抽水試驗於滲漏含水層之洩降模式:考慮延遲效應

The analytical model for drawdown due to constant-rate pumping test in a leaky aquifer: considering lagging effect

林曄辰(Ye-Chen Lin)

指導教授 ： 葉弘德

國立交通大學/工學院/環境工程系所/博士(2018年)

摘要

本論文提出了一個廣義達西定律，其中考慮了水通量和降水梯度中的互相延遲效應，分別反應慣性力與不連續孔隙造成的延遲影響，並建立了用於描述洩漏承壓含水層中定流量抽水引起的水位洩降之數學模式。本模型具有類似於雙孔隙度模型的數學表達式。通過拉普拉斯轉換的技巧，推導出具有井內儲水效應的拉普拉斯域解。利用拉普拉斯轉換和韋伯轉換建立忽略井筒儲存和井半徑情況下時間域的解。基於所推導出的解進行的敏感度分析表明，洩降對導水係數和儲水係數的變化非常敏感。另外，延遲效應對於洩降的影響時間與其延遲參數的值顯著相關。本論文也利用本解用於分析從美國南達科他州裂隙含水層進行的定流量抽水試驗中獲得的洩降資料。結果表明，考慮延遲效應後，模式預測的洩降值非常吻合現場抽水試驗的洩降數據，尤其是在早期抽水時段。另外，上述結果得到的延遲效應值似乎展示出尺度效應。也就是說，延遲效應與麥迪遜含水層的觀測距離呈正相關。

關鍵字

達西定律 ； 延遲效應 ； 滲漏含水層 ； 抽水試驗 ； 尺度效應 ； 雙孔隙模式

並列摘要

This study proposes a generalized Darcy’s law with considering phase lags in both the water flux and drawdown gradient to develop a lagging flow model for describing drawdown induced by constant-rate pumping (CRP) in a leaky confined aquifer. The present model has a mathematical formulation similar to the dual-porosity model. The Laplace-domain solution of the model with the effect of wellbore storage is derived by the Laplace transform method. The time-domain solution for the case of neglecting the wellbore storage and well radius is developed by the use of Laplace transform and Weber transform. The results of sensitivity analysis based on the solution indicate that the drawdown is very sensitive to the change in each of the transmissivity and storativity. Also, a study for the lagging effect on the drawdown indicates that its influence is significant associated with the lag times. The present solution is also employed to analyze a data set taken from a CRP test conducted in a fractured aquifer in South Dakota, USA. The results show the prediction of this new solution with considering the phase lags has very good fit to the field data, especially at early pumping time. In addition, the phase lags seem to have a scale effect as indicated in the results. In other words, the lagging behavior is positively correlated with the observed distance in the Madison aquifer.

並列關鍵字

Darcy’s law ； lagging behavior ； leaky aquifer ； pumping test ； scale effect ； dual porosity model

參考文獻

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