地下水二維污染歷程重建 : 未來連續正規化法

Abstract

當一個污染源釋放污染物進入地下水中，經由傳流及延散作用，會造成地下水污染。當一個場址發現地下水有污染，且其已知污染源位置上曾更替過數個工廠或工廠的經營者時，污染源釋放歷程的重建，可以幫助我們得知地下水中，污染源釋放的濃度歷程，並可釐清各可能責任團體之責任歸屬問題。目前許多地下水污染源歷程重建的方法，只能求得由指數函數所代表的歷程，在重建激變性型態如三角形或階梯形的釋放歷程會產生顯著的誤差。 本研究利用未來連續正規化法(Future-sequential regularization method, FSRM)，針對一個地下水的污染場址作採樣分析，結合地下水污染傳輸控制方程式之基本解，可以重建污染釋放歷程。FSRM可將污染傳輸方程式，由病態的問題(ill-posed problem)轉換成小康構成問題(well-posed problem)，使分析結果滿足穩定狀態且有單一解。我們利用在一個監測井所量得的濃度時間分佈數據，逆推過去文獻提及的地下水二維污染案例；此外，也重建三角形及階梯形的釋放歷程案例。 為了模擬現地可能之情形，本研究分析的案例，除了時間性數據的二維面源傳輸案例，另外含水層可以為有限或無限寬度。本研究除了分析三角及階梯型態的污染源對重建結果的影響，同時也針對幾個問題進行探討，分別是非等間距時間的採樣數據、採樣濃度量測誤差、及其他方法重建歷程結果之比較等。

As a site is found to have groundwater contamination, the reconstruction of the source release history can provide helpful forensic information to identify the responsible parties at a known source location since the owner of the contaminated source changes several times. The objective of this study is to use a full-estimation technique and Future-sequential regularization method (FSRM) incorporated with a fundamental solution of the groundwater transport equation to recover the source release history of a groundwater contamination. This method can transform the plume release function from the ill-posed problem into a well-posed one with a solution satisfying the unique and stable conditions. A lectured two-dimensional (2-D) groundwater contamination case is used to assess the performance of the source identification. In addition, we used two different source release functions (namely the triangle function and the step function) to evaluate the effectiveness of FSRM in recovering the release history. The FSRM is capable of recovering a release history based on the concentration measurements sampled from a monitoring well. With an appropriate value of regularization parameter, FSRM is robust in recovering the optimal release history in terms of the triangle or step source release function. In order to have better representation to the field conditions, the problems of two dimensional plumes are considered to originate from an area source and the aquifer can be of finite or infinite width. Besides, this thesis also investigates the problems of observation data with non-uniform time intervals, data with measurement errors, and comparisons with the solutions obtained by other inverse methods.