Impacts of Non-Darcian Flow in the Fracture on Flow Field and Solute Plumes in a Fracture-Aquifer System
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摘要: 以基岩渗流方向与裂隙轴向呈45度角为例，探讨了当裂隙轴向与基岩水流斜交时，裂隙流的非达西程度对流场及溶质运移的影响.使用Comsol Multiphysics多物理场仿真软件构建了一个在中部包含水平单裂隙的正方形多孔介质模型，裂隙中的非达西流用Izbash方程去刻画，裂隙的上游基岩中存在持续的溶质源.随着裂隙水流的非达西程度逐渐增强，流场及污染物分布表现出如下特征：（1）裂隙中水流流速逐渐增大；流线在裂隙与基岩界面处的折射逐渐偏离折射定律；（2）裂隙水流的流向逐渐偏向基岩水流的渗流方向；（3）溶质羽宽度变宽但对称性逐渐降低；（4）溶质在水平方向上的浓度峰值逐渐降低，右侧浓度逐渐升高；（5）裂隙产生的回弥散对溶质运移作用逐渐增强，使裂隙中更多的溶质运移到了上层基岩中.总体而言，裂隙流的非达西程度对流场及污染物分布有着显著的影响.Abstract: In this study, a mathematical model with the intersection angle between the flow direction and the x axial direction of 45degree was developed to investigate the effect of non-Darcy parameter n on flow field and solute migration when flow is oblique crossing the fracture. The Comsol Multiphysics software was used to do such numerical simulation. The simulation area was assumed to be square with a horizontal fracture embedded in the middle.The flow in the fracture was assumed to be non-Darcian and can be described by the Izbash equation. A constant solute source has been assigned in the upper matrix. The results indicate the following phenomena as the power index in the Izbash equation(n) increases:(1) the fracture flow velocity increases, and the flow line at the matrix-fracture interfaces gradually deviates from the classical fraction law; (2) the flow direction in fracture gradually turns to the direction in the matrix; (3) the width of solute plume increases, while the symmetry of solute plume reduces; (4) the peak solute concentration in the horizontal section diminishes, and the solute concentration on the right sight of the model increases; (5) the effect of back dispersion caused by fracture on solute plume becomes stronger, which results in more solutes in the fracture migrated to the upper matrix. Overall, the non-Darcy flow fracture has a significant impact on the flow field and solute distribution.
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图 2 裂隙下边界流线位移（Dfl）和溶质峰值位移（Dc）示意图
Fig. 2. Schematic diagram of flow line displacement (Dfl) and peak solute concentration displacement (Dc)
图 3 流场及溶质分布示意图
a.模型不存在裂隙；b.存在裂隙且n=1时
Fig. 3. Schematic diagrams of flow field and solute distribution
图 4 不同n取值时，裂隙中流速（V）及其在x和y方向上的分量值（Vx；Vy）
Fig. 4. The velocity and the component of velocity on x and y axes in the fracture for different n values
图 5 不同情况下流线在裂隙与基岩界面处的折射示意图
Fig. 5. Schematic diagram of flow line refraction at the matrix-fracture interfaces for different conditions
图 6 溶质羽的分布
a.不存在裂隙；b. n=1.0；c. n=1.1；d. n=1.2；e. n=1.3；f. n=1.4时
Fig. 6. Solute plume distributions
图 7 不同n取值时裂隙上边界浓度分布
Fig. 7. Solute distributions at the upper boundary of the fracture for different n values
图 8 不同n取值时裂隙下边界浓度分布
Fig. 8. Solute distributions at the bottom boundary of the fracture for different n values
表 1 模型参数及默认值
Table 1. Parameters used in this study and default values
参数名称 符号 默认取值 高渗透性裂隙 PFF 参考等值线浓度 C0 0.001 (mol/m3) 溶质源浓度 Cs 1 (mol/m3) 基岩孔隙度 θm 0.1 基岩渗透系数 Km 1×10-5 (m/s) 纵向弥散度 αl 5×10-3 (m) 横向弥散度 αt 5×10-4(m) 裂隙隙宽 2b 0.01 (m) 裂隙孔隙度 θf 0.2 裂隙渗透系数 Kf 1×10-4 (m/s) 基岩渗流速度 Vm ≈1.44×10-6 (m/s) 裂隙渗流速度 V - 非达西系数 n 1.0~1.4 基岩渗流角度 δ 45° 裂隙渗流角度 θ - 流线位移 Dfl - 裂隙下边界浓度峰值位移 Dc - 
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表 2 Comsol Multiphysics数值解与Robinson and Werner (2017)解析解对比
Table 2. Comparison between numerical results of Comsol Multiphysics and analytical solutions of Robinson and Werner(2017)
2b(cm) 浓度峰值位移Dc (m) 浓度峰值Cb-max (mol/m3) Robinson and Werner (2017) Comsol Multiphysics Robinson and Werner (2017) Comsol Multiphysics 0.25 0.000 95 0.000 95 0.112 88 0.111 44 0.50 0.002 20 0.002 33 0.104 17 0.103 30 1.00 0.040 90 0.041 00 0.028 36 0.028 38 2.00 0.102 86 0.103 00 0.016 46 0.016 46
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表 3 不同情况下裂隙流场的结果.
Table 3. Characteristics of flow field in the fracture
n 不存在裂隙 1.0 1.1 1.2 1.3 1.4 V (m/s) 1.44×10-6 1.00×10-5 2.90×10-5 6.98×10-5 1.46×10-4 2.74×10-4 Vx(m/s) 1.02×10-6 9.95×10-6 2.88×10-5 6.93×10-5 1.45×10-4 2.71×10-4 Vy(m/s) 1.02×10-6 9.95×10-7 3.20×10-6 8.40×10-6 1.90×10-5 3.84×10-5 tanθ 1.00 10.00 9.00 8.25 7.62 7.07 θ(°) 45.0 84.2 83.7 83.0 82.3 81.9
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表 4 不同情况下Cb-max、Dc和Dfl的值
Table 4. Values of Cb-max, Dc and Dfl for different conditions
n 无裂隙 1.0 1.1 1.2 1.3 1.4 Cb-max(mol/m3) 0.089 5 0.023 6 0.015 25 0.009 0 0.005 24 0.003 18 Dfl(m) 0.010 0 0.110 0 0.100 00 0.092 5 0.086 20 0.080 70 Dc(m) 0.010 0 0.050 0 0.060 00 0.070 0 0.078 50 0.086 00
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Basak, P., 1977. Non-Darcy Flow and Its Implications to Seepage Problems. Journal of the Irrigation and Drainage Division, 103(4):459-473. Bear, J., Tsang, C.F., Marsily, G.D., 1993. Flow and Contaminant Transport in Fractured Rock. Journal of the American Mosquito Control Association, 23(3):330-400. http://www.sciencedirect.com/science/book/9780120839803 Berkowitz, B., Miller, C.T., Parlange, M.B., et al., 2002. Characterizing Flow and Transport in Fractured Geological Media:A Review. Advances in Water Resources, 25(8/9/10/11/12):861-884. https://doi.org/10.1016/s0309-1708(02)00042-8 Cheng, H.D., Chai, J.R., Li, Y.M., 2007. Brief Overview on Solute Transport in Fractured Rock Masses. Water Resources and Power, (03):33-37 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-SDNY200703009.htm Gao, Y., Ye, X., Xia, Q., 2016. Numerical Simulation of Single Fracture Seepage Flow Based on the Equivalent Continuous Medium Model. Goundwater, 38(5):40-43(in Chinese). Kessler, J. H., Hunt, J. R., 1994. Dissolved and Colloidal Contaminant Transport in a Partially Clogged Fracture. Water Resources Research, 30(4):1195-1206. https://doi.org/10.1029/93wr03555 Konikow, L. F., 2011. The Secret to Successful Solute-Transport Modeling. Ground Water, 49(2):144-159. https://doi.org/10.1111/j.1745-6584.2010.00764.x Long, J. C. S., Remer, J. S., Wilson, C. R., et al., 1982. Porous Media Equivalents for Networks of Discontinuous Fractures. Water Resources Research, 18(3):645-658. https://doi.org/10.1029/wr018i003p00645 Odling, N. E., Roden, J. E., 1997. Contaminant Transport in Fractured Rocks with Significant Matrix Permeability, Using Natural Fracture Geometries. Journal of Contaminant Hydrology, 27(3/4):263-283. https://doi.org/10.1016/s0169-7722(96)00096-4 Qian, J.Z., Wang, J.Q., Ge, X.G., et al., 2002. Advances in Research for Numerical Simulation of Contaminant Transport and Flow in North China Type Fracture-Karst Media. Advance in Water Science, (4):409-412 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-SKXJ200304022.htm Qin, R.G., Cao, G.Z., Wu, Y.Q., 2014. Review of the Study of Groundwater Flow and Solute Transport in Heterogeneous Aquifer. Advances in Earth Science, 29(1):30-41(in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTotal-DXJZ201401004.htm Robinson, N. I., Werner, A. D., 2017. On Concentrated Solute Sources in Faulted Aquifers. Advances in Water Resources, 104:255-270. https://doi.org/10.1016/j.advwatres.2017.04.008 Sebben, M. L., Werner, A. D., 2016. On the Effects of Preferential or Barrier Flow Features on Solute Plumes in Permeable Porous Media. Advances in Water Resources, 98:32-46. doi: 10.1016/j.advwatres.2016.10.011 Sebben, M. L., Werner, A. D., Graf, T., 2015. Seawater Intrusion in Fractured Coastal Aquifers:A Preliminary Numerical Investigation Using a Fractured Henry Problem. Advances in Water Resources, 85:93-108. doi: 10.1016/j.advwatres.2015.09.013 Song, X.C., Xu, W.Y., 2004. A Study on Conceptual Models of Fluid Flow in Fractured Rock. Rock and Soil Mechanics, (2):226-232 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-YTLX200402015.htm Tsang, C., 2000. Modeling Groundwater Flow and Mass Transport in Heterogeneous Media:Issues and Challenges. Earth Science, 25(5):443-453 (in Chinese with English abstract). http://en.cnki.com.cn/article_en/cjfdtotal-dqkx200005000.htm Vujević, K., Graf, T., Simmons, C. T., et al., 2014. Impact of Fracture Network Geometry on Free Convective Flow Patterns. Advances in Water Resources, 71:65-80. doi: 10.1016/j.advwatres.2014.06.001 Xu, Y., Xue, X.S., Liu, Y.Q., et al., 2014. A Coupled Dracy-Brinkman-NS Simulation Model of Well Bore Effect of an Monitor Well. Earth Science, 39(09):1349-1356 (in Chinese with English abstract). 程汉鼎, 柴军瑞, 李亚盟, 2007.裂隙岩体溶质运移研究简述.水电能源科学, (3):33-37. doi: 10.3969/j.issn.1000-7709.2007.03.010 高瑜, 叶咸, 夏强, 2016.基于等效连续介质模型的单裂隙渗流数值模拟研究.地下水, 38(5):40-43. doi: 10.3969/j.issn.1004-1184.2016.05.016 钱家忠, 汪家权, 葛晓光, 等, 2003.我国北方型裂隙岩溶水流及污染物运移数值模拟研究进展.水科学进展, (4):409-412. http://www.cqvip.com/Main/Detail.aspx?id=8264795 覃荣高, 曹广祝, 仵彦卿, 2014.非均质含水层中渗流与溶质运移研究进展.地球科学进展, 29(1):30-41. http://www.cqvip.com/QK/94287X/201401/48411568.html 宋晓晨, 徐卫亚, 2004.裂隙岩体渗流概念模型研究.岩土力学, (2):226-232. doi: 10.3969/j.issn.1000-7598.2004.02.013 徐亚, 薛祥山, 刘玉强, 等, 2014.地下水观测井井筒效应的多场耦合数值模拟.地球科学, 39(9):1349-1356. doi: 10.3799/dqkx.2014.117 -
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