Abstract
The Silurian Longmaxi formation in the Sichuan Basin, which is the most important gas-producing shale reservoir in China, is characterized by relatively small effective thickness, large in-situ stress difference and highly-developed natural fracture (NF) system. Microseismic monitoring shows that complex hydraulic fracture (HF) networks with relatively small height could be stimulated in the Longmaxi shale reservoirs. Traditional two-dimensional (2D) numerical models cannot capture the three-dimensional (3D) nature of the limited-height HFs, which is not suitable for investigating the fracturing of Longmaxi shale reservoirs. This work develops a fully coupled hydro-mechanical model for HF network propagation based on the discontinuous deformation analysis (DDA) method. A new efficient method is proposed to consider the 3D effect in 2D DDA-based fracturing simulations. Hence an approximate 3D solution of fracture-induced stress and deformation could be obtained. This method is verified against previous works. Then, a series of simulations is performed to investigate the influence of reservoir thickness, in-situ stress difference and NF pattern on the hydraulic stimulation of Longmaxi shale reservoirs. Modeling results show that limited reservoir thickness is favorable to the formation of HF network. Complex and dense fracture network is easily to be formed in thin reservoirs. Large in-situ stress difference will impede the hydraulic stimulation. However, when the reservoir thickness is small, dense fracture network is still likely to be formed under large stress differences. Besides, the NF system is essential for the formation of HF network. The modeling results indicate that as a result of the limited thickness and highly-developed NF system, complex and dense fracture networks could be stimulated in the Longmaxi shale reservoirs. This work partly accounts for the initial success of gas recovery in the Longmaxi shale reservoirs. It also provides a feasible numerical method and theoretical supports for further optimization of shale gas exploitation in China.
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- [Di]:
-
Deformation matrix of the ith block
- u0, v0 :
-
Rigid body translation components (m)
- r 0 :
-
Rigid body rotation (°)
- εx, εy, εxy :
-
Strain components
- x0, y0 :
-
Coordinates of block centroid (m)
- u, v :
-
Displacement components (m)
- [Ti]:
-
Displacement transformation matrix of the ith block
- [K]:
-
Global stiffness matrix
- [D]:
-
Global deformation matrix
- [F]:
-
Global force matrix
- n :
-
Number of blocks
- σn, στ :
-
Normal and shear stress of the bock interface (MPa)
- T 0 :
-
Tensile strength (MPa)
- c :
-
Cohesive strength (MPa)
- φ :
-
Friction angle (°)
- F c :
-
3D constraint force (N)
- Fcx, Fcy :
-
Components of 3D constraint force (N)
- k :
-
Stiffness of constraint spring (MPa)
- ∆d :
-
Displacement vector (m)
- S 0 :
-
Area of block element (m2)
- E :
-
Young’s modulus (MPa)
- G:
-
Coefficient, representing the influence of fracture height on the constraint spring stiffness
- H :
-
Fracture height (m)
- α :
-
Empirically determined constant
- [Fi]:
-
Force matrix of ith block
- q :
-
Volumetric flow rate (m3/s)
- ω :
-
Fracture aperture (m)
- μ :
-
Dynamic viscosity of fluid (mPa·s)
- p :
-
Fluid pressure (MPa)
- p x , p y :
-
Fluid pressure components (MPa)
- c 0 :
-
Fluid injection or leak-off rate (m3/s)
- e m :
-
Average fracture aperture (m)
- r :
-
Fluid pressure ratio
- m :
-
Length of block interface (m)
- σ1, σ2,σ3 :
-
Maximum, intermediate and minimum principal stress (MPa)
- ∆σ :
-
In-situ stress difference (MPa)
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Acknowledgements
The authors would like to thank the Editor and the anonymous reviewers for their helpful and constructive comments. This work was supported by the National Natural Science Foundation of China (No. 51734009), the Second Tibetan Plateau Scientific Expedition and Research Program (STEP) (No. 2019QZKK0904), the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDB10030000), Science Foundation of Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences (No.KLSG201708) and the Joint PhD Training Program of University of Chinese Academy of Sciences (UCAS).
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Hu, Y., Li, X., Zhang, Z. et al. Numerical investigation on the hydraulic stimulation of naturally fractured Longmaxi shale reservoirs using an extended discontinuous deformation analysis (DDA) method. Geomech. Geophys. Geo-energ. Geo-resour. 6, 73 (2020). https://doi.org/10.1007/s40948-020-00195-5
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DOI: https://doi.org/10.1007/s40948-020-00195-5