收斂流場示蹤劑試驗之精確解析解

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姓名

謝秉叡(Bing-Rui Xie) 查詢紙本館藏

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應用地質研究所

論文名稱

收斂流場示蹤劑試驗之精確解析解
(An exact analytical solution for a convergent flow tracer test)

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摘要(中)

移流-延散方程式為用來描述受壓含水層中污染物的傳輸情形，此方程
式需要輸入關鍵的延散度參數，而示蹤劑試驗是決定此參數最有效的方法。進行示蹤劑試驗選用強制梯度系統，相較於自然梯度，強制梯度比較容易控制流場條件與減少實驗時間，強制梯度收斂流場示蹤劑試驗，其優點能回收大部分示蹤劑，減少對環境衝擊。解析解用來描述示蹤劑試驗是非常有效的，但目前可用的解多為半解析(semi-analytical )，需以Laplace 數值逆轉換方式取得原區域濃度值，目前仍無精確解析解。因此本研究以新的方法求解移流-延散方程式，推導過程使用Laplace 轉換以及廣義型積分轉換(generalized integral transform technique, GITT)，消去時間微分項與空間微分項，將偏微分方程轉換成代數方程式，再經由一系列逆轉換求得原時間域之解。將本研究發展的精確解析解與前人發展的半解析進行驗證，結果顯示非常吻合。可以將此方法拓展到其他徑向傳輸問題。

摘要(英)

The advection–dispersion equation (ADE) is generally used to describe the movement of the contaminants in the subsurface environment. Dispersivity is a key input parameter in the ADE. Tracer test is an efficient method for determining dispersivity. Forced gradient tracer tests are preferred over natural gradient experiments because that the flow conditions are well controlled and the duration of the test is reduced. The advantage of the convergent flow tracer tests is the
possibility of achieving high tracer mass recovery. Analytical solutions are useful
for interpreting the results of the field tracer test. Currently available solutions are
mostly limited to semi-analytical solutions. This study develops an explicit analytical solutions for solute transport in a convergent flow tracer test. The solution is achieved by successive applications of integral transform. The robustness and accuracy of the developed solution is proved by excellent agreement between our solution and previous solution.

關鍵字(中)

★ 示蹤劑試驗
★ 移流-延散方程式
★ 解析解
★ 廣義型積分轉換

關鍵字(英)

★ tracer test
★ advection-dispersion equation
★ analytical solution
★ generalized integral transform technique

論文目次

目錄
摘要 i
Abstract ii
目錄 iii
圖目錄 v
表目錄 vi
一、前言 1
1-1 研究背景 1
1-2 文獻回顧 2
1-2-1 地下水示蹤劑試驗 2
1-2-2 徑向流場解析解 4
1-3. 研究目的 9
二、數學模式建立與推導 10
2-1 基本假設與數學模式建立 10
2-1-1 數學模式發展流程 14
2-1-2 數學模式建立 15
2-2. 解析解推導 17
三、結果與討論 26
3-1. 特徵值問題探討 26
3-2. Gaussian quadrature探討 31
3-3. 數值收斂性測試 35
3-4. 模式比較驗證 39
四、結論與建議 42
4-1. 結論 42
4-2. 建議 43
參考文獻 44
附錄 46

參考文獻

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指導教授

陳瑞昇(Jui-Sheng Chen)

審核日期

2016-8-30

推文