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弯曲岩溶管道溶质运移的尺度效应研究

赵小二 王正一 武桂芝 李琪

赵小二,王正一,武桂芝,等. 弯曲岩溶管道溶质运移的尺度效应研究[J]. 水文地质工程地质,2023,50(0): 1-10 doi:  10.16030/j.cnki.issn.1000-3665.202203050
引用本文: 赵小二,王正一,武桂芝,等. 弯曲岩溶管道溶质运移的尺度效应研究[J]. 水文地质工程地质,2023,50(0): 1-10 doi:  10.16030/j.cnki.issn.1000-3665.202203050
ZHAO Xiaoer, WANG Zhengyi, WU Guizhi, et al. Research on the scale effects of solute transport in a bended karst conduit[J]. Hydrogeology & Engineering Geology, 2023, 50(0): 1-10 doi:  10.16030/j.cnki.issn.1000-3665.202203050
Citation: ZHAO Xiaoer, WANG Zhengyi, WU Guizhi, et al. Research on the scale effects of solute transport in a bended karst conduit[J]. Hydrogeology & Engineering Geology, 2023, 50(0): 1-10 doi:  10.16030/j.cnki.issn.1000-3665.202203050

弯曲岩溶管道溶质运移的尺度效应研究

doi: 10.16030/j.cnki.issn.1000-3665.202203050
基金项目: 国家自然科学基金项目(42002259)
详细信息
    作者简介:

    赵小二(1989-),男,博士,主要从事岩溶水文地质方面的研究。E-mail:zhaoxiaoer@qut.edu.cn

  • 中图分类号: 中图分类号

Research on the scale effects of solute transport in a bended karst conduit

  • 摘要: 岩溶管道溶质运移的尺度效应研究对穿透曲线的正确解译非常重要,但目前针对单一弯曲管道中溶质运移尺度效应的研究仍比较缺乏。文章将岩溶管道和溶潭分别概化为透明软管和水箱,基于前期建立的水箱-管道系统(简称“管道系统”),在水箱下游设置不同长度的弯曲管道,通过示踪试验研究管道运移尺度对穿透曲线的影响,并采用暂时存储模型模拟试验曲线。结果表明:(1)随着水箱下游管道长度的增大,峰值质量浓度逐渐缓慢降低,穿透曲线上升段斜率无明显变化,穿透曲线拖尾逐渐缩短,表明运移管道长度增大对溶质运移的影响大于下游管道弯曲;(2)穿透曲线偏度系数、后段溶质羽穿透时间和溶质羽穿透时间与管道系统长度呈良好的负线性相关关系(R2>0.96);(3)当对称和不对称水箱管道系统长度分别增大至154.5 m和164.3 m时,偏度系数接近零,穿透曲线分布接近对称;(4)弥散系数、存储区截面积和交换系数与管道系统长度呈良好的负线性相关关系,当对称和不对称水箱管道系统长度分别增大至159.9 m和178.1 m时,存储区截面积接近零,水箱导致的溶质运移滞后效应基本消失。研究结果对野外岩溶管道穿透曲线的解译具有一定指示作用。
  • 图  1  试验装置示意图(修改自文献[17])

    Figure  1.  Schematic diagram of the experimental setup (modified from Ref. [17])

    图  2  水箱示意图

    Figure  2.  Schematic diagram of the symmetrical pool

    图  3  不同管道长度的水箱管道系统示意图

    Figure  3.  Schematic diagram of the pool-pipe system with different lengths

    图  4  不同长度管道的摆放位置示意图(俯视图)

    Figure  4.  Schematic diagram of the pipe placement with different lengths (top view)

    图  5  典型的穿透曲线及特征参数

    注:Cp为峰值质量浓度;t1为示踪剂最先到达时刻;tp为峰值质量浓度到达时刻;t2为示踪剂最后检出时刻;t0.5Cp为主体溶质穿透时间;tre为后段溶质羽穿透时间;td为溶质羽穿透时间;t0.5ri为浓度上升至一半时峰值质量浓度所对应的时刻,t0.5re为浓度下降至一半时峰值质量浓度所对应的时刻。

    Figure  5.  Typical breakthrough curve and its characteristic parameters

    图  6  水箱下游管道长度对穿透曲线的影响(图中为管道系统长度)

    Figure  6.  Influence of the pipe length downstream of the pool on the breakthrough curve (the length of the pool-pipe system is shown in the figure)

    图  7  穿透曲线特征参数与管道系统长度(L)的关系

    Figure  7.  Relationships between the characteristic parameters of the BTCs and the length (L) of the pipe system

    图  8  模型参数与管道系统长度(L)的关系

    Figure  8.  Relationships between the model parameters and the length (L) of the pipe system

    表  1  穿透曲线特征参数

    Table  1.   Characteristic parameters of breakthrough curve

    特征参数参数分类计算方法
    Cp最大示踪剂浓度${C_p} = \max \left( {C(t)} \right)$
    Rt示踪剂回收率${R_t} = \dfrac{ {\int_0^\infty {C(t)Q(t){\rm{d}}t} } }{M}$
    tm水力参数${t_m} = \dfrac{ {\int_0^\infty {tC(t)Q(t){\rm{d}}t} } }{ {\int_0^\infty {C(t)Q(t){\rm{d}}t} } }$
    v水力参数$v = \dfrac{L}{{{t_m}}}$
    σt2水力参数$\sigma _t^2 = \dfrac{ {\int_0^\infty { { {(t - \overline t )}^2}C(t)Q(t){\rm{d}}t} } }{ {\int_0^\infty {C(t)Q(t){\rm{d}}t} } }$
    CSK水力参数$CSK = \dfrac{ {\int_0^\infty { { {(t - \overline t )}^3}C(t)Q(t){\rm{d}}t} } }{ {\sigma _t^3\int_0^\infty {C(t)Q(t){\rm{d}}t} } }$
    tre水力参数$t_{\rm{re }}= t_2 - t_{\rm{p}} $
    t0.5Cp水力参数$t_{\rm{0.5Cp}} = t_{\rm{0.5re}} - t_{\rm{0.5ri}} $
    td水力参数$t_{\rm{d}} = t_2 - t_1 $
    注:Ct)为在任意t时刻的浓度,Qt)为t时刻的流量,M为示踪剂注入质量。
    下载: 导出CSV

    表  2  不同管道系统长度的穿透曲线特征参数

    Table  2.   Characteristic parameters of the pipe system with different lengths

    水箱结构L/mv/(m·s−1tm/minσt2/min2CSKtre/st0.5Cp/std/sRt/%
    SP1572.250.4472.70040.157680.14721751218791.97
    83.000.4503.07450.15320.12741641217891.92
    93.750.4583.41240.140150.10971481316192.50
    104.50.4673.73170.109960.08891251313789.27
    ASP1572.250.4462.70160.0523050.0847892010594.99
    83.000.4523.05940.048710.072282219896.88
    93.750.4573.42270.045040.062074219091.83
    104.50.4613.77390.0440960.055763217992.36
    下载: 导出CSV

    表  3  不同管道系统长度的模型参数

    Table  3.   Model parameters of the pipe system with different lengths

    水箱结构L/mD/(m2·s−1A/m2As/m2α/(s−1Vs/m3DAI
    SP1572.251.48×10−24.98×10−44.37×10−55.04×10−33.16×10−313.2
    83.001.33×10−25.00×10−43.89×10−54.26×10−33.23×10−312.6
    93.751.27×10−24.97×10−43.42×10−53.76×10−33.21×10−312.4
    104.51.18×10−24.96×10−42.72×10−53.32×10−32.84×10−313.5
    ASP1572.251.87×10−25.09×10−43.54×10−51.04×10−22.56×10−334.7
    83.001.63×10−25.06×10−43.18×10−51.02×10−22.64×10−337.3
    93.751.57×10−25.08×10−42.67×10−58.44×10−22.50×10−336.5
    104.51.34×10−25.04×10−42.52×10−58.42×10−22.63×10−338.0
    下载: 导出CSV
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