XFEM modeling of hydraulic fracture in porous rocks with natural fractures

Tao Wang; ZhanLi Liu; QingLei Zeng; Yue Gao; Zhuo Zhuang

doi:10.1007/s11433-017-9037-3

SCIENCE CHINA Physics, Mechanics & Astronomy

SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 60, Issue 8: 084612(2017) https://doi.org/10.1007/s11433-017-9037-3

XFEM modeling of hydraulic fracture in porous rocks with natural fractures

Tao Wang, ZhanLi Liu, QingLei Zeng, Yue Gao, Zhuo Zhuang

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ReceivedJan 12, 2017
AcceptedApr 11, 2017
PublishedJun 15, 2017

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Abstract

Hydraulic fracture (HF) in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method (XFEM) coupling with Biot theory is developed to study the HF in permeable rocks with natural fractures (NFs). In the recent XFEM based computational HF models, the fluid flow in fractures and interstitials of the porous media are mostly solved separately, which brings difficulties in dealing with complex fracture morphology. In our new model the fluid flow is solved in a unified framework by considering the fractures as a kind of special porous media and introducing Poiseuille-type flow inside them instead of Darcy-type flow. The most advantage is that it is very convenient to deal with fluid flow inside the complex fracture network, which is important in shale gas extraction. The weak formulation for the new coupled model is derived based on virtual work principle, which includes the XFEM formulation for multiple fractures and fractures intersection in porous media and finite element formulation for the unified fluid flow. Then the plane strain Kristianovic-Geertsma-de Klerk (KGD) model and the fluid flow inside the fracture network are simulated to validate the accuracy and applicability of this method. The numerical results show that large injection rate, low rock permeability and isotropic in-situ stresses tend to lead to a more uniform and productive fracture network.

Funded by

Key Project of the National Natural Science Foundation of China(11532008)

Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11532008, and 11372157).

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Figure 1
(Color online) Coupling framework for hydraulic fracture problem, fⁱ is the simplification of the signed distance function fⁱ(X) to describe the location of the fracture.
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Figure 2
(Color online) Hydraulic driving fracture. (a) Orientation of normal and tangent vectors of local fracture surface, and the displacement jump vector; the 3D body with hydro-discontinuity represented by initial configuration (b) and current configuration (c).
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Figure 3
Decomposition of a fractured element into two elements (a), four elements (b): solid and hollow circles denote the original nodes and additional phantom nodes, respectively.
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Figure 4
(Color online) Comparison of the results with analytical solution for the plane strain KGD model with viscosity dominated HF propagation. (a) Fracture opening at injection point; (b) inlet pressure at injection point.
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Figure 5
(Color online) Comparison of the results with analytical solution for the plane strain KGD model with toughness dominated HF propagation. (a) Fracture opening at injection point, (b) inlet pressure at injection point.
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Figure 6
(Color online) Hydraulically induced fracture driven by fluid injection. (a) Boundary value problem. All the sides are mechanically constrained and are assumed to be permeable (p=0?Pa); (b) inlet fluid pressure p in the fracture over total injected time.
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Figure 7
(Color online) Hydraulically induced fracture driven by fluid injection. (a)-(c) Fracture and fluid pressure p; fracture opening width w (d) and fluid pressure (e) along fracture at three times t=1, 5, 20?s, respectively.
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Figure 8
(Color online) Hydraulically induced fracture driven by fluid injection under different media permeability at time t=5?s. (a)-(c) The permeability of media is 2.0×10⁵, 2.0×10⁴ and 2.0×10³ md, respectively.
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Figure 9
(Color online) (a) Hydraulically fracture network driven by fluid injection at current stage, a bridge plug is set to hydraulically isolate the previously stimulated stages; (b) local fracture network domain consists of HF and NFs for studying, lower side of the domain is the symmetry boundary and the other three sides are mechanically constrained and assumed to be permeable.
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Figure 10
(Color online) Inlet fluid pressure of the five NFs over the total injected time.
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Figure 11
(Color online) Fracture evolution morphology for fracture network at different times. (a) t=0?s, (b) t=30?s, (c) t=60?s, (d) t=100?s, respectively.
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Figure 12
(Color online) Fracture network evolution morphology at the same time t=100?s with different inlet fluid flow rates. (a) Q₀=0.000002 m²/s, (b) Q₀=0.00002 m²/s, (c) Q₀=0.0002 m²/s, respectively.
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Figure 13
(Color online) The propagation length of one main fracture and five NFs under different injection rate.
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Figure 14
(Color online) Fracture evolution morphology for fracture network and the fluid pressure contour under different formation conditions. (a) The initial condition and in-situ stress configuration; (b)-(f) the simulation results for different in-situ stresses along x-direction at the same time t=100?s.
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Figure 15
(Color online) (a) The vertical fracture propagation length and total fracture propagation length (one main fracture and five NFs) vs difference of in-situ stress; (b) the final length of five NFs (each point represents the fracture tip position of NF) corresponding to five cases in Figure 14(b)-(f).

Table 1 Input parameters for KGD model

Parameter	Value
E (MPa)	17000
ν	0.2
K _IC $(MPa \sqrt{m})$	1.46
Q₀ (m²/s)	0.0001

Table 2 Material parameters

Parameter	Value
E (MPa)	255
ν	0.3
K _IC $(MPa \sqrt{m})$	0.0167
Q₀ (m²/s)	0.0004
α	1.0
ν _u	0.358
μ (cP)	1.0
k (md) (1 md=9.87×10^?14 m²)	200

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46.15.-x	Computational methods in continuum mechanics (see also 02.70.-c Computational techniques; simulations, in mathematical methods in physics)
46.50.+a	Fracture mechanics, fatigue and cracks (see also 62.20.M- Structural failure of materials in mechanical properties of condensed matter)
91.60.Ba	Elasticity, fracture, and flow
91.60.Ba	Elasticity, fracture, and flo

XFEM modeling of hydraulic fracture in porous rocks with natural fractures

Abstract

Funded by

Acknowledgment

References

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