The Velocity and Shape of Convected Elongated Liquid Drops in Vertical Narrow Gaps
- S. Shad (University of Calgary) | M. Salarieh (University of Calgary) | B.B. Maini (University of Calgary) | I.D. Gates (University of Calgary)
- Document ID
- Society of Petroleum Engineers
- Journal of Canadian Petroleum Technology
- Publication Date
- December 2009
- Document Type
- Journal Paper
- 26 - 31
- 2009. Society of Petroleum Engineers
- 5.2.1 Phase Behavior and PVT Measurements, 4.6 Natural Gas, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 4.1.5 Processing Equipment, 5.3.9 Steam Assisted Gravity Drainage, 4.3.1 Hydrates, 5.3.2 Multiphase Flow, 5.4.6 Thermal Methods, 4.1.2 Separation and Treating, 5.8.6 Naturally Fractured Reservoir, 5.5 Reservoir Simulation, 5.3.1 Flow in Porous Media
- microfractures, two-phase flow
- 3 in the last 30 days
- 267 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
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.
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.
|File Size||987 KB||Number of Pages||6|
1. Bendiksen, K.H. 1985. On the motion of longbubbles in vertical tubes. International Journal of Multiphase Flow11 (6): 797-812. doi:10.1016/0301-9322(85)90025-4.
2. Bretherton F.B. 1961. The motion of long bubblesin tubes. J. Fluid Mech. 10 (2): 166-188.doi:10.1017/S0022112061000160.
3. Eck, W. and Siekmann, J. 1978. On bubble motion in a Hele-Shawcell, a possibility to study two-phase flows under reduced gravity.Archive of Applied Mechanics 47 (3): 153.doi:10.1007/BF01047407.
4. Fairbrother, F. and Stubbs, A.E. 1935. Studies in electro-endosmosis.Part VI. The "bubble tube" method of measurement. J. of Chem. Soc.(1935): 527-529. doi:10.1039/jr9350000527.
5. Helenbrook, B.T. and Edwards, C.F. 2002. Quasi-steady deformationand drag of uncontaminated liquid drops. Int. J. Multiphase Flow28 (10): 1631-1657. doi:10.1016/S0301-9322(02)00073-3.
6. Kopf-Sill, A.R. and Homsy, G.M. 1988. Bubble motion in a Hele-Shawcell. Physics of Fluids 31 (1): 18-27.doi:10.1063/1.866566.
7. Liao, Q. and Zhao, T.S. 2003. Modeling of Taylorbubble rising in a vertical mini noncircular channel filled with a stagnantliquid. International Journal of Multiphase Flow 29 (3):411-434. doi:10.1016/S0301-9322(03)00004-1.
8. Laplace, P.S. 1806. Théorie de l'Action Capillaire; Supplément audixieme livre du Traité de Mécanique Céleste. Courcier, Paris. (Supplémentpp. 80, 1807).
9. Marchessault, R.N. and Mason, S.G. 1960. Flow of Entrapped Bubbles througha Capillary. Industrial and Engineering Chemistry 52 (1):79-84. doi:10.1021/ie50601a051.
10. Maxworthy, T. 1986. Bubble formation, motion andinteraction in a Hele-Shaw cell. J. Fluid Mech. 173: 95-114.doi:10.1017/S002211208600109X.
11. Nicklin, D.J., Wilkes, J.O., and Davidson, J.F. 1962. Two-Phase FilmFlow in Vertical Tubes. Trans. Inst. Chem. Eng. 40: 61-68.
12. Roura, P. 2005. Thermodynamic derivations of themechanical equilibrium conditions for fluid surfaces: Young's and Laplace'sequations. Am. J. Phys. 73 (12): 1139-1147.doi:10.1119/1.2117127.
13. Saffman, P.G. and Taylor, G.I. 1958. The penetration of a fluid into aporous medium or Hele-Shaw cell containing a more viscous liquid. Pro. R.Soc. London Ser. A 245 (1242): 312-329.
14. Saffman, P.F. and Tanveer, S. 1989. Prediction of bubble velocity in ahele-shaw cell: Thin film and contact angle effects. Physics of Fluids A1 (2): 219-223. doi:10.1063/1.857492.
15. Shad, S., Salarieh, M., Maini, B.B., and Gates, I.D. In press.The Velocity and Shape of Convected Elongated Liquid Drops in Narrow HorizontalGaps. J. Pet. Sci. Eng. (submitted 2008).
16. Tanveer, S. 1986. Theeffect of surface tension on the shape of a Hele-Shaw cell bubble. Phys.Fluids 29 (11): 3537-3548. doi:10.1063/1.865831.
17. Tanveer, S. 1987. New solutions for steady bubbles in a Hele-Shaw cell.Physics of Fluids 30 (3): 651-658. doi:10.1063/1.866369.
18. Tanveer, S. 1987. Theeffect of thin film variations and transverse curvature on the shape of fingersin a Hele-Shaw cell. Phys. Fluids 30 (9): 2617.doi:10.1063/1.866105.
19. Taylor, G.I. and Saffman, P.G. 1959. A Note on the Motion of Bubblesin a Hele-Shaw Cell and Porous Medium. J. Mech. Appl. Math. 12(3): 265-279. doi:10.1093/qjmam/12.3.265.