Direct numerical simulation of trapped-phase recirculation at low capillary number

Abstract

Understanding multiphase flow in porous media, especially how velocity is distributed at the pore-scale, has been the aim of several studies. However, these studies address the recirculation behavior inside the trapped phase experimentally without any comprehensive numerical study of the impact of different governing mechanisms related to the fluid configurations and properties, including drag force and capillary number analysis at low capillary number regime. In this study, we analyzed the recirculation phenomenon inside the trapped phase for various displacement mechanisms, fluid configurations, and dynamic properties. To simulate the pore-scale displacement at low capillary number, we used a filtered surface-force formulation of volume of fluid method, which was implemented in a separately available solver for OpenFoam package. The results showed that within the ranges of capillary number of invading phase analyzed in this study (in the order of 1 × 10−7 to 1 × 10−2), the recirculation phenomenon exists in trapped phases. During the imbibition mechanism, two stagnant regions are created adjacent to the fluid-fluid interface inside the invading fluid. Drag-force analysis on fluid-fluid interfaces shows that during imbibition the maximum force is exerted near the center of the interface, whereas during drainage more force is applied on two elongated interface tails on a solid surface. The centroids are elongated parallel to the interface during drainage and perpendicularly during imbibition, which is in concordance with drag-force distribution along with the interface. The existence of a solid surface near the fluid-fluid interface affects the recirculation process in a way that one or more centroids can be created depending on displacement mechanisms. When the ratio of trapped-phase radius to cavity depth is lower, two simultaneous recirculation zones are formed inside the invading and trapped phases While the changes in viscosity ratio and interfacial tension shifted the centroid location inside the trapped zone, the center of rotation seems to be independent of injection velocity. The average velocity of trapped phase is individually a logarithmic function of the surface tension and fluids viscosity ratio. The stationariness of centroid results in a linear relationship between the average velocity inside the trapped zone and injection velocity. For all ranges of viscosity ratios, a linear relationship between the capillary number of invading and trapped phase is obtained. The findings of this study lead to a better understanding of trapping and mobilization mechanisms in microchannels where various forces are acting on fluid-fluid interfaces.