Numerical Simulation of Hydraulic Fractures Intersecting Natural Fractures in Shale With Plastic Deformation
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摘要: 水力压裂中，页岩的塑性变形和大量天然弱界面的存在，给水力裂缝扩展形态的预测带来了巨大的挑战.该文基于有限元法建立了一个完全耦合的弹塑性水力压裂数值模型，并考虑了天然裂缝和层理面.数值模型得到了KGD解析解和Blanton曲线的验证.模拟结果显示：与线弹性的水力压裂结果相比，岩石中的塑性变形使得水力裂缝更容易进入天然弱界面；裂缝扩展过程中，岩石塑性变形区域主要集中在储层内；当岩石发生韧性破坏时，水力裂缝更容易贯穿层理面；水力裂缝在高注入速率下，得益于较大驱动力，裂缝能够直接穿过天然裂缝和层理面.研究结果为页岩储藏中水力裂缝的扩展规律提供了新的认识.Abstract: The plastic deformation and numerous natural joints of shale pose a great challenge for the prediction of the hydraulic fracture geometry extension. Based on the finite element method, a fully coupled numerical model for elastoplastic hydraulic fractures was established with natural fractures and bedding planes considered. The numerical model was validated with the KGD analytical solution and Blanton's curve. The numerical results show that, compared with the numerical model solution of linear elasticity, the hydraulic fractures are prone to enter the natural weak interface due to the rock plastic deformation. The rock plastic deformation area mainly lies in the reservoir layer during the fracture propagation. In the case of rock ductile damage, the hydraulic fracture is more likely to penetrate the bedding plane. Hydraulic fractures can directly penetrate natural fractures and bedding planes at high injection rates due to large driving forces. The study provides new insights in terms of hydraulic fracture extension in elastoplastic formations.
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Key words:
- elastoplastic formation /
- natural fracture /
- bedding plane /
- hydraulic fracture /
- fracture morphology
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图 2 水力裂缝与天然裂缝交叉角度-地应力差曲线图
Figure 2. The approaching angle between the hydraulic fracture and the natural fracture-stress difference curve
图 3 分层页岩模型的几何形状和边界条件
Figure 3. Geometric and boundary conditions of the layered shale model
图 4 不同注入速率下弹性模型(左)和弹塑性模型(右)裂缝几何形态对比
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 4. Comparison of crack morphologies between the elastic model (left) and the elasto-plastic model (right)at different injection rates
图 5 分布在裂缝附近的等效塑性应变
Figure 5. Equivalent plastic strains distributed in the vicinity of the crack
图 6 储层和隔层中水力裂缝在不同强度下的断裂机制(方案A)
Figure 6. Fracture mechanisms of hydraulic fractures in the pay zone and the barrier at different strengths(plan A)
图 7 储层和隔层中水力裂缝在不同强度下的断裂机制(方案B)
Figure 7. Fracture mechanisms of hydraulic fractures in the pay zone and the barrier at different strengths (plan B)
图 8 裂缝形态随水力裂缝与层理面的交叉角度的变化
Figure 8. Variations of the fracture morphology with the approaching angle between the hydraulic fracture and the bedding plane
图 9 裂缝扩展随地应力差的变化
Figure 9. Variations of the crack extension with the stress difference
图 10 裂缝扩展随层理面抗拉强度的变化
Figure 10. Variations of the crack extension with the tensile strength of the bedding plane
图 11 裂缝扩展随注入速率的变化
Figure 11. Variations of the fracture extension with the injection rate
图 12 分层页岩中交叉角度-地应力差的散点图
Figure 12. The scatter plot of the stress difference vs.the approaching angle in the layered shale
表 1 分层页岩的输入参数
Table 1. The input parameters of the layered shale
parameter pay zone barrier bedding plane height H/m 10 10 - elastic modulus E/GPa 15 20 20 Poisson’s ratio ν 0.25 0.2 - permeability k/mD 10 1 - rock tensile strength T/MPa 1 2 1.5 vertical in-situ stress Vmax/MPa 9 9 - minimum horizontal in-situ stress hmin/MPa 5 7 - maximum horizontal in-situ stress hmax/MPa 8 8 - fluid leakoff coefficient (HF & NF) km/(m/(Pa·s)) 1×10-13 1×10-14 1×10-13 fluid viscosity μ/(Pa·s) 0.001 0.001 0.001 
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表 2 页岩的塑性参数
Table 2. The input plastic parameters of the shale
parameter value hardening constant hr0 0.35 hardening parameter ξ 0.01 yield stress c/MPa 11.25 yield parameter α -0.365 yield parameter β 1.980 4 approaching angle θ/(°) 80
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