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变径抽水井降深和涌水量关系的混合井模型

齐跃明 吴佳欣 王旭升 周来 董贵明 刘博 许进鹏 马超 周沛

齐跃明, 吴佳欣, 王旭升, 周来, 董贵明, 刘博, 许进鹏, 马超, 周沛. 变径抽水井降深和涌水量关系的混合井模型[J]. 地质科技通报, 2023, 42(4): 65-74. doi: 10.19509/j.cnki.dzkq.tb20220699
引用本文: 齐跃明, 吴佳欣, 王旭升, 周来, 董贵明, 刘博, 许进鹏, 马超, 周沛. 变径抽水井降深和涌水量关系的混合井模型[J]. 地质科技通报, 2023, 42(4): 65-74. doi: 10.19509/j.cnki.dzkq.tb20220699
Qi Yueming, Wu Jiaxin, Wang Xusheng, Zhou Lai, Dong Guiming, Liu Bo, Xu Jinpeng, Ma Chao, Zhou Pei. Mixed-well model of the relation between drawdown and water inflow in a pumping well with variable-diameter[J]. Bulletin of Geological Science and Technology, 2023, 42(4): 65-74. doi: 10.19509/j.cnki.dzkq.tb20220699
Citation: Qi Yueming, Wu Jiaxin, Wang Xusheng, Zhou Lai, Dong Guiming, Liu Bo, Xu Jinpeng, Ma Chao, Zhou Pei. Mixed-well model of the relation between drawdown and water inflow in a pumping well with variable-diameter[J]. Bulletin of Geological Science and Technology, 2023, 42(4): 65-74. doi: 10.19509/j.cnki.dzkq.tb20220699

变径抽水井降深和涌水量关系的混合井模型

doi: 10.19509/j.cnki.dzkq.tb20220699
基金项目: 

国家重点研发计划课题 2022YFC3702203

国家自然科学基金项目 52274243

国家自然科学基金项目 42272292

江苏省研究生科研创新计划 2766

江苏省研究生科研创新计划 2767

中国矿业大学研究生创新计划项目资助 2023WLJCRCZL003

中国矿业大学研究生创新计划项目资助 2023WLJCRCZL004

详细信息
    作者简介:

    齐跃明(1977—), 男, 副教授, 主要从事水文地质和矿山水害防治方面的教学和科研工作。E-mail: ym_qi@126.com

    通讯作者:

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

  • 中图分类号: P641

Mixed-well model of the relation between drawdown and water inflow in a pumping well with variable-diameter

  • 摘要:

    抽水试验是确定含水层水文地质参数和评价地下水资源的重要手段。对于单井抽水试验分析, 现有井流模型假定抽水井的直径不随深度变化、含水层为单一的潜水或承压含水层, 未考虑抽水井变径及穿越多个含水层的情况。建立多含水层异径抽水的稳定态混合井流模型, 假设地下水仅发生水平流动, 推导出了抽水井涌水量与降深关系的理论解析公式, 探讨根据变径抽水井的单井稳定流抽水试验获取含水层参数的方法, 提出了承压含水层段抽水井等效半径精确解和替代半径计算公式。把混合井流模型用于分析淄河源区的傍河抽水试验, 根据3个流量的阶梯式抽水试验数据确定了涌水量Qw与降深sw的抛物线型关系, 预测允许降深sw为25 m时抽水井涌水量为4 093.8 m3/d, 反算得到潜水含水层渗透系数为1.88 m/d, 用替代半径计算的承压含水层渗透系数约为0.43 m/d, 相对误差小于5%。混合井模型为多含水层抽水井的涌水量预报提供了理论依据, 其适用性也受到假设条件的限制。在完整河情景下忽略三维流将导致反求的渗透系数偏大, 在非完整河情景下解析解反求的渗透系数则偏小。

     

  • 图 1  2种混合井抽水稳定流模型

    r0, r1, r2, …, rn分别为抽水井所揭露第1, 第2, …, 第n+1含水层进水段井半径(m);K0, K1, K2, …, Kn分别为抽水井所揭露第1, 第2, …, 第n+1含水层水平渗透系数(m/d);z1, z2, z3, …, zn, zb分别为抽水井所揭露第1, 第2, …, 第n+1含水层底部标高(m);M1, M2, M3, …, Mn分别为抽水井所揭露第2, 第3, …, 第n+1含水层厚度(m);Qw为混合抽水井抽水流量(m3/d);hR为圆岛外边界定水头水位(m);hw为开采井中水位(m);R为开采井中心距圆岛外边界水平距离(m);L为开采井中心与定水头边界的水平距离(m); 下同
    a.圆岛中心抽水;b.定水头边界附近抽水

    Figure 1.  Two types of steady state flow models for a multilayer mixed pumping well

    图 2  淄河附近XK1钻孔剖面特征

    Figure 2.  Profile map of the borehole XK1 near the Zi River

    图 3  稳定流抽水试验降深(sw)与涌水量(Qw)的关系

    Figure 3.  Relationship between the drawdown(sw) and pumping rate(Qw) in steady-state pumping test

    图 4  三维有限差分模型及其模拟结果

    a.三维模型网格;b.抽水井水位下降20 m时含水层底部降深分布;c.抽水井水位下降20 m中心剖面降深分布;d.抽水井涌水量与降深关系曲线

    Figure 4.  3D finite-difference model and its simulation modeling results

    表  1  抽水井分段特征

    Table  1.   Sectional characteristics of the pumping well

    编号 底面深度/m 井孔直径/mm 揭露地层 含水层岩性 有效厚度/m 分段体积/m3 分段侧面积m2
    顶层 16.3 426 Q、O2b 砂层、白云岩 套管阻隔、侧面不进水
    26.1 377 O2b 白云岩 潜水含水层段
    105.9 377 O2b、O2d、∈4O1s、∈4O1ĉ 白云岩、灰岩 79.8 8.91 94.5
    250.2 325 4O1s、∈4O1ĉ 白云岩、灰岩 144.3 11.97 147.3
    353.2 273 4O1ĉ 灰岩为主 74.2 4.34 63.6
    注:Q.第四系;O2b.北奄庄组;O2d.东黄山组;∈4O1s.三山子组;∈4O1ĉ.炒米店组
    下载: 导出CSV

    表  2  不同解析模型涌水量计算值相对数值模拟结果的误差

    Table  2.   Errors of the flow rate estimated from different analytical models with respect to numerical simulations

    抽水井降深sw/m 单井涌水量
    数值模拟Qw/(m3·d-1) 传统解析模型(定半径均质含水层) 混合井解析模型
    rw=136.5 mm rw=188.5 mm 涌水量Qw/ (m3·d-1) 相对误差/ %
    Qw/(m3·d-1) 相对误差/% Qw/(m3·d-1) 相对误差/%
    5 939.0 789.9 -15.9 835.6 -11.0 924.4 -1.6
    10 1 877.0 1 568.4 -16.4 1 659.1 -11.6 1 795.9 -4.3
    15 2 813.0 2 335.4 -17.0 2 470.5 -12.2 2 614.7 -7.1
    20 3 679.2 3 091.0 -16.0 3 269.8 -11.1 3 380.6 -8.1
    25 4 154.5 3 835.2 -7.7 4 057.0 -2.3 4 093.8 -1.5
    30 4 985.8 4 567.9 -8.4 4 832.1 -3.1 4 754.2 -4.6
    35 5 816.1 5 289.2 -9.1 5 595.1 -3.8 5 361.8 -7.8
    下载: 导出CSV
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  • 收稿日期:  2022-12-22
  • 录用日期:  2023-05-04
  • 修回日期:  2023-04-11

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