結合禁忌演算法與模擬退火演算法推求三維空間地下水污染源

Abstract

本研究提出一個方法，融合禁忌演算法與模擬退火演算法的優點，並結合美國地質調查局所研發之三維地下水流與傳輸模擬模式MODFLOW-GWT，做為污染源鑑定的工具，針對在監測井測得的污染分佈，推求地下水污染源的位置、釋放時間、及釋放濃度。在本研究中，先設定在自由含水層中，一個污染源位置為已知（以下稱實際污染源）且某污染物連續釋放三年，利用MODFLOW-GWT模式模擬下游的濃度分布。在模擬時，將此含水層以等厚度分為四層，可算得在已知位置的監測井中，於不同深度時的實際濃度值。其後，在實際污染源周圍，選擇一個區域列為可疑的污染源區域，並將此區域內格網的節點位置，皆視為候選污染源的釋放點，並設定各監測井的深度，要逆推的未知數，為各候選污染源三維空間的位置、釋放濃度、及釋放時間。 在進行污染源推求時，利用禁忌演算法及模擬退火演算法不同的演算特性，分別產生一系列污染源位置、污染物釋放時間、及釋放濃度的試誤解，利用禁忌演算法選取候選污染源位置的試誤解，並以模擬退火演算法產生釋放濃度及時間的可能解，隨後用MODFLOW-GWT進行污染物的傳輸模擬，得到在各監測井的模擬濃度值。當所得結果滿足所設定的目標函數時，亦即模擬濃度與實際濃度差值的平方和最小時，即表示求得污染源的位置與所釋放污染物的濃度和釋放時間。由數值模擬的結果顯示，即使觀測濃度包含誤差，本研究所發展的方法依然能得到精確的推估結果。此外，本研究由數值模擬結果，提出最佳的監測井個數與有效鑑定污染源的準則。

An approach, combining the tabu search, simulated annealing, and a three-dimensional groundwater flow and solute transport model (MODFLOW-GWT) is developed to estimate the source information including source location, release concentration, and length of release period. At the development stage of the proposed approach, the measured concentrations at sampling points are simulated by MODFLOW-GWT with the assumed release concentration at known source location (hereinafter referred to as real source). In the source information estimation process, a suspicious source area covering the real source is delimited at beginning. Then the source location is chosen by tabu search from the suspicious source area and a series of trial solutions for release concentration and release period are generated by simulated annealing. The MODFLOW-GWT is employed with those generated source information to simulate the plume concentrations at sampling points. The source estimation process is terminated when the sum of square error between simulated concentration and measured concentration is minimized. The proposed approach gives good estimate results even the measured concentrations contain measurement errors. In addition, a guideline regarding to the optimal number of sampling points and the condition for effectively estimating source information is also concluded in this thesis.