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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.

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Figures

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)

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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

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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.

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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

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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

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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.

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Fig. 8

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

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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

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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

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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

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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

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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.

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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

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Fig. 15

Superposition of the stress for the fracking problem

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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

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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

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