Poro-elasto-plastic modeling of complex hydraulic fracture propagation: simultaneous multi-fracturing and producing well interference

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• 作者：HanYi Wang
• 刊名：Acta Mechanica
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：227
• 期：2
• 页码：507-525
• 全文大小：2,562 KB
• 参考文献：1.Economides M., Nolte K.: Reservoir Stimulation, 3rd edn. Wiley, Chichester (2000)
  2.Khristianovich, S., Zheltov, Y.: Formation of vertical fractures by means of highly viscous fluids. In: Proceedings of 4th World Petroleum Congress, Rome, Sec. II, pp. 579–586 (1955)
  3.Geertsma J., De Klerk F.: A rapid method of predicting width and extent of hydraulic induced fractures. J. Pet. Technol. 246, 1571–1581 (1969)CrossRef
  4.Perkins, T., Kern, L.: Widths of hydraulic fractures. J. Pet. Technol. 222, 937--949 (1961) (Trans. AIME)
  5.Nordgren R.: Propagation of vertical hydraulic fractures. J. Pet. Technol. 253, 306–314 (1972)
  6.Karihaloo B.L., Xiao Q.Z.: Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Comput. Struct. 81, 119–129 (2003)CrossRef
  7.Lecampion B.: An extended finite element method for hydraulic fracture problems. Commun. Numer. Methods Eng. 25, 121–133 (2009)CrossRef MathSciNet MATH
  8.Dahi-Taleghani A., Olson J.E.: Numerical modeling of multistranded-hydraulic-fracture propagation: accounting for the interaction between induced and natural fractures. SPE J. 16(03), 575–581 (2011)CrossRef
  9.Leonhart D., Meschke D.: Extended finite element method for hydro-mechanical analysis of crack propagation in porous materials. Proc. Appl. Math. Mech. 11, 161–162 (2011)CrossRef
  10.Gordeliy E., Peirce A.: Implicit level set schemes for modeling hydraulic fractures using the XFEM. Comput. Methods Appl. Mech. Eng. 266, 125–143 (2013)CrossRef MathSciNet MATH
  11.Papanastasiou P.: The influence of plasticity in hydraulic fracturing. Int. J. Fract. 84, 61–79 (1997)CrossRef
  12.Papanastasiou P.: The effective fracture toughness in hydraulic fracturing. Int. J. Fract. 96, 127–147 (1999)CrossRef
  13.Germanovich L.N., Astakhov D.K., Shlyapobersky J., Mayerhofer M.J., Dupont C., Ring L.M.: Modeling multi-segmented hydraulic fracture in two extreme cases: no leak-off and dominating leak-off. Int. J. Rock Mech. Min. Sci. 35, 551–554 (1998)CrossRef
  14.Van Dam D.B., Papanastasiou P., De Pater C.J.: Impact of rock plasticity on hydraulic fracture propagation and closure. SPE Prod. Facil. 17, 149–159 (2002)CrossRef
  15.Sone, H., Zoback, M.D.: Visco-plastic properties of shale gas reservoir rocks. Presented at the 45th US Rock Mechanics/Geomechanics Symposium, June 26–29, San Francisco, California (2011)
  16.Parker, M., Petre, E., Dreher, D., Buller, D.: Haynesville shale: hydraulic fracture stimulation approach. Paper 0913 Presented at the International Coalbed and Shale Gas Symposium, Tuscaloosa, Alabama, USA, 18–22 May 2009
  17.Barenblatt G.I.: The formation of equilibrium cracks during brittle fracture: general ideas and hypothesis, axially symmetric cracks. J. Appl. Math. Mech. 23, 622–636 (1959)CrossRef MathSciNet MATH
  18.Barenblatt, G.I.: The Mathematical Theory of Equilibrium Cracks in Brittle Fracture. Advanced in Applied Mechanics, pp. 55–129. Academic Press, New York (1962)
  19.Dugdale D.S.: Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, 100–104 (1960)CrossRef
  20.Griffith A.A.: The phenomena of rupture and flow in solids. Philos. Trans. R. Soc. 221, 163–198 (1921)CrossRef
  21.Griffith, A.A.: The theory of rupture. In: Proceedings of 1st International Congress for Applied Mechanics, Delft, The Netherlands, pp. 55–63 (1924)
  22.Mokryakov V.: Analytical solution for propagation of hydraulic fracture with Barenblatt’s cohesive tip zone. Int. J. Fract. 169, 159–168 (2011)CrossRef MATH
  23.Yao Y.: Linear elastic and cohesive fracture analysis to model hydraulic fracture in brittle and ductile rocks. Rock Mech. Rock Eng. 45, 375–387 (2012)CrossRef
  24.Wang, H., Marongiu-Porcu, M., Economides, M.J.: Poroelastic and poroplastic modeling of hydraulic fracturing in brittle and ductile formations. SPE Prod Oper (2015, in press)
  25.Busetti S., Mish K., Reches Z.: Damage and plastic deformation of reservoir rocks: Part 1. Damage fracturing. AAPG Bull. 96, 1687–1709 (2012)CrossRef
  26.Busetti S., Mish K., Hennings P., Reches Z.: Damage and plastic deformation of reservoir rocks: Part 2. Propagation of a hydraulic fracture. AAPG Bull. 96, 1711–1732 (2012)CrossRef
  27.Boone T.J., Ingraffea A.R.: A numerical procedure for simulation of hydraulically driven fracture propagation in poroelastic media. Int. J. Numer. Anal. Methods Geomech. 14, 27–47 (1990)CrossRef
  28.Biot M.A.: General theory of three dimensional consolidation. J. Appl. Phys. 12(2), 155–164 (1941)CrossRef MATH
  29.Ghassemi, A.: Three-dimensional poroelastic hydraulic fracture simulation using the displacement discontinuity method. PhD dissertation, University of Oklahoma, Norman, Oklahoma (1996)
  30.Vermeer P.A., de Borst R.: Non-associated plasticity for soils, concrete and rock. Heron 29, 3–64 (1984)
  31.Belytschko T., Black T.: Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Methods Eng. 45, 601–620 (1999)CrossRef MathSciNet MATH
  32.Melenk J., Babuska I.: The partition of unity finite element method: basic theory and applications. Comput. Methods Appl. Mech. Eng. 39, 289–314 (1996)CrossRef MathSciNet
  33.Fries T.P., Baydoun M.: Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description. Int. J. Numer. Methods Eng. 89(12), 1527–1558 (2012)CrossRef MathSciNet MATH
  34.Sukumar N., Huang Z.Y., Prevost J.-H., Suo Z.: Partition of unity enrichment for bimaterial interface cracks. Int. J. Numer. Methods Eng. 59, 1075–1102 (2004)CrossRef MATH
  35.Sukumar N., Prevost J.-H.: Modeling quasi-static crack growth with the extended finite element method Part I: computer implementation. Int. J. Solids Struct. 40, 7513–7537 (2003)CrossRef MATH
  36.Elguedj T., Gravouil A., Combescure A.: Appropriate extended functions for X-FEM simulation of plastic fracture mechanics. Comput. Methods Appl. Mech. Eng. 195, 501–515 (2006)CrossRef MATH
  37.Tomar V., Zhai J., Zhou M.: Bounds for element size in a variable stiffness cohesive finite element model. Int. J. Numer. Methods Eng. 61, 1894–1920 (2004)CrossRef MATH
  38.Kanninen M.F., Popelar C.H.: Advanced fracture mechanics, 1st edn. Oxford University Press, Oxford (1985)
  39.Turon A., Camanho P.P., Costa J., Davila C.G.: A damage model for the simulation of delamination in advanced composites under variable-model loading. Mech. Mater. 38, 1072–1089 (2006)CrossRef
  40.Benzeggagh M.L., Kenane M.: Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus. Compos. Sci. Technol. 56, 439–449 (1996)CrossRef
  41.Rabczuk T., Zi G., Gerstenberger A., Wall A.: A new crack tip element for the phantom-node method with arbitrary cohesive cracks. Int. J. Numer. Methods Eng. 75, 577–599 (2008)CrossRef MATH
  42.Song J.H., Areias P.M.A., Belytschko T.: A method for dynamic crack and shear band propagation with phantom nodes. Int. J. Numer. Methods Eng. 67, 868–893 (2006)CrossRef MATH
  43.Remmers J.J.C., de Borst R., Needleman A.: The simulation of dynamic crack propagation using the cohesive segments method. J. Mech. Phys. Solids 56, 70–92 (2008)CrossRef MathSciNet MATH
  44.Roussel N.P., Sharma M.M.: Optimizing fracture spacing and sequencing in horizontal well fracturing. SPE Prod. Oper. 26, 173–184 (2010)CrossRef
  45.Wu K., Olson J.E.: Simultaneous multifracture treatments: fully coupled fluid flow and fracture mechanics for horizontal wells. SPE J. 20, 337–346 (2015)CrossRef
  46.Afrouz A.: Practical handbook of rock mass classification systems and modes of ground failure, 1st edn. CRC Press, Boca Raton (1992)
  47.Peza, E., Hand, R., Happer, W., Jayakumar, R., Wood, D., Wigger, E., Dean, B., Al-Jaial, Z., Ganpule,S.: How Fracture Interference Impacts Woodford Shale Gas Production. Schlumberger ShaleTech Report, pp. 10–14 (2015)
  
• 作者单位：HanYi Wang (1)
  
  1. Petroleum and Geosystems Engineering Department, The University of Texas at Austin, 200 E. Dean Keeton St., Stop C0300, Austin, TX, USA
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Mechanics, Fluids and Thermodynamics
  Continuum Mechanics and Mechanics of Materials
  Structural Mechanics
  Vibration, Dynamical Systems and Control
  Engineering Thermodynamics and Transport Phenomena
  
• 出版者：Springer Wien
• ISSN：1619-6937

文摘

With the increasing wide use of hydraulic fractures in the petroleum industry, it is essential to accurately predict the behavior of fractures based on the understanding of fundamental mechanisms governing the process. For effective reservoir exploration and development, hydraulic fracture pattern, geometry and associated dimensions are critical in determining well stimulation efficiency. In shale formations, non-planar, complex hydraulic fractures are often observed, due to the activation of preexisting natural fractures and the interaction between multiple, simultaneously propagating hydraulic fractures. The propagation of turning non-planar fractures due to the interference of nearby producing wells has also been reported. Current numerical simulation of hydraulic fracturing generally assumes planar crack geometry and weak coupling behavior, which severely limits the applicability of these methods in predicting fracture propagation under complex subsurface conditions. In addition, the prevailing approach for hydraulic fracture modeling also relies on linear elastic fracture mechanics (LEFM) by assuming the rock behaves purely elastically until complete failure. LEFM can predict hard rock hydraulic fracturing processes reasonably, but often fails to give accurate predictions of fracture geometry and propagation pressure in ductile and quasi-brittle rocks, such as poorly consolidated/unconsolidated sands and ductile shales, even in the form of simple planar geometry. In this study, we present a fully coupled poro-elasto-plastic model for hydraulic fracture propagation based on the theories of extend finite element, cohesive zone method and Mohr–Coulomb plasticity, which is able to capture complex hydraulic fracture geometry and plastic deformations in reservoir rocks explicitly. To illustrate the capabilities of the model, example simulations are presented including ones involving simultaneously propagating multiple hydraulic fractures and producing well interference. The results indicate that both stress shadow effects and producing well interference can alter hydraulic fracture propagation behavior substantially, and shear failure in ductile reservoir rocks can indeed make a significant difference in fracturing pressure and final fracture geometry.