Research Papers

Simulation-Based Unitary Fracking Condition and Multiscale Self-Consistent Fracture Network Formation in Shale

[+] Author and Article Information
Qinglei Zeng, Tao Wang, Zhanli Liu

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

Zhuo Zhuang

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

1Corresponding author.

Manuscript received December 27, 2016; final manuscript received March 7, 2017; published online March 24, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(5), 051004 (Mar 24, 2017) (7 pages) Paper No: JAM-16-1623; doi: 10.1115/1.4036192 History: Received December 27, 2016; Revised March 07, 2017

Hydraulic fracturing (fracking) technology in gas or oil shale engineering is highly developed last decades, but the knowledge of the actual fracking process is mostly empirical and makes mechanicians and petroleum engineers wonder: why fracking works? (Bažant et al., 2014, “Why Fracking Works,” ASME J. Appl. Mech., 81(10), p. 101010) Two crucial issues should be considered in order to answer this question, which are fracture propagation condition and multiscale fracture network formation in shale. Multiple clusters of fractures initiate from the horizontal wellbore and several major fractures propagate simultaneously during one fracking stage. The simulation-based unitary fracking condition is proposed in this paper by extended finite element method (XFEM) to drive fracture clusters growing or arresting dominated by inlet fluid flux and stress intensity factors. However, there are millions of smeared fractures in the formation, which compose a multiscale fracture network beyond the computation capacity by XFEM. So, another simulation-based multiscale self-consistent fracture network model is proposed bridging the multiscale smeared fractures. The purpose of this work is to predict pressure on mouth of well or fluid flux in the wellbore based on the required minimum fracture spacing scale, reservoir pressure, and proppant size, as well as other given conditions. Examples are provided to verify the theoretic and numerical models.

Copyright © 2017 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]
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]
Miller, C. K. , Waters, G. A. , and Rylander, E. I. , 2011, “Evaluation of Production Log Data From Horizontal Wells Drilled in Organic Shales,” North American Unconventional Gas Conference and Exhibition, Society of Petroleum Engineers, The Woodlands, Texas, Paper No. SPE-144326-MS.
Xu, D. D. , Liu, Z. L. , Liu, X. M. , Zeng, Q. L. , and Zhuang, Z. , 2014, “ Modeling of Dynamic Crack Branching by Enhanced Extended Finite Element Method,” Comput. Mech., 54(2), pp. 489–502. [CrossRef]
Chau, V. T. , Bažant, Z. P. , and Su, Y. , 2016, “ Growth Model for Large Branched Three-Dimensional Hydraulic Crack System in Gas or Oil Shale,” Philos. Trans. R. Soc. A, 374(2078), p. 20150418.
Geertsma, J. , and De Klerk, F. , 1969, “ A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures,” J. Pet. Technol., 21(12), pp. 1571–1581. [CrossRef]
Khristianovic, S. A. , and Zheltov, Y. P. , 1955, “ Formation of Vertical Fractures by Means of Highly Viscous Liquid,” 4th World Petroleum Congress, Rome, Italy, June 6–15, Paper No. WPC-6132.
Nordgren, R. P. , 1972, “ Propagation of a Vertical Hydraulic Fracture,” Soc. Pet. Eng. J., 12(4), pp. 306–314. [CrossRef]
Perkins, T. K. , and Kern, L. R. , 1961, “ Widths of Hydraulic Fractures,” J. Pet. Technol., 13(9), pp. 937–949. [CrossRef]
Adachi, J. , 2001, “ Fluid-Driven Fracture in Permeable Rock,” Ph.D. thesis, University of Minnesota, Minneapolis, MN.
Detournay, E. , 2004, “ Propagation Regimes of Fluid-Driven Fractures in Impermeable Rocks,” Int. J. Geomech., 4(1), pp. 35–45. [CrossRef]
Garagash, D. I. , 2006, “ Propagation of a Plane-Strain Hydraulic Fracture With a Fluid Lag: Early-Time Solution,” Int. J. Solids Struct., 43(18–19), pp. 5811–5835. [CrossRef]
Savitski, A. A. , and Detournay, E. , 2002, “ Propagation of a Penny-Shaped Fluid-Driven Fracture in an Impermeable Rock: Asymptotic Solutions,” Int. J. Solids Struct., 39(26), pp. 6311–6337. [CrossRef]
Olson, J. E. , and Taleghani, A. D. , 2009, “ Modeling Simultaneous Growth of Multiple Hydraulic Fractures and Their Interaction With Natural Fractures,” SPE Hydraulic Fracturing Technology Conference, Society of Petroleum Engineers, The Woodlands, TX, Paper No. SPE-119739-MS.
Taleghani, A. D. , 2011, “ Modeling Simultaneous Growth of Multi-Branch Hydraulic Fractures,” 45th U.S. Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association, San Francisco, CA, June 26–29, Paper No. ARMA-11-436.
Bunger, A. P. , 2013, “ Analysis of the Power Input Needed to Propagate Multiple Hydraulic Fractures,” Int. J. Solids Struct., 50(10), pp. 1538–1549. [CrossRef]
Bunger, A. P. , Jeffrey, R. G. , and Zhang, X. , 2014, “ Constraints on Simultaneous Growth of Hydraulic Fractures From Multiple Perforation Clusters in Horizontal Wells,” SPE J., 19(4), pp. 608–620. [CrossRef]
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]
Wu, K. , and Olson, J. E. , 2015, “ Mechanisms of Simultaneous Hydraulic-Fracture Propagation From Multiple Perforation Clusters in Horizontal Wells,” SPE J., 21(3), pp. 1–9.
Zeng, Q. , Liu, Z. , Wang, T. , Gao, Y. , and Zhuang, Z. , 2017, “ Fully Coupled Simulation of the Propagation of Multiple Hydraulic Fractures From a Horizontal Wellbore,” Comput. Mech., (submitted).
Zhuang, Z. , Liu, Z. , Cheng, B. , and Liao, J. , 2014, Extended Finite Element Method, Elsevier & Tsinghua University Press, Oxford, UK.
Fox, R. W. , McDonald, A. T. , and Pritchard, P. J. , 2010, Introduction to Fluid Mechanics, Wiley, New York.
Crump, J. B. , and Conway, M. W. , 1988, “ Effects of Perforation-Entry Friction on Bottomhole Treating Analysis,” J. Pet. Technol., 40(8), pp. 1041–1048. [CrossRef]
Wang, H. , Liu, Z. , Xu, D. , Zeng, Q. , and Zhuang, Z. , 2016, “ Extended Finite Element Method Analysis for Shielding and Amplification Effect of a Main Crack Interacted With a Group of Nearby Parallel Microcracks,” Int. J. Damage Mech., 25(1), pp. 4–25. [CrossRef]
Bažant, Z. P. , Ohtsubo, H. , and Aoh, K. , 1979, “ Stability and Post-Critical Growth of a System of Cooling or Shrinkage Cracks,” Int. J. Fract., 15(5), pp. 443–456. [CrossRef]
Bažant, Z. P. , and Tabbara, M. R. , 1992, “ Bifurcation and Stability of Structures With Interacting Propagating Cracks,” Int. J. Fract., 53(3), pp. 273–289.
Nemat-Nasser, S. , Keer, L. M. , and Parihar, K. S. , 1978, “ Unstable Growth of Thermally Induced Interacting Cracks in Brittle Solids,” Int. J. Solids Struct., 14(6), pp. 409–430. [CrossRef]
Nemat-Nasser, S. , Sumi, Y. , and Keer, L. M. , 1980, “ Unstable Growth of Tension Cracks in Brittle Solids: Stable and Unstable Bifurcations, Snap-Through, and Imperfection Sensitivity,” Int. J. Solids Struct., 16(11), pp. 1017–1035. [CrossRef]


Grahic Jump Location
Fig. 1

Simultaneous propagation of multiple fractures during one fracking stage

Grahic Jump Location
Fig. 2

Simultaneous propagation of four HFs

Grahic Jump Location
Fig. 3

Fluid partitioning and evolution of f for case 1

Grahic Jump Location
Fig. 4

Fluid partitioning and evolution of f for case 2

Grahic Jump Location
Fig. 5

Fluid partitioning and evolution of f for case 3

Grahic Jump Location
Fig. 6

Fluid partitioning and evolution of f for case 4

Grahic Jump Location
Fig. 7

Global fracture network from local fracture SRV model

Grahic Jump Location
Fig. 8

The smallest fracture spacing 0.1 m is established after five scale reduction from the largest scale level at 30 m

Grahic Jump Location
Fig. 9

The fracture propagation process at the smallest scale

Grahic Jump Location
Fig. 10

Fracture width and formation deformation contour at different scales

Grahic Jump Location
Fig. 11

Average fracture width versus minimum fracture spacing at different scales



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