The Extended Thiem's solution: Including the impact of heterogeneity
The Extended Thiem's solution: Including the impact of heterogeneity
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扩展蒂姆的解决方案：包括异质性的影响
DOI：
10.1029/2012wr011852
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发表时间：
2012
影响因子：
5.4
通讯作者：
S. Attinger
中科院分区：
文献类型：
--
作者：
A. Zech;C. Schneider;S. Attinger
本文提出了一个有效描述非均质各向异性多孔介质三维稳态抽水试验平均降深的水头公式。通过将水力传导系数K（x→）建模为空间随机函数并使用粗粒化方法，我们成功地导出了封闭形式的解hefw（r），我们将其理解为Thiem公式对非均质介质的扩展。解hefw（r）不仅依赖于径向距离r，而且还考虑了K（x→）的统计量，即几何平均KG、方差σ2、水平相关长度λ和各向异性比e。我们对hefw（r）的参数进行了敏感性分析，并实现了逆估计策略。利用数值抽水试验，我们证明了hefw（r）在解释水位降深数据上的适用性。这将针对两者、整体测试以及单次抽水测试进行。利用逆估计方法，我们发现估计的参数与初始值，特别是水平相关长度的良好协议。
In this study we present a formula for the hydraulic head describing the mean drawdown of a three dimensional steady state pumping test in heterogeneous anisotropic porous media effectively. By modeling the hydraulic conductivity K(x→) as spatial random function and using the upscaling method Coarse Graining we succeed in deriving a closed form solution hefw (r) which we understand as an extension of Thiem's formula to heterogeneous media. The solution hefw (r) does not only depend on the radial distance r but accounts also for the statistics of K(x→) , namely geometric mean KG, variance σ2, horizontal correlation length ℓ and anisotropy ratio e. We perform a sensitivity analysis on the parameters of hefw (r) and implement an inverse estimation strategy. Using numerical pumping tests we show the applicability of hefw (r) on the interpretation of drawdown data. This will be done for both, an ensemble of as well as for single pumping tests. Making use of the inverse estimation method we find excellent agreement of estimated parameters with initial values, in particular for the horizontal correlation length.