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    越流含水层中抽水井附近非达西流两区模型近似解析解

    文章 黄冠华 刘壮添 李健

    文章, 黄冠华, 刘壮添, 李健, 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, 36(6): 1165-1172. doi: 10.3799/dqkx.2011.123
    引用本文: 文章, 黄冠华, 刘壮添, 李健, 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, 36(6): 1165-1172. doi: 10.3799/dqkx.2011.123
    WEN Zhang, HUANG Guan-hua, LIU Zhuang-tian, LI Jian, 2011. An Approximate Analytical Solution for Two-Region Non-Darcian Flow Toward a Well in a Leaky Aquifer. Earth Science, 36(6): 1165-1172. doi: 10.3799/dqkx.2011.123
    Citation: WEN Zhang, HUANG Guan-hua, LIU Zhuang-tian, LI Jian, 2011. An Approximate Analytical Solution for Two-Region Non-Darcian Flow Toward a Well in a Leaky Aquifer. Earth Science, 36(6): 1165-1172. doi: 10.3799/dqkx.2011.123

    越流含水层中抽水井附近非达西流两区模型近似解析解

    doi: 10.3799/dqkx.2011.123
    基金项目: 

    国家自然科学基金项目 41002082

    国家自然科学基金项目 50979106

    中央高校基本科研业务费专项资金资助项目 CUG110401

    高等学校博士学科点专项科研基金 20100145120004

    水利部公益性行业科研专项 200901083

    详细信息
      作者简介:

      文章(1982-), 男, 讲师, 博士, 主要从事地下水非达西流动的研究.E-mail: wenzhangcau@gmail.com

    • 中图分类号: P641.2

    An Approximate Analytical Solution for Two-Region Non-Darcian Flow Toward a Well in a Leaky Aquifer

    • 摘要: 构建了越流含水层中抽水井附近非达西流动的两区模型, 即距离抽水井较近的区域为非达西流, 而相对较远区域为达西流, 两区之间的临界半径可根据临界雷诺数确定.采用线性化近似方法和Laplace变换相结合分别得到了非达西流区域和达西流区域的水位降深在拉氏空间下的解析解, 应用数值Laplace逆变换—Stehfest方法得到其在实空间下的水位降深, 并与相应的全达西模型和全非达西模型进行了比较, 结果表明: 在抽水初期不同临界半径情况下非达西流区域的水位降深曲线互相重合, 并与全非达西模型所得到的结果相吻合; 在抽水后期的结果与全非达西流模型存在明显的差异.在抽水初期, 非达西渗透系数kD越大, 非达西流区域和达西流区域的水位降深越大; 在抽水后期, kD越大, 非达西流区域水位降深越小, 而kD的变化对达西流区域的水位降深影响较小.越流补给在非达西流情况下对水位降深的影响与达西流情况下的结果基本类似, 且只存在于抽水后期.考虑井储影响后, 不同kD和越流补给因子BD情况下抽水初期井中的水位降深在双对数坐标表现为直线且相互重合.

       

    • 图  1  越流含水层中抽水井附近两区模型示意

      Fig.  1.  The schematic diagram of the studied system

      图  2  非达西流区域水位降深与Wen et al.(2008a)全非达西流动模型比较

      Fig.  2.  Comparison of the solution in this study with Wen et al. (2008a)

      图  3  不同kD(a)和不同BD(b)非达西流区域水位降深规律

      Fig.  3.  Drawdowns in non-Darcian flow region for different kD values (a) and BD values (b)

      图  4  不同kD(a)和不同BD(b)达西流区域水位降深规律

      Fig.  4.  Drawdowns in Darcian flow region for different kD values (a) and BD values (b)

      图  5  考虑井储影响后不同kD(a)和不同BD(b)井中水位降深曲线

      Fig.  5.  Drawdowns inside the well for different kD values (a) and BD values (b) with wellbore storage

      表  1  无量纲变量

      Table  1.   Dimensionless variables used in this study

      ${r_D} = \frac{r}{m}$ ${r_{wD}} = \frac{{{r_w}}}{m}$ ${r_{cD}} = \frac{{{r_c}}}{m}$
      ${R_{cD}} = \frac{{{R_c}}}{m}$ ${q_D} = - \frac{{4\pi {m^2}}}{Q}q$ ${s_D} = \frac{{4\pi {k_2}m}}{Q}s$
      ${k_D} = \frac{{{k_1}}}{{{k_2}}}{\left[ {\frac{Q}{{4\pi {m^2}}}} \right]^{1 - n}}$ ${t_D} = \frac{{{k_2}t}}{{Sm}}$ ${B_D} = \frac{{B{k_2}}}{{{m^2}}}$
      下载: 导出CSV
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    出版历程
    • 收稿日期:  2011-05-08
    • 网络出版日期:  2021-11-10
    • 刊出日期:  2011-06-15

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