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潜水稳定井流的剖面二维数值模拟方法

王旭升 谢永桦 陈崇希

王旭升, 谢永桦, 陈崇希. 潜水稳定井流的剖面二维数值模拟方法[J]. 地质科技通报, 2023, 42(4): 27-36. doi: 10.19509/j.cnki.dzkq.tb20230024
引用本文: 王旭升, 谢永桦, 陈崇希. 潜水稳定井流的剖面二维数值模拟方法[J]. 地质科技通报, 2023, 42(4): 27-36. doi: 10.19509/j.cnki.dzkq.tb20230024
Wang Xusheng, Xie Yonghua, Chen Chongxi. Sectional 2D numerical modelling method for steady state well-flow in an unconfined aquifer[J]. Bulletin of Geological Science and Technology, 2023, 42(4): 27-36. doi: 10.19509/j.cnki.dzkq.tb20230024
Citation: Wang Xusheng, Xie Yonghua, Chen Chongxi. Sectional 2D numerical modelling method for steady state well-flow in an unconfined aquifer[J]. Bulletin of Geological Science and Technology, 2023, 42(4): 27-36. doi: 10.19509/j.cnki.dzkq.tb20230024

潜水稳定井流的剖面二维数值模拟方法

doi: 10.19509/j.cnki.dzkq.tb20230024
基金项目: 

国家自然科学基金项目 41972263

国家自然科学基金项目 41772249

详细信息
    作者简介:

    王旭升(1974—), 男, 教授, 博士生导师, 主要从事地下水动力学和水文模型研究工作。E-mail: wxsh@cugb.edu.cn

  • 中图分类号: P641

Sectional 2D numerical modelling method for steady state well-flow in an unconfined aquifer

  • 摘要:

    经典Dupuit井流模型与考虑入渗的改进Dupuit井流模型, 都受到Dupuit假定的影响, 可能存在系统误差。建立反映三维流或轴对称二维流特性的潜水井流数值模型, 是检验Dupuit模型可靠性的重要手段。提出一种模拟潜水稳定井流的剖面二维数值模拟方法, 通过参数转换把柱坐标系的渗流方程变换为等效的直角坐标系方程, 利用MODFLOW方体网格有限差分模型实现剖面二维流场模拟。数值模型以抽水井的井中水位为已知条件, 渗出面的排水量按照Darcy定律差分公式计算, 潜水面则通过MODFLOW对干-湿单元的处理加以识别, 抽水流量经水均衡计算得到。通过采用精细化网格建立典型案例模型, 获得模拟精度很高的结果, 使反算抽水井流量的相对误差不超过0.2%。以此检验Dupuit井流模型, 发现解析公式得到的水位线总体与数值模拟结果一致, 仅在抽水井附近由于没有考虑水跃而偏低, 且误差受到含水层渗透系数各向异性的影响。在有入渗的情况下, 分水岭附近的渗流违反Dupuit假定。然而, 改进的Dupuit井流公式计算的分水岭水位相对误差低于1%。这一数值模拟方法简单实用, 但也受到MODFLOW本身局限性的约束。

     

  • 图 1  直角坐标系(a)和柱坐标系(b)的潜水面示意图(z为相对高度; x为横向距离; r为径向距离;后同)

    Figure 1.  Schematics of the phreetic surface in the cartesian (a) and cylindrical (b) coordinate systems

    图 2  含水层网格单元与井孔的关系示意图

    a.井壁渗出面相邻单元;b.井孔饱水带相邻单元;rw为抽水井半径;Δx为单元长度;Δz为单元厚度;Δy为单元宽度;Qx为侧面流量;zw为井中水位;z(k)为单元中点高度;H(k)为单元格点水头

    Figure 2.  Schematics of the relationship between grid blocks of the aquifer and the well

    图 3  潜水井流模型示意图

    x, r为距离;R为圆岛半径;LR为外侧边界水跃;H(r, z)为水头分布函数;hw为井中水位;Lw为井壁水跃

    Figure 3.  Diagrammatic map of the model for the wellflow in an unconfined aquifer

    图 4  情景A模拟水位与经典Dupuit模型解析解的局部对比

    Figure 4.  Local comparison between the modelled groundwater level of the scenario-A and the analytical solution of the classical Dupuit model

    图 5  情景B模拟水位与改进Dupuit模型解析解的对比

    a.整体范围;b.抽水井附近

    Figure 5.  Comparison between the modelled groundwater level of scenario-B and the analytical solution of the modified Dupuit model

    图 6  情景C的模拟水位与改进Dupuit模型解析解的对比

    a.抽水井附近;b.全部范围

    Figure 6.  Comparison between the modelled groundwater level of scenario-C and the analytical solution of the modified Dupuit model

    图 7  情景D的模拟结果

    Figure 7.  Numerical modelling results of scenario-D

    表  1  模拟情景编号和参数

    Table  1.   Code and parameters of modelling scenarios

    模拟情景 水平方向渗透系数Kh/(m·d-1) 各向异性比值Kv/Kh 入渗补给强度ε/(mm·d-1) 井中水位hw/m
    A 10 1 0.0 35
    B 10 1 1.0 35
    C 10 0.1, 10.0 1.0 35
    D 1 0.1 1.0 20
    下载: 导出CSV
  • [1] Dupuit A J E J. Etudes theoretiques et pratiques sur le mouvement des eaux[M]. Paris: Dunod, 1863.
    [2] Каменский Г И. Основы дина-мики подземных вод[M]. Москва: Госгеолиздат, 1943(in Russian).
    [3] Haitjema H M. Analytic element modeling of groundwater flow[M]. San Diego: Academic Press, Inc., 1995.
    [4] 陈崇希. Dupuit模型的改进: 具入渗补给[J]. 水文地质工程地质, 2020, 47(5): 1-4. https://www.cnki.com.cn/Article/CJFDTOTAL-SWDG202106001.htm

    Chen C X. Improvement of Dupuit model: With infiltration recharge[J]. Hydrogeology & Engineering Geology, 2020, 47(5): 1-4(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-SWDG202106001.htm
    [5] Чарный И A. Строгое доказателъство формулм дюпюидля безнапорной филътрации с промеҗутком высачнвания[J]. Докл. АН СССР, 1951, 79(6): 937-948. https://www.cnki.com.cn/Article/CJFDTOTAL-NWYJ202105015.htm
    [6] 陈崇希, 林敏. 地下水动力学[M]. 武汉: 中国地质大学出版社, 1999.

    Chen C X, Lin M. Groundwater hydraulics[M]. Wuhan: China University of Geosciences Press, 1999(in Chinese).
    [7] Boulton N S. The flow pattern near a gravity well in a uniform water-bearing medium[J]. Journal of the ICE, 1951, 36(10): 534-550.
    [8] 张有龄. 河床地下水运动的供水理论分析[M]. 北京: 科学出版社, 1958.

    Zhang Y L. Theoretical analysis on water yield from groundwater flow beneath riverbed[M]. Beijing: Science Press, 1958(in Chinese).
    [9] Taylor G S, Luthin J N. Computer methods for transient analysis of water-table aquifers[J]. Water Resources Research, 1969, 5(1): 144-152. doi: 10.1029/WR005i001p00144
    [10] Neuman S P, Witherspoon P A. Finite element method of analyzing steady seepage with a free surface[J]. Water Resources Research, 1970, 6(3): 889-897. doi: 10.1029/WR006i003p00889
    [11] McDonald M G, Harbaugh A W. A modular three-dimensional finite-difference ground-water flow model[R]. Denver: Techniques of Water-Resources Investigations of the U.S. Geological Survey, Chapter A1, Book 6, 1988.
    [12] 王旭升, 万力. 地下水运动方程[M]. 北京: 地质出版社, 2011.

    Wang X S, Wan L. Equations of groundwater movements[M]. Beijing: Geological Publishing House, 2011(in Chinese).
    [13] 陈崇希, 林敏, 成建梅. 地下水动力学[M]. 北京: 地质出版社, 2011.

    Chen C X, Lin M, Cheng J M. Groundwater hydraulics[M]. Beijing: Geological Publishing House, 2011(in Chinese).
    [14] Samani N, Kompani-Zarea M, Barry D. MODFLOW equipped with a new method for the accurate simulation of axisymmetric flow[J]. Advances in Water Resources, 2004, 27(1): 31-45. doi: 10.1016/j.advwatres.2003.09.005
    [15] Langevin C D. Modeling axisymmetric flow and transport[J]. Groundwater, 2008, 46(4): 579-590. doi: 10.1111/j.1745-6584.2008.00445.x
    [16] Louwyck A, Vandenbohede A, Bakker M, et al. MODFLOW procedure to simulate axisymmetric flow in radially heterogeneous and layered aquifer systems[J]. Hydrogeology Journal, 2014, 22(5): 1217-1226. doi: 10.1007/s10040-014-1150-0
    [17] 董佩, 王旭升. MODFLOW模拟自由面渗流的应用与讨论[J]. 工程勘察, 2009(7): 27-30. https://www.cnki.com.cn/Article/CJFDTOTAL-GCKC200907009.htm

    Dong P, Wang X S. Application and discussion of MODFLOW's simulation to the seepage of free surface[J]. Journal of Geotechnical Investigation & Surveying, 2009(7): 27-30(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-GCKC200907009.htm
    [18] Hill M C. Preconditioned conjugate-gradient 2 (PCG2), a computer program for solving, ground-water flow equations[R]. Water-Resources Investigations Report 90-4048, Denver: U.S. Geological Survey, 1990.
    [19] Pollock D W. User's Guide for MODPATH/MODPATH-PLOT, Version 3: A Particle tracking post-processing package for MODFLOW, the U.S. Geological survey finite difference groundwater flow model[R]. Open-file report 94-464, Denver: U.S. Geological Survey, 1994.
    [20] 陈崇希, 唐仲华, 胡立堂. 地下水流数值模拟理论方法及模型设计[M]. 北京: 地质出版社, 2014.

    Chen C X, Tang Z H, Hu L T. Theory, method and model design for numerical simulation of groundwater flow[M]. Beijing: Geological Publishing House, 2014 (in Chinese).
    [21] 成建梅, 罗一鸣. 岩溶多重介质地下水模拟技术及应用进展[J]. 地质科技通报, 2022, 41(5): 220-229. doi: 10.19509/j.cnki.dzkq.2022.0220

    Chen J M, Luo Y M. Overview of groundwater modeling technology and its application in karst areas with multiple-void media[J]. Bulletin of Geological Science and Technology, 2022, 41(5): 220-229(in Chinese with English abstract). doi: 10.19509/j.cnki.dzkq.2022.0220
    [22] 郑小康, 杨志兵. 岩溶含水层饱和-非饱和流动与污染物运移数值模拟[J]. 地质科技通报, 2022, 41(5): 357-366. doi: 10.19509/j.cnki.dzkq.2022.0211

    Zheng X K, Yang Z B. Numerical simulation of saturated-unsaturated groundwater flow and contaminant transport in a karst aquifer[J]. Bulletin of Geological Science and Technology, 2022, 41(5): 357-366(in Chinese with English abstract). doi: 10.19509/j.cnki.dzkq.2022.0211
    [23] Wen Z, Liu Z T, Jin M G, et al. Numerical modeling of Forchheimer flow to a pumping well in a confined aquifer using the strong-form mesh-free method[J]. Hydrogeology Journal, 2014, 22(5): 1207-1215. doi: 10.1007/s10040-014-1136-y
    [24] Wang Q R, Zhan H B, Tang Z H, et al. Forchheimer flow to a well-considering time-dependent critical radius[J]. Hydrology and Earth System Sciences, 2014, 18(6): 2437-2448. doi: 10.5194/hess-18-2437-2014
    [25] 陈崇希, 林敏, 叶善士, 等. 地下水混合井流的理论及应用[M]. 武汉: 中国地质大学出版社, 1998.

    Chen C X, Lin M, Ye S S, et al. Theory of multi-layer mixed well flow and its application[M]. Wuhan: China University of Geosciences Press, 1998(in Chinese).
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出版历程
  • 收稿日期:  2023-01-13
  • 录用日期:  2023-04-19
  • 修回日期:  2023-04-14

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