地下水污染源歷程重建-模擬退火演算法

Abstract

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，重建污染源釋放歷程將可協助釐清各可能責任團體之責任歸屬問題。本研究利用函數擬合技巧，結合模擬退火演算法(simulated annealing, SA)與地下水污染傳輸控制方程式之基本解，來推算地下水污染源釋放歷程。其重建步驟為:首先，將已知釋放地點之真實污染源釋放函數代入地下水污染傳輸控制方程式之基本解中，計算得到監測井的污染物濃度值，然後設定此值為採樣濃度。其次視該污染源的釋放函數為未知，並假設其由多項指數函數所組成；利用SA試誤產生未知函數中的參數值，得到試誤之污染源釋放函數。隨後，將試誤函數代入地下水污染傳輸控制方程式之基本解中，計算出監測井的模擬濃度值。根據模擬濃度與採樣濃度之最小誤差平方和，SA最後能搜尋到假設函數中之最佳參數值；若將此函數算出或畫出圖形曲線，則得以重建地下水污染源的釋放歷程。 為了模擬現地可能之情形，本研究分析的案例，從一維點源傳輸問題擴展至二維與三維非點源傳輸案例；另外考慮含水層為有限寬度與無限寬度兩種不同狀況。本研究除了調查監測井與污染源的距離對重建結果的影響，同時也針對幾項問題進行探討，分別是時間性數據與空間性數據在污染源釋放歷程重建上之應用、兩個獨立污染源釋放歷程之鑑定、地下水污染傳輸之延散效應與生物降解反應、及採樣濃度量測誤差與採樣濃度數據數目多寡對歷程重建結果之影響等。最後，整合所有結果的分析，提出一個重建污染源歷程的準則。

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 function-fitting technique and simulated annealing (SA) incorporated with a fundamental solution of the groundwater transport equation to recover the source release history of a groundwater contamination. The source release history is recovered via a two-step process. In the first step, the fundamental solution for a “true” contaminant release function at a known source location is used to create the sampling concentrations at monitoring wells. In the second step, the “true” source release function, an unknown to be recovered, is assumed as a combination of several exponential functions; the SA generates trial values for the parameters in the assumed release function. The simulated concentrations are then obtained from the fundamental solution with the trial source release function. While minimizing the sum of square errors between the simulated and sampling concentrations, SA can determine the optimal parameters of the assumed release function. The curve of source release history can be drawn based on the obtained parameters of the release function. In order to have better representation to the field conditions, the problems of two- and three-dimensional plume originated from a non-point source are taken into account. In addition, two different aquifer configurations are considered; one has infinite width while the other has finite width. Besides, topics of measurement errors, contaminant biodegradation, the degree of dispersion, the location of monitoring well, the number of sampling data, the use of temporal concentration data or spatial concentration data, and the existence of two contaminated sources are also studied. Finally, a guideline for the optimal sampling strategy to reconstruct the source release history is recommended.