In the oil production industry, it is of significance to measure and predict the form of multi-phase flow and gas flow that are present within petroleum production and processing pipelines. One component which has received little attention is the characteristics of bubbly flow around production pipelines. Rising bubble behavior in a wellbore changes with various factors, of which temperature leading to variations of liquids properties is one of the important factors. Herein, using an improved drag coefficient model to investigate bubble rising behavior at different temperatures is considered to calculate bubble flow velocities for drilling design, operation and wellbore pressure control. Firstly, a series of simulated laboratory experiments were conducted at 5–100 °C in four Newtonian fluids to obtain liquid properties and bubble parameters, such as bubbles shape, terminal velocity and trajectory. Then, compared with terminal velocities obtained by using the drag coefficients models CD = 0.95, which was considered to be constant by many literature at high Reynolds region (Re > 135), the modified drag coefficient model CD = 1.227 yielded better satisfactory prediction results for bubbles terminal rising velocity. Additionally, a new correlation using Reynolds number, Eötvös number, Weber number is proposed to predict bubble terminal velocity at low Reynolds number (Re < 135) based on experimental data and the Schiller–Naumann model. The results showed excellent agreement with the experimental data, with standard error of 5.32%.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Alam, T., Li, W., Yang, F., Chang, W., Li, J., Wang, Z., et al. (2016). Force analysis and bubble dynamics during flow boiling in silicon nanowire microchannels. International Journal of Heat and Mass Transfer,101, 915–926.
Amirnia, S., de Bruyn, J. R., Bergougnou, M. A., & Margaritis, A. (2013). Continuous rise velocity of air bubbles in non-Newtonian biopolymer solutions. Chemical Engineering Science,94, 60–68.
Behnia, S., Mobadersani, F., Yahyavi, M., & Rezavand, A. (2013). Chaotic behavior of gas bubble in non-Newtonian fluid: A numerical study. Nonlinear Dynamics,74(3), 559–570.
Cai, Z., Bao, Y., & Gao, Z. (2010). Hydrodynamic behavior of a single bubble rising in viscous liquids. Chinese Journal of Chemical Engineering,18(6), 923–930.
Celata, G. P., D’Annibale, F., di Marco, P., Memoli, G., & Tomiyama, A. (2007). Measurements of rising velocity of a small bubble in a stagnant fluid in one-and two-component systems. Experimental Thermal and Fluid Science,31(6), 609–623.
Chan, I. H., Sishtla, C., & Knowlton, T. M. (1987). The effect of pressure on bubble parameters in gas-fluidized beds. Powder Technology,53(3), 217–235.
Funfschilling, D., & Li, H. Z. (2006). Effects of the injection period on the rise velocity and shape of a bubble in a non-Newtonian fluid. Chemical Engineering Research and Design,84(10), 875–883.
Guan, X., Li, Z., Wang, L., & Cheng, Y. (2014). CFD simulation of bubble dynamics in bubble columns with internals. Industry and Engineering Chemical Research,53(42), 16529–16538.
Huang, C., Wang, L., Chen, X., Wei, X., & Liang, J. (2018). The rising behaviors of single bubbles in stagnant turpentine and pine resin solutions. Experimental Thermal and Fluid Science,98, 170–180.
Ishii, M., & Chawla, T. C. (1979). Local drag laws in dispersed two-phase flow. Argonne National Lab., IL, USA, NUREG/CR-1230, pp 79–105.
Jamialahmadi, M., Branch, C., & Müuller-Steinhagen, H. (1994). Terminal bubble rise velocity in liquids. Chemical Engineering Research and Design,72, 119–122.
Karamanev, D. G. (1994). Rise of gas bubbles in quiescent liquids. AIChE Journal,40(8), 1418–1421.
Karamanev, D. G. (1996). Equations for calculation of the terminal velocity and drag coefficient of solid spheres and gas bubbles. Chemical Engineering Communications,147(1), 75–84.
Kelbaliyev, G., & Ceylan, K. (2007). Development of new empirical equations for estimation of drag coefficient, shape deformation, and rising velocity of gas bubbles or liquid drops. Chemical Engineering Communications,194, 1623–1637.
Kishore, N., Chhabra, R. P., & Eswaran, V. (2007). Drag on a single fluid sphere translating in power-law liquids at moderate Reynolds numbers. Chemical Engineering Science,62(9), 2422–2434.
Kishore, N., Chhabra, R. P., & Eswaran, V. (2008). Bubble swarms in power-law liquids at moderate Reynolds numbers: Drag and mass transfer. Chemical Engineering Research and Design,86(1), 39–53.
Kupferberg, A., Jameson, G. J., & Eng, C. (1969). Bubble formation at a submerged orifice above a gas chamber of finite volume. Transaction of Institution of Chemical Engineers,49, 241–250.
Leifer, I., Patro, R. K., & Bowyer, P. (2000). A study on the temperature variation of rise velocity for large clean bubbles. Journal of Atmospheric and Oceanic Technology,17(10), 1392–1402.
Liu, N., Ju, B., Chen, X., Brantson, E. T., Mu, S., Yang, Y., et al. (2019a). Experimental study of the dynamic mechanism on gas bubbles migration, fragment, coalescence and trapping in a porous media. Journal of Petroleum Science and Engineering,181, 106192.
Liu, N., Ju, B., Yang, Y., Brantson, E. T., Wang, J., & Tian, Y. (2019b). Experimental study of different factors on dynamic characteristics of dispersed bubbles rising motion behavior in a liquid-saturated porous media. Journal of Petroleum Science and Engineering,180, 396–405.
Liu, L., Yan, H., & Zhao, G. (2015). Experimental studies on the shape and motion of air bubbles in viscous liquids. Experimental Thermal and Fluid Science,62, 109–121.
Loth, E. (2008). Quasi-steady shape and drag of deformable bubbles and drops. International Journal of Multiphase Flow,34(6), 523–546.
Margaritis, A. (1999). Bubble rise velocities and drag coefficients in non-Newtonian polysaccharide solutions. Biotechnology and Bioengineering,64(3), 257–266.
Mendelson, H. D. (1967). The prediction of bubble terminal velocities from wave theory. AIChE Journal,13(2), 250–253.
Merritt, R. M., & Subramanian, R. S. (1988). The migration of isolated gas bubbles in a vertical temperature gradient. Journal of Colloid and Interface Science,125(1), 333–339.
Moore, D. W. (1965). The velocity of rise of distorted gas bubbles in a liquid of small viscosity. Journal of Fluid Mechanics,23, 749–766.
Myint, W., Hosokawa, S., & Tomiyama, A. (2006). Terminal velocity of single drops in stagnant liquids. Journal of Fluid Science and Technology,1, 72–81.
Myint, W., Hosokawa, S., & Tomiyama, A. (2007). Shapes of single drops rising through stagnant liquids. Journal of Fluid Science and Technology,2, 184–195.
Nalajala, V. S., Kishore, N., & Chhabra, R. P. (2014). Effect of contamination on rise velocity of bubble swarms at moderate Reynolds numbers. Chemical Engineering Research and Design,92(6), 1016–1026.
Nickens, H. V., & Yannitell, D. W. (1987). The effects of surface tension and viscosity on the rise velocity of a large gas bubble in a closed, vertical liquid-filled tube. International Journal of Multiphase Flow,13(1), 57–69.
Peebles, F. N., & Garber, H. J. (1953). Studies on the motion of gas bubbles in liquids. Chemical Engineering Progress,49, 88–97.
Rodi, W., & Fueyo, N. (2002). Engineering turbulence modelling and experiments 5. In Proceedings of the 5th international symposium on engineering turbulence modelling and measurements. Mallorca, Spain, 16–18 September, 2002.
Rodrigue, D. (2001a). Drag coefficient-Reynolds number transition for gas bubbles rising steadily in viscous fluids. Canada Journal of Chemical Engineering,79(1), 119–123.
Rodrigue, D. (2001b). Generalized correlation for bubble motion. AIChE Journal,47(1), 39–44.
Ruzica, D., Bonnie, L., & Warren, S. G. (2010). Migration of air bubbles in ice under a temperature gradient, with application to “Snowball Earth”. Journal of Geophysical Research Atmosphere,115, D18125.
Sawi, M. E. (1974). Distorted gas bubbles at large Reynolds number. Journal of Fluid Mechanics,62(1), 163–183.
Schiller, L., & Naumann, Z. (1935). A drag coefficient correlation. Zeitschrift des Vereins Deutscher Ingenieure,77, 318–320.
Shreve, R. L. (1967). Migration of air bubbles, vapor figures, and brine pockers in ice under a temperature gradient. Journal of Geophysical Research,72(16), 4093–4100.
Simonnet, M., Gentric, C., Olmos, E., & Midoux, N. (2007). Experimental determination of the drag coefficient in a swarm of bubbles. Chemical Engineering Science,62(3), 858–866.
Speight, M. V. (1964). The migration of gas bubbles in material subject to a temperature gradient. Journal of Nuclear Materials,13(2), 207–209.
Stehle, N. S. (1967). Migration of bubbles in ice under a temperature gradient. In Physics of snow and ice: Proceedings of the international conference on low temperature science. Hokkaido Univ., Sapporo, Japan, pp. 219–232.
Stubington, J. F., Barrett, D., & Lowry, G. (1984). On the minimum fluidizing velocity of coal-derived chars at elevated temperatures. Chemical Engineering Science,39(10), 1516–1518.
Sun, B., Guo, Y., Sun, W., Gao, Y., Hao, L., Wang, Z., et al. (2018a). Multiphase flow behavior for acid-gas mixture and drilling fluid flow in vertical wellbore. Journal of Petroleum Science and Engineering,165, 388–396.
Sun, B., Guo, Y., Wang, Z., Yang, X., Gong, X., Wang, J., et al. (2015). Experimental study on the drag coefficient of single bubbles rising in static non-Newtonian fluids in wellbore. Journal of Natural Gas Science and Engineering,26, 867–872.
Sun, F., Yao, Y., Chen, M., Li, X., Zhao, L., Meng, Y., et al. (2017). Performance analysis of superheated steam injection for heavy oil recovery and modeling of wellbore heat efficiency. Energy,125, 795–804.
Sun, F., Yao, Y., & Li, X. (2018b). The heat and mass transfer characteristics of superheated steam coupled with non-condensing gases in horizontal wells with multi-point injection technique. Energy,143, 995–1005.
Sun, F., Yao, Y., Li, G., & Li, X. (2018c). Geothermal energy extraction in CO2 rich basin using abandoned horizontal wells. Energy,158, 760–773.
Sun, F., Yao, Y., Li, G., & Li, X. (2018d). Performance of geothermal energy extraction in a horizontal well by using CO2 as the working fluid. Energy Conversation Management,171, 1529–1539.
Sun, F., Yao, Y., Li, G., & Li, X. (2018e). Geothermal energy development by circulating CO2 in a U-shaped closed loop geothermal system. Energy Conversation Management,174, 971–982.
Tomiyama, A., Celata, G. P., Hosokawa, S., & Yoshida, S. (2002). Terminal velocity of single bubbles in surface tension force dominant regime. International Journal of Multiphase Flow,28(9), 1497–1519.
Tomiyama, A., Kataoka, I., Zun, I., & Sakaguchi, T. (1998). Drag coefficients of single bubbles under normal and micro gravity conditions. JSME International Journal Series B,41(2), 472–479.
Tripathi, M. K., Sahu, K. C., Karapetsas, G., & Sefiane, K. (2015). Non-isothermal bubble rise: Non-monotonic dependence of surface tension on temperature. Journal of Fluid Mechanics,763, 82–108.
Wittmann, K., Helmrich, H., & Schügerl, K. (1981). Measurements of bubble properties in continuously operated fluidized bed reactors at elevated temperatures. Chemical Engineering Science,36(10), 1673–1677.
Yoshida, K., Sakane, J., & Shimizu, F. (1982). A new probe for measuring fluidized bed characteristics at high temperatures. Industrial and Engineering Chemistry Fundamentals,21(1), 83–85.
Zhang, Y., Sam, A., & Finch, J. A. (2003). Temperature effect on single bubble velocity profile in water and surfactant solution. Colloids and Surfaces A: Physicochemical and Engineering Aspects,223(1), 45–54.
The research was supported by the Fundamental Research Funds for National Science and Technology Major Projects (2016ZX05011-002 and 2017ZX05009-005). The authors would like to thank the editors and anonymous referees for their valuable comments and suggestions.
About this article
Cite this article
Liu, N., Yang, Y., Wang, J. et al. Experimental Investigations of Single Bubble Rising in Static Newtonian Fluids as a Function of Temperature Using a Modified Drag Coefficient. Nat Resour Res 29, 2209–2226 (2020). https://doi.org/10.1007/s11053-019-09537-x
- Rising bubble velocity
- Visual observation
- Newtonian fluids
- Drag coefficient
- Reynolds number