徑向雙層受限含水層之定流量試驗洩降閉合解

Abstract

本研究考慮井半徑與井膚層效應之情況下，求受限含水層中徑向雙層介質之定流量抽水試驗水位洩降閉合解。推導過程中經由拉普拉斯轉換求得拉普拉斯域的洩降解，而後應用Bromwich積分方法求得時間域的洩降閉合解。在不考慮井半徑影響之情況下，研究結果可簡化為Butler(1993)的拉普拉斯域解。在求時間域的洩降閉合解值的過程中，本研究應用Bisection尋根方法、Gaussian quadrature積分方法及Shanks加速收斂方法，並將計算值與拉普拉斯域洩降解經由修正Crump方法計算值比較，結果頗為一致。研究結果也顯示此一閉合解可有效反應在受限含水層中雙層介質洩降在時間、空間上的變化；同時也說明井膚層型態、膚層厚度及井半徑對水位洩降的影響情況。

A mathematical model is presented for describing the groundwater flow in a radial two-layer confined aquifer system with a constant-flux pumping well that has a wellbore skin and finite well radius. The Laplace-domain solution for the model is first derived by the Laplace transforms; and the time-domain solution in terms of the aquifer drawdown is then obtained form the Laplace inversion using the Bromwich integral method. When neglecting the well radius, our Laplace-domain solution is shown to reduce to a Laplace-domain solution given by Butler (1988). A unified numerical approach including a root search approach, the Gaussian quadrature, and the Shanks method is employed for evaluating this time-domain solution. The evaluated results of the solution agree well with those of the Laplace-domain solution estimated by the modified Crump algorithm. This new solution can be used either to predict the spatial and temporal drawdown distributions in both the skin and formation zones or to investigate the effects of the skin type, skin thickness and well radius on the drawdown distribution.