| 摘要: | 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。
;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. |
