徑向發散流場移流-延散方程之全解析解

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姓名

陳緯愷(Wei-Kai Chen) 查詢紙本館藏

畢業系所

應用地質研究所

論文名稱

徑向發散流場移流-延散方程之全解析解

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至系統瀏覽論文 (2025-7-20以後開放)

摘要(中)

徑向流場中溶質傳輸的解析解在抽注/發散/收斂流示踪試驗中的傳輸研究、通過抽水整治含水層以及含水層儲存回抽中具有多種實際應用。然而徑向移流-延散傳輸的解析解已被證明難以開發。過去研究提出的大多數徑向移流-延散傳輸的解通常為半解析解，最終濃度值是借助數值Laplace逆轉換獲得。本研究採用了較新穎的方式來求解徑向發散流場移流-延散傳輸問題。首先執行關於時間變數的Laplace轉換和關於空間變數的廣義積分轉換技術，以將暫態控制偏微分方程轉換為代數方程。使用簡單的代數操作來求解代數方程，從而在轉換域中容易地求得解。通過Laplace逆轉換和相應的廣義積分逆轉換連續應用，最終求得原始域中的解。使用發散流示踪劑試驗證明了所提出的方法的穩定性，該方法用於推導徑向發散流場移流-延散傳輸問題的全解析解。將本研究的解析解模式計算結果與Laplace轉換有限差分法（LTFD）進行比較，以驗證解的正確性。通過LTFD驗證了所開發的解析解，結果表明，本研究的全解析解與LTFD非常吻合。

摘要(英)

An analytical solution for solute transport in a radial flow field has a variety of practical applications in the study of the transport in push-pull/divergent/convergent flow tracer tests, aquifer remediation by pumping and aquifer storage and recovery. However, an analytical solution for radial advective-dispersive transport has been proven very difficult to develop. Most of the solutions for radial advective-dispersive transport presented in the past have generally been solved semi-analytically with the final concentration values being obtained with the help of a numerical Laplace inversion. This study uses a novel solution strategy for analytically solving the radial divergent flow field advective-dispersive transport problem. A Laplace transform with respect to the time variable and a generalized integral transform technique with respect to the spatial variable are first performed to convert the transient governing partial differential equations into an algebraic equation. Subsequently, the algebraic equation is solved using simple algebraic manipulations, easily yielding the solution in the transformed domain. The solution in the original domain is ultimately obtained by successive applications of the Laplace and corresponding generalized integral transform inversions. A divergent flow tracer test is used to demonstrate the robustness of the proposed method for deriving an exact analytical solution to the radial advective-dispersive transport problem. The computational results of the analytical solution model of this study will be compared with the use of the modified Laplace transform finite difference method (LTFD) to verify the correctness of the solution. The developed analytical solution is verified against a LTFD. The results show perfect agreement between this study exact analytical solution and the LTFD.

關鍵字(中)

★ 全解析解
★ 徑向移流-延散傳輸
★ Laplace轉換
★ 發散示蹤劑試驗
★ 廣義型積分轉換

關鍵字(英)

★ Exact analytical solution
★ Radial advection-dispersion transport
★ Divergent flow tracer test
★ Laplace transform
★ Generalized integral transform

論文目次

摘要 i
Abstract ii
致謝 iii
目錄 iv
圖目錄 v
表目錄 vi
符號說明 vii
一、前言 1
1-1 研究動機 1
1-2 文獻回顧 3
1-3 研究目的 6
二、數學模式建立與推導 7
2-1 基本假設與數學模式建立 7
2-1-1 數學模式發展流程 10
2-1-2 數學模式建立 11
2-2 解析解推導 13
三、結果與討論 21
3-1 模式驗證 21
3-2敏感性分析 43
3-3 正弦週期函數 53
四、結論與建議 56
4-1 結論 56
4-2建議 57
文獻參考 58
附錄 61

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指導教授

陳瑞昇(Jui-Sheng Chen)

審核日期

2023-7-24

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