# Simulating fully 3D non-planar evolution of hydraulic fractures

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## Abstract

Three-dimensional model of fracture propagation is proposed. The model simultaneously accounts rock deformation in the vicinity of a fracture and a cavity, fluid flow inside the fracture and its propagation in the direction that is selected by a growth criterion. The results of the sensitivity analysis of model solution to the variation of model parameters are presented.

## Keywords

3D boundary element method Fracture initiation 2D fluid flow Hydraulic fracture propagation Numerical simulation Fully coupled## Notes

### Acknowledgments

Authors gratefully acknowledge the financial support of this research by the Russian Scientific Fund under grant number 14-11-00234.

## Supplementary material

## References

- Abe H, Mura T, Keer LM (1976) Growth rate of a penny-shaped crack in hydraulic fracturing of rocks. J Geophys Res 81(29):5335–5340CrossRefGoogle Scholar
- Aidagulov G, Alekseenko O, Chang F, Bartko K, Cherny S, Esipov D, Kuranakov D, Lapin V (2015) Model of hydraulic fracture initiation from the notched open hole. In: Proceedings 2015 annual technical symposium & exhibition, Al Khobar, Saudi Arabia, April 21–23, SPE-178027-MS, pp 1–12Google Scholar
- Alekseenko OP, Esipov DV, Kuranakov DS, Lapin VN, Cherny SG (2011) 2D step-by-step model of hydrofracturing Vestnik. Quart J Novosib State Univ Ser: Math Mech Inf 11(3):36–60 (in Russian)Google Scholar
- Alekseenko OP, Potapenko DI, Cherny SG, Esipov DV, Kuranakov DS, Lapin VN (2013) 3D Modeling of fracture initiation from perforated non-cemented wellbore. SPE J 18(3):589–600CrossRefGoogle Scholar
- Aliabadi MH (2002) The boundary element method: vol 2 (applications in solids and structures). Wiley, New YorkGoogle Scholar
- Barr DT (1991) Leading-edge analysis for correct simulation of interface separation and hydraulic fracturing. Massachusetts Institute of Technology, Department of Mechanical EngineeringGoogle Scholar
- Blandford GE, Ingraffea AR, Liggett JA (1981) Two-dimensional stress intensity factor computations using the boundary element method. Int J Numer Meth Eng 17(3):387–404CrossRefGoogle Scholar
- Briner A, Chavez JC, Nadezhdin S, Alekseenko O, Gurmen N, Cherny S, Kuranakov D, Lapin V (March 2015) Impact of perforation tunnel orientation and length in horizontal wellbores on fracture initiation pressure in maximum tensile stress criterion model for tight gas fields in the Sultanate of Oman SPE Middle East Oil & Gas Show and Conference, Manama, Bahrain, 8–11, pp 1–12, SPE 172663Google Scholar
- Briner A, Florez JC, Nadezhdin S, Gurmen N, Cherny S, Kuranakov D, Lapin V (September 2015) Impact of wellbore orientation on fracture initiation pressure in maximum tensile stress criterion model for unconventional gas field in the Sultanate of Oman. In: Proceedings of North Africa technical conference and exhibition, Cairo, Egypt, 14–16, pp 1–13, SPE-175725-MSGoogle Scholar
- Bueckner HF (1973) Field singularities and related integral representations. In: Sih GC (ed) Mechanics of fracture, vol 1: methods of analysis and solutions of crack problems. Nordhoff, Leyden, pp 239–314CrossRefGoogle Scholar
- Carbonell R, Desroches J, Detournay E (1999) A comparison between a semi-analytical and a numerical solution of a twodimensional hydraulic fracture. Int J Solids Struct 36(31–32):4869–4888CrossRefGoogle Scholar
- Carter BJ, Desroches J, Ingraffea AR, Wawrzynek PA (2000) Simulating fully 3D hydraulic fracturing. In: Zaman M, Booker J, Gioda G (eds) Modeling in Geomechanics. Wiley Publishers, New York, pp 525–557Google Scholar
- Carter BJ (1992) Size and stress gradient effects on fracture around cavities. Rock Mech Rock Eng 25(3):167–186CrossRefGoogle Scholar
- Chang F, Bartko K, Dyer S, Aidagulov G, Suarez-Rivera R, Lung J (2014) Multiple fracture initiation in openhole without mechanical isolation: first step to fulfill an ambition. SPE-168638-MS, pp 1–18Google Scholar
- Chen JT, Hong H-K (1999) Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series. Appl Mech Rev 52(1):17–33CrossRefGoogle Scholar
- Cherepanov GP (1979) Mechanics of brittle fracture (translated from the Russian by A. L. Peabody; ed. R. de Wit and W.C. Cooley). McGraw-Hill, LondonGoogle Scholar
- Cherny S, Chirkov D, Lapin V, Muranov A, Bannikov D, Miller M, Willberg D (2009) Two-dimensional modeling of the near-wellbore fracture tortuosity effect. Int J Rock Mech Min Sci 36(6):992–1000CrossRefGoogle Scholar
- Cherny S, Esipov D, Kuranakov D, Lapin V, Chirkov D, Astrakova A (2015) Numerical method for solving a 3D problem of fracture initiation from a cavity in an elastic media presented in the international journal of fracture in 2015Google Scholar
- Cooke ML, Pollard DD (1996) Fracture propagation paths under mixed mode loading within rectangular blocks of polymethyl methacrylate. J Geophys Res 101(B2):3387–3400Google Scholar
- Crouch SL (1976) Solution of plane elasticity problems by the displacement discontinuity method. Int J Numer Methods Eng 10:301–343CrossRefGoogle Scholar
- Cruse TA (1972) Numerical evaluation of elastic stress intensity factors by the boundary-integral equation method. Surfase cracks: physical problems and computational solutions, pp 153–170Google Scholar
- Cruse TA (1973) Application of the boundary-integral equation method to three dimensional stress analysis. Comput Struct 3:509–527CrossRefGoogle Scholar
- Desroches J, Thiercelin M (1993) Modeling propagation and closure of micro-hydraulic fractures. Int J Rock Mech Min Sci 30:1231–1234CrossRefGoogle Scholar
- Dobroskok A, Ghassemi A, Linkov A (2005) Extended structural criterion for numerical simulation of crack propagation and coalescence under compressive loads. Int J Fract 133:223–246CrossRefGoogle Scholar
- Erdogan F, Sih GC (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng 85:519–525CrossRefGoogle Scholar
- Esipov DV, Cherny SG, Kuranakov DS, Lapin VN (2011) Multiple-zone boundary element method modeling of hydraulic fracture initiation from perforated cased wellbore. In: Proceedings of international conference “Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications”, devoted to the 90th anniversary of professor N. N. Yanenko (Novosibirsk, Russia, 30 May–4 June 2011). “Informregistr”. - Novosibirsk. - http://conf.nsc.ru/files/conferences/niknik-90/fulltext/40532/47467/EsipovDV
- Esipov DV, Kuranakov DS, Lapin VN, Cherny SG (2011) Multiple-zone boundary element method and its application to the problem of hydraulic fracture initiation from cased perforated wellbore. Comp Technol 16(6):13–26 (in Russian)Google Scholar
- Esipov DV, Kuranakov DS, Lapin VN, Cherny SG (2014) Mathematical models of hydraulic fracturing. Comp Technol 19(2):33–61 (in Russian)Google Scholar
- Germanovich LN, Cherepanov GP (1995) On some general properties of strength criteria. Int J Fract 71:37–56CrossRefGoogle Scholar
- Goldstein RV, Salganik RL (1974) Brittle fracture of solids with arbitrary cracks. Int J Fract 10:507–523CrossRefGoogle Scholar
- Gupta P, Duarte CAM (2014) Simulation of non-planar three dimensional hydraulic fracture propagation. Int J Nume Anal Methods Geomech 38(13):1397–1430CrossRefGoogle Scholar
- Hong H-K, Chen JT (1988) Derivation of integral equations in elasticity. J Eng Mech 114(6):1028–1044CrossRefGoogle Scholar
- Leblond J-B, Frelat J (2000) Crack kinking from an initially closed crack. Int J Solids Struct 37:1595–1614CrossRefGoogle Scholar
- Leblond J-B, Frelat J (2001) Crack kinking from an interface crack with initial contact between the crack lips. Eur J Mech A: Solids 20:937–951CrossRefGoogle Scholar
- Leblond JB, Frelat J (2004) Crack king from an initially closed, ordinary or interface crack, in the presence of friction. Eng Fract Mech 71:289–307CrossRefGoogle Scholar
- Liu YJ, Li YX (2014) Revisit of the equivalence of the displacement discontinuity method and boundary element method for solving crack problems. Eng Anal Bound Elem 47:64–67CrossRefGoogle Scholar
- Mi Y, Aliabadi MH (1992) Dual boundary element method for three-dimensional fracture mechanics analysis. Eng Anal 10(2):161–171Google Scholar
- Mi Y, Aliabadi MH (1994) Three-dimensional crack growth simulation using BEM. Comput Struct 52(5):871–878CrossRefGoogle Scholar
- Murakami Y (Editor-in-Chief) Stress intensity factors handbook. Pergamon Press, Oxford (1987)Google Scholar
- Napier JAL, Detournay E (2013) Propagation of non-planar pressurized cracks from a borehole. In: Proceedings of the 5th international conference on structural engineering, mechanics and computation, SEMC 2013, pp 597–602Google Scholar
- Neuber HK (1937) Verlag Julius Springer, BerlinGoogle Scholar
- Novozhilov VV (1969) On a necessary and sufficient criterion for brittle strength. J Appl Math Mech 33(2):201–210CrossRefGoogle Scholar
- Nuismer RJ (1975) An energy release rate criterion for mixed mode fracture. Int J Fract 11:245–250CrossRefGoogle Scholar
- Paris A, Erdogan F (1963) A critical analysis of crack propagation law. J Basic Eng 85:528–534CrossRefGoogle Scholar
- Pereira JPA (2010) Generalized finite element methods for three-dimensional crack growth simulations. PhD Dissertation in Civil Engineering, University of IllinoisGoogle Scholar
- Portela A, Aliabadi MH, Rooke DP (1991) The dual boundary element method: efficient implementation for cracked problems. Int J Numer Methods Eng 32:445–470CrossRefGoogle Scholar
- Richard HA, Fulland M, Sander M (2005) Theoretical crack path prediction. Fatigue Fract Eng Mater Struct 28:3–12CrossRefGoogle Scholar
- Rizzo FJ (1967) An integral equation approach to boundary value problems of classical elastostatics. Quart J Appl Math 25:83–95Google Scholar
- Rungamornrat J (2004) A computational procedure for analysis of fractures in three dimensional anisotropic media. Ph.D. Dissertation, Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at AustinGoogle Scholar
- Rungamornrat J, Wheeler MF, Mear ME (2005) A numerical technique for simulating nonplanar evolution of hydraulic fractures. Paper SPE 96968:1–9Google Scholar
- Savitski AA, Detournay E (2002) Propagation of a fluid-driven pennyshaped fracture in an impermeable rock: asymptotic solutions. Int J Solids Struct 39(26):6311–6337CrossRefGoogle Scholar
- Schollmann M, Richard HA, Kullmer G, Fulland M (2002) A new criterion for the prediction of crack development in multiaxially loaded structures. Int J Fract 117:129–141CrossRefGoogle Scholar
- Sedov LI (1997) Mechanics of continuous media. World Scientific, SingaporeCrossRefGoogle Scholar
- Sneddon IN, Elliott HA (1946) The opening of a griffith crack under internal pressure. Quart Appl Math 4:262Google Scholar
- Snyder MD, Cruse TA (1975) Boundary-integral equation analysis of cracked anisotropic plates. Int J Fract 11(2):315–328CrossRefGoogle Scholar
- Sousa JL, Carter BJ, Ingraffea AR (1993) Numerical methods of 3D hydraulic fracture using Newtonian and power-law fluids. Int J Rock Mech Mining Sci Geomech Abst 30(7):1265–1271CrossRefGoogle Scholar
- Tada H, Paris P, Irwin G (2000) The stress analysis of cracks handbook, 3rd edn. ASME Press, New YorkCrossRefGoogle Scholar
- Vandamme L, Curran JH (1989) A three-dimensional hydraulic fracturing simulator. Int J Numer Methods Eng 28:909–927CrossRefGoogle Scholar
- Watson JO (1982) Hermitian cubic boundary elements for plane problems of fracture mechanics. Res Mechanica 4:23–42Google Scholar
- Watson JO (1986) Hermitian cubic and singular elements for plane strain. In: Banerjee PK, Watson JO (eds) Developments in boundary element methods - 4, Chapter 1. Elsevier Applied Science Publishers, London, pp 1–28Google Scholar
- Weber W, Kuhn G (2008) An optimized predictor–corrector scheme for fast 3d crack growth simulations. Eng Fract Mech 75:452–460. doi: 10.1016/j.engfracmech.2007.01.005 International Conference of Crack PathsCrossRefGoogle Scholar

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