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研究生:蘇威名
研究生(外文):Wei-Ming Su
論文名稱:利用孔頸系集模型推估濕潤相流體特徵曲線掃瞄迴圈之研究
論文名稱(外文):Deriving Wetting Phase Fluid Hydraulic Conductivity Scanning Loops Using Unit-Pore-Throat Ensemble Model Framework
指導教授:李天浩李天浩引用關係
指導教授(外文):Tim-Hau Li
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:土木工程學研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:中文
論文頁數:123
中文關鍵詞:特徵曲線孔頸單元掃瞄迴圈孔頸系集模型
外文關鍵詞:scanning looppore-throat unitunit-pore-throat emsemble model
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繼鄭安孺(2004)、馮智勇(2006)等由土壤水-空氣毛細壓力與飽合度關係掃描曲線,透過孔頸單元系集模型,推估水與微溶性非水相液體(Non-Aqueous Phase Liquid, NAPL)在相同土壤中的毛細壓力與飽合度關係掃描曲線,以及毛細壓力與水的傳導係數關係曲線之研究方向。本研究的目標,除了增加孔頸單元組數,以達到「系集」目標外,另外,從模擬案例中找尋孔頸單元毛細壓力和水力傳導係數的簡化規則,以期能更有效率的達到推估目標。

研究方法是以鄭安孺(2004)利用實驗真實土壤保水曲線,反演導出水力等價的孔頸單元系集模型,使用Surface Evolver軟體在不同毛細壓力下,導出在每個孔頸單元中水-NAPL的界面位置和兩液相飽和度;再以計算流體動力學軟體CFDRC計算孔頸單元的相對傳導度;最後,統計整合所有孔頸單元的模擬結果,估計該土壤的水-NAPL特徵曲線( Curve)。

除了以上主要目標外,本研究在模擬流程中解決以下三項問題:
1. 為了節省計算資源、保留孔單元計算結果,未來針對不同的土壤可以結合不同的管長因子,透過測試決定孔單元合適的基本管長,並且證實基本管長孔單元和管單元水力傳導數的組合,和完整管長孔單元計算結果一致。
2. 透過比較不同孔頸單元相對水力傳導係數的模擬結果,找出能簡化代表各孔頸單元在臨界毛細壓力時,相對水力傳導係數和管徑尺寸關係的規則。並利用此規則內插推估其他尺寸,未實際計算的孔頸單元相對水力傳導係數。
3. 利用上項規則,可以減少計算需求,以較有效率的方式,增加孔頸單元分佈樣本,改善系集模型因為有限孔頸單元,造成 關係曲線在某些地方曲折較大問題,得到較細緻化的曲線。
Abstract

Following the research of Jheng(2004)and Fong(2006), based on Unit-Pore-Throat Ensemble Model (UPTEM), using the water-air soil retention curve( Curve), to estimate the relationship of “capillary pressure-saturation”( ) and “capillary pressure-permeability”( ) caused by water and Non-Aqueous Phase Liquid(NAPL) in the same soil. One objective of this research is reaching whole ensemble curve by increasing the number of UPT. The other objective is estimating curve more efficiently by finding a simple rule to get the relationship of capillary pressure and hydraulic conductivity.

Main method is like Jheng(2004) establishing a hydraulic equivalent unit-pore-throat ensemble model by using experimental retention curve. Using the software - Surface Evolver to find water-NAPL interface and saturation of all pore-throat units in different capillary pressure. And then calculate the hydraulic conductance of pore-throat unit by hydraulic kinetics calculating software - CFDRC. At last, integrate the simulating results of all pore-throat units by statistics and estimate water-NAPL Curve of the soil sample.

There are three problems solved in this research with the above-mentioned procedure:
1. In order to save time, keep the calculating results and combine different length factor in different soil samples, decide the unit length factor by testing. The effect of hydraulic conductance when length factor changes is provided that the result and relative conductance value calculated from original pore-throat unit are the same.
2. A simple rule to get the relationship between hydraulic conductance and throat size in different critical capillary pressure is found out by comparing the simulation results of different pore-throat units. So the hydraulic conductance of new inserted pore-throat units can be calculated by using the rule.
3. By using the simple rule, more hydraulic conductance can be calculated more easily and more efficiently. So the curve can be refined by inserting more pore-throat units.
目錄

謝 誌.................................................................................................................................I
摘 要................................................................................................................................II
Abstract...............................................................................................................................III
目 錄................................................................................................................................V
表目錄...............................................................................................................................VII
圖目錄.............................................................................................................................. VII
第1章 緒論....................................................................................................................1-1
1.1 研究動機與問題概述.......................................................................................1-1
1.2 相關研究回顧....................................................................................................1-3
1.2.1 Brooks & Corey模型............................................................................1-3
1.2.2 van Genuchten模型...............................................................................1-4
1.2.3 比例化技術...........................................................................................1-5
1.2.4 孔頸網絡模型......................................................................................1-6
1.3 研究目標............................................................................................................1-9
1.4 內容概述............................................................................................................1-9
第2章 模型理論............................................................................................................2-1
2.1 孔頸單元模型....................................................................................................2-1
2.2 孔頸系集模型....................................................................................................2-6
2.3 軟體使用簡介..................................................................................................2-10
2.3.1 系統能量概述....................................................................................2-11
2.3.2 孔頸單元的流體靜態界面模擬......................................................2-12
2.3.3 濕潤相流體相對傳導度的求取......................................................2-14
2.4 研究流程..........................................................................................................2-16
第3章 模型推論與分析...............................................................................................3-1
3.1 單元分析流程與結果.......................................................................................3-1
3.2 系集分析流程與結果.....................................................................................3-14
第4章 曲線精緻化..........................................................................................4-1
4.1 精緻化方法........................................................................................................4-1
4.2 結果討論...........................................................................................................4-21
第5章 結論與建議........................................................................................................5-1
5.1結論.......................................................................................................................5-1
5.2 建議.....................................................................................................................5-3
參考文獻............................................................................................................................6-1
附錄A................................................................................................................................A-1
附錄B................................................................................................................................B-1
附錄C................................................................................................................................C-1












表目錄

表3.1-1 反演20種孔頸單元頸管內切圓半徑的發生機率與大頸管孔頸徑比值分 布................................................................................................................................3-3
表3.2-1 控制折曲過大部分的對應頸管編號表......................................................3-15
表4.1-1 大頸管同為No. 18的迴歸結果表.................................................................4-9
表4.1-2 大頸管同為No. 18的迴歸結果表.................................................................4-9
表4.1-3 大頸管編號18的所有孔頸單元組合依比例求 誤差表...............4-11
表4.1-4 大頸管編號09的所有孔頸單元組合依比例求 誤差表...............4-13

圖目錄

圖1.2.1-1 平行管束示意圖...........................................................................................1-3
圖1.2.2-1 Mualem(1976)模式兩段管示意圖...............................................................1-5
圖1.2.4-1 R. Lenormand et al., 1983設計的鑄模溝槽示意圖....................................1-8
圖1.2.4-2 R. Lenormand et al., 1983管網流體置換示意圖........................................1-8
圖2.1-1 單個孔頸單元示意圖......................................................................................2-2
圖2.1-2 半孔頸單元幾何示意圖.................................................................................2-3
圖2.2-1 反演頸管管徑分布示意圖.............................................................................2-7
圖2.2-2 頸管管徑分布離散計劃示意圖 (摘自鄭安孺(2004))................................2-9
圖2.2-3 孔頸徑比值條件分布離散計劃示意圖 (摘自鄭安孺(2004))..................2-10
圖2.3.1-1 =(0.389,0.369)案例, 10未滿管的模擬情形...................2-13
圖2.3.1-2 =(0.389,0.369)案例, 5.4小頸管攫斷後的模擬情形......2-13
圖2.3.1-3 =(0.389,0.369)案例, 5.1大頸管也攫斷後的模擬情形.2-14
圖2.3.2-1 利用軟體CFDRC模擬孔頸單元計算 示意圖..................................2-15
圖2.4-1 研究大致流程圖............................................................................................2-18
圖3.1-1 所有171組孔頸單元的搭配示意圖..............................................................3-5
圖 3.1-2 完全飽和的孔頸單元排退至大頸管與孔只剩角隅流,小頸管仍為滿管 的範例模擬情形.......................................................................................................3-7
圖3.1-3 完全飽和的孔頸單元排退至大頸管與孔只剩角隅流,小頸管仍為滿管 的範例 Curve與 Curve....................................................................3-7
圖3.1-4 小頸管由滿管排退剩角隅流的範例模擬情形...........................................3-8
圖3.1-5 小頸管由滿管排退剩角隅流的範例 Curve與 Curve........3-8
圖3.1-6 排退至殘餘含水量的範例 Curve與 Curve.........................3-9
圖3.1-7 小頸管攫斷前的模擬界面示意圖................................................................3-9
圖3.1-8 由殘餘含水量汲取至小頸管攫斷前的 Curve與 Curve..3-10
圖3.1-9 小頸管攫斷後的模擬界面示意圖..............................................................3-10
圖3.1-10 大頸管攫斷前的模擬界面示意圖............................................................3-11
圖3.1-11 小頸管攫斷後繼續汲取至大頸管攫斷前的 Curve與 Curve.........................................................................................................................3-11
圖3.1-12 大頸管攫斷後非濕潤相入陷的模擬界面示意圖...................................3-12
圖3.1-13 大頸管攫斷後非濕潤相入陷的 Curve與 Curve.............3-12
圖3.1-14 完整的單個孔頸單元 Curve與 Curve..............................3-13
圖3.2-1 模擬實際土樣的首次排退及主汲取 Curve.....................................3-14
圖3.2-2 模擬實際土樣的首次排退及主汲取 Curve.....................................3-16
圖3.2-3 管徑分布離散區間取20組與取80組的整體 Curve比較圖..........3-17
圖4.1-1 增加頸管管徑分布區間示意圖 (修改自鄭安孺(2004))............................4-2
圖4.1-2 增加區間後的孔頸單元組合示意圖............................................................4-4
圖4.1-3 =(0.389,0.369)時的首次退水 Curve...........................................................................................................................4-5
圖4.1-4 =(0.389,0.369)時的首次退水 Curve (為圖4.1-3中B點至 原點的放大圖) .........................................................................................................4-6
圖4.1-5 45.955 、 0.389的所有孔頸單元組合之 圖.........4-7
圖4.1-6 24.745 、 0.902的所有孔頸單元組合之 圖.........4-8
圖4.1-7 大頸管同為No. 18各組於點B、C、D的 與 值比較圖及誤差圖...4-14
圖4.1-8 大頸管同為No. 09各組於點B、C、D的 與 值比較圖及誤差圖...4-15
圖4.1-9 20.032 的所有孔頸單元組合之 圖...........................4-17
圖4.1-10 增加區間後的孔頸單元組合示意圖........................................................4-18
圖4.1-11 曲線精緻化大致流程圖.............................................................................4-20
圖4.2-1 增加20組區間後的整體土樣p-S Curve.....................................................4-21
圖4.2-2 增加20組區間後的整體土樣 Curve................................................4-22
圖4.2-3 增加20組區間後分別與原18組區間及80組區間的 Curve做比 較..............................................................................................................................4-23
圖4.2-4 增加20組區間後與原18組區間的 Curve比較圖...........................4-24
參考文獻

1.Bear, J., Hydraulics of Groundwater. McGraw-Hill, Inc., 1979
2.Brooks, R. H. and C. T. Corey, “Hydraulic Properties of Porous Media”, Hydrol. Paper 3. Colorado State University, Fort Collins, 1964
3.Corey, A. T., “Mechanics of Immiscible Fluids in Porous Media”, Water Resources Publications, 2nd print, Littleton, Colorado, 1990.
4.Legait, B., “Laminar Flow of Two Phases through a Capillary Tube with Variable Square Cross Section”, Journal of Colloid and Interface Science, vol.96, no.1, pp.28-38, 1983.
5.Lenhard, R. J. and J. C. Parker, ”Measurement and Prediction of Saturation-Pressure Relationships in Three-Phase Porous Media Systems”, Journal of Contaminant Hydrology, vol.1, pp.407-424, 1987a
6.Lenhard R. J. and J. C. Parker, “A Model for Hysteretic Constitutive Relations Governing Multiphase Flow: 2. Permeability-Saturation Relations”, Water Resource Research, vol.23, no.12, pp.2197-2204, 1987b.
7.Lenormand, R., Zarcone, C. and A. Sarr, “Mechanism of the displacement of one fluid by another in a network of capillary ducts”. Journal of Fluid Mechanics, 135, 337-353, 1983
8.Maša Prodanovi´c, Steven L. Bryant, “A level set method for determining critical curvatures for drainage and imbibition”, Journal of Colloid and Interface Science 304 442–458, 2006
9.Mualem, Y. “A New Model for Predicting the Hydraulic Conductivity of Unsaturated Porous Media”, Water Resource Research, vol.12, no.3, pp.513-522, 1976.
10.Parker, J. C. and J. R. Lenhard, “A Model for Hysteretic Constitutive Relations Governing Multiphase Flow: 1. Saturation-Pressure Relations”, Water Resource Research, vol.23, no.12, pp.2187-2196, 1987.
11.Parker, J. C., “Multiphase Flow and Transport in Porous Media”, Reviews of Geophysics, vol. 27, no. 3, pp. 311-328, 1989.
12.Patzek T.W. and J.G. Kristensen, “Shape factor correlations of hydraulic conductance in noncircular capillaries. II. Two-phase creeping flow”, Journal of Colloid and Interface Science, vol. 236, pp.305-317, 2001
13.Ransohoff, T. C. and C. J. Radke, “Laminar Flow of a Wetting Liquid along the Corners of a Predominatly Gas-Occupied Noncircular Pore”. Journal of Colloid and Interface Science, 121, 392-401, 1988
14.van Genuchten, M. Th. A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. v.44, pp.892-898, 1980
15.Wardlaw, N. C., “The effects of geometry, wettability, viscosity and interfacial tension on trapping in single pore-throat pairs”, Journal of Canadian Petroleum Technology, pp.21-27, 1982.
16.Wardlaw, N. C. and Y. Li, “Fluid Topology, Pore Size and Aspect Ratio during Imbibition”, Transport in Porous Media, vol. 3, pp.17-34, 1988.
17.鄭安孺,「建構單元孔頸系集模型推估毛細壓力與飽和度關係之研究」,國立台灣大學土木工程學研究所博士論文,2004
18.馮智勇,「以孔頸單元系集模型推估濕潤相流體未飽和水力傳導係數之研究」,國立台灣大學土木工程學研究所博士論文,2006
19.李居正,「運用雙伽碼射線量測土壤二相流飽和度之研究」,國立台灣大學土木工程學研究所碩士論文,2006
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