The motion and shape of a liquid drop through another continuous liquid phase (conveying phase) in a vertical Hele- Shaw cell with different 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 cell, the velocity of droplets in vertical fracture is different from that of 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.
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, and 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 size rectangular ducts or pipes due to 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. In the case of a smooth-walled fracture, the slug shape can be regular elongated drops (or bubbles) flowing through the conveying phase. The elongated drops (or bubbles) can have a rounded leading edge and occupy a considerable portion of the gap with length of several times to several hundred times that of the gap. The behavior of single elongated drops (or bubbles) through a continuous liquid phase problem is as rich and complex as the viscous fingering problem6. The conditions corresponding to a swarm of the elongated drops can be inferred by considering the behavior of a single drop (bubble) and their conglomeration. The interaction of many drops or bubbles across the flow cross section can also be inferred from single drop or bubble dynamics. A firm understanding of the behavior of drop or bubble flow in a single fracture is prerequisite to build predictive models for flow in complex fracture systems.
