多相流問題在日常生活中非常常見，並且也是水文地質學中非常重要的一個課題。在多相流問題中，兩相流問題尤其最受廣泛討論，而兩相流為多相流的一個特例。在傳統孔隙介質水流的分析中，大部分情況下只考慮單相流。然而在未飽和帶中，空氣的存在會影響水的流動，在單純只考慮單相流的情境下，水於孔隙介質流動過程中，空氣對水的影響無法看見。一旦水流動受空氣影響，水於孔隙介質的流動過程中，水和空氣即必須被同時考慮。本研究進行兩相流的流動特性分析，兩相流模式採用Buckley-Leverett模式。兩相流模式中，水於孔隙介質流動由三個機制所組成，分別為流動性、重力作用與擴散作用。當不同作用機制被考慮下，水於孔隙介質流動會有不同的特性。兩相流於孔隙介質的分析結果可與單相流結果做比較，單相流與兩相流的數值模擬採用COMSOL數值軟體執行。結果顯示兩相流模式下水於孔隙介質流動對比單相流模式下較為緩慢，而在兩相流模式中考慮不同作用機制下，孔隙介質中水飽和度隨時間的分佈會有顯著的差異。此外，不同機制對於孔隙介質中潮濕峰的移動貢獻亦可由數值模擬分別得出。

Multiphase flow problems are widely used in our life, and they are also important in the hydrogeology. In multiphase problems, two-phase flow problems are discussed the most commonly, and the two-phase flow is a particular case of the multiphase flow. In the traditional analysis of water flow in porous media, the single-phase flow is considered in most cases. In the unsaturated zone, however, the existence of air may influence the flow of water. When the one-phase flow was taken into account, the influence of air is neglected in the flowing process. Since the flow of water is influenced by air, water and air have to be considered simultaneously to analyze the flowing procedure in the porous medium. This study investigates the flowing characteristics of the two-phase flow, and Buckley-Leverett model is chosen as the two-phase flow model. The flow of water in the two-phase flow in the porous medium is composed of three mechanisms including the mobility, the gravity and the diffusion. When the different mechanisms in the two-phase flow are considered, the flow of water has different characteristics in the porous medium. The results of the two-phase flow are compared with that of the one-phase flow using Richards’ equation. The numerical simulations of the one-phase and two-phase flow in this study are conducted by COMSOL. The results demonstrate that the flow of water is slower in the two-phase flow comparing with that in the one-phase flow in the porous medium. Since the different mechanisms are taken into account in the two-phase flow, the distribution of the water saturation by time is quite different in the porous medium. In addition, the contribution to the movement of the wetting front from different mechanisms can be identified in the numerical simulation.

Abstract I
摘要 II
誌謝 III
Content IV
List of Table VII
List of Figure VIII
Notation XII
Chapter 1 Introduction 1
1.1 Background and motivation 1
1.2 Literature review 5
1.3 Flow chart 8
Chapter 2 Methodology 9
2.1 One-phase flow 9
2.1.1 Darcy’s law 9
2.1.2 Richards’ equation 9
2.1.3 Richards’ equation in expressions of the water content 11
2.1.4 Richards’ equation in expressions of the capillary pressure head 12
2.1.5 van Genuchten model 12
2.2 Two-phase flow model 15
2.2.1 Buckley-Leverett model 15
2.2.2 Relative permeability 18
2.2.3 Buckley-Leverett model with the effect of the mobility only 20
2.2.4 Buckley-Leverett model with the effect of the mobility and the gravity 21
2.2.5 Buckley-Leverett model with the effect of the mobility, the gravity and the diffusion 23
2.2.6 Determination of the total flux 24
Chapter 3 Numerical Simulation 25
3.1 COMSOL Multiphysics 25
3.2 Parameters of the fluids and the porous medium for the numerical simulations 25
3.3 One-phase flow 26
3.3.1 Scenario 1 27
3.3.2 Scenario 2 28
3.4 Two-phase flow 29
3.4.1 Scenario 1 29
3.4.2 Scenario 2 30
3.4.3 Scenario 3 30
3.5 Numerical oscillation 31
Chapter 4 Results and Discussions 33
4.1 One-phase flow 33
4.1.1 Scenario 1 37
4.1.2 Scenario 2 42
4.2 Two-phase flow 46
4.2.1 Determination of the total flux 48
4.2.2 Scenario 1 52
4.2.3 Scenario 2 56
4.2.4 Scenario 3 58
4.3 Comparisons of the one-phase and two-phase flow 61
4.4 Sensitivity analysis in the two-phase flow 64
4.4.1 Initial condition 64
4.4.2 Permeability 67
4.5 Contributions to the wetting front for the different mechanisms 68
Chapter 5 Conclusions and Suggestions 73
5.1 Conclusions 73
5.2 Suggestions 74
References 75

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