Ferer M, Bromhal Grant S, Smith Duane H
U.S. DOE, National Energy Technology Laboratory, Morgantown, West Virginia 26507-0880, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Oct;76(4 Pt 2):046304. doi: 10.1103/PhysRevE.76.046304. Epub 2007 Oct 4.
Using a standard pore-level model, which includes both viscous and capillary forces, we have studied the injection of a viscous, nonwetting fluid into a two-dimensional porous medium saturated with a less viscous, wetting fluid, i.e., drainage with favorable viscosity ratios, M> or =1 . We have observed a crossover from fractal capillary fingering to standard compact flow at a characteristic time, which decreases with increased capillary number and/or viscosity ratio. We have tested an earlier prediction for the dependence of this crossover upon viscosity ratio and capillary number using our data for a wide-but-physical range of capillary numbers and viscosity ratios. We find good agreement between the predicted behavior and our results from pore-level modeling. Furthermore, we show that this agreement is not affected by changes in the random distribution of pore throat radii or by changes in the coordination number, suggesting that the prediction is universal, i.e., valid for any porous medium structure, as expected from the general nature of the derivation of the prediction. Furthermore, this agreement indicates that the prediction correctly accounts for dependence of the flow upon capillary number and viscosity ratios, thereby enabling predictions for interfacial advance and width as well as saturation and fractional flow profiles. Also this agreement supports the validity of the general theoretical development lending credence to the three-dimensional predictions.
使用一个包含粘性力和毛细力的标准孔隙尺度模型，我们研究了将粘性非润湿性流体注入充满低粘性润湿性流体的二维多孔介质中，即粘度比有利（M≥1）的驱替过程。我们观察到在一个特征时间处，从分形毛细指进转变为标准的致密流，该特征时间随着毛细数和/或粘度比的增加而减小。我们使用在广泛但符合实际的毛细数和粘度比范围内的数据，检验了先前关于这种转变对粘度比和毛细数依赖性的预测。我们发现预测行为与孔隙尺度建模结果之间有很好的一致性。此外，我们表明这种一致性不受孔隙喉道半径随机分布变化或配位数变化的影响，这表明该预测具有普遍性，即对于任何多孔介质结构都是有效的，正如该预测推导的一般性质所预期的那样。此外，这种一致性表明该预测正确地考虑了流动对毛细数和粘度比的依赖性，从而能够预测界面推进和宽度以及饱和度和分流曲线。而且这种一致性支持了一般理论发展的有效性，为三维预测提供了可信度。
