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Experimental Investigations of Single Bubble Rising in Static Newtonian Fluids as a Function of Temperature Using a Modified Drag Coefficient

  • Nannan Liu
  • Yong Yang
  • Jian Wang
  • Binshan JuEmail author
  • Eric Thompson Brantson
  • Yapeng Tian
  • Yintao Dong
  • B. M. Mahlalela
Original Paper

Abstract

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%.

Keywords

Temperature Rising bubble velocity Visual observation Newtonian fluids Drag coefficient Reynolds number 

Notes

Acknowledgments

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.

References

  1. 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.CrossRefGoogle Scholar
  2. 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.CrossRefGoogle Scholar
  3. 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.CrossRefGoogle Scholar
  4. 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.CrossRefGoogle Scholar
  5. 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.CrossRefGoogle Scholar
  6. 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.CrossRefGoogle Scholar
  7. 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.CrossRefGoogle Scholar
  8. 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.CrossRefGoogle Scholar
  9. 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.CrossRefGoogle Scholar
  10. 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.Google Scholar
  11. Jamialahmadi, M., Branch, C., & Müuller-Steinhagen, H. (1994). Terminal bubble rise velocity in liquids. Chemical Engineering Research and Design, 72, 119–122.Google Scholar
  12. Karamanev, D. G. (1994). Rise of gas bubbles in quiescent liquids. AIChE Journal, 40(8), 1418–1421.CrossRefGoogle Scholar
  13. 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.CrossRefGoogle Scholar
  14. 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.CrossRefGoogle Scholar
  15. 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.CrossRefGoogle Scholar
  16. 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.CrossRefGoogle Scholar
  17. 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.Google Scholar
  18. 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.CrossRefGoogle Scholar
  19. 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.CrossRefGoogle Scholar
  20. 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.CrossRefGoogle Scholar
  21. 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.CrossRefGoogle Scholar
  22. Loth, E. (2008). Quasi-steady shape and drag of deformable bubbles and drops. International Journal of Multiphase Flow, 34(6), 523–546.CrossRefGoogle Scholar
  23. Margaritis, A. (1999). Bubble rise velocities and drag coefficients in non-Newtonian polysaccharide solutions. Biotechnology and Bioengineering, 64(3), 257–266.CrossRefGoogle Scholar
  24. Mendelson, H. D. (1967). The prediction of bubble terminal velocities from wave theory. AIChE Journal, 13(2), 250–253.CrossRefGoogle Scholar
  25. 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.CrossRefGoogle Scholar
  26. 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.CrossRefGoogle Scholar
  27. Myint, W., Hosokawa, S., & Tomiyama, A. (2006). Terminal velocity of single drops in stagnant liquids. Journal of Fluid Science and Technology, 1, 72–81.CrossRefGoogle Scholar
  28. Myint, W., Hosokawa, S., & Tomiyama, A. (2007). Shapes of single drops rising through stagnant liquids. Journal of Fluid Science and Technology, 2, 184–195.CrossRefGoogle Scholar
  29. 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.CrossRefGoogle Scholar
  30. 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.CrossRefGoogle Scholar
  31. Peebles, F. N., & Garber, H. J. (1953). Studies on the motion of gas bubbles in liquids. Chemical Engineering Progress, 49, 88–97.Google Scholar
  32. 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.Google Scholar
  33. 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.CrossRefGoogle Scholar
  34. Rodrigue, D. (2001b). Generalized correlation for bubble motion. AIChE Journal, 47(1), 39–44.CrossRefGoogle Scholar
  35. 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.CrossRefGoogle Scholar
  36. Sawi, M. E. (1974). Distorted gas bubbles at large Reynolds number. Journal of Fluid Mechanics, 62(1), 163–183.CrossRefGoogle Scholar
  37. Schiller, L., & Naumann, Z. (1935). A drag coefficient correlation. Zeitschrift des Vereins Deutscher Ingenieure, 77, 318–320.Google Scholar
  38. 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.CrossRefGoogle Scholar
  39. 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.CrossRefGoogle Scholar
  40. Speight, M. V. (1964). The migration of gas bubbles in material subject to a temperature gradient. Journal of Nuclear Materials, 13(2), 207–209.CrossRefGoogle Scholar
  41. 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.Google Scholar
  42. 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.CrossRefGoogle Scholar
  43. 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.CrossRefGoogle Scholar
  44. 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.CrossRefGoogle Scholar
  45. 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.CrossRefGoogle Scholar
  46. 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.CrossRefGoogle Scholar
  47. Sun, F., Yao, Y., Li, G., & Li, X. (2018c). Geothermal energy extraction in CO2 rich basin using abandoned horizontal wells. Energy, 158, 760–773.CrossRefGoogle Scholar
  48. 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.CrossRefGoogle Scholar
  49. 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.CrossRefGoogle Scholar
  50. 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.CrossRefGoogle Scholar
  51. 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.CrossRefGoogle Scholar
  52. 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.CrossRefGoogle Scholar
  53. 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.CrossRefGoogle Scholar
  54. 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.CrossRefGoogle Scholar
  55. 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.CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geosciences 2019

Authors and Affiliations

  • Nannan Liu
    • 1
    • 2
  • Yong Yang
    • 3
  • Jian Wang
    • 5
  • Binshan Ju
    • 1
    • 4
    Email author
  • Eric Thompson Brantson
    • 5
  • Yapeng Tian
    • 1
    • 2
  • Yintao Dong
    • 1
    • 2
  • B. M. Mahlalela
    • 1
    • 2
  1. 1.School of Energy ResourcesChina University of Geosciences (Beijing)Haidian District, BeijingChina
  2. 2.Key Laboratory of Marine Reservoir Evolution and Hydrocarbon Enrichment MechanismMinistry of EducationBeijingChina
  3. 3.Research Institute of Petroleum Exploration and Development of Shengli Oilfield, Sinopec Corp.DongyingChina
  4. 4.Key Laboratory of Geological Evaluation and Development Engineering of Unconventional Natural Gas EnergyBeijingChina
  5. 5.Department of Petroleum Engineering, Faculty of Mineral Resources TechnologyUniversity of Mines and TechnologyTarkwaGhana

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