scholar 

  47. Cundall, P.A.: PFC User Manual. Itasca Consulting Group Inc., Mineapolis (2004)

    Google Scholar 

  48. Snow, D.T.: Anisotropic permeability of fractured media. Water Resour. Res. 5, 1273–1289 (1969). https://doi.org/10.1029/WR005i006p01273

    Article  ADS  Google Scholar 

  49. Nasseri, M.H.B., Tatone, B.S.A., Grasselli, G., Young, R.P.: Fracture toughness and fracture roughness interrelationship in thermally treated Westerly granite. Pure Appl. Geophys. 166, 801–822 (2009)

    Article  ADS  Google Scholar 

  50. Nakajima, H., Takeda, M., Zhang, M.: Evaluation and application of the constant flow technique in testing low-permeability geo-materials. In: WM'07: 2007 Waste Management Symposium - Global Accomplishments in Environmental and Radioactive Waste Management: Education and Opportunity for the Next Generation of Waste Management Professionals, Tucson, AZ (United States), 25 Feb–1 Mar 2007 (2007)

  51. Olsen, H.W.: Darcy’s law in saturated kaolinite. Water Resour. Res. 2, 287–295 (1966)

    Article  ADS  Google Scholar 

  52. Brace, W., Walsh, J.B., Frangos, W.T.: Permeability of granite under high pressure. J. Geophys. Res. 73, 2225–2236 (1968)

    Article  ADS  Google Scholar 

  53. Kipp, M.E., Grady, D.E., Chen, E.P.: Strain-rate dependent fracture initiation. Int. J. Fract. 16, 471–478 (1980)

    Article  Google Scholar 

  54. Kirsch, G.: Die Theorie der Elastizität und die Bedürfnisse der Festigkeitslehre. Zeitschrift des Vereines Dtsch. Ingenieure. 42, 797–807 (1898)

    Google Scholar 

  55. Govender, N., Wilke, D.N., Wu, C.-Y., Khinast, J., Pizette, P., Xu, W.: Hopper flow of irregularly shaped particles (non-convex polyhedra): GPU-based DEM simulation and experimental validation. Chem. Eng. Sci. 188, 34–51 (2018). https://doi.org/10.1016/J.CES.2018.05.011

    Article  Google Scholar 

  56. Munjiza, A., Latham, J.P.: Comparison of experimental and FEM/DEM results for gravitational deposition of identical cubes. Eng. Comput. 21, 249–264 (2004). https://doi.org/10.1108/02644400410519776

    Article  MATH  Google Scholar 

  57. Frash, L.: Laboratory simulation of an enhanced geothermal reservoir (2014). https://dspace.library.colostate.edu/bitstream/handle/10217/76804/Frash_mines_0052N_10026.pdf?sequence=1&isAllowed=y. Accessed 3 Jan 2020

  58. Frash, L.P., Gutierrez, M.S.: Laboratory-scale study of hydraulic fracturing in heterogeneous media for enhanced geothermal systems and general well stimulation (2014). https://mountainscholar.org/handle/11124/17002. Accessed 3 Jan 2020

  59. Hampton, J.C.: Laboratory Hydraulic Fracture Characterization Using Acoustic Emission. Colorado School of Mines, Golden (2012)

    Google Scholar 

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Funding

This study was funded by the U.S. Department of Energy under DOE Grant No. DE-FE0002760. The opinions expressed in this paper are those of the authors and not the DOE.

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Authors and Affiliations

  1. Department of Structural Engineering, University of California San Diego, 9500 Gilman Drive #0412, La Jolla, CA, 92093-0412, USA

    Ingrid Tomac

  2. Department of Civil and Environmental Engineering, Colorado School of Mines, 1610 Illinois St., Golden, CO, 80401, USA

    Marte Gutierrez

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  1. Ingrid Tomac
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Correspondence to Ingrid Tomac.

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Tomac, I., Gutierrez, M. Micromechanics of hydraulic fracturing and damage in rock based on DEM modeling. Granular Matter 22, 56 (2020). https://doi.org/10.1007/s10035-020-01023-z

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