於自由含水層抽水引致河川滲漏量的通解

Abstract

本研究考慮未來可能發生地表水匱乏問題，提出利用在河畔抽取水地下 水，引致河川滲漏而補注含水層，使河川水間接變成供水的水源。針對河畔抽取 地下水問題，本計畫將先建立一個數學模式，以描述前述情景的地下水位的變 化，並推導出相關的水位和河川滲漏量(Stream depletion rate, SDR)的解析解。針 對在河畔抽取水地下水問題，我們曾在2010 及2011 年，分別探討傾斜井在受壓 含水層和水平井在自由含水層中抽水，引致鄰近河川滲漏補注水層的問題，並導 出SDR 的解析解。 本兩年期的研究計畫，著重於探討河床低滲透性對SDR 的影響和發展出新 的閉合解。第一年考慮在鄰近河川的輻射井抽水，而該河川的河床具低滲透性， 擬先發展一個描述地下水位與SDR 的解析解，藉由發展出來的解析解，探討低 滲透性河床對SDR 的影響，並估算抽水引致的河川滲漏量。此解析解不但可評 估一個場址是否適合設置抽水井，而且可用來當設計抽水井系統的工具。第二年 將參考並整合過去的研究成果，考慮抽水井為垂直井、水平井、或輻射井情況， 發展出一個在受壓水層或自由水層抽水所引致水位變化與SDR 的閉合解。此閉 合解將有計算簡單與精度高的優點。此外，我們將說明過去多數的SDR 解析解， 為此新閉合解的特例。

This proposal aims at developing a general mathematical model for describing drawdown distributions due to pumping in a confined or unconfined aquifer which has a stream nearby. The solution of the model can be used to derive the formula of SDR. We had developed two analytical solutions for describing the behaviors of SDR in the years of 2010 and 2011, one for a slanted well in a confined and the other for a horizontal well in an unconfined aquifer, respectively. In this proposal, we will concentrate the effect of low permeable streambed on SDR and develop a closed-form solution for the model. The proposal is basically a two-year project. In the first year, we will derive an analytical solution for describing SDR induced by a radial well in an unconfined aquifer with a low permeable streambed. The effect of the low permeability of streambed on SDR will be investigated through the use of the solution. The solution can be used to estimate the infiltration rate from the nearby stream and assess whether a site is suitable for installing a pumping well. In the second year, we will develop a closed-form solution for three different well types (i.e., vertical well, horizontal well, and radial well) in a confined or unconfined aquifer. This new closed-form solution will have the merits of easy computing and good accuracy. In addition, some of the existing SDR solutions can be shown as the special cases of the present solution.