Rock Mechanics and Rock Engineering

, Volume 51, Issue 2, pp 491–511 | Cite as

Effect of Random Natural Fractures on Hydraulic Fracture Propagation Geometry in Fractured Carbonate Rocks

  • Zhiyuan Liu
  • Shijie Wang
  • Haiyang Zhao
  • Lei Wang
  • Wei Li
  • Yudi Geng
  • Shan Tao
  • Guangqing Zhang
  • Mian Chen
Original Paper


Natural fractures have a significant influence on the propagation geometry of hydraulic fractures in fractured reservoirs. True triaxial volumetric fracturing experiments, in which random natural fractures are created by placing cement blocks of different dimensions in a cuboid mold and filling the mold with additional cement to create the final test specimen, were used to study the factors that influence the hydraulic fracture propagation geometry. These factors include the presence of natural fractures around the wellbore, the dimension and volumetric density of random natural fractures and the horizontal differential stress. The results show that volumetric fractures preferentially formed when natural fractures occurred around the wellbore, the natural fractures are medium to long and have a volumetric density of 6–9%, and the stress difference is less than 11 MPa. The volumetric fracture geometries are mainly major multi-branch fractures with fracture networks or major multi-branch fractures (2–4 fractures). The angles between the major fractures and the maximum horizontal in situ stress are 30°–45°, and fracture networks are located at the intersections of major multi-branch fractures. Short natural fractures rarely led to the formation of fracture networks. Thus, the interaction between hydraulic fractures and short natural fractures has little engineering significance. The conclusions are important for field applications and for gaining a deeper understanding of the formation process of volumetric fractures.


Fractured reservoir Carbonate rock Natural fracture Volumetric fracturing Fracture propagation 

List of symbols


Fracture length


Cohesion strength of the natural fracture

\(C_{W}^{\text{NF}} (i)\)

Cohesion strength of the natural fracture in location i


Fracturing thickness


Stress intensity factors of mode-I and mode-II


Rock fracture toughness of mode-I and mode-II


Fluid pressure in the hydraulic fracture


Breakdown pressure of the rock matrix


Opening pressure of the natural fracture

\(p_{\text{NF}} \left( i \right)\)

Opening pressure of the natural fracture in location i


Formation pressure


Bottom hole pressure


Injection rate


Fracturing radius


Tensile strength of the rock matrix


Maximum injection volume of volumetric fracturing in single stage


Biot coefficient


Angle between the normal nature fracture and σ 1


Component of the polar coordinates at the fracture tip


Horizontal differential stress


Maximum stress difference to overcome in the fracture area


Poroelastic stress coefficient


Circumferential angle


Fracturing fluid viscosity

σ1, σ3

Maximum and minimum principle stress at wellbore


Maximum horizontal in situ stress


Minimum horizontal in situ stress


Normal stress acting on the natural fracture


Stresses induced by the pressurized hydraulic fracture

\(\sigma_{n}^{\text{NF}} (i)\)

Normal stress acting on the natural fracture in location i


Stresses induced by the opening and sliding of natural fractures

\(\sigma_{n}^{\infty }\)

Far-field in situ stresses

σr, σθ, σz

Components of wellbore stress in the polar coordinates


Overburden stress


Shearing stress acting on the natural fracture


Poisson’s ratio


Angle between the hydraulic fracture and natural fracture



This study was supported by the National Science and Technology Major Projects (No. 2016ZX05014-005-003).


  1. Aliabadian Z, Sharafisafa M, Mortazavi A (2012) Investigation of the effect of in-situ stresses and loading rate on blasting induced fracture propagation. Paper ARMA 12-146. The 46th US rock mechanics/geomechanics symposium. Chacago, IL, USA, American Rock Mechanics AssociationGoogle Scholar
  2. Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Meth Eng 45:601–620CrossRefGoogle Scholar
  3. Beugelsdijk LJL, Pater CJD, Sato K (2000) Experimental hydraulic fracture propagation in a multi-fractured medium. Paper SPE 59419. SPE Asia Pacific conference on integrated modelling for asset management. Yokohama, Japan, Society of Petroleum EngineersGoogle Scholar
  4. Blanton TL (1982) An experimental study of interaction between hydraulically induced and pre-existing fractures. Paper SPE 10847. SPE unconventional gas recovery symposium. Pittsburgh, Pennsylvania, Society of Petroleum Engineers of AIMEGoogle Scholar
  5. Blanton TL (1986) Propagation of hydraulically and dynamically induced fractures in naturally fractured reservoirs. Paper SPE 15261. SPE unconventional gas technology symposium. Louisville, Kentucky, Society of Petroleum EngineersGoogle Scholar
  6. Chen WF (1988) Plasticity for structural engineers. Springer, New YorkCrossRefGoogle Scholar
  7. Chudnovsky A, Fan J (1996) A new hydraulic fracture tip mechanism in a statistically homogeneous medium. Paper SPE 36442. SPE annual technical conference and exhibition. Denver, Colorado, Society of Petroleum Engineers, IncGoogle Scholar
  8. Chuprakov DA, Zhubayev AS (2010) A variational approach to analyze a natural fault with hydraulic fracture based on the strain energy density criterion. Theor Appl Fract Mech 53(3):221–232CrossRefGoogle Scholar
  9. Chuprakov D, Melchaeva O, Prioul R (2013) Hydraulic fracture propagation across a weak discontinuity controlled by fluid injection. Proceedings of the international conference for effective and sustainable hydraulic fracturing. Brisbane, Australia, International Society for Rock MechanicsGoogle Scholar
  10. Chuprakov D, Melchaeva O, Prioul R (2014) Injection-sensitive mechanics of hydraulic fracture interaction with discontinuities. Rock Mech Rock Eng 47:1625–1640CrossRefGoogle Scholar
  11. Clifton RJ, Abou-Sayed AS (1979) On the computation of the three-dimensional geometry of hydraulic fractures. Paper SPE 7943. Symposium on low permeability gas reservoirs. Denver, Colorado, USA, Society of Petroleum EngineersGoogle Scholar
  12. Damjanac B, Cundall P (2016) Application of distinct element methods to simulation of hydraulic fracturing in naturally fractured reservoirs. Comput Geotech 71:283–294CrossRefGoogle Scholar
  13. Daneshy AA (1974) Hydraulic fracture propagation in the presence of planes of weakness. Paper SPE 4852. SPE European Spring Meeting. Amsterdam, Netherlands, American Institute of Mining, Metallurgical, and Petroleum Engineers, IncGoogle Scholar
  14. De Pater CJ, Cleary MP, Quinn TS, Barr DT, Johnson DE, Weijers L (1994) Experimental verification of dimensional analysis for hydraulic fracturing. Paper SPE 24994. SPE European petroleum conference. Cannes, French, Society of Petroleum EngineersGoogle Scholar
  15. Erdogan F, Sih GC (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng 85(4):519–527CrossRefGoogle Scholar
  16. Fairhurst C (2013) Fractures and fracturing: hydraulic fracturing in jointed rock. In: Proceedings of the international conference for effective and sustainable hydraulic fracturing. Brisbane, Australia, International Society for Rock MechanicsGoogle Scholar
  17. Fajer E, Holt RM, Horsrud P, Raaen AM, Risnes R (2008) Petroleum related rock mechanics. Elsevier, OxfordGoogle Scholar
  18. Fan TG, Zhang GQ (2014) Laboratory investigation of hydraulic fracture networks in formations with continuous orthogonal fractures. Energy 74:164–173CrossRefGoogle Scholar
  19. Ge WF, Chen M, Jin Y (2010) Analysis of the external pressure on casings induced by salt-gypsum creep in build-up sections for horizontal wells. Rock Mech Rock Eng 44:711–723CrossRefGoogle Scholar
  20. Gu H, Weng X, Lund J, Mack M, Ganguly U, Suarez-Rivera R (2011) Hydraulic fracture crossing natural fracture at nonorthogonal angles: a criterion and its validation. Paper SPE 139984. SPE Hydraulic Fracturing Technology Conference and exhibition. Woodlands, Texas, USA, Society of Petroleum EngineersGoogle Scholar
  21. Gudmundsson A (2011) Rock fractures in geological processes. Cambridge University Press, Cambridge, p 578CrossRefGoogle Scholar
  22. Gudmundsson A, Brenner SL (2001) How hydrofractures become arrested. Terra Nova 13(6):456–462CrossRefGoogle Scholar
  23. Jaeger JC, Cook NGW, Zimmerman RW (2007) Fundamentals of rock mechanics. Blackwell, OxfordGoogle Scholar
  24. Jaimes MG, Castillo RD, Mendoza SA (2012) High energy gas fracturing: a technique of hydraulic prefracturing to reduce the pressure losses by friction in the near wellbore—a colombian field application. Paper SPE 152886. SPE Latin American and Caribbean Petroleum Engineering Conference. Mexico City, Mexico, Society of Petroleum EngineersGoogle Scholar
  25. Jin Y, Yuan JB, Chen M, Chen KP, Lu YH, Wang HY (2011) Determination of rock fracture toughness KIIC and its relationship with tensile strength. Rock Mech Rock Eng 44:621–627CrossRefGoogle Scholar
  26. Krugman DG (1985) A brittle fracture theory for understanding high energy gas fracturing. Paper SPE 1568. Society of Petroleum Engineers.
  27. Lamont N, Jessen F (1963) The effects of existing fractures in rocks on the extension of hydraulic fractures. Paper SPE 419. The 37th annual fall meeting of SPE. Los Angeles, CA, USA, Society of Petroleum EngineersGoogle Scholar
  28. Li JH, Zhang LM (2011) Connectivity of a network of random discontinuities. Comput Geotech 38(2):217–226CrossRefGoogle Scholar
  29. Liu GH, Pang F, Chen ZX (2000) Development of scaling laws for hydraulic fracture simulation tests. J Univ Pet 24(5):45–48 (in Chinese) Google Scholar
  30. Liu ZY, Chen M, Zhang GQ (2014) Analysis of the influence of a natural fracture network on hydraulic fracture propagation in carbonate formations. Rock Mech Rock Eng 47(2):575–587CrossRefGoogle Scholar
  31. Liu P, Ju Y, Ranjith PG, Zheng ZM, Chen JL (2016a) Experimental investigation of the effects of heterogeneity and geostress difference on the 3D growth and distribution of hydrofracturing cracks in unconventional reservoir rocks. J Nat Gas Sci Eng 35:541–554CrossRefGoogle Scholar
  32. Liu ZY, Jin Y, Chen M, Hou B (2016b) Analysis of non-planar multi-fracture propagation from layered-formation inclined-well hydraulic fracturing. Rock Mech Rock Eng 49:1747–1758CrossRefGoogle Scholar
  33. Long JCS, Witherspoon PA (1985) The relationship of the degree of inter connectivity to permeability in fracture networks. J Geophys Res 90(B4):3087–3097CrossRefGoogle Scholar
  34. Min KB, Jing L, Stephansson O (2004) Determining the equivalent permeability tensor for fractured rock masses using a stochastic REV approach: method and application to the field data from Sellafield, UK. Hydrol J 12(5):497–510Google Scholar
  35. Nadimi S, Miscovic I, McLennan J (2016) A 3D peridynamic simulation of hydraulic fracture process in a heterogeneous medium. J Petrol Sci Eng 145:444–452CrossRefGoogle Scholar
  36. Olson JE (2008) Multi-fracture propagation modeling: applications to hydraulic fracturing in shales and tight gas sands. Paper ARMA 08-327. The 42nd U.S. Rock Mechanics Symposium (USRMS). San Francisco, American Rock Mechanics AssociationGoogle Scholar
  37. Olson JE, Taleghani AD (2009) Modeling simultaneous growth of multiple hydraulic fractures and their interaction with natural fractures. Paper SPE 119739. SPE Hydraulic Fracturing Technology Conference. The Woodlands, Texas, Society of Petroleum EngineersGoogle Scholar
  38. Pirayehgar A, Dusseault MB (2014) The stress ratio effect on hydraulic fracturing in the presence of natural fractures. Paper ARMA 14-7138. The 48th US rock mechanics/geomechanics symposium. Minneapolis, MN, USA, American Rock Mechanics AssociationGoogle Scholar
  39. Potluri NK, Zhu D, Hill AD (2005) The effect of natural fractures on hydraulic fracture propagation. Paper SPE 94568. SPE European formation damage conference. Sheveningen, The Netherlands, Society of Petroleum EngineersGoogle Scholar
  40. Rahman MM, Aghighi MA, Rahman S, Ravoof S (2009a) Interaction between induced hydraulic fracture and pre-existing natural fracture in a poro-elastic environment: effect of pore pressure change and the orientation of natural fractures. Paper SPE 122574. Asia Pacific oil and gas conference & exhibition. Jakarta, Indonesia, Society of Petroleum EngineersGoogle Scholar
  41. Rahman MM, Aghighi MA, Shaik AR (2009b) Numerical modeling of fully coupled hydraulic fracture propagation in naturally fractured poro-elastic reservoirs. Paper SPE 121903. EUROPEC/EAGE conference and exhibition. Amsterdam, The Netherlands, Society of Petroleum EngineersGoogle Scholar
  42. Renshaw CE, Pollard DD (1995) An experimentally verified criterion for propagation across unbonded frictional interfaces in brittle, linear elastic materials. Int J Rock Mech Min Sci 32(3):237–249CrossRefGoogle Scholar
  43. Shi GH (1992) Manifold method of material analysis. In: Transactions of the 9th army conference on applied mathematics computing, Minneapolis, USA, pp 57–76Google Scholar
  44. Shimizu H, Hiyama M, Ito T, Tamagawa T, Tezuka K (2014) Flow-coupled dem simulation for hydraulic fracturing in pre-fractured rock. Paper ARMA 14-7365. The 48th US rock mechanics/geomechanics symposium. Minneapolis, MN, USA, American Rock Mechanics AssociationGoogle Scholar
  45. Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48:175–209CrossRefGoogle Scholar
  46. Taleghani AD, Olson JE (2009) Numerical modeling of multi-stranded hydraulic fracture propagation: accounting for the interaction between induced and natural fractures. Paper SPE 124884. SPE annual technical conference and exhibition. New Orleans, Louisiana, Society of Petroleum EngineersGoogle Scholar
  47. Thiecelin M, Roegiers JC, Boone TJ, Ingraffea AR (1987) An investigation of the material parameters that govern the behavior of fractures approaching rock interfaces. In: The 6th international congress of rock mechanics, pp 263–269Google Scholar
  48. Thiercelin M, Makkhyu E (2007) Stress field in the vicinity of a natural fault activated by the propagation of an induced hydraulic fracture. Paper ARMA 07-201. American Rock Mechanics AssociationGoogle Scholar
  49. Wang WW, Olson JE, Prodanović M (2013) Natural and hydraulic fracture interaction study based on semi-circular bending experiments. Paper SPE 168714. Unconventional resources technology conference. Denver, Colorado, USA, Society of Petroleum EngineersGoogle Scholar
  50. Wang S, Zhao JZ, Li YM (2014) Hydraulic fracturing simulation of complex fractures growth in naturally fractured shale gas reservoir. Arab J Sci Eng 39:7411–7419CrossRefGoogle Scholar
  51. Warpinski NR (1991) Hydraulic fracturing in tight, fissured media. Paper SPE 20154. SPE J Pet Technol 43(2): 146–151, 208–209Google Scholar
  52. Warpinski NR, Teufel LW (1987) Influence of geologic discontinuities on hydraulic fracture propagation (includes associated papers 17011 and 17074). Paper SPE 13224. SPE. J Pet Technol 39(2):209–220CrossRefGoogle Scholar
  53. Warpinski NR, Schmidt RA, Cooper PW, Walling HC, Northrop DA (1979) High-energy gas Frac: multiple fracturing in a wellbore. The 20th U.S. symposium on rock mechanics. Austin, TexasGoogle Scholar
  54. Warpinski NR, Kramm RC, Heinze JR, Waltman CK (2005) Comparison of single and dual-array microseismic mapping techniques in the barnett shale. Paper SPE 95568. Presented at the 2005 SPE annual technical conference and exhibition. Dallas, Texas, Society of Petroleum EngineersGoogle Scholar
  55. Weng XW, Kresse O, Chuprakov D, Cohen C-E, Prioul R, Ganguly U (2014) Applying complex fracture model and integrated workflow in unconventional reservoirs. J Pet Sci Eng 124:468–483CrossRefGoogle Scholar
  56. Yew CH, Weng XW (2015) Mechanics of hydraulic fracturing. Elsevier, OxfordGoogle Scholar
  57. Yoon JS, Zang A, Stephansson O (2014) Numerical investigation on optimized stimulation of intact and naturally fractured deep geothermal reservoirs using hydro-mechanical coupled discrete particles joints model. Geothermics 52:165–184CrossRefGoogle Scholar
  58. Zhang GQ, Chen M (2010) Dynamic fracture propagation in hydraulic re-fracturing. J Pet Sci Eng 70(3–4):266–272CrossRefGoogle Scholar
  59. Zhang Z, Ghassemi A (2011) Simulation of hydraulic fracture propagation near a natural fracture using virtual multidimensional internal bonds. Int J Numer Anal Meth Geomech 35(4):480–495CrossRefGoogle Scholar
  60. Zhang F, Nagel N, Sheibani F (2014) Evaluation of hydraulic fractures crossing natural fractures at high angles using a hybrid discrete-continuum model. Paper ARMA 14-7540. The 48th US rock mechanics/geomechanics symposium. Minneapolis, MN, USA, American Rock Mechanics AssociationGoogle Scholar
  61. Zhao HF, Chen M (2010) Extending behavior of hydraulic fracture when reaching formation interface. J Pet Sci Eng 74(1–2):26–30CrossRefGoogle Scholar
  62. Zhou XP, Wang YT (2016) 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 89:235–249Google Scholar
  63. Zhou XP, Yang HQ (2012) Multiscale numerical modeling of propagation and coalescence of multiple cracks in rock masses. Int J Rock Mech Min Sci 55:15–27Google Scholar
  64. Zhou J, Chen M, Jin Y, Zhang GQ (2008) Analysis of fracture propagation behavior and fracture geometry using a tri-axial fracturing system in naturally fractured reservoirs. Int J Rock Mech Min Sci 45(7):1143–1152CrossRefGoogle Scholar
  65. Zhou J, Jin Y, Chen M (2010) Experimental investigation of hydraulic fracturing in random naturally fractured blocks. Int J Rock Mech Min Sci 47(7):1193–1199CrossRefGoogle Scholar
  66. Zhou XP, Bi J, Qian QH (2015) Numerical simulation of crack growth and coalescence in rock-like materials containing multiple pre-existing flaws. Rock Mech Rock Eng 48:1097–1114CrossRefGoogle Scholar
  67. Zhou J, Huang H, Deo M (2016) Simulation of hydraulic and natural fracture interaction using a coupled DFN-DEM model. Paper ARMA 16-739. The 50th US rock mechanics/geomechanics symposium. Houston, Texas, USA, American Rock Mechanics AssociationGoogle Scholar
  68. Zou YS, Ma XF, Zhang SC, Zhou T, Li H (2016) Numerical investigation into the influence of bedding plane on hydraulic fracture network propagation in shale formations. Rock Mech Rock Eng 49(9):3597–3614CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria 2017

Authors and Affiliations

  • Zhiyuan Liu
    • 1
  • Shijie Wang
    • 1
  • Haiyang Zhao
    • 1
  • Lei Wang
    • 1
  • Wei Li
    • 1
  • Yudi Geng
    • 1
  • Shan Tao
    • 1
  • Guangqing Zhang
    • 2
  • Mian Chen
    • 2
  1. 1.Sinopec Northwest Oilfield BranchResearch Institute of Petroleum EngineeringÜrümqiChina
  2. 2.State Key Laboratory of Petroleum Resources and ProspectingChina University of PetroleumBeijingChina

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