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


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%.


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



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.


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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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