Experimental study on characterization hydraulic fracturing coal fracture network and evolution of fracture forming performance
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摘要:
煤裂隙网络的准确表征可以有效评估深部煤层经水力压裂后的压裂效果，为了定量评估煤层经水力压裂后的复杂程度，利用自制的真三轴试验系统进行了煤的水力压裂试验，结合CT扫描，重建了具有拓扑结构的孔裂隙网络，用分形理论和拓扑学定量表征了断裂网络的复杂程度。探究了在真三轴应力条件下，中间主应力对裂缝网络复杂程度的影响。结果表明：压裂后煤样的二维分形维数变化率K为1.03%~7.10%，三维分形维数的变化率为3.50%～9.18%，经过水力压裂后煤样的二维和三维分形维数均显著增大。基于分形理论和拓扑学的方法能有效表征水力压裂的裂缝结构和造缝能力。压裂后煤样的二维拓扑参数为1.18～1.52，与压裂前后煤样的二维分形维数变化率呈正相关关系，二维分形维数变化率的增加速率随着拓扑参数的增大逐渐减小。重构的内部结构和裂缝分布表明，压裂后的三维分形维数比二维分形维数更具优势，压裂后煤样的三维拓扑参数为1.82～1.93，随着三维分形维数变化率的增加而增大，三维分形维数变化率的增加速率随着拓扑参数的增大而增大。中间主应力对煤层的造缝能力存在积极影响。水力压裂前后的分形维数和拓扑参数都随着中间主应力的增大而增大，即随着中间主应力的增大而增大，产生的裂缝网络更复杂，连通性更好，水力压裂的造缝能力更强。
Abstract:The accurate characterization of coal fracture network can effectively evaluate the fracturing effect of the deep coal seam after hydraulic fracturing. In order to quantitatively evaluate the complexity of coal seam after hydraulic fracturing, the hydraulic fracturing test of coal was carried out by using the self-made true triaxial test system, combined with CT scan, the pore network and fracture network with topological structure are reconstructed, and the complexity of the fracture network is quantitatively characterized by fractal theory and topology. The effect of the intermediate principal stress on the complexity of the fracture networks under the condition of true triaxial stress is explored. The results showed that the change rate of the two-dimensional fractal dimension (K) are 1.03% ~ 7.10%, and the change rate of three-dimensional fractal dimension are 3.50% ~ 9.18%, the two-dimensional and three-dimensional fractal dimensions of coal samples after hydraulic fracturing increase significantly. The method based on fractal theory and topology can effectively characterize the fracture structure and fracture forming ability of hydraulic fracturing. The two-dimensional topological parameter of coal samples after fracturing are1.18 ~ 1.52, which is positively correlated with the change rate of two-dimensional fractal dimension．Increasing rate of change rate of two-dimensional fractal dimension decreases with the increase of topological parameters. The reconstructed internal structure and fracture distribution showed that the three-dimensional fractal dimension after fracturing is more advantaged than the two-dimensional fractal dimension. The three-dimensional topological parameters of coal samples after fracturing are 1.82-1.93, increased with the increase of the change rate of three-dimensional fractal dimension. The intermediate principal stress has a positive effect on the seam forming ability of coal seam. The fractal dimension and topological parameters increase with the increase of intermediate principal stress before and after hydraulic fracturing. In other words, Increased with the intermediate principal stress, the resulting fracture network is more complex, the connectivity is better, and the fracture forming ability of hydraulic fracturing is stronger.
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图 7 煤样C1、C2和C3压裂前后的三维重构模型
Figure 7. 3D reconstruction model of C1、C2 and C3 specimen before and after hydraulic fracturing
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图 8 水力压裂前、后煤样的宏观裂隙图像
Figure 8. Image of macroscopic fracture of coal sample before and after hydraulic
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图 9 水力压裂前后煤样的宏观裂隙分形维数线性拟合
Figure 9. Linear fitting of two-dimensional fractures before and after hydraulic
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图 13 二维拓扑网络计算原理图和不同应力条件下二维分形维数变化率与拓扑参数的分布
Figure 13. Fracture networks in two-dimensional and distribution of 2D fractures and topological parameters of fractures under different stress
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图 15 三维拓扑网络计算原理图和不同应力条件下三维分形维数变化率与拓扑参数的分布
Figure 15. Fracture networks in three-dimensional and distribution of 3D fractures and topological parameters of fractures under different stress
表 1 试样的物理力学性质
Table 1 Physical properties of samples
孔隙率/
%天然密度/
(g·m−3)抗拉强度/
MPa弹性模量/
GPa单轴抗压强度/
MPa6.021 1.756 1.743 5.49 10.43 
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表 2 真三轴水力压裂试验参数
Table 2 True triaxial hydraulic fracturing test parameters
试件
编号($ {\mathrm{\sigma }}_{\mathrm{t}1}/{\mathrm{\sigma }}_{\mathrm{n}}/{\mathrm{\sigma }}_{\mathrm{t}2} $)/
MPa垂向应力
差异系数水平应力
差异系数水平
应力比注入速度/
(mL·min−1)C1 25/40/20 1 0.25 1.25 60 C2 30/40/20 1 0.50 1.50 C3 35/40/20 1 0.75 1.75 注：垂向地应力差异系数$k_{\mathrm{v} }=\left(\sigma_{\rm{n}}-\sigma_{ {\rm{t} } 2}\right) / \sigma_{ {\rm{t} } 2}$；水平应力差异系数$k_{\mathrm{H}}=\left(\sigma_{{\rm{t}} 1}-\sigma_{{\rm{t}} 2}\right) / \sigma_{{\rm{t}} 2}$。
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表 3 煤样裂缝的相关参数
Table 3 Relevant parameters of coal cracks
试件
编号压裂前裂缝数量 压裂后裂缝数量 压裂后裂缝形态 C1 0 7 主裂缝为弧形裂缝 C2 1 7 主裂缝为横向贯穿裂缝 C3 0 8 网状裂缝网络
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表 4 压裂前后煤样的三维分形维数
Table 4 Three-dimensional fractal dimension of coal samples before and after hydraulic
试件编号 Da Db K/% 水平应力比 C1 2.167 72 2.24369 3.50 1.25 C2 2.206 16 2.31075 4.74 1.5 C3 2.155 92 2.35386 9.18 1.75
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表 5 压裂前后煤样的二维拓扑参数
Table 5 Two dimensional topological parameters of coal samples be-fore and after hydraulic fracturing
试件
编号节点数量 Na Nb NI NX NY C1 9 1 3 11 1.18 C2 9 0 5 12 1.25 C3 8 1 7 16.5 1.52
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表 6 压裂前后煤样的三维拓扑参数
Table 6 Three-dimensional topological parameters of coal samples before and after hydraulic
试件
编号节点数量 Na Nb NI NX NY C1 1 1 2 5.5 1.82 C2 1 1 3 7 1.86 C3 1 3 5 14 1.93
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