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有入渗补给的层状非均质含水层圆岛潜水井流模型

陈崇希 唐仲华 谢永桦 王旭升

陈崇希, 唐仲华, 谢永桦, 王旭升. 有入渗补给的层状非均质含水层圆岛潜水井流模型[J]. 地质科技通报, 2023, 42(4): 15-26. doi: 10.19509/j.cnki.dzkq.tb20220723
引用本文: 陈崇希, 唐仲华, 谢永桦, 王旭升. 有入渗补给的层状非均质含水层圆岛潜水井流模型[J]. 地质科技通报, 2023, 42(4): 15-26. doi: 10.19509/j.cnki.dzkq.tb20220723
Chen Chongxi, Tang Zhonghua, Xie Yonghua, Wang Xusheng. A well flow model for a stratified heterogenous unconfined aquifer in a round island with infiltration recharge[J]. Bulletin of Geological Science and Technology, 2023, 42(4): 15-26. doi: 10.19509/j.cnki.dzkq.tb20220723
Citation: Chen Chongxi, Tang Zhonghua, Xie Yonghua, Wang Xusheng. A well flow model for a stratified heterogenous unconfined aquifer in a round island with infiltration recharge[J]. Bulletin of Geological Science and Technology, 2023, 42(4): 15-26. doi: 10.19509/j.cnki.dzkq.tb20220723

有入渗补给的层状非均质含水层圆岛潜水井流模型

doi: 10.19509/j.cnki.dzkq.tb20220723
基金项目: 

国家自然科学基金项目 41972263

详细信息
    作者简介:

    陈崇希(1933—), 男, 教授, 博士生导师, 主要从事地下水运动解析模型与数值模拟方法的研究与教学工作。E-mail: ccx33@163.com

  • 中图分类号: P641

A well flow model for a stratified heterogenous unconfined aquifer in a round island with infiltration recharge

  • 摘要:

    作为圆岛状均质含水层稳定井流模型, 经典的Dupuit井流模型既没有考虑普遍存在的降水入渗补给, 也不适用于层状非均质含水层系统, 有必要加以完善。在考虑降水入渗补给改进Dupuit井流模型的基础上, 进一步将其拓展到层状非均质潜水含水层。引入Гиринский(吉林斯基)势函数, 根据水均衡原理建立极坐标下的地下水流微分方程, 再依边界条件解析得到了相应的流量方程、水位方程和分水岭公式。以双层结构为例, 观察30组不同参数条件的典型水位曲线组, 发现不同渗透系数的水位曲线交于一点的特殊现象并从理论上给出了证明。解析模型仍引入Dupuit假定, 且没有考虑抽水井的井壁"水跃"现象, 为判断这些条件对解析公式适用能力的影响, 建立轴对称剖面二维流数值模型并做了对比研究。除抽水井附近外, 水位解析方程产生的相对误差一般低于4%, 在最偏离Dupuit假定的分水岭处, 距离和水位的解析误差均小于0.1%。Dupuit假定并没有严重影响解析模型的适用性。

     

  • 图 1  层状非均质含水层具入渗补给的圆岛状潜水井流模型图

    K0, K1, K2, …, Kn分别为第1, 第2, …, 第n介质层渗透系数(m/d);Qw为抽水流量(m3/d);hR为圆岛外边界水位(m);hw为开采井中水位(m);R为圆岛半径(m);a为无分水岭水位曲线;b为有分水岭水位曲线

    Figure 1.  Model map of well flow in a round island with a stratified heterogeneous unconfined aquifer obtaining infiltration recharge

    图 2  层状非均质含水层吉林斯基势函数定义要素图

    z1, z2, …, zn分别为抽水井所揭露第1, 第2, …, 第n介质层底部标高(m);M1, M2, …, Mn分别为第1, 第2, …, 第n介质层的水带厚度(m)

    Figure 2.  Elements of Girinskii's potential function for a stratified heterogeneous aquifer

    图 3  双层结构含水层天然状态水位曲线计算案例(ε.入渗强度;K2.水平渗透系数; 下同)

    Figure 3.  Estimated results of groundwater level curves in the natural state for an aquifer of the bilayer structure

    图 4  双层结构含水层在Qw=5 000 m3/d抽水状态水位曲线计算案例

    Figure 4.  Estimated results of groundwater level curves in the pumping state of Qw=5 000 m3/d for an aquifer of the bilayer structure

    图 5  解释交叉点的f(r/R)函数曲线

    Figure 5.  Function curve of f(r/R) used to interpret the intersection poi

    图 6  双层结构含水层轴对称剖面二维流概念模型示意图

    Figure 6.  Schematic diagram of two-dimensional flow conceptual model in axisymmetric section of bilayer structure aquifer

    图 7  利用表 1~2K2=1 m/d. ε=0.000 75 m/d条件数值模拟结果绘制的流网图

    Figure 7.  Flow net map drawn with numerical modelling results for the condition of K2=1 m/d, and ε=0.000 75 m/d as that listed in tables 1 and 2

    图 8  抽水井附近解析水位误差随距离的变化曲线图

    Figure 8.  Relationship between the error of the analytical groundwater level and the distance near the pumping well

    图 9  分水岭处解析水位误差随K2的变化曲线图

    Figure 9.  Relationship between the error of the analytical groundwater level and the K2 value on the groundwater divide

    表  1  Qw=0 m3/d时不同K2r=0处水位峰值hp

    Table  1.   Maximum groundwater level, hp at r=0 for different K2 values when Qw=0 m3/d

    ε/(m·d-1) 水位峰值hp/m
    K2=1 K2=5 K2=10 K2=20 K2=100
    0.000 75 52.34 51.85 51.48 51.06 50.32
    0.001 53.11 52.46 51.96 51.40 50.43
    0.001 5 54.65 53.67 52.92 52.08 50.64
    注:K2单位为m/d
    下载: 导出CSV

    表  2  Qw=5 000 m3/d时不同K2值抽水井的井中水位hw

    Table  2.   Water level within the pumping well for different K2 values when Qw=5 000 m3/d

    ε/(m·d-1) 井中水位hw/m
    K2=1 K2=5 K2=10 K2=20 K2=100
    0.000 75 26.72 29.56 32.77 37.63 46.66
    0.001 27.64 30.40 33.52 38.17 46.78
    0.001 5 29.39 32.03 34.98 39.23 47.03
    注:K2单位为m/d
    下载: 导出CSV

    表  3  Qw=5 000 m3/d时分水岭和交叉点特征

    Table  3.   Characteristics of groundwater divide and intersection point for Qw=5 000 m3/d

    ε/(m·d-1) 分水岭位置rd/m 不同K2值(m/d)对应分水岭处水位hd(m) 交叉点位置rc/m 交叉点水位hc/m
    K2=1 K2=5 K2=10 K2=20 K2=100
    0.000 75 1 456.732 50.31 50.25 50.20 50.14 50.04 974.95 50.000
    0.001 1 261.567 50.73 50.59 50.47 50.33 50.10 650.02 50.000
    0.0015 1 030.065 51.79 51.42 51.14 50.81 50.25 318.55 50.000
    注:K2单位为m/d
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-12-31
  • 录用日期:  2023-02-24
  • 修回日期:  2023-02-22

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