異質多孔介質指形流之模擬

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余昭諭(Jau-Yu Yu) 查詢紙本館藏

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機械工程學系

論文名稱

異質多孔介質指形流之模擬

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摘要(中)

兩黏度不同的不互溶流體在隨機分布的多孔介質中，若以黏度較低的流體驅替較高的流體，由於兩流體之間的黏度差異、表面張力與濕潤性，導致流動不穩定而產生指形流，造成驅替效果下降。本研究為了確認一種新的提升驅替效果方法是否可行，使用商用軟體Ansys Fluent，以有限體積法模擬兩相流在準二維多孔介質(quasi-two dimensional porous media)驅替的流動情況。模擬之模型採用層流及不可壓縮流，並利用二維暫態納維爾史托克方程式加上額外的達西項與物體力來描述流體在兩平板間流動的黏滯力與毛細力，再以流體體積(Volume of fluid, VOF)演算法追蹤多相流之介面。
研究方法為嘗試不同大小的顆粒，來控制多孔介質的毛細壓力，以高毛細壓力阻擋指形的概念探討驅替效果提升的效果。模擬之裝置由兩玻璃板平板構成的Hele-Shaw Cell，平板間充滿尺寸為常態分布、位置隨機分布的圓柱形顆粒，顆粒有分兩區，上游區為大顆粒，下游區為小顆粒，大顆粒平均半徑皆為1mm，小顆粒平均半徑依序設計為1 mm、0.7 mm、0.5 mm、0.45 mm與0.4mm，其毛細壓力差值分別代表效果為無、弱、中、強、更強，共五種情況。
模擬流程為一開始多孔介質充滿黏度相對較高的水，接著出口端抽水，入口端進入空氣，直到最後空氣離開多孔介質。模擬結果以實驗比對與網格收斂測試來驗證模擬的可靠性。模擬結果顯示，異質孔徑之小顆粒從1mm到0.5mm，驅替效果越來越好，0.5mm之後則開始變差。提升效果的區域主要分布在靠近異質孔徑介面的大顆粒區，並呈現扇形的分布形態。驅替效果無法提升的原因主要有兩個：一、如果異質孔徑界面被空氣填滿，大顆粒區的水就排不出去，無法增加驅替量；二、指形尖端到異質孔徑介面的黏滯壓降大於毛細壓力差值，故毛細阻力不足以阻擋指形前進。

摘要(英)

When one fluid displaces another in a disordered porous medium, the displacement can be unstable that leads to the reduction of displacement efficience. Viscous fingering is an unstable phenomenon that occurs when a less viscous fluid displaces a more viscous one, depending on different viscosities, surface tension, and wettability between the two fluids. In order to confirm the feasibility of a new method for enhancing displacement effects, this study used the commercial software ANSYS Fluent to simulate the two-phase flow in a quasi two-dimensional porous media. The flow was considered to be laminar and incompressible, and the two-dimensional transient Navier-Stokes equation with additional source terms of Darcy resistance and continuous surface force to describe the viscous force induced by the boundary and capillary forces between the two fluids. The fluid volume (VOF) algorithm was used to track the interface of the two-phase flow.
The physical domain is a thin porous medium sandwitched between two solid flate plates. Mirco cylindrical obstacles were used to produce two porous media with different capillary pressures. The upstream region was filled with big obstacles, and the downstream region was filled with small obstacles. The displacement efficiency was improved by increasing finger movement resistance at the heterogeneous interface. Five different radius ratios (1:1, 1:0.7, 1;0.5, 1:0.45, 1:0.4) of big obstacles region to small obstacles region were considered. The five situations represented five kinds of capillary pressure differences.
The porous medium was initially filled with water. Next, the water exited porous medium from outlet and the air entered porous medium from inlet. The simulation model was verified by experimental comparisons and grid convergence tests. The simulation results showed that the displacement effect was getting better when the radius ratios were from 1: 1 to 1: 0.5. However, the displacement efficiency started getting worse from 1:0.5 to 1:0.4. The areas of air were mainly distributed in the big obstacle regions near the heterogeneous pore-scale boundary, and had a fan-shaped distribution pattern. There were two main reasons why the displacement efficiency could not be improved for pore-size ratio getting smaller: First, if the air fully filled the heterogeneous pore-scale boundary, the water in the big region cannot be drained; second, the viscous pressure drop from the fingertip to heterogeneous pore-scale boundary is larger than the capillary pressure difference, so the capillary resistance was not sufficient anymore to resist the fingers.

關鍵字(中)

★ 多孔介質
★ 異質孔徑介面
★ 指形流

關鍵字(英)

★ porous medium
★ heterogeneous pore-scale boundary
★ fingering flow

論文目次

中文摘要 i
Abstract ii
符號說明 iv
英文字母 iv
希臘字母 v
上下標 vi
目錄 vii
圖目錄 x
表目錄 xiii
第一章緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 研究目的 5
第二章數學模型 11
2.1 問題描述 11
2.1.1 物理系統 12
2.1.2 多孔介質粒徑生成方法 13
2.1.3 流體性質與基本假設 14
2.2 統御方程式 15
2.2.1 質量守恆方程式 15
2.2.2 動量守恆方程式 15
2.2.3 體積分率方程式 16
2.3 VOF模型 16
2.4 CSF模型 17
2.5 接觸角與濕潤性 18
2.6 邊界條件與初始條件 18
2.6.1 邊界條件 18
2.6.2 初始條件 19
2.7 數值方法 20
2.7.1 Ansys Fluent簡介 20
2.7.2 網格設定 20
2.7.3 方程式與空間離散求解演算法設定 21
2.7.4 鬆弛因子 21
2.7.5 收斂標準 21
2.7.6 模擬設備與計算時間 22
第三章結果與討論 30
3.1 多孔隙介質流動壓力 30
3.1.1 壓力與座標定義 30
3.1.2 多孔隙介質流動壓力關係式 30
3.2 模擬驗證 31
3.2.1 網格收斂性 31
3.2.2 實驗比較 33
3.3 多孔介質性質量測 34
3.3.1 孔隙率 34
3.3.2 粒徑大小分布 34
3.3.3 孔隙大小分布 35
3.3.4 以孔隙大小推估毛細壓力 35
3.3.5 滲透度 36
3.4 異質孔徑驅替過程分析 36
3.4.1 顆粒粒徑比1: 1，流率30 mL/min 36
3.4.2 顆粒粒徑比1: 0.7，流率30 mL/min 37
3.4.3 顆粒粒徑比1: 0.5，流率30 mL/min 39
3.4.4 顆粒粒徑比1: 0.45，流率30 mL/min 41
3.4.5 顆粒粒徑比1: 0.4，流率30 mL/min 43
3.4.6 各數據比較 44
3.5 驅替效果分析 45
3.5.1 毛細壓力差對於驅替效果的影響 45
3.5.2 毛細壓力與黏性阻力相對大小的影響 45
3.6 指形行走特性 46
3.7 指形的水黏性阻力 47
3.8 指形的空氣黏性阻力 47
第四章結論與未來展望 77
4.1 結論 77
4.2 未來展望 78
參考文獻 79

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指導教授

鍾志昂(Chih-Ang Chung)

審核日期

2018-8-21

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