多孔介質指形流實驗

張奐文(Huan-wen Chang)

指導教授 ： 鍾志昂

國立中央大學/工學院/機械工程學系/碩士(2014年)

摘要

本文以適用於徑向流動的修正毛細數來分析流動不穩定現象。利用不同顆粒直徑釔鋯球構成多孔介質，進行矽油與空氣在不同孔徑的二維Hele-Shaw多孔介質中相互推動的實驗。藉由改變顆粒直徑與注入流率來觀察流動過程，並透過壓力計量測不同注入流量對應的壓力與時間關係。本實驗觀察到三種流動型態：穩定移動、毛細指形與黏性指形。
由矽油（大黏度）推動空氣（小黏度）的實驗結果可以發現，矽油皆穩定的往出口端移動，矽油與空氣介面為維持平整的穩定移動的流動過程，且對於不同注入流量，此特性的結果一致。
由空氣（小黏度）推動矽油（大黏度）的實驗結果可以發現，提升修正毛細數可使毛細指形轉變為黏性指形。在相同注入流量條件，較小顆粒直徑構成的多孔介質結構對應的修正毛細數較高，故較容易隨著流量的增加而產生指形轉換。

關鍵字

多孔介質 ； 指形不穩定 ； 毛細壓力 ； 黏性效應

並列摘要

This research presents the modified capillary number for determining the fingering instability in radial flow. Experiments were conducted using the silicon oil and air pushing each other in the two dimensional Hele-Shaw porous media of different pore sizes. Two kinds of zirconia particles with different average diameters of 1 mm and 0.1 mm respectively were used to form different pore sizes. The processes of flow were recorded by a CCD camera and the pressures of the pushing fluid were monitored by installing a pressure sensor at the fluid inlet for different particle sizes and injection rates.
Results showed that three flow regimes could be identified from the experiments: stable displacement, capillary finger and viscous finger. In the case of silicon oil (large viscosity) pushing air (small viscosity), silicon oil was continuously moving towards the outlet. The silicon oil and the air maintained a stable and smooth interface during the entire flow course at different injection rates and pore sizes. Oppositely when air (small viscosity) was used to push silicon oil (large viscosity), two flow types were observed, which could be referred to as the capillary fingering and the viscous fingering flows. The capillary fingers dominated by the capillary pressure transited into the viscous fingers dominated by the viscous force as the modified capillary numbers were increased. The small pore size corresponded to a higher modified capillary number in the same injection rates, so the fingering transition occurred more easily for the small pore size than the big one.

參考文獻

Furuberg, L., Måløy, K. J. and Feder, J., 1996, "Intermittent behavior in slow drainage," Physical Review E, Vol. 53, pp. 966- 977.

Holtzman, R., Szulczewski, M. L. and Juanes, R., 2012, "Capillary fracturing in granular media, " Physical review letters, Vol. 108, pp. 264504.

IPCC, 2005：IPCC Special report on carbon dioxide capture and storage.

Lenormand, R., Touboul, E. and Zarcone, C., 1988, "Numerical models and experiments on immiscible displacements in porous media," Journal of fluid mechanics, Vol. 189, pp. 165- 187.

Løvoll, G., Méheust, Y., Toussaint, R., Schmittbuhl, J. and Måløy, K. J., 2004, "Growth activity during fingering in a porous Hele-Shaw cell," Physical Review E, Vol. 70, pp. 026301.