Crossover from fractal capillary fingering to compact flow: The effect of stable viscosity ratios

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.