雙孔隙率自由含水層定流量抽水之三維半解析解

Abstract

本研究發展一個三維地下水數學模式，以描述雙孔隙率非受壓含水層受抽水影響的水力水頭分佈。考慮水層水平方向的四個邊界皆為有限寬，且皆設定為第三類邊界條件。於垂直方向，水層上邊界為自由液面，下邊界為不透水層。應用拉普拉斯轉換和雙重積分轉換，可求得模式的半解析解，透過Stehfest method數值逆轉，可得到時間域的結果。若水層上邊界改為不透水邊界所求得的時間域的洩降分佈，在相同水文地質條件下，會與二維雙孔隙率受壓含水層模式模擬的結果吻合。本文所發展的半解析模式，可探討垂直流與比出水對於雙孔隙率含水層洩降分佈的影響，以及單孔隙率和雙孔隙率之間的差異。由敏感度分析可以探討雙孔隙率水層在非受壓含水層內的洩降變化，會出現兩個延遲現象的原因，一個是受到雙介質補注的影響，而另一個則是受到自由液面的影響。根據Green et al. (1999) 提供的數據驗證，本研究可提供做為雙孔隙率有限非受壓含水層之地下水預測洩降變動之參考。

This study develops a three-dimensional mathematical model for evaluating the drawdown distribution in a double-porosity unconfined aquifer due to pumping at a fully penetrating well. The aquifer is of finite extent in the horizontal direction and with the Robin condition at the outer boundary. The upper boundary of the aquifer is a water table with a linearized free-surface equation, whereas the lower boundary is impervious considered a no-flow condition. The semi-analytical solutions of the proposed model can be obtained using the methods of Laplace transform and double-integral transform. The time domain results can be obtained using the Stehfest method. The derived semi-analytical solutions are used in evaluating the effects of the vertical flow and specific yield on the temporal drawdowns. Furthermore, a sensitivity analysis was performed and the results indicated that the double-porosity unconfined aquifer exhibits two flat periods in the temporal drawdown curves. One is caused by the replenishment from the matrix storage, and the other is caused by the effect of the free surface. Compared the results with Green et al. (1999), the model proposed in this study can be used in predicting the drawdown changes in the double-porosity aquifer.