Skip to main content
SpringerLink
Log in

Investigation of the Influence of Natural Cavities on Hydraulic Fracturing Using Phase Field Method

  • Research Article - Petroleum Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

In this paper, the influence of natural cavities on the propagation of hydraulic fractures is investigated using the phase field method. The deflection behaviour of a fracture during its propagation is firstly verified against published experimental data. Then, a sensitivity analysis on the mechanical behaviour of fracture propagation near a cavity is conducted. The fracture deflection is quantified in terms of the deviation distance and deflection point. The influence of the Young’s modulus ratio between the cavity and rock mass (Er= Ecave/Erock), the differential stress (Sd= Sx − Sy) and the relative spatial position of the fracture and cavity (lr) on the propagation trajectory are considered. Simulation results show that with the decrease in Er, crack path deviation becomes more prominent. With the increase in Sd, hydraulic fractures tend to propagate along the direction of maximum horizontal geostress. As lr varies, the deflection of the hydraulic fracture can be classified into three regimes: (1) the deflection is negligible; (2) the hydraulic fracture deflects and approaches the natural cavity, but does not connect with it; (3) the hydraulic fracture deflects and connects with the natural cavity. The results could be used as guidance for field design of stimulation scheme in carbonate oil/gas reservoirs.

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
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29

Similar content being viewed by others

Abbreviations

Ω :

The domain of a brittle medium

U :

Displacement field

\({\varvec{\upvarepsilon}}({\mathbf{u}})\) :

Strain tensor

\(\sigma_{ij}\) :

Stress

Γ :

Crack set

\(\bar{\gamma }\) :

Body force

\({\bar{\mathbf{t}}}\) :

Surface traction

\(\varPi ({\mathbf{u}},\varGamma )\) :

Energy functional

\(\psi ({\varvec{\upvarepsilon}}({\mathbf{u}}))\) :

Strain energy density

G c :

Critical energy release rate

S :

Phase field

\(\epsilon\) :

The width of the transition zone of s

\(\dot{E}\) :

The evolution of the degrading strain energy

D :

Dissipation of the fracture

P :

External power

\(\psi_{0}^{ + } ({\varvec{\upvarepsilon}}({\mathbf{u}}))\) :

Strain energy density function for extension state

\(\psi_{0}^{ - } ({\varvec{\upvarepsilon}}({\mathbf{u}}))\) :

Strain energy density function for compression state

λ :

First lame constant

μ :

Shear modulus

\(\phi\) :

Crack dissipation per unit volume

\(\beta\) :

Driving force field

\(\eta\) :

Viscosity parameter

\(\gamma\) :

Crack surface density function

L :

Regularization parameter

Ρ :

The bulk density of brittle rock

η d :

Damping viscosity

p :

Fluid pressure

α :

Biot coefficient

References

  1. Kazemi, H.: Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution. Soc. Petrol. Eng. J. 9(04), 451–462 (2013). https://doi.org/10.2118/2156-a

    Article  Google Scholar 

  2. Tang, X.; Wu, S.; Zheng, C.; Zhang, J.: A novel virtual node method for polygonal elements. Appl. Math. Mech. 30(10), 1233 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. 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)

    Article  Google Scholar 

  4. Warren, J.; Root, P.J.: The behavior of naturally fractured reservoirs. Soc. Petrol. Eng. J. 3(03), 245–255 (1963)

    Article  Google Scholar 

  5. Dokhani, V.; Yu, M.; Gao, C.; Bloys, J.: Investigating the relation between sorption tendency and hydraulic properties of shale formations. J. Energy Res. Technol. 140(1), 012902 (2017). https://doi.org/10.1115/1.4037480

    Article  Google Scholar 

  6. Rui, Z.; Cui, K.; Wang, X.; Lu, J.; Chen, G.; Ling, K.; Patil, S.: A quantitative framework for evaluating unconventional well development. J. Petrol. Sci. Eng. 166, 900–905 (2018). https://doi.org/10.1016/j.petrol.2018.03.090

    Article  Google Scholar 

  7. Rui, Z.; Guo, T.; Feng, Q.; Qu, Z.; Qi, N.; Gong, F.: Influence of gravel on the propagation pattern of hydraulic fracture in the glutenite reservoir. J. Petrol. Sci. Eng. 165, 627–639 (2018). https://doi.org/10.1016/j.petrol.2018.02.067

    Article  Google Scholar 

  8. Yang, T.H.; Tham, L.G.; Tang, C.A.; Liang, Z.Z.; Tsui, Y.: Influence of heterogeneity of mechanical properties on hydraulic fracturing in permeable rocks. Rock Mech. Rock Eng. 37(4), 251–275 (2004). https://doi.org/10.1007/s00603-003-0022-z

    Article  Google Scholar 

  9. Dahi Taleghani, A.; Olson, J.E.: How natural fractures could affect hydraulic-fracture geometry. SPE J. 19(01), 161–171 (2013)

    Article  Google Scholar 

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

    Google Scholar 

  11. Potluri, N.; Zhu, D.; Hill, A.D.: The effect of natural fractures on hydraulic fracture propagation. In: SPE European Formation Damage Conference 2005. Society of Petroleum Engineers

  12. Weng, X.; Kresse, O.; Cohen, C.E.; Wu, R.; Gu, H.: Modeling of hydraulic fracture network propagation in a naturally fractured formation. In: SPE Hydraulic Fracturing Technology Conference 2011. Society of Petroleum Engineers

  13. Williams, B.B.: Fluid loss from hydraulically induced fractures. J. Petrol. Technol. 22, 882 (1970)

    Article  Google Scholar 

  14. Carter, R.: Derivation of the general equation for estimating the extent of the fractured area. Appendix I of “Optimum Fluid Characteristics for Fracture Extension,” Drilling and Production Practice, GC Howard and CR Fast, New York, New York, USA, American Petroleum Institute, pp. 261–269 (1957)

  15. Settari, A.: A new general model of fluid loss in hydraulic fracturing. Soc. Petrol. Eng. J. 25(04), 491–501 (1985)

    Article  Google Scholar 

  16. Geertsma, J.; Klerk, F.D.: A rapid method of predicting width and extent of hydraulically induced fractures. J. Petrol. Technol. 21(12), 1571–1581 (1969)

    Article  Google Scholar 

  17. Zheltov, A.: 3. Formation of vertical fractures by means of highly viscous liquid (1955)

  18. Nordgren, R.P.: Propagation of a vertical hydraulic fracture. Soc. Petrol. Eng. J. 12(04), 306–314 (1972). https://doi.org/10.2118/3009-pa

    Article  Google Scholar 

  19. Perkins, T.K.; Kern, L.R.: Widths of hydraulic fractures. J. Petrol. Technol. 13(09), 937–949 (1961). https://doi.org/10.2118/89-pa

    Article  Google Scholar 

  20. Ren, Q.; Dong, Y.; Yu, T.: Numerical modeling of concrete hydraulic fracturing with extended finite element method. Sci. China Ser. E: Technol. Sci. 52(3), 559–565 (2009). https://doi.org/10.1007/s11431-009-0058-8

    Article  MATH  Google Scholar 

  21. Lecampion, B.: An extended finite element method for hydraulic fracture problems. Int. J. Numer. Methods Biomed. Eng. 25(2), 121–133 (2009)

    MathSciNet  MATH  Google Scholar 

  22. Belytschko, T.; Black, T.: Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Meth. Eng. 45(5), 601–620 (1999)

    Article  MATH  Google Scholar 

  23. Moës, N.; Dolbow, J.; Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Meth. Eng. 46(1), 131–150 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  24. 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  MathSciNet  MATH  Google Scholar 

  25. Olson, J.: Fracture pattern development: the effects of subcritical crack growth and mechanical interaction. J. Geophys. Res. 93, 12251–12265 (1993)

    Article  Google Scholar 

  26. Olson, J.E.: Predicting fracture swarms—the influence of subcritical crack growth and the crack-tip process zone on joint spacing in rock. Geol. Soc. Lond. Spec. Publ. 231(1), 73–88 (2004)

    Article  Google Scholar 

  27. Shou, K.J.; Crouch, S.L.: A higher order displacement discontinuity method for analysis of crack problems. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 32(1), 49–55 (1995). https://doi.org/10.1016/0148-9062(94)00016-v

    Article  Google Scholar 

  28. Olson, J.E.: Multi-fracture propagation modeling: applications to hydraulic fracturing in shales and tight gas sands (2008)

  29. Olson, J.E.; Taleghani, A.D.: Modeling simultaneous growth of multiple hydraulic fractures and their interaction with natural fractures. In: SPE Hydraulic Fracturing Technology Conference. Society of Petroleum Engineers (2009)

  30. Wu, K.; Olson, J.E.: Investigation of critical in situ and injection factors in multi-frac treatments: guidelines for controlling fracture complexity. In: SPE Hydraulic Fracturing Technology Conference. Society of Petroleum Engineers (2013)

  31. Wu, K.; Olson, J.E.: Simultaneous multifracture treatments: fully coupled fluid flow and fracture mechanics for horizontal wells. SPE journal 20(02), 337–346 (2015)

    Article  Google Scholar 

  32. Zhang, X.; Jeffrey, R.G.: Fluid-driven multiple fracture growth from a permeable bedding plane intersected by an ascending hydraulic fracture. J. Geophys. Res. Solid Earth 117(B12), 12402 (2012)

    Article  Google Scholar 

  33. Zhang, X.; Jeffrey, R.G.: Role of overpressurized fluid and fluid-driven fractures in forming fracture networks. J. Geochem. Explor. 144, 194–207 (2014)

    Article  Google Scholar 

  34. Boone, T.J.; Ingraffea, A.R.: A numerical procedure for simulation of hydraulically-driven fracture propagation in poroelastic media. Int. J. Numer. Anal. Meth. Geomech. 14(1), 27–47 (1990)

    Article  Google Scholar 

  35. Chen, Z.; Bunger, A.P.; Zhang, X.; Jeffrey, R.G.: Cohesive zone finite element-based modeling of hydraulic fractures. Acta Mech. Solida Sin. 22(5), 443–452 (2009). https://doi.org/10.1016/s0894-9166(09)60295-0

    Article  Google Scholar 

  36. Carrier, B.; Granet, S.: Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model. Eng. Fract. Mech. 79, 312–328 (2012)

    Article  Google Scholar 

  37. Mohammadnejad, T.; Khoei, A.: An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model. Finite Elem. Anal. Des. 73, 77–95 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  38. 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 

  39. 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  Google Scholar 

  40. Zhang, G.X.; Xu, L.I.; Haifeng, L.I.: Simulation of hydraulic fracture utilizing numerical manifold method. Sci. China Technol. Sci. 58(9), 1542–1557 (2015)

    Article  Google Scholar 

  41. Paluszny, A.; Tang, X.H.; Zimmerman, R.W.: Fracture and impulse based finite-discrete element modeling of fragmentation. Comput. Mech. 52(5), 1071–1084 (2013). https://doi.org/10.1007/s00466-013-0864-5

    Article  MATH  Google Scholar 

  42. Zhao, Q.; Lisjak, A.; Mahabadi, O.; Liu, Q.; Grasselli, G.: Numerical simulation of hydraulic fracturing and associated microseismicity using finite-discrete element method. J. Rock Mech. Geotechn. Eng. 6(6), 574–581 (2014). https://doi.org/10.1016/j.jrmge.2014.10.003

    Article  Google Scholar 

  43. Liu, Q.; Sun, L.; Tang, X.; Chen, L.: Simulate intersecting 3D hydraulic cracks using a hybrid “FE-Meshfree” method. Eng. Anal. Boundary Elem. 91, 24–43 (2018). https://doi.org/10.1016/j.enganabound.2018.03.005

    Article  MathSciNet  MATH  Google Scholar 

  44. Liu, Q.; Sun, L.; Tang, X.; Guo, B.: Modelling hydraulic fracturing with a point-based approximation for the maximum principal stress criterion. Rock Mech. Rock Eng. 52(6), 1781–1801 (2018)

    Article  Google Scholar 

  45. Yang, Y.; Tang, X.; Zheng, H.: Construct ‘FE-Meshfree’ Quad4 using mean value coordinates. Eng. Anal. Bound. Elem. 59, 78–88 (2015). https://doi.org/10.1016/j.enganabound.2015.04.011

    Article  MathSciNet  MATH  Google Scholar 

  46. Kachanov, L.M.: Rupture time under creep conditions. Int. J. Fract. 97(1), 11–18 (1999). https://doi.org/10.1023/a:1018671022008

    Article  Google Scholar 

  47. Jirásek, M.: Mathematical analysis of strain localization. Rev. Eur. Génie Civ. 11(7–8), 977–991 (2007)

    Article  Google Scholar 

  48. Simo, J.C.; Ju, J.W.: Strain- and stress-based continuum damage models—I. Formul. Math. Comput. Model. 12(3), 378 (1987)

    MATH  Google Scholar 

  49. Bažant, Z.P.; Belytschko, T.B.; Chang, T.-P.: Continuum theory for strain-softening. J. Eng. Mech. 110(12), 1666–1692 (1984)

    Article  Google Scholar 

  50. Pijaudier-Cabot, G.; Bažant, Z.P.: Nonlocal damage theory. J. Eng. Mech. 113(10), 1512–1533 (1987)

    Article  MATH  Google Scholar 

  51. Frémond, M.; Nedjar, B.: Damage, gradient of damage and principle of virtual power. Int. J. Solids Struct. 33(8), 1083–1103 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  52. Lorentz, E.; Andrieux, S.: A variational formulation for nonlocal damage models. Int. J. Plast 15(2), 119–138 (1999)

    Article  MATH  Google Scholar 

  53. Pham, K.; Amor, H.; Marigo, J.J.; Maurini, C.: Gradient damage models and their use to approximate brittle fracture. Int. J. Damage Mech 20(4), 618–652 (2010)

    Article  Google Scholar 

  54. Bourdin, B.; Francfort, G.A.; Marigo, J.-J.: The variational approach to fracture. J. Elast. 91(1–3), 5–148 (2008). https://doi.org/10.1007/s10659-007-9107-3

    Article  MathSciNet  MATH  Google Scholar 

  55. Miehe, C.; Hofacker, M.; Welschinger, F.: A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput. Methods Appl. Mech. Eng. 199(45–48), 2765–2778 (2010). https://doi.org/10.1016/j.cma.2010.04.011

    Article  MathSciNet  MATH  Google Scholar 

  56. Tanné, E.; Li, T.; Bourdin, B.; Marigo, J.J.; Maurini, C.: Crack nucleation in variational phase-field models of brittle fracture. J. Mech. Phys. Solids 110, 80–99 (2018). https://doi.org/10.1016/j.jmps.2017.09.006

    Article  MathSciNet  Google Scholar 

  57. Nguyen, T.T.; Yvonnet, J.; Bornert, M.; Chateau, C.; Sab, K.; Romani, R.; Le Roy, R.: On the choice of parameters in the phase field method for simulating crack initiation with experimental validation. Int. J. Fract. 197(2), 213–226 (2016)

    Article  Google Scholar 

  58. Ambati, M.; Gerasimov, T.; Lorenzis, L.D.: Phase-field modeling of ductile fracture. Comput. Mech. 55(5), 1017–1040 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  59. Amiri, F.; Millán, D.; Shen, Y.; Rabczuk, T.; Arroyo, M.: Phase-field modeling of fracture in linear thin shells. Theor. Appl. Fract. Mech. 69(2), 102–109 (2014)

    Article  Google Scholar 

  60. 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 

  61. Wilson, Z.A.; Landis, C.M.: Phase-field modeling of hydraulic fracture. J. Mech. Phys. Solids 96, 264–290 (2016). https://doi.org/10.1016/j.jmps.2016.07.019

    Article  MathSciNet  Google Scholar 

  62. Miehe, C.; Mauthe, S.: Phase field modeling of fracture in multi-physics problems Part III Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media. Comput. Methods Appl. Mech. Eng. 304, 619–655 (2016). https://doi.org/10.1016/j.cma.2015.09.021

    Article  MathSciNet  MATH  Google Scholar 

  63. Miehe, C.; Mauthe, S.; Teichtmeister, S.: Minimization principles for the coupled problem of Darcy–Biot-type fluid transport in porous media linked to phase field modeling of fracture. J. Mech. Phys. Solids 82, 186–217 (2015). https://doi.org/10.1016/j.jmps.2015.04.006

    Article  MathSciNet  Google Scholar 

  64. Francfort, G.A.; Marigo, J.J.: Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46(8), 1319–1342 (1998). https://doi.org/10.1016/S0022-5096(98)00034-9

    Article  MathSciNet  MATH  Google Scholar 

  65. Miehe, C.; Welschinger, F.; Hofacker, M.: Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations. Int. J. Numer. Meth. Eng. 83(10), 1273–1311 (2010). https://doi.org/10.1002/nme.2861

    Article  MathSciNet  MATH  Google Scholar 

  66. Biot, M.A.; Tolstoy, I.: Acoustics, elasticity, and thermodynamics of porous media: twenty-one papers. Acoustical Society of Amer, New York (1992)

    Google Scholar 

  67. Crouch, S.L.; Starfield, A.M.; Rizzo, F.: Boundary element methods in solid mechanics. J. Appl. Mech. 50, 704 (1983)

    Article  Google Scholar 

  68. Lardner, T.J.; Ritter, J.E.; Shiao, M.L.; Lin, M.R.: Behavior of indentation cracks near free surfaces and interfaces. Int. J. Fract. 44(2), 133–143 (1990). https://doi.org/10.1007/bf00047064

    Article  Google Scholar 

  69. Guo, J.; Lu, Q.; Chen, H.; Wang, Z.; Tang, X.; Chen, L.: Quantitative phase field modeling of hydraulic fracture branching in heterogeneous formation under anisotropic in situ stress. J. Nat. Gas Sci. Eng. 56, 455–471 (2018). https://doi.org/10.1016/j.jngse.2018.06.009

    Article  Google Scholar 

  70. Chen, M.; Zhang, G.Q.: Laboratory measurement and interpretation of the fracture toughness of formation rocks at great depth. J. Petrol. Sci. Eng. 41(1), 221–231 (2004)

    Article  Google Scholar 

  71. Josh, M.; Esteban, L.; Piane, C.D.; Sarout, J.; Dewhurst, D.N.; Clennell, M.B.: Laboratory characterisation of shale properties. J. Petrol. Sci. Eng. 88–89(2), 107–124 (2012)

    Article  Google Scholar 

  72. Senseny, P.; Pfeifle, T.: Fracture toughness of sandstones and shales (1984)

  73. Li, Y.; Hou, J.; Ma, X.: Data integration in characterizing a fracture-cavity reservoir, Tahe oilfield, Tarim basin, China. Arab. J. Geosci. 9(8), 532 (2016)

    Article  Google Scholar 

  74. Weng, Z.; Zhang, Y.; Wu, Y.; Fan, K.; Wang, F.: An experimental study on the influence of caves in reservoirs on hydraulic fractures propagation. Reservoir Evaluation and Development (2019). (in press)

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 41602296) and the National Science and Technology Major Project (2016ZX05014-005-003). Special thanks are due to Lei Chen of Mississippi State University for his source codes and Dr. Xiaoguang Wang for his valuable suggestions.

Author information

Authors and Affiliations

  1. Sinopec Northwest Oilfield Company, Research Institute of Petroleum Engineering Technology, Urumqi, 830011, China

    Zhiyuan Liu

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

    Qianli Lu

  3. School of Civil and Architectural Engineering, Wuhan University, Wuhan, 430072, China

    Yuan Sun, Xuhai Tang, Zuliang Shao & Zheng Weng

Authors
  1. Zhiyuan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qianli Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuan Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xuhai Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zuliang Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zheng Weng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuan Sun.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Z., Lu, Q., Sun, Y. et al. Investigation of the Influence of Natural Cavities on Hydraulic Fracturing Using Phase Field Method. Arab J Sci Eng 44, 10481–10501 (2019). https://doi.org/10.1007/s13369-019-04122-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-019-04122-z

Keywords

Search

Navigation