Skip to main content
Log in

A poroelastic simulator with hydraulic fracture propagation using cohesive finite elements

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

Oil and gas production projects rely on hydraulic fracturing for improved well stimulation and profitability. Research progress on numerical simulation enables design teams to estimate rock behavior and ensure the success of such operations. Stimulation operations usually take only a few hours, and fluid diffusion around the well is normally unimportant. In long-term improved oil recovery injection projects, however, injected water and gas significantly modify reservoir pore pressure and geomechanical conditions around injection wells. This paper proposes a fully coupled hydromechanical full-field reservoir simulator to consider the effects of such coupled effects in the propagation of tensile hydraulic fractures in short- and long-term processes. The numerical approach uses finite elements to represent the poroelastic medium and lower dimension cohesive interface elements to represent fragile interfaces. Numerical accuracy is validated against asymptotic analytical solutions. The results show significant impact of fluid injection and production history in the attributes of the fracture generated. For long-term projects, designers must avoid the use of off-the-shelf hydraulic fracturing simulators designed typically for stimulation operations. This paper encourages using fully coupled, full-field reservoir simulators and considering, in detail, the variety of physical phenomena present in the process. The main contributions of this work comprise an incremental damage control algorithm for fracture propagation and a geometrical analysis technique for avoiding mesh overlap on damaged compressive interfaces.

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

Access this article

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

Instant access to the full article PDF.

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

Similar content being viewed by others

References

  1. Peirce A (2016) Implicit level set algorithms for modelling hydraulic fracture propagation. Philos Trans R Soc A 374(2078):20150423

    Article  MathSciNet  Google Scholar 

  2. Detournay E (2016) Mechanics of hydraulic fractures. Annu Rev Fluid Mech 48(1):311–339. https://doi.org/10.1146/annurev-fluid-010814-014736

    Article  MathSciNet  MATH  Google Scholar 

  3. Hyman JD et al (2016) Understanding hydraulic fracturing: a multi-scale problem. Philos Trans A Math Phys Eng Sci. https://doi.org/10.1098/rsta.2015.0426

    Article  Google Scholar 

  4. Perkins TK, Gonzalez JA (1985) The effect of thermoelastic stresses on injection well fracturing. Soc Pet Eng J 25(01):78–88

    Article  Google Scholar 

  5. Lecampion B, Bunger A, Zhang X (2017) Numerical methods for hydraulic fracture propagation: a review of recent trends. J Nat Gas Sci Eng 49:66–83

    Article  Google Scholar 

  6. Obeysekara A et al (2016) A fluid-solid coupled approach for numerical modeling of near-wellbore hydraulic fracturing and flow dynamics with adaptive mesh refinement. In: 50th US rock mechanics/geomechanics symposium

  7. Manzoli OL, Cleto PR, Sánchez M, Guimarães LJN, Maedo MA (2019) On the use of high aspect ratio finite elements to model hydraulic fracturing in deformable porous media. Comput Methods Appl Mech Eng 350:57–80

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  9. Tatomir A-B (2012) From discrete to continuum concepts of flow in fractured porous media. University of Stuttgart, Stuttgart

    Google Scholar 

  10. Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids. https://doi.org/10.1016/0022-5096(60)90013-2

    Article  Google Scholar 

  11. Barenblatt GI (1962) The mathematical theory of equilibrium cracks formed in brittle fracture. Zhurnal Prikl Mekhaniki i Tec

  12. Yan C, Zheng H, Sun G, Ge X (2016) Combined finite-discrete element method for simulation of hydraulic fracturing. Rock Mech Rock Eng 49(4):1389–1410. https://doi.org/10.1007/s00603-015-0816-9

    Article  Google Scholar 

  13. Munjiza A, Andrews KRF, White JK (1999) Combined single and smeared crack model in combined finite-discrete element analysis. Int J Numer Methods Eng 44(1):41–57

    Article  Google Scholar 

  14. Patil RU, Mishra BK, Singh IV (2018) An adaptive multiscale phase field method for brittle fracture. Comput Methods Appl Mech Eng 329:254–288. https://doi.org/10.1016/j.cma.2017.09.021

    Article  MathSciNet  MATH  Google Scholar 

  15. Dontsov EV, Peirce AP (2017) A multiscale Implicit level set algorithm (ILSA) to model hydraulic fracture propagation incorporating combined viscous, toughness, and leak-off asymptotics. Comput Methods Appl Mech Eng 313:53–84. https://doi.org/10.1016/j.cma.2016.09.017

    Article  MathSciNet  MATH  Google Scholar 

  16. Flemisch B et al (2018) Benchmarks for single-phase flow in fractured porous media. Adv Water Resour 111:239–258. https://doi.org/10.1016/j.advwatres.2017.10.036

    Article  Google Scholar 

  17. Oliver J, Huespe AE, Cante JC (2008) An implicit/explicit integration scheme to increase computability of non-linear material and contact/friction problems. Comput Methods Appl Mech Eng 197(21–24):1865–1889. https://doi.org/10.1016/j.cma.2007.11.027

    Article  MATH  Google Scholar 

  18. Munjiza A, Andrews KRF (1998) NBS contact detection algorithm for bodies of similar size. Int J Numer Methods Eng 43(1):131–149. https://doi.org/10.1002/(SICI)1097-0207(19980915)43:1%3c131::AID-NME447%3e3.0.CO;2-S

    Article  MATH  Google Scholar 

  19. Lei Q, Latham JP, Xiang J, Tsang C-F (2015) Polyaxial stress-induced variable aperture model for persistent 3D fracture networks. Geomech Energy Environ 1:34–47. https://doi.org/10.1016/j.gete.2015.03.003

    Article  Google Scholar 

  20. Biot MA (1941) General theory of three-dimensional consolidation. J Appl Phys 12(2):155–164

    Article  Google Scholar 

  21. Witherspoon PA, Wang JSY, Iwai K, Gale JE (1980) Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour Res 16(6):1016–1024

    Article  Google Scholar 

  22. Zoback MD (2010) Reservoir geomechanics. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  23. Fabri A, Giezeman G, Kettner L, Schirra S, Schönherr S (2000) On the design of CGAL a computational geometry algorithms library. Softw Pract Exp 30(11):1167–1202

    Article  Google Scholar 

  24. Kirk BS, Peterson JW, Stogner RH, Carey GF (2006) libMesh : a C++ library for parallel adaptive mesh refinement/coarsening simulations. Eng Comput 22(3–4):237–254. https://doi.org/10.1007/s00366-006-0049-3

    Article  Google Scholar 

  25. Abhyankar S, Brown J, Constantinescu EM, Ghosh D, Smith BF, Zhang H (2018) PETSc/TS: a modern scalable ODE/DAE solver library. 5(212):1–29. [Online]. Available: http://arxiv.org/abs/1806.01437

  26. Wang HF (2000) Theory of linear poroelasticity with applications to geomechanics and hydrogeology. Princeton University Press, Princeton

    Google Scholar 

  27. Cheng AH-D (2016) Poroelasticity, vol 27. Springer, Cham

    Book  Google Scholar 

  28. Maliska CR, Honório HT, Coelho Jr J (2017) A non-oscillatory staggered grid algorithm for the pressure-displacement coupling in geomechanics. In: IACM 19th international conference in flow problems–FEF

  29. Mandel J (1953) Consolidation des sols (étude mathématique). Geotechnique 3(7):287–299

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge Petrobras and the University of São Paulo for the administrative and technical support to this project.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Renato Poli or Ronaldo Carrion.

Additional information

Technical Editor: Celso Kazuyuki Morooka.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Poli, R., Gioria, R. & Carrion, R. A poroelastic simulator with hydraulic fracture propagation using cohesive finite elements. J Braz. Soc. Mech. Sci. Eng. 43, 175 (2021). https://doi.org/10.1007/s40430-020-02787-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-020-02787-4

Keywords

Navigation