承压含水层中非完整井附近“非达西-达西”两区渗流模型近似解析解

文章; 刘凯; 陈晓恋

doi:10.3799/dqkx.2015.076

承压含水层中非完整井附近“非达西-达西”两区渗流模型近似解析解

doi: 10.3799/dqkx.2015.076

文章^1,,
刘凯^{1, 2},
陈晓恋¹

1.
中国地质大学环境学院，湖北武汉 430074
2.
中国交通建设股份有限公司第二公路勘察设计研究院有限公司，湖北武汉 430056

基金项目:

国家自然科学基金项目 41372253

国家自然科学基金项目 41002082

国家重点基础研究发展计划项目 2010CB428802

中央高校基本科研业务费专项基金项目 CUG140501

中央高校基本科研业务费专项基金项目 CUG120113

详细信息

作者简介:
文章(1982-)，男，博士，副教授，主要从事地下水渗流、污染物迁移等方面的研究.E-mail: wenzhangcau@gmail.com

中图分类号: P641.2
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出版历程
- 收稿日期: 2014-09-15
- 刊出日期: 2015-05-15

Approximate Analytical Solutions for Two-Region Non-Darcian Flow to a Partially Penetrating Well

1.
School of Environmental Studies, China University of Geosciences, Wuhan 430074, China
2.
Second Highway Consultants Co.Ltd., China Communications Construction Co.Ltd., Wuhan 430056, China

摘要

摘要: 抽水井附近由于流速过快往往发生非达西流，而远离抽水井随着流速下降又变为达西流.为了描述这些特征，建立了承压含水层中非完整井附近“非达西-达西”两区渗流模型，即距离抽水井较近的区域由于流速较快假设发生非达西渗流，并利用Izbash公式刻画，而距离抽水井较远由于流速较慢假设仍然满足达西定律，含水层中垂向流速较小也利用达西定律描述.通过线性化近似方法结合Laplace变换和有限Fourier余弦变换对模型进行了求解，分析探讨了该两区模型下水位降深曲线特征.结果表明：抽水初期，非达西渗流区域水位降深与全非达西渗流模型结果吻合，而抽水后期两区模型非达西渗流区域的水位降深与全达西模型水位降深基本一致，但大于全非达西渗流模型的水位降深；抽水初期，两区模型中达西渗流区域的水位降深比全达西渗流模型结果大，但比全非达西渗流模型结果小；对不同时间的水位降深随井距变化曲线分析发现非达西渗流区域水位降深随Izbash公式中的幂指数n增大而减小，而在达西渗流区域水位降深基本不受n值的影响.研究成果对非完整井抽水试验参数反演具有重要理论意义.
- 非达西流 /
- 两区模型 /
- 非完整井 /
- 线性化 /
- 地下水
Abstract: Non-Darcian flow is likely to occur in the region near a pumping well because of high velocities, while flow becomes Darcian again in the region far away from the pumping well as the velocity decreases. To describe these characteristics, a two-region non-Darcian flow model toward a partially penetrating well is developed in this study. The flow in the region near the pumping well is assumed to be non-Darcian which can be described by the Izbash equation. The flow in the region far away from the pumping well was assumed to be Darcian as well as the vertical flow due to the low velocities. A linearization procedure associated with the Laplace transform and finite cosine transform is used to work out such two-region non-Darcian flow model. The characteristics of the drawdowns under such flow conditions are examined. It is concluded that: (1) the drawdown in the non-Darcian flow region is the same as that of the fully non-Darcian flow model at early times, and it is the same at that of the fully Darcian flow model and larger than that of the fully non-Darcian flow model at late times. (2) the drawdown in the Darcian flow region is larger than that of the fully Darcian flow model and smaller than that of the full non-Darcian flow model at early times; (3) the drawdown-distance behavior indicates that the drawdown in the non-Darcian flow region increases as the power index n in the Izbash equation increases, while the value of n has a little effect on the drawdown in the Darcian flow region. The results of this study will be of great theoretical significance for the aquifer parameters estimation with the pumping test data in a partially penetrating well.
- non-Darcian flow /
- two-region model /
- partially penetrating well /
- linearization /
- ground water

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图 1 非完整抽水井附近两区模型渗流物理模型

Fig. 1. The schematic of two-region model near a partially penetrating well

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图 2 简化模型与Hantush模型结果比较

Fig. 2. Comparison between the results of this study and the solution of Hantush model for Darcian flow case

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图 3 不同抽水模型下非达西区域水位降深对比

Fig. 3. Comparison of the drawdown in non-Darcian flow region under for different models

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图 4 不同抽水模型下达西区域水位降深对比

Fig. 4. Comparison of the drawdown in Darcian flow region under for different models

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图 5 不同n值时含水层水位降深-距离曲线

Fig. 5. Drawdown-distance behavior for different n values

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图 6 不同抽水时间下含水层水位降深-距离曲线

Fig. 6. Drawdown-distance behavior for different pumping times

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参考文献(22)

[1]	Chang, A.D., Guo, J.Q., Wang, H.S., 2000. The Analytical Solution of Unsteady Well Flow with Two Flow Regimes. Journal of Hydraulic Engineering, 31(6): 49-53, 66 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-SLXB200006008.htm
[2]	Crump, K.S., 1976. Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation. Journal of the ACM, 23(1): 89-96. doi: 10.1145/321921.321931
[3]	de Hoog, F.R., Knight, J.H., Stokes, A.N., 1982. An Improved Method for Numerical Inversion of Laplace Transforms. SIAM Journal on Scientific and Statistical Computing, 3(3): 357-366. doi: 10.1137/0903022
[4]	Hantush, M.S., 1964. Hyraulics of Wells. In: Chow, V.T., ed., Advances in Hydroscience, Academic Press, Inc., New York.
[5]	Mathias, S.A., Butler, A.P., Zhan, H.B., 2008. Approximate Solutions for Forchheimer Flow to a Well. Journal of Hydraulic Engineering, 134(9): 1318-1325. doi: 10.1061/(ASCE)0733-9429(2008)134:9(1318)
[6]	Sen, Z., 1988. Type Curves for Two-Regime Well Flow. Journal of Hydraulic Engineering, 114(12): 1461-1484. doi: 10.1061/(ASCE)0733-9429(1988)114:12(1461)
[7]	Stehfest, H., 1970a. Algorithm 368: Numerical Inversion of Laplace Transforms [D5]. Communications of the ACM, 13(1): 47-49. doi: 10.1145/361953.361969
[8]	Stehfest, H., 1970b. Remark on Algorithm 368: Numerical Inversion of Laplace Transforms. Communications of the ACM, 13(10): 624-625. doi: 10.1145/355598.362787
[9]	Wan, J.W., Huang, K., Chen, C.X., 2013. Reassessing Darcy' Law on Water Flow in Porous Media. Earth Science—Journal of China University of Geosciences, 38(6): 1327-1330 (in Chinese with English abstract). doi: 10.3799/dqkx.2013.130
[10]	Wang, P.J., 1996. Theory for Two-Regime Well Flow in Confined Aquifers. Irrigation and Drainage, 15(4): 1-9 (in Chinese with English abstract).
[11]	Wang, Q.R., Tang, Z.H., Wen, Z., et al., 2012. Numeric Simulation for Flow to a Pumping Well with Moving Boundary of the Non-Darcian Flow Region in a Leaky Aquifer. Journal of Hydraulic Engineering, 43(10): 1171-1178 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTotal-SLXB201210008.htm
[12]	Wen, Z., Huang, G.H., Liu, Z.T., et al., 2011. An Approximate Analytical Solution for Two-Region Non-Darcian Flow toward a Well in a Leaky Aquifer. Earth Science—Journal of China University of Geosciences, 36(6): 1165-1172 (in Chinese with English abstract).
[13]	Wen, Z., Huang, G.H., Zhan, H.B., 2008a. Non-Darcian Flow toward a Finite-Diameter Vertical Well in a Confined Aquifer. Pedosphere, 18(3): 288-303. doi: 10.1016/S1002-0160(08)60019-3
[14]	Wen, Z., Huang, G.H., Zhan, H.B., et al., 2008b. Two-Region Non-Darcian Flow toward a Well in a Confined Aquifer. Advances in Water Resources, 31(5): 818-827. doi: 10.1016/j.advwatres.2008.01.014
[15]	Wen, Z., Huang, G.H., Zhan, H.B., 2009. A Numerical Solution for Non-Darcian Flow to a Well in a Confined Aquifer Using the Power Law Function. Journal of Hydrology, 364(1-2): 99-106. doi: 10.1016/j.jhydrol.2008.10.009
[16]	Wen, Z., Liu, K., Chen, X.L., 2013. Approximate Analytical Solution for Non-Darcian Flow toward a Partially Penetrating Well in a Confined Aquifer. Journal of Hydrology, 498(8): 124-131. doi: 10.1016/j.jhydrol.2013.06.027
[17]	Wu, Y.S., 2001. Non-Darcy Displacement of Immiscible Fluids in Porous Media. Water Resources Research, 37(12): 2943-2950. doi: 10.1029/2001WR000389
[18]	常安定, 郭建青, 王洪胜, 2000. 两种流态区域条件下的井流问题的解析解. 水利学报, 31(6): 49-53, 66. https://www.cnki.com.cn/Article/CJFDTOTAL-SLXB200006008.htm
[19]	万军伟, 黄琨, 陈崇希, 2013. 达西定律成立吗. 地球科学——中国地质大学学报, 38(6): 1327-1330. https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX201306020.htm
[20]	王鹏举, 1996. 考虑非达西流情况下地下水向集水建筑物运动的非稳定理论的研究. 灌溉排水, 15(4): 1-9. https://www.cnki.com.cn/Article/CJFDTOTAL-GGPS604.000.htm
[21]	王全荣, 唐仲华, 文章, 等, 2012. 越流含水层抽水井附近非达西流与达西流区界面位置变化规律研究. 水利学报, 43(10): 1171-1178. https://www.cnki.com.cn/Article/CJFDTOTAL-SLXB201210008.htm
[22]	文章, 黄冠华, 刘壮添, 等, 2011. 越流含水层中抽水井附近非达西流两区模型近似解析解. 地球科学——中国地质大学学报, 36(6): 1165-1172 https://www.cnki.com.cn/Article/CJFDTOTAL-DQKX201106023.htm