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A Comprehensive Model of a Hydraulic Fracture Interacting with a Natural Fracture: Analytical and Numerical Solution

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Abstract

In this paper, a comprehensive model combining analytical and numerical solution has been developed to study the interaction between a hydraulic fracture (HF) and a natural fracture (NF). A new analytical solution is presented to analyze the interaction mechanism with consideration of fluid lag and stress singularities near the HF tip, and to predict whether the HF crosses the NF when the propagating tip reaches the interface and the fluid front remains farther back. A new numerical solution based on the displacement discontinuity method and finite-volume method is derived to solve the problem of coupled rock deformation, fluid transport, stress interference, interface slipping, and opening, and to investigate the interaction between an HF and an NF after the fluid front reaching the interface. Based on the comprehensive model, sensitivity analyses of key influence parameters are implemented. The analyses indicate that the HF tends to cross the NF under conditions of high principal stress difference, high intersection angle, high interfacial friction, high injection rate, high fracturing fluid viscosity, and low initial conductivity of the NF. Moreover, the morphology of HF is significantly affected by two engineering parameters, the injection rate and the fracturing fluid viscosity. The same value of the product of these two parameters results in the same HF morphology at the times of the same injected fluid volumes. The new comprehensive model is validated with published analytical and numerical criterions and laboratory tests.

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Abbreviations

σ x :

Principal stress component along the x-axis

σ y :

Principal stress component along the y-axis

α :

Intersection angle

P frac :

Fluid pressure in the hydraulic fracture

\(\sigma _{{\text{n}}}^{\infty }\) :

Remote boundary normal stress

\(\sigma _{{\text{s}}}^{{{\text{local}}}}\) :

Locally applied shear traction

\(\sigma _{{\text{s}}}^{\infty }\) :

Remote boundary shear stress

\({\text{D}}_{{\text{s}}}^{j},D_{{\text{n}}}^{j}\) :

Shear and normal displacement discontinuities of element j

\(A_{{{\text{ss}}}}^{{i,j}},A_{{{\text{sn}}}}^{{i,j}},A_{{{\text{ns}}}}^{{i,j}},A_{{{\text{nn}}}}^{{i,j}}\) :

Boundary influence coefficients for the stresses

q :

Injection volume rate per unit fracture height

A :

Cross-sectional area of the fracture

q L :

Fluid leak-off rate

µ :

Fracturing fluid viscosity

Q 0 :

Injection volume rate per unit fracture height at the inlet

\({\phi _{{\text{nf}}}}\) :

Porosity of NF

C nf :

Compressibility of NF

k nf :

Permeability of NF

p 0 :

Original formation pressure

p int :

Internal fluid pressure of HF/NF intersection point

L nf :

Distance from the intersection point to the tip of the NF

θ 0 :

Extend direction relative to the current direction

K I, K II :

Mode I and II stress intensity factors

E :

Young’s modulus

a :

Half element length

v :

Poisson’s ratio

K IC :

Tensile fracture toughness

σ H :

Maximum horizontal principal stress

σ h :

Minimum horizontal principal stress

r, θ :

Polar coordinates at the fracture tip

r c :

Critical radius

τ 0 :

Inherent shear strength of the NF plane

K f :

Coefficient of friction of NF surface

T :

Tensile strength of rock

τ nf :

Shear stress acting on NF surface

σ nf :

Normal stress acting on NF surface

\(K_{{{\text{IC}}}}^{{{\text{nf}}}}\) :

Tensile fracture toughness of NF

κ :

Dimensionless toughness

References

  • Adachi J, Siebrits E, Peirce A, Desroches J (2007) Computer simulation of hydraulic fractures. Int J Rock Mech Min Sci 44(5):739–757

    Article  Google Scholar 

  • Aud WW, Wright TB, Cipolla CL, Harkrider JD (1994) The effect of viscosity on near-wellbore tortuosity and premature screenouts. In: SPE 69th annual technical conference and exhibition held in New Orleans, LA, USA, 25–28 September

  • Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, London

    Google Scholar 

  • Behnia M, Goshtasbi K, Marji MF, Golshani A (2015) Numerical simulation of interaction between hydraulic and natural fractures in discontinuous media. Acta Geotech 10(4):533–546

    Article  Google Scholar 

  • Beugelsdijk LJL, Pater CJD, Sato K (2000) Experimental hydraulic fracture propagation in a multi-fractured medium. Paper SPE 59419. In: SPE Asia Pacific conference on integrated modelling for asset management, Yokohama, Japan

  • Blanton TL (1982) An experimental study of interaction between hydraulically induced and pre-existing fractures. In: Society of petroleum engineers unconventional gas technology symposium, Pittsburgh, May 16–18

  • Blanton TL (1986) Propagation of hydraulically and dynamically induced fractures in naturally fractured reservoirs. In: Society of petroleum engineers unconventional gas technology symposium, Louisville, May 18–21

  • Broek D (1982) Elementary engineering fracture mechanics, 4th edn. Martinus Nijhoff Publishers, The Hague

    Book  Google Scholar 

  • Bunger AP, Kear J, Jeffrey RG, Prioul R, Chuprakov D (2015) Laboratory investigation of hydraulic fracture growth through weak discontinuities with active ultrasound monitoring. In: Proceedings of the 13th international congress on rock Mechanics, Montreal, May 10–13, ISRM

  • Chen P, Rahman MM (2015) A novel approach to predict interaction between hydraulic fracture and natural fracture using artificial neural networks. In: SPE/IATMI Asia Pacific oil and gas conference and exhibition, Bali, Indonesia, October 20–22

  • Chen P, Rahman MM, Sarma HK (2014) Interaction between hydraulic fracture and natural fracture-a new prediction model by adaptive neuro-fuzzy inference system (ANFIS). In: Abu Dhabi international petroleum exhibition and conference, Abu Dhabi, UAE, November 10–13

  • Chen Z, Jeffrey RG, Zhang X, Kear J (2017) Finite-element simulation of a hydraulic fracture interacting with a natural fracture. SPE J 22(01):219–234

    Article  Google Scholar 

  • Cheng W, Jin Y, Chen Y, Zhang Y, Diao C, Wang Y (2014a) Experimental investigation about influence of natural fracture on hydraulic fracture propagation under different fracturing parameters. In: ISRM International symposium-8th Asian rock mechanics symposium, Sapporo, Japan, October 14–16

  • Cheng W, Jin Y, Chen M, XU T, Zhang YK, Ce D (2014b) A criterion for identifying hydraulic fractures crossing natural fractures in 3D space. Pet Explor Dev 41(3):371–376

    Article  Google Scholar 

  • Cheng W, Jin Y, Chen M (2015) Reactivation mechanism of natural fractures by hydraulic fracturing in naturally fractured shale reservoirs. J Nat Gas Sci Eng 27:1357–1365

    Article  Google Scholar 

  • Chuprakov D, Akulich AV, Siebrits E, Thiercelin M (2011) Hydraulic-fracture propagation in a naturally fractured reservoir. SPE Prod Oper 26(01):88–97

    Google Scholar 

  • Chuprakov D, Melchaeva O, Prioul R (2013) Hydraulic fracture propagation across a weak discontinuity controlled by fluid injection. Effective and sustainable hydraulic fracturing. InTech, London, pp 157–181. https://doi.org/10.5772/55941

    Google Scholar 

  • Chuprakov D, Melchaeva O, Prioul R (2014) Injection-sensitive mechanics of hydraulic fracture interaction with discontinuities. Rock Mech Rock Eng 47(5):1625–1640

    Article  Google Scholar 

  • Crank J (1979) The mathematics of diffusion. Oxford University Press, Oxford

    Google Scholar 

  • Crouch SL, Starfield AM (1983) Boundary element methods in solid mechanics. George Allen & Unwin, London

    Book  Google Scholar 

  • Daneshy AA (1974) Hydraulic fracture propagation in the presence of planes of weakness. In: SPE European spring meeting, 29–30 May, Amsterdam, The Netherlands

  • Detournay E (2004) Propagation regimes of fluid-driven fractures in impermeable rocks. Int J Geomech 4(1):35–45

    Article  Google Scholar 

  • Erdogan F, Sih GC (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng 85(4):519–525

    Article  Google Scholar 

  • Fatahi H, Hossain M, Sarmadivaleh M (2017) Numerical and experimental investigation of the interaction of natural and propagated hydraulic fracture. J Nat Gas Sci Eng 37:409–424

    Article  Google Scholar 

  • Fu P, Cruz L, Moos D, Settgast RR, Ryerson FJ (2015) Numerical investigation of a hydraulic fracture bypassing a natural fracture in 3D. In: American rock mechanics association 49th US rock mechanics/geomechanics symposium, San Francisco, CA, June 28–July 1

  • Garagash DI (2006) Propagation of a plane-strain hydraulic fracture with a fluid lag: early-time solution. Int J Solids Struct 43(18–19):5811–5835

    Article  Google Scholar 

  • Gu H, Weng X (2010) Criterion for fractures crossing frictional interfaces at non-orthogonal angles. In: 44th US rock mechanics symposium and 5th U.S.–Canada rock mechanics symposium, Salt Lake City, UT, June 27–30

  • Gu H, Weng X, Lund JB, Mack MG, Ganguly U, Suarez-Rivera R (2012) Hydraulic fracture crossing natural fracture at nonorthogonal angles: a criterion and its validation. SPE Prod Oper 27(01):20–26

    Google Scholar 

  • Guo T, Zhang S, Qu Z, Zhou T, Xiao Y, Gao J (2014) Experimental study of hydraulic fracturing for shale by stimulated reservoir volume. Fuel 128:373–380

    Article  Google Scholar 

  • Hou B, Chen M, Jin Y, Lin B, Diao C, Zhang X (2015) Optimum condition of hydraulic fracture–natural fracture interaction in shale block experiments. In: American rock mechanics association 49th US rock mechanics/geomechanics symposium, San Francisco, California, June 28–July 1

  • Jaeger JC, Cook NGW (1976) Fundamentals of rock mechanics. Halsted Press, New York

    Google Scholar 

  • Jamison W, Azad A (2017) The hydraulic fracture–natural fracture network configuration in shale reservoirs: geological limiting factors. J Pet Sci Eng 159:205–229

    Article  Google Scholar 

  • Jeffrey RG, Vandamme L, Roegiers JC (1987) Mechanical interactions in branched or subparallel hydraulic fractures. In: Society of petroleum engineers low permeability reservoirs symposium, Denver, Colorado, May 18–19

  • Jeffrey RG, Bunger A, Lecampion B, Zhang X, Chen ZR, Van AA, Allison DP, De BW, Dudley JW, Siebrits E, Thiercelin MJ (2009) Measuring hydraulic fracture growth in naturally fractured rock. In: SPE annual technical conference and exhibition, Louisiana, October 4–7

  • Jeffrey RG, Kear J, Kasperczyk D, Zhang X, Chuprakov D, Prioul R, Chouten J (2015) A 2D experimental method with results for hydraulic fractures crossing discontinuities. In: 49th US rock mechanics/geomechanics symposium, San Francisco, CA, June 28–July 1

  • Jiang T, Zhang J, Wu H (2016) Experimental and numerical study on hydraulic fracture propagation in coalbed methane reservoir. J Nat Gas Sci Eng 35:455–467

    Article  Google Scholar 

  • Kear J, Kasperczyk D, Zhang X, Jeffrey RG, Chuprakov D, Prioul R (2017) 2D experimental and numerical results for hydraulic fractures interacting with orthogonal and inclined discontinuities. In: 51st US rock mechanics/geomechanics symposium, San Francisco, CA, June 25–28

  • Keshavarzi R, Jahanbakhshi R (2013) Investigation of hydraulic and natural fracture interaction: numerical modeling or artificial intelligence? Effective and sustainable hydraulic fracturing. InTech, London, pp 1039–1058. https://doi.org/10.5772/56382

    Google Scholar 

  • Kresse O, Weng X (2013) Hydraulic fracturing in formations with permeable natural fractures. Effective and sustainable hydraulic fracturing. InTech, London, pp 287–310

    Google Scholar 

  • Kresse O, Weng X, Chuprakov D, Prioul R, Cohen C (2013) Effect of flow rate and viscosity on complex fracture development in UFM model. Effective and sustainable hydraulic fracturing. InTech, London, pp 183–210. https://doi.org/10.5772/56406

    Google Scholar 

  • Lamont N, Jessen F (1963) The effects of existing fractures in rocks on the extension of hydraulic fractures. JPT 20(2):203–209

    Article  Google Scholar 

  • Llanos EM, Jeffrey RG, Hillis R, Zhang X (2017) Hydraulic fracture propagation through an orthogonal discontinuity: a laboratory, analytical and numerical study. Rock Mech Rock Eng 50(8):2101–2118

    Article  Google Scholar 

  • McClure MW, Horne RN (2013) Discrete fracture network modeling of hydraulic stimulation: coupling flow and geomechanics. Springer Science & Business Media, New York

    Book  Google Scholar 

  • Medlin WL, Masse L (1984) Laboratory experiments in fracture propagation. SPE J 24(03):256–268

    Google Scholar 

  • Olson JE (1991) Fracture mechanics analysis of joints and veins. Dissertation, Stanford University

  • Olson JE (2007) Fracture aperture, length and pattern geometry development under biaxial loading: a numerical study with applications to natural, cross-jointed systems. Geol Soc Lond Spec Publ 289(1):123–142

    Article  Google Scholar 

  • Olson JE, Bahorich B, Holder J (2012) Examining hydraulic fracture: natural fracture interaction in hydrostone block experiments. In: SPE hydraulic fracturing technology conference, Texas, February 6–8

  • Potluri NK, Zhu D, Hill AD (2005) The effect of natural fractures on hydraulic fracture propagation. In: SPE European formation damage conference. Society of Petroleum Engineers, Scheveningen, Netherlands, May 25–27

  • 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):237–249

    Article  Google Scholar 

  • Sarmadivaleh M, Rasouli V (2014) Modified Reinshaw and Pollard criteria for a non-orthogonal cohesive natural interface intersected by an induced fracture. Rock Mech Rock Eng 47(6):2107–2115

    Article  Google Scholar 

  • Sesetty V, Ghassemi A (2012) Simulation of hydraulic fractures and their interactions with natural fractures. In: American rock mechanics association 46th US rock mechanics/geomechanics symposium, Texas, June 24–27

  • Suarez RR, Connor B, Kieschnick J, Green S (2006) Laboratory experiments of hydraulic fracturing on glass plates help investigating basic conditions for fracture branching and fracture containment along interfaces. In: The 41st U.S. symposium on rock mechanics (USRMS), Golden, Colorado, June 17–21

  • Taheri-Shakib J, Ghaderi A, Hosseini S, Hashemi A (2016) Debonding and coalescence in the interaction between hydraulic and natural fracture: accounting for the effect of leak-off. J Nat Gas Sci Eng 36:454–462

    Article  Google Scholar 

  • Taleghani AD, Olson JE (2011) Numerical modeling of multi-stranded hydraulic fracture propagation: accounting for the interaction between induced and natural fractures. SPE J 16(03):575–581

    Article  Google Scholar 

  • Taleghani AD, Olson JE (2013) How natural fractures could affect hydraulic-fracture geometry. SPE J 19(01):161–171

    Article  Google Scholar 

  • Taleghani AD, Gonzalez-Chavez M, Hao H, Asala H (2018) Numerical simulation of hydraulic fracture propagation in naturally fractured formations using the cohesive zone model. J Pet Sci Eng 165:42–57

    Article  Google Scholar 

  • Tan P, Jin Y, Han K, Hou B, Chen M, Guo X, Gao J (2017) Analysis of hydraulic fracture initiation and vertical propagation behavior in laminated shale formation. Fuel 206:482–493

    Article  Google Scholar 

  • Teufel L, Clark J (1984) Hydraulic fracture propagation in layered rock: experimental studies of fracture containment. SPE J 24(1):19–32

    Google Scholar 

  • Thiercelin M, Roegiers JC, Boone TJ, Ingraffea AR (1987) An investigation of the material parameters that govern the behavior of fractures approaching rock interfaces. In: 6th International congress of rock mechanics, pp 263–269

  • Van Dam DB, De Pater CJ, Romijn R (2000) Analysis of hydraulic fracture closure in laboratory experiments. SPE Prod Facil 15(03):151–158

    Article  Google Scholar 

  • Wang X, Shi F, Liu C, Lu D, Liu H, Wu H (2018) Extended finite element simulation of fracture network propagation in formation containing frictional and cemented natural fractures. J Nat Gas Sci Eng 50:309–324

    Article  Google Scholar 

  • Warpinski NR (1985) Measurement of width and pressure in a propagating hydraulic fracture. SPE J 25(01):46–54

    Google Scholar 

  • Warpinski NR, Teufel LW (1987) Influence of geologic discontinuities on hydraulic fracture propagation. J Pet Technol 39:209–220

    Article  Google Scholar 

  • Wasantha PLP, Konietzky H (2016) Fault reactivation and reservoir modification during hydraulic stimulation of naturally-fractured reservoirs. J Nat Gas Sci Eng 34:908–916

    Article  Google Scholar 

  • Wasantha PLP, Konietzky H, Weber F (2017) Geometric nature of hydraulic fracture propagation in naturally-fractured reservoirs. Comput Geotech 83:209–220

    Article  Google Scholar 

  • Williams JG, Ewing PD (1972) Fracture under complex stress—the angled crack problem. Int J Fract Mech 8(4):441–446

    Google Scholar 

  • Yao Y, Wang W, Keer LM (2017) An energy based analytical method to predict the influence of natural fractures on hydraulic fracture propagation. Eng Fract Mech 189:232–245

    Article  Google Scholar 

  • Zhang X, Jeffrey RG (2008) Reinitiation or termination of fluid driven fractures at frictional bedding interfaces. J Geophys Res Solid Earth 113(B08416):1–16 (Artn B08416)

    Google Scholar 

  • Zhang X, Jeffrey RG (2016) Fluid-driven nucleation and propagation of splay fractures from a permeable fault. J Geophys Res Solid Earth 121(7):5257–5277

    Article  Google Scholar 

  • Zhang X, Jeffrey RG, Thiercelin M (2007a) Deflection and propagation of fluid-driven fractures at frictional bedding interfaces: a numerical investigation. J Struct Geol 29(3):396–410

    Article  Google Scholar 

  • Zhang X, Thiercelin MJ, Jeffrey RG (2007b) Effects of frictional geological discontinuities on hydraulic fracture propagation. In: Society of petroleum engineers hydraulic fracturing technology conference, Texas, USA, January 29–31

  • 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):1143–1152

    Article  Google Scholar 

  • 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):1193–1199

    Article  Google Scholar 

  • Zou C, Zhang G, Yang Z et al (2013) Geological concepts, characteristics, resource potential and key techniques of unconventional hydrocarbon: on unconventional petroleum geology. Pet Explor Dev 40(4):385–399

    Article  Google Scholar 

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Acknowledgements

The authors gratefully acknowledge the support of the Major Program of the National Natural Science Foundation of China (Grant no. 51490653), Sichuan Youth Science and Technology Innovation Research Team Program (2017TD0013) and Sichuan Science and Technology Innovation Seedling Project (2018055). Wenjun Xu gratefully acknowledges the support of China Scholarship Council (CSC) for sponsoring the visit to University of New South Wales to complete this research study.

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Authors and Affiliations

  1. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610500, China

    Wenjun Xu, Jinzhou Zhao & Yongming Li

  2. School of Minerals and Energy Resources Engineering, University of New South Wales, Sydney, 2052, Australia

    Wenjun Xu, Sheik S. Rahman & Yudong Yuan

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  1. Wenjun Xu
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Correspondence to Jinzhou Zhao.

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Xu, W., Zhao, J., Rahman, S.S. et al. A Comprehensive Model of a Hydraulic Fracture Interacting with a Natural Fracture: Analytical and Numerical Solution. Rock Mech Rock Eng 52, 1095–1113 (2019). https://doi.org/10.1007/s00603-018-1608-9

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