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Journal of Applied Mechanics | Volume 84 | Issue 6 | research-article
Research Papers

The Enigma of Large-Scale Permeability of Gas Shale: Pre-Existing or Frac-Induced?

[+] Author and Article Information
Viet T. Chau, Saeed Rahimi-Aghdam

Department of Civil and Environmental Engineering,
Northwestern University,
Evanston, IL 60208

Cunbao Li

Department of Civil and Environmental Engineering,
Northwestern University,
Evanston, IL 60208;Key Laboratory of Energy Engineering Safety
and Disaster Mechanics Ministry of Education,
Sichuan University,
Chengdu 610065, China;College of Architecture and Environment,
Sichuan University,
Chengdu 610065, China

Zdeněk P. Bažant

McCormick Institute Professor
W.P. Murphy Professor of Civil and Mechanical
Engineering and Materials Science,
Northwestern University,
Evanston, IL 60208
e-mail: z-bazant@northwestern.edu

1V. T. Chau, C. Li, and S. Rahimi-Aghdam contributed equally to this work.

2Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 11, 2017; final manuscript received April 7, 2017; published online April 25, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(6), 061008 (Apr 25, 2017) (11 pages) Paper No: JAM-17-1140; doi: 10.1115/1.4036455 History: Received March 11, 2017; Revised April 07, 2017
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Citing Articles

The existing commercial programs for simulation of hydraulic fracturing (aka fracking, or frac) of gas (or oil) shale predict parallel vertical cracks to spread in vertical parallel planes, with no lateral branching. These cracks emanate from the perforation clusters on the horizontal wellbore casing, typically spaced 10 m apart or more. For such a large spacing, the rate of gas production observed at the wellhead can be explained only upon making the hypothesis that the large-scale (or regional) permeability of shale is (even at 3 km depth) about 10,000 times higher than the gas permeability of shale measured in the lab on drilled (nondried) shale cores under confining pressures corresponding to shale at the depth of about 3 km. This hypothesis has recently been rendered doubtful by a new three-phase medium theory that takes into account the body forces due to pressure gradients of pore water diffusing into the pores. This theory predicts the fracking to produce a dense system of branched vertical hydraulic cracks with the spacing of about 0.1 m. This value matches the crack spacing deduced from the gas production rate at wellhead based on the actual lab-measured permeability. It is calculated that, to boost the permeability 10,000 times, the width of the pre-existing open (unfilled) natural cracks or joints (whose ages are distributed from one to several hundred million years) would have to be about 2.8 μm (not counting possible calcite deposits in the cracks). But this width is improbably high because, over the geologic time span, the shale must exhibit significant primary and secondary creep or flow. It is shown that the creep must close all the cracks tightly (except for residual openings of the order of 10 nm) even if the cracks are propped open by surface asperities. The inevitability of secondary creep (or steady-state flow) is explained theoretically by activation of new creep sites at stress concentrations caused by prior creep deformation. The time of transition from primary to secondary creep is taken equal to the Maxwell time estimate from geology. The overall conclusion is that the 10,000-fold increase of large-scale permeability is most likely not pre-existing but frac-induced. Although this conclusion will make little difference for long-term forecasts, it would make a major difference for the understanding and control of the frac process.
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Figures

Grahic Jump Location
Fig. 1

Parallel hydraulic cracks as predicted in current practice (a single crack per perforation cluster, with no branching), pictured before localization [2]

+Parallel hydraulic cracks as predicted in current practice (a single crack per perforation cluster, with no branching), pictured before localization [2]
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Parallel hydraulic cracks as predicted in current practice (a single crack per perforation cluster, with no branching), pictured before localization [2]
Grahic Jump Location
Fig. 5

(a) Three phases of creep evolution under constant stress, (b) creep evolution over 200 million years when only the primary creep terms are considered, and (c) the same when the secondary creep (or flow) is included

+(a) Three phases of creep evolution under constant stress, (b) creep evolution over 200 million years when only the primary creep terms are considered, and (c) the same when the secondary creep (or flow) is included
View Large  |  Save Figure  |  Download Slide (.ppt)
(a) Three phases of creep evolution under constant stress, (b) creep evolution over 200 million years when only the primary creep terms are considered, and (c) the same when the secondary creep (or flow) is included
Grahic Jump Location
Fig. 2

Crack branching in a horizontal frac domain 5 m × 5 m simulated in Ref. [3] by three-phase medium theory with body forces due to pore pressure gradients: (a) for full fracture energy Gf and tensile strength ft of crack band model [12] and (b) for Gf=ft=0 [3] (the horizontal wellbore lies at the bottom of each square shown, and the frac water is injected at constant pressure from three perforations clusters on the wellbore)

+Crack branching in a horizontal frac domain 5 m × 5 m simulated in Ref. [3] by three-phase medium theory with body forces due to pore pressure gradients: (a) for full fracture energy Gf and tensile strength ft of crack band model [12] and (b) for Gf=ft=0 [3] (the horizontal wellbore lies at the bottom of each square shown, and the frac water is injected at constant pressure from three perforations clusters on the wellbore)
View Large  |  Save Figure  |  Download Slide (.ppt)
Crack branching in a horizontal frac domain 5 m × 5 m simulated in Ref. [3] by three-phase medium theory with body forces due to pore pressure gradients: (a) for full fracture energy Gf and tensile strength ft of crack band model [12] and (b) for Gf=ft=0 [3] (the horizontal wellbore lies at the bottom of each square shown, and the frac water is injected at constant pressure from three perforations clusters on the wellbore)
Grahic Jump Location
Fig. 3

Permeability of shale: (a) the effect of volumetric (or hydrostatic) confining stress (test data reported in Ref. [16]) and (b) the effect of creep (test data reported in Ref. [19])

+Permeability of shale: (a) the effect of volumetric (or hydrostatic) confining stress (test data reported in Ref. [16]) and (b) the effect of creep (test data reported in Ref. [19])
View Large  |  Save Figure  |  Download Slide (.ppt)
Permeability of shale: (a) the effect of volumetric (or hydrostatic) confining stress (test data reported in Ref. [16]) and (b) the effect of creep (test data reported in Ref. [19])
Grahic Jump Location
Fig. 4

Idealized array of parallel planar pre-existing natural cracks, assumed to calculate gas transport to adjacent primary hydraulic cracks spaced at L = 10 m

+Idealized array of parallel planar pre-existing natural cracks, assumed to calculate gas transport to adjacent primary hydraulic cracks spaced at L = 10 m
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Idealized array of parallel planar pre-existing natural cracks, assumed to calculate gas transport to adjacent primary hydraulic cracks spaced at L = 10 m
Grahic Jump Location
Fig. 7

Sequence of creep closure of the cross section of an elliptical channel, calculated for the expected and greatly increased values of Maxwell time τM of shale

+Sequence of creep closure of the cross section of an elliptical channel, calculated for the expected and greatly increased values of Maxwell time τM of shale
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Sequence of creep closure of the cross section of an elliptical channel, calculated for the expected and greatly increased values of Maxwell time τM of shale
Grahic Jump Location
Fig. 6

Active creep sites (left) and newly created creep sites (right) of bond breakage at stress concentrations in the nanoscale of shale subjected to shear under confining pressure: (a) during the primary (or transient) creep, (b) during the secondary creep (or steady-state flow), and (c) creep sites (stress concentrations)

+Active creep sites (left) and newly created creep sites (right) of bond breakage at stress concentrations in the nanoscale of shale subjected to shear under confining pressure: (a) during the primary (or transient) creep, (b) during the secondary creep (or steady-state flow), and (c) creep sites (stress concentrations)
View Large  |  Save Figure  |  Download Slide (.ppt)
Active creep sites (left) and newly created creep sites (right) of bond breakage at stress concentrations in the nanoscale of shale subjected to shear under confining pressure: (a) during the primary (or transient) creep, (b) during the secondary creep (or steady-state flow), and (c) creep sites (stress concentrations)
Grahic Jump Location
Fig. 8

(a) Idealization of planar crack in shale kept open by asperities imagined as rectangular pillar walls and (b) subsequent states of creep closure for the expected and greatly increased values of Maxwell time τM of shale

+(a) Idealization of planar crack in shale kept open by asperities imagined as rectangular pillar walls and (b) subsequent states of creep closure for the expected and greatly increased values of Maxwell time τM of shale
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(a) Idealization of planar crack in shale kept open by asperities imagined as rectangular pillar walls and (b) subsequent states of creep closure for the expected and greatly increased values of Maxwell time τM of shale

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