Инд. авторы:	Cherny S.G., Lapin V.N., Kuranakov D.S., Alekseenko O.P.
Заглавие:	3D model of transversal fracture propagation from a cavity caused by Herschel–Bulkley fluid injection
Библ. ссылка:	Cherny S.G., Lapin V.N., Kuranakov D.S., Alekseenko O.P. 3D model of transversal fracture propagation from a cavity caused by Herschel–Bulkley fluid injection // International Journal of Fracture. - 2018. - Vol.212. - Iss. 1. - P.15-40. - ISSN 0376-9429. - EISSN 1573-2673.
Внешние системы:	DOI: 10.1007/s10704-018-0289-4; РИНЦ: 35762317; РИНЦ: 41781535; РИНЦ: 38607951; SCOPUS: 2-s2.0-85046705786; WoS: 000438103600002;
Реферат:	rus: The paper presents an extension of authors’ previous model for a 3D hydraulic fracture with Newtonian fluid, which aims to account for the Herschel–Bulkley fluid rheology and to study the associated effects. This fluid rheology model is the most suitable for description of modern complex fracturing fluids, in particular, for description of foamed fluids that have been successfully utilized recently as fracturing fluids in tight and ultra-tight unconventional formations with high clay contents. Another advantage of using Herschel–Bulkley rheological law in the hydraulic fracture model consists in its generality as its particular cases allow describing the behavior of the majority of non-Newtonian fluids employed in hydraulic fracturing. Except the Herschel–Bulkley fluid flow model the considered model of hydraulic fracturing includes the model of the rock stress state. It is based on the elastic equilibrium equations that are solved by the dual boundary element method. Also the hydraulic fracturing model contains the new mixed mode propagation criterion, which states that the fracture should propagate in the direction in which mode II and mode III stress intensity factors both vanish. Since it is not possible to make both modes zero simultaneously the criterion proposes a functional that depends on both modes and is minimized along the fracture front in order to obtain the direction of propagation. Solution for Herschel–Bulkley fluid flow in a channel is presented in detail, and the numerical algorithm is described. The developed model has been verified against some reference solutions and sensitivity of fracture geometry to rheological fluid parameters has been studied to some extent. eng: The paper presents an extension of authors' previous model for a 3D hydraulic fracture with Newtonian fluid, which aims to account for the Herschel-Bulkley fluid rheology and to study the associated effects. This fluid rheology model is the most suitable for description of modern complex fracturing fluids, in particular, for description of foamed fluids that have been successfully utilized recently as fracturing fluids in tight and ultra-tight unconventional formations with high clay contents. Another advantage of using Herschel-Bulkley rheological law in the hydraulic fracture model consists in its generality as its particular cases allow describing the behavior of the majority of non-Newtonian fluids employed in hydraulic fracturing. Except the Herschel-Bulkley fluid flow model the considered model of hydraulic fracturing includes the model of the rock stress state. It is based on the elastic equilibrium equations that are solved by the dual boundary element method. Also the hydraulic fracturing model contains the new mixed mode propagation criterion, which states that the fracture should propagate in the direction in which mode and mode stress intensity factors both vanish. Since it is not possible to make both modes zero simultaneously the criterion proposes a functional that depends on both modes and is minimized along the fracture front in order to obtain the direction of propagation. Solution for Herschel-Bulkley fluid flow in a channel is presented in detail, and the numerical algorithm is described. The developed model has been verified against some reference solutions and sensitivity of fracture geometry to rheological fluid parameters has been studied to some extent.
Ключевые слова:	Dual boundary element method; ROCK; STRESS; MECHANICS; SIMULATION; DRIVEN FRACTURE; HYDRAULIC FRACTURE; POWER-LAW FLUID; BOUNDARY-ELEMENT METHOD; 3D mixed mode crack front deflection criterion; 3D mixed mode crack front deflection criterion; Dual boundary element method; Herschel–Bulkley fluid flow in fracture; 3D model of hydraulic fracture propagation; 3D model of hydraulic fracture propagation; Herschel-Bulkley fluid flow in fracture;
Издано:	2018
Физ. характеристика:	с.15-40
Цитирование:	1. Abass HH, Brumley JL, Venditto JJ et al (1994) Oriented perforations-a rock mechanics view. In: SPE annual technical conference and exhibition 2. Adachi JI, Detournay E (2002) Self-similar solution of a plane-strain fracture driven by a power-law fluid. Int J Numer Anal Methods Geomech 26:579–604 3. Adachi JI, Detournay E (2008) Plane strain propagation of a hydraulic fracture in a permeable rock. Eng Fract Mech 75(16):4666–4694 4. Aliabadi MH (2002) The boundary element method, applications in solids and structures, vol 2. Wiley, Chichester 5. Aud WW, Wright TB, Cipolla CL, Harkrider JD (1994) The effect of viscosity on near-wellbore tortuosity and premature screenouts. In: SPE annual technical conference and exhibition, New Orleans, Louisiana. Society of Petroleum Engineers 6. Barati R, Liang J-T (2014) A review of fracturing fluid systems used for hydraulic fracturing of oil and gas wells. J Appl Polym Sci 131(16):1–11 7. Barati R, Hutchins RD, Friedel T, Ayoub JA, Dessinges M-N, England KW (2009) Fracture impact of yield stress and fracture-face damage on production with a three-phase 2D model. SPE Product Oper 24(02):336–345 (SPE-111457-PA) 8. Bunger AP, Detournay E (2007) Early-time solution for a radial hydraulic fracture. J Eng Mech 133(5):534–540 9. Bunger AP, Detournay E, Garagash DI (2005) Toughness-dominated hydraulic fracture with leak-off. Int J Fract 134(2):175–190 10. Chen J-T, Hong H-K (1999) Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series. Appl Mech Rev 52(1):17–33 11. Cherny SG, Lapin VN (2016) 3D model of hydraulic fracture with Herschel–Bulkley compressible fluid pumping. Procedia Struct Integr 2:2479–2486 12. Cherny S, Chirkov D, Lapin V, Muranov A, Bannikov D, Miller M, Willberg D, Medvedev O, Alekseenko O (2009) Two-dimensional modeling of the near-wellbore fracture tortuosity effect. Int J Rock Mech Min Sci 46(6):992–1000 13. Cherny S, Lapin V, Esipov D, Kuranakov D, Avdyushenko A, Lyutov A, Karnakov P (2016) Simulating fully 3D non-planar evolution of hydraulic fractures. Int J Fract 201(2):181–211. 10.1007/s10704-016-0122-x 14. Cleary MP, Johnson DE, Kogsbøll H-H, Owens KA, Perry KF, de Pater CJ, Stachel A, Schmidt H, Mauro T (1993) Field implementation of proppant slugs to avoid premature screen-out of hydraulic fractures with adequate proppant concentration. In: Low permeability reservoirs symposium, Denver, Colorado. Society of Petroleum Engineers 15. Cooke ML, Pollard DD (1996) Fracture propagation paths under mixed mode loading within rectangular blocks of polymethyl methacrylate. J Geophys Res 101(B2):3387–3400 16. Detournay E (2004) Propagation regimes of fluid-driven fractures in impermeable rocks. Int J Geomech 4(1):35–45 17. Detournay E (2016) Mechanics of hydraulic fractures. Annu Rev Fluid Mech 48(1):311–339 18. Dontsov EV (2016) An approximate solution for a penny-shaped hydraulic fracture that accounts for fracture toughness, fluid viscosity and leak-off. R Soc Open Sci 3(12):160737 19. Dontsov EV, Kresse O (2018) A semi-infinite hydraulic fracture with leak-off driven by a power-law fluid. J Fluid Mech 837:210–229 20. Economides MJ, Nolte KG (2000) Reservoir stimulation, 3rd edn. Wiley, Chichester 21. Esipov DV, Kuranakov DS, Lapin VN, Cherny SG (2014) Mathematical models of hydraulic fracturing of a reservoir. Comput Technol 19(2):33–61 (in Russian) 22. Garagash DI (2006) Transient solution for a plane-strain fracture driven by a shear-thinning, power-law fluid. Int J Numer Anal Methods Geomech 30(14):1439–1475 23. Garagash D, Detournay E (2000) The tip region of a fluid-driven fracture in an elastic medium. J Appl Mech 67(1):183–192 24. Herschel WH, Bulkley R (1926) Konsistenzmessungen von gummi-benzollösungen. Kolloid-Zeitschrift 39(4):291–300 25. Hong H-K, Chen J-T (1988) Derivations of integral equations of elasticity. J Eng Mech 114(6):1028–1044 26. Kauzlarich JJ, Greenwood JA (1972) Elastohydrodynamic lubrication with Herschel–Bulkley model greases. ASLE Trans 15(4):269–277 27. Kuranakov DS, Esipov DV, Lapin VN, Cherny SG (2016) Modification of the boundary element method for computation of three-dimensional fields of strain-stress state of cavities with cracks. Eng Fract Mech 153:302–318 28. Linkov A (2015) Bench-mark solution for a penny-shaped hydraulic fracture driven by a thinning fluid. ArXiv e-prints arXiv:1508.07968 29. Mi Y, Aliabadi MH (1992) Dual boundary element method for three-dimensional fracture mechanics analysis. Eng Anal Bound Elem 10(2):161–171 30. Mi Y, Aliabadi MH (1994) Three-dimensional crack growth simulation using BEM. Comput Struct 52(5):871–878 31. Mitsoulis E (2007) Flows of viscoplastic materials: models and computations. In: Rheology Reviews 2007. British Society of Rheology 32. Nuismer RJ (1975) An energy release rate criterion for mixed mode fracture. Int J Fract 11(2):245–250 33. Ouyang S, Carey GF, Yew CH (1997) An adaptive finite element scheme for hydraulic fracturing with proppant transport. Int J Numer Methods Fluids 24:645–670 34. Pereira JPA (2010) Generalized finite element methods for three-dimensional crack growth simulations. Ph.D. thesis, Department of Civil and Environmental Engineering, University of Illinois, Urbana-Champaign, p 221 35. Rungamornrat J, Wheeler MF, Mear MF (2005) Coupling of fracture/non-newtonian flow for simulating nonplanar evolution of hydraulic fractures. In: SPE annual technical conference and exhibition, SPE-96968-MS 36. Savitski AA, Detournay E (2002) Propagation of a penny-shaped fluid-driven fracture in an impermeable rock: asymptotic solutions. Int J Solids Struct 39(26):6311–6337 37. Shokin Yu, Cherny S, Esipov D, Lapin V, Lyutov A, Kuranakov D (2015) Three-dimensional model of fracture propagation from the cavity caused by quasi-static load or viscous fluid pumping. Commun Comput Inf Sci. 10.1007/978-3-319-25058-8-15 38. Sousa JL, Carter BJ, Ingraffea AR (1993) Numerical simulation of 3D hydraulic fracture using newtonian and power-law fluids. Int J Rock Mech Min Sci Geomech Abstr 30(7):1265–1271