博碩士論文 103624006 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:13 、訪客IP:3.236.231.61
姓名 謝秉叡(Bing-Rui Xie)  查詢紙本館藏   畢業系所 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)
相關論文
★ 單井垂直循環流場追蹤劑試驗數學模式發展★ 斷層對抽水試驗洩降反應之影響
★ 漸近型式尺度延散度之一維移流-延散方程式之Laplace轉換級數解★ 延散效應對水岩交互作用反應波前的影響
★ 異向垂直循環流場溶質傳輸分析★ 溶解反應對碳酸岩孔隙率與水力傳導係數之影響
★ 濁水溪沖積扇地下水硝酸鹽氮污染潛勢評估與預測模式建立★ 異向含水層部分貫穿井溶質傳輸分析
★ 溶解與沈澱反應對碳酸鈣礦石填充床孔隙率與水力傳導係數變化之影響★ 有限長度圓形土柱實驗二維溶質傳輸之解析解
★ 第三類注入邊界條件二維圓柱座標移流-延散方程式解析解發展★ 側向延散對雙井循環流場追蹤劑試驗溶質傳輸的影響
★ 關渡平原地下水流動模擬★ 應用類神經網路模式推估二維徑向收斂流場追蹤劑試驗縱向及側向延散度
★ 關渡濕地沉積物中砷之地化循環與分布★ 結合水質變異與水流模擬模式評估屏東平原地下水適合飲用之區域
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   至系統瀏覽論文 (2021-8-31以後開放)
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 [1] T. Ptak, M. Piepenbrink, E. Martac, “Tracer tests for
the investigation of heterogeneous porous media and
stochastic modelling of flow and transport-a review
of some recent developments”, J. Hydrol., 294, 122-
163, 2004.
[2] P. A. Hsieh, “A new formula for the analytical
solution of the radial dispersion problem”, Water
Resour. Res., 22(11), 1597-1605, 1986.
[3] A. J. Valocchi, “Effect of radial flow on deviations
from local equilibrium during sorbing solute
transport through homogeneous soils”, Water Resour.
Res., 22(12), 1693–1701, 1986.
[4] C. S. Chen, “Analytical solution for radial
dispersion problem with Cauchy boundary at injection
well”, Water Resour. Res. 23(7), 1217–1224, 1987.
[5] A. F. Moench, “Convergent radial dispersion: a
Laplace transform solution for aquifer tracer
testing”, Water Resour. Res., 25(3), 439–447, 1989.
[6] A. F. Moench, “Convergent radial dispersion: a note
on evaluation of the Laplace transform solution”,
Water Resour. Res., 27(12), 3261–3264, 1991.
[7] A. F. Moench, “Convergent radial dispersion in a
double-porosity aquifer with fracture skin:
analytical solution and application to a field
experiment in fractured chalk”, Water Resour. Res.,
31(8), 1823–1835, 1995.
[8] K. S. Novakowski, “The analysis of tracer experiments
conducted in divergent radial flow fields”, Water
Resour. Res., 28(12), 3215-3225, 1992.
[9] J. S. Chen, C. W. Liu, C. S. Chen, H. D. Yeh, “A
Laplace transform solution for tracer tests in a
radially convergent flow field with upstream
dispersion”, J. Hydrol., 183, 263–275, 1996.
[10] D. Tomasko, G. P. Williams, K. Smith, “An analytical
model for simulating step-function injection in a
radial geometry”, Math. Geol., 33(2), 155–165, 2001.
[11] J. S. Chen, C. W. Liu, C. M. Liao, “A novel
analytical power series solution for solute
transport in a radially convergent flow field”, J.
Hydrol., 266, 120–138, 2002.
[12] J. S. Chen, C. W. Liu, H. T. Hsu, C. M. Liao, “A
Laplace transform power series solution for solute
transport in a convergent flow field with scale-
dependent dispersion”, Water Resour. Res., 39(8):
1229, 2003.
[13] J. S. Chen, C. S. Chen, C. Y. Chen, “Analysis of
solute transport in a radially divergent flow tracer
test with scale-dependent dispersion”, Hydrol.
Processes, 21, 2526-2536, 2007.
[14] J. S. Chen, “Analytical model for fully three-
dimensional radial dispersion in a finite-thickness
aquifer”, Hydrol. Processes, 24, 934–945, 2010.
[15] E. J. M. Veling, “Radial transport in a porous
medium with Dirichlet, Neumann and Robin-type
inhomogeneous boundary values and general initial
data: analytical solution and evaluation”, J. Eng.
Math., 75, 173-189, 2012.
[16] Q. Wang and H. Zhan, “Radial reactive solute
transport in an aquifer–aquitard system”, Adv. Water
Resour. 61, 51–61, 2013.
[17] J. Q. Huang, “Analytical solutions for efficient
interpretation of single-well push-pull tracer
tests”, Water Resour. Res., 46, 2010.
[18] C. S. Chen and G. D. Woodside “Analytical solution
for aquifer decontamination by pumping”, Water
Resour. Res., 24(8), 1329–1338, 1988.
[19] M. N. Goltz and M. E. Oxley, “Analytical modeling of
aquifer decontamination by pumping when transport is
affected by rate-limited sorption”, Water Resour.
Res., 27(4), 547–556, 1991.
[20] C. F. Harvey, R. Haggerty, S. M. Gorelick, “Aquifer
remediation: a method for estimating mass transfer
rate coefficients and evaluation of pulsed pumping”,
Water Resour. Res., 30(7), 1979–1991, 1994.
[21] C. Lu, P. Du, Y. Chen, J. Luo, “Recovery efficiency
of aquifer storage and recovery (ASR) with mass
transfer limitation”, Water Resour. Res., 47, 2011.
[22] D. H. Tang and D. K. Babu, “Analytical solution of a
velocity dependent dispersion problem”, Water
Resour. Res., 15(6), 1471–1478, 1979.
[23] A. F. Moench and A. Ogata, “A numerical inversion of
the Laplace transform solution to radial dispersion
in a porous medium”, Water Resour. Res., 17(1), 250–
252, 1981.
[24] C. S. Chen, “Analytical and approximate solutions to
radial dispersion from an injection well to a
geological unit with simultaneous diffusion into
adjacent strata”, Water Resour. Res., 21(8), 1069–
1076, 1985.
[25] J. S. Pérez Guerrero and T. H. Skaggs, “Analytical
solution for one-dimensional advection-dispersion
transport equation with distance-dependent
coefficients”, J. Hydrol., 390, 57–65, 2010.
指導教授 陳瑞昇(Jui-Sheng Chen) 審核日期 2016-8-30
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明