有限長度圓形土柱實驗二維溶質傳輸之解析解

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陳寬哲(Kuan-jhe Chen) 查詢紙本館藏

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應用地質研究所

論文名稱

有限長度圓形土柱實驗二維溶質傳輸之解析解
(An analytical solution for two-dimensional radial transport in a finite soil)

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摘要(中)

二維徑向土柱實驗配合數學模式可推估縱向及側向延散係數，在現有的相關研究中，數學模式常假設土柱長度為無窮大，此假設較不符合實際情況。本研究發展在有限長土柱之二維圓柱座標系統移流－延散方程式之解析解，以描述圓柱形之二維溶質傳輸，分別利用finite Hankel轉換與通用積分轉換方法（GITT）求得解析解，所發展的解析解與Laplace轉換有限差分法（LTFD）進行驗證，驗證結果兩者十分吻合。因為執行積分轉換後的解析解包含finite Hankel與GITT逆轉換級數，當Peclet number較大與延散度比很小時，需要比較高的累加次數才能夠讓解收斂。和前人發展的解析解比較並對邊界條件的影響進行討論，Peclet number較小時若以無窮大邊界的數學模式進行推估可能會低估延散係數。發展的解析解進一步可應用於分析土柱實驗所得濃度穿透曲線，推估孔隙率、縱向與側向延散係數。

摘要(英)

Two-dimensional radial column experiment combine with mathematical models to estimate longitudinal and transverse dispersion coefficient. Existing research of mathematical models assumed infinite length of column, but this assumption is not conforming to the actual circumstances. In this research, we developed a analytical solution of the two-dimensional advection-dispersion equations in cylindrical coordinates with a finite soil column for describing solute transport in two-dimensional cylindrical geometry. This analytical solution is obtained in the use of finite Hankel transform and generalized integral transform technique (GITT). Development of analytical solution is verified with Laplace transform finite difference (LTFD). This analytical solution consists of two infinite series expansions after the finite Hankel and GITT inverse transforms. When Peclet number larger and the dispersion ratio is very small, it needs more the number of summed terms for solution convergence. We compared with the previous development of analytical solution, and discussed the effect of different boundary conditions. When the Peclet number are smaller, the concentration of infinite boundary will be lower. If the analytical solutions with infinite boundary condition are used to estimate the solute transport parameters, and therefore underestimate the dispersion coefficients. We further used to analyze the concentration breakthrough curve of column test and estimated porosity, longitudinal and transverse dispersion coefficients.

關鍵字(中)

★ 通用積分轉換
★ 土柱實驗
★ 延散係數
★ finite Hankel轉換

關鍵字(英)

★ general integral transform technique
★ finite Hankel transform
★ dispersion coefficient
★ column test

論文目次

摘要 I
Abstract II
目錄 III
符號說明 VIII
一、研究背景與目的 1
1-1前言 1
1-2文獻回顧 3
1-3研究目的 4
二、有限長度之二維圓柱座標移流－延散方程式求解 6
2-1二維圓柱座標移流－延散方程式與邊界設定 9
2-2數學模式求解 14
三、實驗設備與步驟 24
3-1二維徑向土柱實驗 24
3-2 砂樣準備 25
3-3 儀器設備 25
3-4 實驗步驟 28
四、結果與討論 29
4-1模式驗證 29
4-2參數敏感度分析 44
4-2-1延散度異相比敏感度分析 45
4-2-2 Peclet number敏感度分析 45
4-3邊界條件效應 49
4-4參數推估 51
五、結論與建議 53
參考文獻 55
附錄一　求解正規化特徵函數與特徵值 58
附錄二　無限長度之解析解 59

參考文獻

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指導教授

陳瑞昇(Jui-sheng Chen)

審核日期

2010-7-29

推文