Numerical study on permeability properties of three-dimensional rock fracture under coupled stress-seepage-dissolution process
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摘要: 基于格子Boltzmann方法采用双分布函数分别模拟渗流速度场与溶质浓度场的演化过程，建立了三维岩石裂隙应力-渗流-溶蚀耦合作用机制的数值计算模型，并讨论了渗流流速、法向应力、溶蚀反应速率等因素对裂隙渗透特性演化规律的影响。结果表明：在渗流流速较低时，壁面溶蚀出来的离子得不到及时输运，使得出口处浓度较高溶蚀速度慢，裂隙结构呈“喇叭口”状。增大法向应力会减小裂隙开度，减慢溶质的运移速率，使得裂隙出口处的溶蚀速率显著降低，从而限制了其渗透率的发展。当壁面溶蚀反应速率较小时，裂隙渗透率呈持续缓慢增长的状态；随着溶蚀反应速率增加，出口处的溶蚀量会明显小于入口处，导致出口处壁面发生显著溶蚀之前，裂隙渗透率发展缓慢，此后渗透率便呈急速突变增长趋势。研究成果能够为酸蚀作用下岩石裂隙渗透能力的定量评价提供重要理论支撑。
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关键词:
- 岩石裂隙 /
- 应力-渗流-溶蚀耦合 /
- 渗透特性 /
- 格子Boltzmann方法 /
- 数值计算
Abstract: Based on the lattice Boltzmann method, the evolution of seepage velocity field and solute concentration field is simulated by the double-distribution functions, and a numerical model is proposed to study the coupling mechanism of stress-seepage-dissolution in three-dimensional rock fracture. The evolution of fracture permeability properties is discussed considering the effects of seepage velocity, normal stress and dissolution rate. The results show that when the seepage velocity is low, the ions dissolved from the fracture wall cannot be transported in time, which results in a higher concentration and a lower dissolution rate at the outlet, the dissolved fracture is shaped as a "bell mouth". Increasing the normal stress decreases the fracture width and slows down the solute transport rate, which significantly reduces the dissolution at the fracture outlet, limiting the development of its permeability. When the wall dissolution rate is low, the fracture permeability shows a continuous and slow growth. As the dissolution rate increases, the dissolution amount at the outlet is significantly less than that at the inlet, which leads to a slow development of fracture permeability until the wall surface at the outlet exhibits significant dissolution, and the fracture permeability shows a rapid growth trend. The results can provide important theoretical support for the quantitative evaluation of permeability of rock fracture under acid corrosion. -
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图 3 中心插值法生成的三维粗糙裂隙面
Figure 3. Three-dimensional rough fracture surface generated by midpoint interpolation method
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图 4 三维粗糙裂隙结构构建示意图
Figure 4. Diagram for generating three-dimensional rough fracture structure
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图 5 不同法向应力作用下的裂隙开度分布
Figure 5. Distribution of fracture aperture under different normal stresses
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图 7 溶质浓度分布的本文数值解与解析解对比
Figure 7. Comparison between proposed numerical and analytical solutions for solute concentration distribution
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图 9 本文数值解与解析解的浓度等值线图对比
Figure 9. Comparison between proposed numerical of iso- concentrations contours and analytical solution
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图 10 不同渗流流速作用下的裂隙溶蚀形貌
Figure 10. Corrosion morphology of fractures under different flow velocities
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图 11 不同渗流流速作用下的溶质浓度分布
Figure 11. Distribution of solute concentration under different flow velocities
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图 12 不同渗流流速作用下裂隙渗透率时程演化曲线
Figure 12. Evolution curves of time history of fracture permeability under different flow velocities
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图 13 不同法向应力作用下裂隙的溶蚀形貌
Figure 13. Corrosion morphologies of fractures under different normal stresses
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图 14 不同法向应力作用下的溶质浓度分布
Figure 14. Distribution of solute concentration under different normal stresses
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图 15 不同法向应力作用下裂隙渗透率时程演化曲线
Figure 15. Evolution curves of time history of fracture permeability under different normal stresses
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图 16 不同溶蚀反应速率作用下的裂隙溶蚀形貌
Figure 16. Corrosion morphology of fractures under different sdissolution rates
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图 17 不同溶蚀反应速率作用下的溶质浓度分布
Figure 17. Distribution of solute concentration under different dissolution rates
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图 18 不同溶蚀反应速率作用下裂隙渗透率时程演化曲线
Figure 18. Evolution curves of time history of fracture permeability under different dissolution rates
表 1 格子步长对计算结果影响
Table 1 Influences of lattice space on computational results
格子步长/mm 计算网格 最大相对误差/% 计算耗时/s 0.4 25×5×5 0.150 0.13 0.2 50×10×10 0.036 1.67 0.1 100×20×20 0.009 49 0.05 200×40×40 0.002 1323 
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