The Velocity and Shape of Convected Elongated Liquid Drops in Vertical Narrow Gaps

Abstract

Abstract The motion and shape of a liquid drop through another continuous liquid phase (conveying phase) in a vertical Hele-Shaw cell with two different apertures were investigated experimentally. Two different liquid/liquid systems were tested. In all cases, the continuous phase was more viscous and wetted the bounding walls. In the capillarity-dominated region, the irregular shape of the discontinuous phase changed with time and distance, with much lower velocity than that of the conveying phase. In contrast to gas/liquid systems, the velocity of these stabilized, elongated drops was 2.5 to almost 5 times higher than that of conveying liquid. Despite the similarities between flow in vertical and horizontal Hele-Shaw cells, the velocity of droplets in a vertical fracture is different from that of a horizontal fracture. A new correlation is derived from dimensionless analysis and the experimental data to predict the elongated drop velocity as a function of the dimensionless parameters governing the system. Introduction Two-phase flow in micro-fractures is fundamental to many different fields of advanced science and technology, such as chemical process engineering, bioengineering, medical and genetic engineering, as well as petroleum engineering. For instance, understanding the flow of two-phase fluids in near-parallel gaps through fractured rocks has a significant effect on design of different recovery methods for naturally fractured reservoir. The flow pattern of two-phase immiscible flow in a fracture depends on the flow rates of the phases, the geometry, aperture, roughness of the fracture, the flow properties of the phases and interfacial tension between the phases. The flow patterns in a fracture are different from that in macro-sized rectangular ducts or pipes because of the small aperture, which can enhance capillary effects. The flow structure in the fracture affects the flow and transport through the surrounding porous matrix blocks. The slug flow pattern in a fracture, which occurs over a wide range of parameters, is frequently encountered in oil-wet fractured reservoirs during the immiscible displacement of viscous oil. It also occurs in natural gas reservoirs during displacement of water during gas production.