Research Papers

Theoretical and Numerical Models to Predict Fracking Debonding Zone and Optimize Perforation Cluster Spacing in Layered Shale

[+] Author and Article Information
Tao Wang, Yue Gao, Qinglei Zeng

Applied Mechanics Laboratory,
School of Aerospace Engineering,
Tsinghua University,
Beijing 100084, China

Zhanli Liu

Applied Mechanics Laboratory,
School of Aerospace Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: liuzhanli@tsinghua.edu.cn

Zhuo Zhuang

Applied Mechanics Laboratory,
School of Aerospace Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: zhuangz@tsinghua.edu.cn

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 19, 2017; final manuscript received October 16, 2017; published online November 9, 2017. Editor: Yonggang Huang.

J. Appl. Mech 85(1), 011001 (Nov 09, 2017) (14 pages) Paper No: JAM-17-1520; doi: 10.1115/1.4038216 History: Received September 19, 2017; Revised October 16, 2017

Shale is a typical layered and anisotropic material whose properties are characterized primarily by locally oriented anisotropic clay minerals and naturally formed bedding planes. The debonding of the bedding planes will greatly influence the shale fracking to form a large-scale highly permeable fracture network, named stimulated reservoir volume (SRV). In this paper, both theoretical and numerical models are developed to quantitatively predict the growth of debonding zone in layered shale under fracking, and the good agreement is obtained between the theoretical and numerical prediction results. Two dimensionless parameters are proposed to characterize the conditions of tensile and shear debonding in bedding planes. It is found that debonding is mainly caused by the shear failure of bedding planes in the actual reservoir. Then the theoretical model is applied to design the perforation cluster spacing to optimize SRV, which is important in fracking. If the spacing is too small, there will be overlapping areas of SRV and the fracking efficiency is low. If the spacing is too large, there will be stratum that cannot be stimulated. So another two dimensionless parameters are proposed to evaluate the size and efficiency of stimulating volume at the same time. By maximizing these two parameters, the optimal perforation cluster spacing and SRV can be quantitatively calculated to guide the fracking treatment design. These results are comparable with data from the field engineering.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Bažant, Z. P. , Salviato, M. , Chau, V. T. , Visnawathan, H. , and Zubelewicz, A. , 2014, “ Why Fracking Works,” ASME J. Appl. Mech., 81(10), p. 101010. [CrossRef]
Fisher, M. K. , Wright, C. A. , Davidson, B. M. , Goodwin, A. K. , Fielder, E. O. , Buckler, W. S. , and Steinsberger, N. P. , 2002, “ Integrating Fracture Mapping Technologies to Optimize Stimulations in the Barnett Shale,” SPE Annual Technical Conference and Exhibition, Sept. 29–Oct. 2, San Antonio, TX, SPE Paper No. SPE-77441-MS.
Maxwell, S. C. , Urbancic, T. I. , Steinsberger, N. , and Zinno, R. , 2002, “ Microseismic Imaging of Hydraulic Fracture Complexity in the Barnett Shale,” SPE Annual Technical Conference and Exhibition, Sept. 29–Oct. 2, San Antonio, TX, SPE Paper No. SPE-77440-MS.
Nassir, M. , Settari, A. , and Wan, R. G. , 2014, “ Prediction of Stimulated Reservoir Volume and Optimization of Fracturing in Tight Gas and Shale With a Fully Elasto-Plastic Coupled Geomechanical Model,” SPE J., 19(5), pp. 771–785. [CrossRef]
Li, W. , Rezakhani, R. , Jin, C. , Zhou, X. , and Cusatis, G. , 2017, “ A Multiscale Framework for the Simulation of the Anisotropic Mechanical Behavior of Shale,” Int. J. Numer. Anal. Methods Geomech., 41(14), pp. 1494–1522.
Bennett, K. C. , Berla, L. A. , Nix, W. D. , and Borja, R. I. , 2015, “ Instrumented Nanoindentation and 3D Mechanistic Modeling of a Shale at Multiple Scales,” Acta Geotech., 10(1), pp. 1–14. [CrossRef]
Bobko, C. , and Ulm, F.-J. , 2008, “ The Nano-Mechanical Morphology of Shale,” Mech. Mater., 40(4–5), pp. 318–337. [CrossRef]
Slatt, R. M. , and Abousleiman, Y. , 2011, “ Merging Sequence Stratigraphy and Geomechanics for Unconventional Gas Shales,” Leading Edge, 30(3), pp. 274–282. [CrossRef]
Gale, J. F. W. , Laubach, S. E. , Olson, J. E. , Eichhuble, P. , and Fall, A. , 2014, “ Natural Fractures in Shale: A Review and New Observations,” AAPG Bull., 98(11), pp. 2165–2216. [CrossRef]
Blanton, T. L. , 1986, “ Propagation of Hydraulically and Dynamically Induced Fractures in Naturally Fractured Reservoirs,” SPE Unconventional Gas Technology Symposium, Louisville, Kentucky, May 18–21, SPE Paper No. SPE-15261-MS.
Warpinski, N. R. , and Teufel, L. W. , 1987, “ Influence of Geologic Discontinuities on Hydraulic Fracture Propagation,” SPE J., 39(2), pp. 209–220.
Zhou, J. , Chen, M. , Jin, Y. , and Zhang, G.-Q. , 2008, “ Analysis of Fracture Propagation Behavior and Fracture Geometry Using a Tri-Axial Fracturing System in Naturally Fractured Reservoirs,” Int. J. Rock Mech. Min. Sci., 45(7), pp. 1143–1152. [CrossRef]
Chuprakov, D. , Melchaeva, O. , and Prioul, R. , 2013, “ Injection-Sensitive Mechanics of Hydraulic Fracture Interaction With Discontinuities,” 47th U.S. Rock Mechanics/Geomechanics Symposium, San Francisco, CA, June 23–26, Paper No. ARMA-2013-252. https://www.onepetro.org/conference-paper/ARMA-2013-252
Potluri, N. K. , Zhu, D. , and Hill, A. D. , 2005, “ The Effect of Natural Fractures on Hydraulic Fracture Propagation,” SPE European Formation Damage Conference, Sheveningen, The Netherlands, May 25–27, SPE Paper No. SPE-94568-MS.
Beugelsdijk, L. J. L. , de Pater, C. J. , and Sato, K. , 2000, “ Experimental Hydraulic Fracture Propagation in a Multi-Fractured Medium,” SPE Asia Pacific Conference on Integrated Modelling for Asset Management, Yokohama, Japan, Apr. 25–26, SPE Paper No. SPE-59419-MS.
Zhang, X. , Jeffrey, R. G. , and Thiercelin, M. , 2009, “ Mechanics of Fluid-Driven Fracture Growth in Naturally Fractured Reservoirs With Simple Network Geometries,” J. Geophys. Res. Solid Earth, 114(B12), p. B12406.
Dahi-Taleghani, A. , and Olson, J. E. , 2011, “ Numerical Modeling of Multistranded-Hydraulic-Fracture Propagation: Accounting for the Interaction Between Induced and Natural Fractures,” SPE J., 16(3), pp. 575–581. [CrossRef]
Guo, J. , Zhao, X. , Zhu, H. , Zhang, X. , and Pan, R. , 2015, “ Numerical Simulation of Interaction of Hydraulic Fracture and Natural Fracture Based on the Cohesive Zone Finite Element Method,” J. Nat. Gas Sci. Eng., 25, pp. 180–188. [CrossRef]
Jang, Y. , Kim, J. , Ertekin, T. , and Sung, W. , 2016, “ Fracture Propagation Model Using Multiple Planar Fracture With Mixed Mode in Naturally Fractured Reservoir,” J. Pet. Sci. Eng., 144, pp. 19–27. [CrossRef]
Miehe, C. , Mauthe, S. , and Teichtmeister, S. , 2015, “ Minimization Principles for the Coupled Problem of Darcy–Biot-Type Fluid Transport in Porous Media Linked to Phase Field Modeling of Fracture,” J. Mech. Phys. Solids, 82, pp. 186–217. [CrossRef]
Wang, T. , Liu, Z. L. , Zeng, Q. L. , Gao, Y. , and Zhuang, Z. , 2017, “ XFEM Modeling of Hydraulic Fracture in Porous Rocks With Natural Fractures,” Sci. China-Phys. Mech. Astron., 60(8), p. 084612.
Renshaw, C. E. , and Pollard, D. D. , 1995, “ An Experimentally Verified Criterion for Propagation Across Unbounded Frictional Interfaces in Brittle, Linear Elastic Materials,” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 32(3), pp. 237–249. [CrossRef]
Taleghani, A. D. , and Olson, J. E. , 2014, “ How Natural Fractures Could Affect Hydraulic-Fracture Geometry,” SPE J., 19(1), pp. 161–171. [CrossRef]
Gu, H. , and Weng, X. , 2010, “ Criterion for Fractures Crossing Frictional Interfaces at Non-Orthogonal Angles,” 44th U.S. Rock Mechanics Symposium and Fifth U.S.–Canada Rock Mechanics Symposium, Salt Lake City, Utah, June 27–30, Paper No. ARMA-10-198 https://www.onepetro.org/conference-paper/ARMA-10-198.
Zhang, X. , and Jeffrey, R. G. , 2006, “ The Role of Friction and Secondary Flaws on Deflection and Re-Initiation of Hydraulic Fractures at Orthogonal Pre-Existing Fractures,” Geophys. J. Int., 166(3), pp. 1454–1465. [CrossRef]
Chau, V. T. , Bazant, Z. P. , and Su, Y. , 2016, “ Growth Model for Large Branched Three-Dimensional Hydraulic Crack System in Gas or Oil Shale,” Philos. Trans. Ser. A, 374(2078), p. 20150418.
Chau, V. T. , Li, C. , Rahimi-Aghdam, S. , and Bažant, Z. P. , 2017, “ The Enigma of Large-Scale Permeability of Gas Shale: Pre-Existing or Frac-Induced?,” ASME J. Appl. Mech., 84(6), p. 061008. [CrossRef]
Mayerhofer, M. J. , Lolon, E. , Warpinski, N. R. , Cipolla, C. L. , Walser, D. W. , and Rightmire, C. M. , 2010, “ What Is Stimulated Reservoir Volume?,” SPE Prod. Oper., 25(1), pp. 89–98. [CrossRef]
Grassl, P. , Fahy, C. , Gallipoli, D. , and Wheeler, S. J. , 2015, “ On a 2D Hydro-Mechanical Lattice Approach for Modelling Hydraulic Fracture,” J. Mech. Phys. Solids, 75, pp. 104–118. [CrossRef]
Zeng, X. , and Wei, Y. , 2017, “ Crack Deflection in Brittle Media With Heterogeneous Interfaces and Its Application in Shale Fracking,” J. Mech. Phys. Solids, 101, pp. 235–249. [CrossRef]
Li, C. , Caner, F. C. , Chau, V. T. , and Bažant, Z. P. , 2017, “ Spherocylindrical Microplane Constitutive Model for Shale and Other Anisotropic Rocks,” J. Mech. Phys. Solids., 103, pp. 155–178.
Bažant, Z. P. , and Chau, V. T. , 2016, “ Recent Advances in Global Fracture Mechanics of Growth of Large Hydraulic Crack Systems in Gas or Oil Shale: A Review,” New Frontiers in Oil and Gas Exploration, C. Jin and G. Cusatis , eds., Springer International Publishing, Cham, Switzerland, pp. 435–460. [CrossRef]
Cipolla, C. L. , Weng, X. , Mack, M. G. , Ganguly, U. , Gu, H. , Kresse, O. , and Cohen, C. E. , 2011, “ Integrating Microseismic Mapping and Complex Fracture Modeling to Characterize Hydraulic Fracture Complexity,” SPE Hydraulic Fracturing Technology Conference, The Woodlands, TX, Jan. 24–26, SPE Paper No. SPE-140185-MS.
Weng, X. , Kresse, O. , Cohen, C.-E. , Wu, R. , and Gu, H. , 2011, “ Modeling of Hydraulic-Fracture-Network Propagation in a Naturally Fractured Formation,” SPE Prod. Oper., 26(4), pp. 368–380. [CrossRef]
Wu, R. , Kresse, O. , Weng, X. , Cohen, C.-E. , and Gu, H. , 2012, “ Modeling of Interaction of Hydraulic Fractures in Complex Fracture Networks,” SPE Hydraulic Fracturing Technology Conference, The Woodlands, TX, Feb. 6–8, SPE Paper No. SPE-152052-MS.
Wu, K. , and Olson, J. E. , 2015, “ Simultaneous Multifracture Treatments: Fully Coupled Fluid Flow and Fracture Mechanics for Horizontal Wells,” SPE J., 20(2), pp. 337–346. [CrossRef]
Zeng, Q. , Liu, Z. , Wang, T. , Gao, Y. , and Zhuang, Z. , 2017, “ Fully Coupled Simulation of Multiple Hydraulic Fractures to Propagate Simultaneously From a Perforated Horizontal Wellbore,” Comput. Mech., epub.
Lecampion, B. , and Desroches, J. , 2015, “ Simultaneous Initiation and Growth of Multiple Radial Hydraulic Fractures From a Horizontal Wellbore,” J. Mech. Phys. Solids, 82, pp. 235–258. [CrossRef]
Peirce, A. , and Bunger, A. , 2015, “ Interference Fracturing: Nonuniform Distributions of Perforation Clusters That Promote Simultaneous Growth of Multiple Hydraulic Fractures,” SPE J., 20(2), p. 172500-PA.
Liu, C. , Shi, F. , Zhang, Y. , Zhang, Y. , Deng, D. , Wang, X. , Liu, H. , and Wu, H. , 2017, “ High Injection Rate Stimulation for Improving the Fracture Complexity in Tight-Oil Sandstone Reservoirs,” J. Nat. Gas Sci. Eng., 42, pp. 133–141. [CrossRef]
Shi, F. , Wang, X. , Liu, C. , Liu, H. , and Wu, H. , 2017, “ An XFEM-Based Method With Reduction Technique for Modeling Hydraulic Fracture Propagation in Formations Containing Frictional Natural Fractures,” Eng. Fract. Mech., 173, pp. 64–90. [CrossRef]
Zhao, J. , Chen, X. , Li, Y. , and Fu, B. , 2016, “ Simulation of Simultaneous Propagation of Multiple Hydraulic Fractures in Horizontal Wells,” J. Pet. Sci. Eng., 147, pp. 788–800. [CrossRef]
Lecampion, B. , Desroches, J. , Weng, X. , Burghardt, J. , and Brown, J. E. , 2015, “ Can We Engineer Better Multistage Horizontal Completions? Evidence of the Importance of Near-Wellbore Fracture Geometry From Theory, Lab and Field Experiments,” SPE Hydraulic Fracturing Technology Conference, The Woodlands, TX, Feb. 3–5, SPE Paper No. SPE-173363-MS.
Nagel, N. , Zhang, F. , Sanchez-Nagel, M. , Lee, B. , and Agharazi, A. , 2013, “ Stress Shadow Evaluations for Completion Design in Unconventional Plays,” SPE Unconventional Resources Conference, Calgary, AB, Canada, Nov. 5–7, SPE Paper No. SPE-167128-MS.
Chen, Z. , 2012, “ Finite Element Modelling of Viscosity-Dominated Hydraulic Fractures,” J. Pet. Sci. Eng., 88–89, pp. 136–144. [CrossRef]
Hoek, E. , Kaiser, P. K. , and Bawden, W. F. , 1995, Support of Underground Excavations in Hard Rock, Taylor & Francis, Rotterdam, The Netherlands.
Soundararaiah, Q. Y. , Karunaratne, B. S. B. , and Rajapakse, R. M. G. , 2009, “ Montmorillonite Polyaniline Nanocomposites: Preparation, Characterization and Investigation of Mechanical Properties,” Mater. Chem. Phys., 113(2–3), pp. 850–855. [CrossRef]
Liu, Y. , 2015, “ Fracture Toughness Assessment of Shales By Nanoindentation,” Master's thesis, University of Massachusetts Amherst, Amherst, MA. http://scholarworks.umass.edu/cee_geotechnical/4/
Kahraman, S. , and Altindag, R. , 2004, “ A Brittleness Index to Estimate Fracture Toughness,” Int. J. Rock Mech. Min. Sci., 41(2), pp. 343–348. [CrossRef]
Stoeckhert, F. , Molenda, M. , Brenne, S. , and Alber, M. , 2015, “ Fracture Propagation in Sandstone and Slate—Laboratory Experiments, Acoustic Emissions and Fracture Mechanics,” J. Rock Mech. Geotech. Eng., 7(3), pp. 237–249. [CrossRef]
Muskhelishvili, N. I. , 2013, Some Basic Problems of the Mathematical Theory of Elasticity, Springer Science & Business Media, Berlin.
Detournay, E. , 2004, “ Propagation Regimes of Fluid-Driven Fractures in Impermeable Rocks,” Int. J. Geomech., 4(1), pp. 35–45. [CrossRef]
Hu, J. , and Garagash, D. I. , 2010, “ Plane-Strain Propagation of a Fluid-Driven Crack in a Permeable Rock With Fracture Toughness,” ASCE J. Eng. Mech., 136(9), pp. 1152–1166. [CrossRef]


Grahic Jump Location
Fig. 1

(a) Typical weak interfaces such as bedding planes in shale outcrops in Changning, Sichuan Province, China and (b) HFs debond bedding planes and form high-permeability zones (SRV)

Grahic Jump Location
Fig. 2

The shale formation and its surrounding environment. Typical fracking process (here present three stages (stage N–2, N–1, and N) with different perforation cluster spacing (sN−2, sN−1 and sN)) and the in situ stress status. The horizontal wellbore is in the direction of the minimum horizontal in situ stress σh; the HFs would propagate across the weak regions and debond the bedding planes to form SRV under the influence of fluid pressure pf, with in situ stresses σh and σV.

Grahic Jump Location
Fig. 3

Geometry of the problem and the applied in situ stresses and uniform internal pressure: (a) bedding plane is not debonded and (b) as fracture propagates, the bedding plane is partially debonded

Grahic Jump Location
Fig. 4

Dimensionless debonding zone caused by the tensile stress in front of HF tip for different dimensionless parameters χ. The dots at the end of the dotted lines represent the positions where the maximum tensile debonding width ξmaxT occurs and the dots on x-axis represent the maximum dimensionless distances dmaxT where the debonding begins to occur.

Grahic Jump Location
Fig. 5

(a) The maximum dimensionless tensile debonding width ξmaxT as a function of dimensionless parameter χ and (b) the maximum dimensionless distance dmaxT as a function of dimensionless parameter χ

Grahic Jump Location
Fig. 6

(a) Dimensionless debonding zone caused by shear stress in front of the HF tip for different dimensionless parameter γ, the dot represents the position where the maximum shear debonding length ξmaxS occurs and (b) the maximum dimensionless shear debonding length ξmaxS as a function of the dimensionless parameter χ

Grahic Jump Location
Fig. 7

The tensile (a)–(d) and shear (e)–(h) debonding zones under pressure evolution with different HF propagation length (a=10 m, a=20 m, a=40 m, a=80 m). The x-axis represents the coordinates along the HF direction, and the y-axis represents the coordinates perpendicular to the HF direction.

Grahic Jump Location
Fig. 8

The upper envelope of (a) tensile and (b) shear debonding zone under different material parameters and geomechanical conditions

Grahic Jump Location
Fig. 9

Finite element models for the numerical calculation of HF in a layered rock: (a) the HF in the layered shale, (b) the partial enlarged view of the HF tip, and (c) the connection form of cohesive elements at intersection between HF and bedding planes

Grahic Jump Location
Fig. 10

Numerical Solutions of debonding zone under different dimensionless parameters γ and layers spacing Ls: (a) γ=1.0, Ls=0.2 m, (b) γ=0.5, Ls=0.5 m, and (c) comparison between numerical and analytical solutions

Grahic Jump Location
Fig. 11

The comparison between numerical results and analytical solutions for debonding zones at different time (corresponding to different HF extension length): (a) t=13.74 s, a=10 m, (b) t=37.91 s, a=20 m, and (c) t=68.02 s, a=30 m

Grahic Jump Location
Fig. 12

The schematic diagram of definition for the parameters stimulating volume ratio α (the ratio of the volume at the middle part to the left part) and stimulating efficiency β (the ratio of the volume at the middle part to the right part): (a) the perforation cluster spacing is relatively small, (b) the perforation cluster spacing is relatively large, and (c) three-dimensional view of the debonding zones

Grahic Jump Location
Fig. 13

Stimulating volume ratio α and stimulating efficiency β versus perforation cluster spacing under different material parameters. The large right point marker indicates the optimal perforation cluster spacing to ensure the stimulating volume ratio α and the left point is that to ensure the stimulating efficiency β.

Grahic Jump Location
Fig. 14

Fast prediction of optimal perforation cluster spacing and SRV by using the limit half-width of envelope: (a) the actual debonding zones and (b) the equivalent debonding zones for fast prediction

Grahic Jump Location
Fig. 15

Superposition of the stress for the fracking problem

Grahic Jump Location
Fig. 16

Comparison of the results with analytical solution for the plane strain KGD model with viscosity-dominated HF propagation (a) fracture opening at injection point and (b) inlet pressure at injection point

Grahic Jump Location
Fig. 17

Comparison of the results with analytical solution for the plane strain KGD model with toughness-dominated HF propagation (a) fracture opening width at injection point and (b) inlet pressure at injection point



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In