Initiation and extension of gas-driven fracture during compound perforation
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摘要: 结合线弹性断裂力学的裂缝尖端应力强度因子判据，建立了复合射孔爆燃气体压裂裂缝的起裂扩展模型，通过建立与多个变量相关的缝内气体压力分布函数，利用迭代法实现了模型的数值求解，获得了缝内气体压力分布随时间的动态变化规律，并分析了不同特征参数对裂缝起裂扩展与止裂过程的影响。实例计算结果表明：(1)随着裂缝扩展的进行，爆燃气体流动尖端与裂缝尖端经历了由重合到不重合再到重合的过程；(2)地应力越大，裂缝起裂扩展越困难，爆燃气体有效致裂作用时间越短，最终得到的裂缝扩展长度也越小；(3)初始裂缝越长，裂缝更容易起裂扩展，爆燃气体能量利用率越高，裂缝扩展更长；(4)岩石断裂韧性的改变对裂缝起裂、止裂和裂缝扩展长度没有明显的影响；(5)升压速率越小，爆燃气体有效致裂作用时间越长，最终裂缝扩展也更长，但对裂缝起裂压力与止裂压力几乎没有影响。Abstract: Combined with the crack tip stress intensity factor criterion of linear elastic fracture mechanics, the model of initiation and extension of gas-driven fractures by compound perforation is established.A function with multiple variables describing gas pressure distribution in crack is proposed herein to realize the numerical resolution of the model using the iteration method, and the dynamic change law of gas pressure distribution in fracture with time is obtained.In addition, the effect of different characteristic parameters on the process of fracture initiation and extension as well as fracture arrest is analyzed.The example calculation shows: (1)with the progress of fracture extension, the leading edge of the flow and the fracture tip will experience the process from coincidence to noncoincidence and then to coincidence; (2)the fracture initiation and extension are more difficult as in-situ stress is greater, which makes the effective time of gas-driven and the fracture shorter; (3)the fracture initiation and extension are easier and the utilization of gas energy is higher as the initial crack is longer, resulting in the longer crack; (4)the change of fracture toughness has no obvious influence on the crack initiation and extension as well as the fracture arrest; (5)both the effective time of gas-driven and the fracture are longer as the rate of pressure rise is smaller, but its change has nearly no impact on the pressure of the fracture initiation and arrest.
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图 1 缝内气体压力分布的2种情况
Figure 1. Gas pressure distribution in fracture of two different types
图 2 缝口气体压力与爆燃气体温度随时间的变化
Figure 2. Gas pressure at the inlet and gas temperature varied with time
图 4 不同地应力下裂缝长度随时间的变化
Figure 4. Fracture length versus time for various in-situ stresses
图 5 不同初始裂缝长度下裂缝长度随时间的变化
Figure 5. Fracture length varied with time for various initial crack lengths
图 6 不同岩石断裂韧性下裂缝长度随时间的变化
Figure 6. Fracture length with time for various fracture toughnesses
图 7 不同升压速率下缝口气体压力随时间的变化
Figure 7. Gas pressure at the inlet with varied time at various rates of pressure rise
图 8 不同升压速率下裂缝长度随时间的变化
Figure 8. Fracture lengths varied with time at various rates of pressure rise
表 1 不同地应力下的裂缝扩展情况
Table 1. Fracture extension under different in-situ stresses
σ/MPa ti/ms pi/MPa ta/ms pa/MPa L/m 22 22.3 24.17 157.2 23.61 4.93 25 23.8 27.22 131.8 26.78 3.85 28 25.4 30.47 112.0 30.22 2.93 
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表 2 不同初始裂缝长度下的裂缝扩展情况
Table 2. Fracture extension under differentinitial crack lengths
L0/m ti/ms pi/MPa ta/ms pa/MPa L/m 0.10 24.3 28.23 130.3 26.98 3.53 0.45 23.8 27.22 131.8 26.78 3.85 1.00 23.7 27.02 133.5 26.55 4.31
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表 3 不同岩石断裂韧性下的裂缝扩展情况
Table 3. Fracture extension under different fracture toughnesses
KIC/(MPa·m0.5) ti/ms pi/MPa ta/ms pa/MPa L/m 0.5 23.8 27.22 131.8 26.78 3.85 1.0 24.1 27.83 130.2 26.99 3.82 2.0 24.7 29.05 128.7 27.20 3.76
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表 4 不同升压速率下的裂缝扩展情况
Table 4. Fracture extension at different rates of pressure rise
vp/(MPa·ms-1) ti/ms pi/MPa ta/ms pa/MPa L/m 1.70 23.8 27.22 131.8 26.78 3.85 1.22 27.5 27.22 161.7 26.65 4.39 0.92 31.4 27.22 185.4 26.50 4.83
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