層狀地質介質溶質傳輸之解析解

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田傑仁(Chieh-Jen Tien) 查詢紙本館藏

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應用地質研究所

論文名稱

層狀地質介質溶質傳輸之解析解
(Analytical solutions for solute transport in layered geological media)

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摘要(中)

汙染物在層狀介質的傳輸行為經常可以在自然環境或人造環境觀察到，例如汙染物經過層狀土壤、掩埋襯墊、人工障壁等，故汙染物在層狀介質的傳輸行為為重要議題。本研究推導一維層狀地質介質中移流-延散方程式之解析解，方程式考慮移流傳輸、延散作用、線性平衡吸附，以及溶質一階衰減反應等影響。解析解主要利用Laplace轉換消去時間微分項和廣義型積分轉換(generalized integral transform)消去空間微分項，使微分方程式轉換為代數方程式，再進行一系列逆轉換可求得時間域下之解。此解析解與有限差分等數值方法進行驗證工作，目前在模擬時間較大或兩層介質Pelect number相差較小情況下兩者濃度分布曲線可重合進行驗證，在模擬時間較小或兩層Pelect number相差較大情況下解析解與數值模式產生顯著誤差。本研究提出之解析方法可擴展至層狀介質非平衡吸附傳輸、層狀介質多物種傳輸之解析解。

摘要(英)

Contaminant transport in layered geological media is often observed, either in natural environments such as stratified soils, or in constructed environments such as landfill clay liner and barrier system. This study presents an analytical solution for one-dimensional advection-dispersion equation in layered geological media. The governing equations include terms accounting for advection, dispersion, linear equilibrium sorption, and first order decay processes. The analytical solution is derived by using the Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate. The analytical solutions are verified against the numerical solutions using a finite difference scheme. In the case of large time or the small difference of Pelect number between two layers, the result shows agreement between the analytical and numerical solution. Current and future developers of transport model may extend the ideas of solution method expounded to develop analytical models for problem of coupled nonequilibrium sorption or multi-species transport in layered geological media.

關鍵字(中)

★ 層狀介質
★ 移流-延散方程式
★ 解析解

關鍵字(英)

論文目次

目錄
摘要 i
Abstract ii
目錄 iii
圖目錄 v
表目錄 viii
符號說明 ixx
一、緒論 1
1-1 研究背景 1
1-2 研究目的 5
1-3 研究方法 6
1-4 論文架構 7
二、文獻回顧 9
三、層狀地質介質溶質傳輸解析解數學模式 14
3-1 基本假設與模式建立 14
3-2 控制方程式與邊界條件 18
3-3 層狀介質溶質傳輸解析解推導 20
四、結果與討論 37
4-1 特徵值問題探討 37
4-2 解析模式數值收斂測試 45
4-3 解析解模式比較 49
五、結論與建議 63
5-1 結論 63
5-2 建議 64
參考文獻 65
附錄一廣義型積分轉換分段討論部分 69
附錄二有限差分模式建立 77

參考文獻

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指導教授

陳瑞昇(Jui-Sheng Chen)

審核日期

2013-8-27

推文