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題名 | 多層半拘限含水層系統有限半徑抽水井抽水洩降解析解=Analytical Solution of Drawdown in a Multiple Semi-Confined Aquifer System Due to Pumping from a Finite-Diameter Pumping Well |
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作 者 | 徐年盛; | 書刊名 | 農業工程學報 |
卷期 | 43:1 1997.03[民86.03] |
頁次 | 頁49-60 |
分類號 | 443.67 |
關鍵詞 | 多層含水層系統; 有效井徑; 洩降; 解析解; 敏感度分析; Multiple-layered aquifer system; Effective well diameter; Drawdown; Analytical solution; Sensitivity analysis; |
語文 | 中文(Chinese) |
中文摘要 | 本文旨在求得自一有限半徑抽水井,由一多層半拘限含水層系統抽水所造成洩降 及水位變化之解析解,並進行敏感度分析以探討抽水時各含水層參數對各層水位變化之影響 程度。 在建立解析解時,本文首先解出單井單層抽水之穩態解,然後根據疊加原理求得單井多層抽 水情況下之穩態解。由於非穩態下各含水層之出水量為時變狀態,因此本文引進脈衝反應函 數及摺合積分之方法,分別求得非穩態固定抽水總量下之單層與多層抽水時之解析解。在進 行模式中參數之敏感度分析,本文採用影響係數法以計算水位對參數之偏導數,再利用變異 數矩陣判斷各參數對水位變化之敏感度。 最後本文以數值算例來說明解析解之特性,以及井半徑大小對非穩態下水位變化之影響。結 果顯示當井半徑增加時,觀測點之洩降趨於穩定之時間亦相對增長。此算例亦應用於參數之 敏感度分析上,結果顯示在單井多層抽水情況下,各參數均有相近之敏感程度,因此可做為 決定各含水層參數之抽水試驗設計;此結果可用以替代成本較高之多井分別貫穿不同水層之 抽水試驗。 |
英文摘要 | The purpose of this paper is to develop an analytical solution of drawdown in a multiple semiconfined aquifer system due to pumping from a finite-diameter well. Also performed in the study is the sensitivity analysis of the parmeters of each layer with respect to drawdown of all aquifers. The parameters considered are the hydraulics conductivity and storage coefficient of each aquifer and the leakance of each aquitard. In the development of the analytical solution, the steady state solution for pumping from any single layer is derived first. The steady state solution for pumping from multiple layers is then obtained by using the principle of superposition. The solution of steady flow is then used as the initial conditions for developing the solution for unsteady flow cases due to constant pumping. To obtain the unsteady solution for time-varying pumping rate, a pulse response function is developed first and the discrete convolution is then performed. In the sensitivity analysis, sensitivity coeffcient of parameters with respect to drawdown are computed using the influence coefficient method. The covariance matrix is then computed and is used to investigate the relative sensitivity of the parameters with respect to drawdown. A numerical example is provided to depict the characteristics of the analytical solution and the effect of well diameter on the unsteady state solution. Results show that when the well diameter gets larger, it takes more time for the drawdown to reach steady state at a given location. Sensitivity analysis is also performed by using the same example. Results show that, in order to have an equalweighted sensitivity of the parameters with respect to drawdown, water should be pumped from all layers by a single well that penetrates through all layers. An expensive alternative is also effective if water is pumped by multiple wells with each well penetrates an individual layer. |
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