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XFEM-Based CZM for the Simulation of 3D Multiple-Cluster Hydraulic Fracturing in Quasi-Brittle Shale Formations

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Abstract

The cohesive zone model (CZM) honors the softening effects and plastic zone at the fracture tip in a quasi-brittle rock, e.g., shale, which results in a more precise fracture geometry and pumping pressure compared to those from linear elastic fracture mechanics. Nevertheless, this model, namely the planar CZM, assumes a predefined surface on which the fractures propagate and therefore restricts the fracture propagation direction. Notably, this direction depends on the stress interactions between closely spaced fractures and can be acquired by integrating CZM as the segmental contact interaction model with a fully coupled pore pressure–displacement model based on extended finite element method (XFEM). This integrated model, called XFEM-based CZM, simulates the fracture initiation and propagation along an arbitrary, solution-dependent path. In this work, we modeled a single stage of 3D hydraulic fracturing initiating from three perforation clusters in a single-layer, quasi-brittle shale formation using planar CZM and XFEM-based CZM including slit flow and poroelasticity for fracture and matrix spaces, respectively, in Abaqus. We restricted the XFEM enrichment zones to the stimulation regions as enriching the whole domain leads to extremely high computational expenses and unrealistic fracture growths around sharp edges. Moreover, we validated our numerical technique by comparing the solution for a single fracture with KGD solution and demonstrated several precautionary measures in using XFEM in Abaqus for faster solution convergence, for instance the initial fracture length and mesh refinement. We demonstrated the significance of the injection rate and stress contrast in fracture aperture, injection pressure, and the propagation direction. Moreover, we showed the effect of the stress distribution on fracture propagation direction comparing the triple-cluster fracturing results from planar CZM with those from XFEM-based CZM. We found that the stress shadowing effect of hydraulic fractures on each other can cause these fractures to coalesce, grow parallel, or diverge depending on cluster spacing. We investigated the effect of this arbitrary propagation direction on not only the fractures’ length, aperture, and the required injection pressure, but also the fractures’ connection to the wellbore. This connection can be disrupted due to the near-wellbore fracture closure which may embed proppant grains on the fracture wall or screen out the fracture at early times. Our results verified that the near-wellbore fracture closure strongly depends on the following: (1) the implemented model, planar or XFEM-based CZM; and (2) fracture cluster spacing. Ultimately, we proposed the best fracturing scenario and cluster spacing to maintain the fractures connected to the wellbore.

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Abbreviations

t :

Traction size (ML−1 T−2), kPa

\(t_{m}^{0}\) :

Mixed-mode traction in damage initiation (ML−1 T−2), kPa

\(\overline{t}\) :

Post-damage elastic traction component (ML−1 T−2), kPa

\(K_{m}\) :

Cohesive layer stiffness (ML−1 T−2), kPa

\(\delta_{m}^{0}\) :

Mixed-mode separation in damage initiation (L), m

\(\delta_{m}^{f}\) :

Final mixed-mode separation (L), m

\(\delta_{m}^{ \hbox{max} }\) :

Maximum mixed-mode separation at partial damage D (L), m

D :

Inviscid cohesive damage variable

G:

Fracture energy release rate (MT−2), kN/m

\(G^{c}\) :

Critical energy release rate (MT−2), kN/m

\(S_{{h,\hbox{min} ,{\text{tot}}}}\) :

Total minimum horizontal stress (ML−1 T−2), kPa

\(S_{{H,\hbox{max} ,{\text{tot}}}}\) :

Total maximum horizontal stress (ML−1 T−2), kPa

\(u^{h} \left( x \right)\) :

Displacement at location x (L), m

\(N_{I} \left( x \right)\) :

Conventional FEM shape function

\(u_{I}\) :

Nodal degree of freedom (L), m

\(H\left( x \right)\) :

Heaviside enrichment function

\(a_{I}\) :

Nodal enrichment degree of freedom for jump discontinuity on fracture walls

\(F_{\alpha } \left( x \right)\) :

Crack tip enrichment (asymptotic) function

\(b_{I}^{\alpha }\) :

Nodal degree of freedom for the crack tip enrichments (L), m

ϕ :

Porosity

K:

Soil permeability (L2), mD

E :

Young’s modulus (ML−1 T−2), GPa

ν :

Poisson’s ratio

GIc :

Opening-mode energy release rate (MT−2), kN/m

GIIc :

Shearing-mode energy release rate (MT−2), kN/m

References

  • Abaqus Analysis User’s Manual (2014) Version 6.14-2. Dassault Systémes Simulia Corp., Providence, RI

  • Abaqus Benchmarks Guide (2014) Version 6.14-2. Dassault Systémes Simulia Corp., Providence, RI

  • Adachi J, Siebrits E, Peirce A, Desroches J (2007) Computer simulation of hydraulic fractures. Int J Rock Mech Min Sci 44:739–757

    Article  Google Scholar 

  • Babuska I, Melenk JM (1997) The partition of unity method. Int J Numer Meth Eng 40:727–758

    Article  Google Scholar 

  • Bazant ZP (1998) Fracture and size effect in concrete and other quasibrittle materials. CRC Press LLC, Boca Raton

    Google Scholar 

  • Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Method Biomed Eng 45:601–620

    Article  Google Scholar 

  • Benzeggagh ML, Kenane M (1996) Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus. Compos Sci Technol 56:439–449

    Article  Google Scholar 

  • Cipolla C, Weng X, Mack M, Ganguly U, Gu H, Kresse O, Cohen C. (2001) Integrating microseismic mapping and complex fracture modeling to characterize fracture complexity. In: Proceedings of the SPE hydraulic fracturing technology conference and exhibition, HFTC2011, 24–26 January 2011, The Woodlands, Texas, USA

  • Cipolla CL, Warpinski NR, Mayerhofer MJ, Lolon EP (2008) The relationship between fracture complexity, reservoir properties, and fracture treatment design. In: Proceedings of the SPE annual technical conference and exhibition, ATCE2008, 21–24 September 2008, Denver, Colorado, USA

  • Crouch SL (1976) Solution of plane elasticity problems by the displacement discontinuity method. Int J Numer Methods Engrg 10:301–343

    Article  Google Scholar 

  • Crouch SL, Starfield AM (1983) bouNdary element methods in solid mechanics. Allen & Unwin, London

    Google Scholar 

  • Daneshy A (2011) Hydraulic fracturing of horizontal wells: issues and insights. In: Proceedings of the SPE Hydraulic fracturing technology conference and exhibition, HFTC2011, 24–26 January 2011, The Woodlands, Texas, USA

  • Fjaer E, Holt RM, Horsrud P, Raaen AM, Risnes R (2008) Petroleum related rock mechanics. In: Developments in petroleum science (2nd ed.). Elsevier, UK

  • Fu P, Johnson SM, Carrigan CR (2012) An explicitly coupled hydro-geomechanical model simulating hydraulic fracturing in arbitrary discrete fracture networks. Int J Numer Anal Meth Geomech

  • Geertsma J, de Klerk F (1969) A rapid method of predicting width and extent of hydraulically induced fractures. J Pet Technol 21:1571–1581

    Article  Google Scholar 

  • Gonzalez M, Dahi Taleghani A (2015) A cohesive model for modeling hydraulic fractures in naturally fractured formations. In: Proceedings of the SPE hydraulic fracturing technology conference, HFTC2015, 3–5 February 2015, Woodlands, Texas, USA. doi:10.2118/173384-MS

  • Haddad M, Sepehrnoori K (2014a) Cohesive fracture analysis to model multiple-stage fracturing in quasibrittle shale formations. In: Proceedings of the SIMULIA community conference, SCC2014, 19–21 May 2014, Providence, Rhode Island, USA. http://www.3ds.com/products-services/simulia/resources/

  • Haddad M, Sepehrnoori K (2014b) Simulation of multiple-stage fracturing in quasibrittle shale formations using pore pressure cohesive zone model. In: Proceedings of the SPE/AAPG/SEG unconventional resources technology conference, URTeC2014, 25–27 August 2014, Denver, Colorado, USA. doi:10.15530/urtec-2014-1922219

  • Haddad M, Sepehrnoori K (2015) Simulation of hydraulic fracturing in quasi-brittle shale formations using characterized cohesive layer: stimulation controlling factors. J Unconventional Oil Gas Resourc 9:65–83. doi:10.1016/j.juogr.2014.10.001

    Article  Google Scholar 

  • Haddad M, Du J, Vidal-Gilbert S (2016) Integration of dynamic microseismic data with a true 3D modeling of hydraulic fracture propagation in Vaca Muerta Shale. In: Proceedings of the SPE hydraulic fracturing technology conference, HFTC2016, 9–11 February 2016. The Woodlands, Texas, USA. doi:10.2118/179164-MS

  • Hansbo A, Hansbo P (2004) A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput Methods Appl Mech Eng 193:3523–3540

    Article  Google Scholar 

  • Hansford J, Fisher Q (2009) The influence of fracture closure from petroleum production from naturally fractured reservoirs: a simulation modeling approach. In: Proceedings of the AAPG annual convention, AAPG2009, Search and Discovery Article No. 40442

  • Howard GC, Fast CR (1957) Optimum fluid characteristics for fracture extension. In: Proceedings of the spring meeting of the mid-continent district, division of production, April 1957, Tulsa, Oklahoma, USA

  • Huang K, Zhang Z, Ghassemi A (2012) Modeling three-dimensional hydraulic fracture propagation using virtual multidimensional internal bonds. Int J Numer Anal Meth Geomech. 2012

  • Moes N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Method Biomed Eng 46:131–150

    Article  Google Scholar 

  • Mohammadnejad T, Khoei AR (2013) 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

    Article  Google Scholar 

  • Muskhelishvili NI (1953) Some basic problems of the mathematical theory of elasticity. Nordhoof, Holland

    Google Scholar 

  • Platts.com (2014) US oil export debate: a platts.com news feature. Platts, a division of the McGraw-Hill Companies, Inc. McGraw-Hill. http://www.platts.com/news-feature/2014/oil/us-oil-export-debate/crude-oil-exports-priority

  • Rickman R., Mullen M., Petre E., Grieser B., Kundert D. A Practical Use of Shale Petrophysics for Stimulation Design Optimization: All Shale Plays Are Not Clones of the Barnett Shale. In: Proceedings of the SPE annual technical conference and exhibition, ATCE2008, 21–24 September 2008, Denver, Colorado, USA

  • Secchi S, Schrefler BA (2012) A method for 3-D hydraulic Fracturing simulation. Int J Fract 178:245–258

    Article  Google Scholar 

  • Sneddon IN (1973) Integral transform methods. In: Sih GC (ed) Mechanics of Fracture I. Methods of Analysis and Solutions of Crack Problems, Nordhoff International, Leyden, p 1973

    Google Scholar 

  • Song J, Areias PM, Belytschko T (2006) A method for dynamic crack and shear band propagation with phantom nodes. Int J Numer Meth Eng 67:868–893

    Article  Google Scholar 

  • Valko P, Economides MJ (1995) Hydraulic fracture mechanics. Wiley, Chichester

    Google Scholar 

  • Vermeer PA, Verruijt A (1981) An accuracy condition for consolidation by finite elements. Int J Numer Anal Meth Geomech 5:1–14

    Article  Google Scholar 

  • Warpinski NR, Mayerhofer MJ, Agarwal K, Du J. (2012) Hydraulic fracture geomechanics and microseismic source mechanisms. In: Proceedings of the SPE annual technical conference and exhibition, ATCE2012, 8–10 October, San Antonio, Texas, USA

  • Weng X, Kresse O, Cohen C, Wu R, Gu H (2011) Modeling of hydraulic-fracture-network propagation in a naturally fractured formation. SPE Journal of Production and Operations 26(4):368–380

    Article  Google Scholar 

  • Wong S, Geilikman M, Xu G (2013) The geomechanical interaction of multiple hydraulic fractures in horizontal wells. In: Effective and sustainable hydraulic fracturing (ed. R. Jeffrey). doi:10.5772/56385

  • Ziarani AS, Chen C, Cui A, Quirk D, Roney D (2014) Fracture and wellbore spacing optimization in multistage fractured horizontal wellbores: learnings from our experience on canadian unconventional resources. In: Proceedings of the international petroleum technology conference, IPTC2014, 10–12 December 2014, Kuala Lumpur, Malaysia

  • Zielonka MG, Searles KH, Ning J, Buechler SR (2014) Development and validation of fully-coupled hydraulic fracturing simulation capabilities. In: Proceedings of the SIMULIA community conference, SCC2014, 19–21 May 2014, Providence, Rhode Island, USA

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Acknowledgments

The authors would like to acknowledge Dassault Systemes Simulia Corporation and Chief Oil and Gas Company for providing Abaqus software program and financial support, respectively. Furthermore, the authors gratefully acknowledge Professor John T. Foster for his critical comments on the paper manuscript and his promotion and advice to validate our numerical model.

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Authors and Affiliations

  1. Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, 200 E. Dean Keeton, Stop C0304, CPE 4.148, Austin, TX, 78712-1575, USA

    Mahdi Haddad & Kamy Sepehrnoori

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  1. Mahdi Haddad
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  2. Kamy Sepehrnoori
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Correspondence to Mahdi Haddad.

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Haddad, M., Sepehrnoori, K. XFEM-Based CZM for the Simulation of 3D Multiple-Cluster Hydraulic Fracturing in Quasi-Brittle Shale Formations. Rock Mech Rock Eng 49, 4731–4748 (2016). https://doi.org/10.1007/s00603-016-1057-2

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