Flow patterns and pressure gradient correlation for oil–water core–annular flow in horizontal pipes

  • Haili HuEmail author
  • Jiaqiang JingEmail author
  • Jiatong Tan
  • Guan Heng Yeoh
Research Article


The water-lubricated transportation of heavy oil seems to be an attractive method for crude oil production with significant savings in pumping power. With oil surrounded by water along the pipe, oil–water core–annular flow forms. In this paper, the characteristics of oil–water core–annular flow in a horizontal acrylic pipe were investigated. Plexiglas pipes (internal diameter = 14 mm and length = 7.5 m) and two types of white oil (viscosity = 0.237 and 0.456 Pa·s) were used. Flow patterns were observed with a high-speed camera and rules of flow pattern transition were discussed. A pressure loss model was modified by changing the friction coefficient formula with empirical value added. Totally 224 groups of experimental data were used to evaluate pressure loss theoretical models. It was found the modified model has been improved significantly in terms of precision compared to the original one. With 87.4% of the data fallen within the deviation of ± 15%, the new model performed best among the five models.


oil–water flow core–annular flow (CAF) flow pattern transition pressure gradient empirical correlations 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 51779212 and 51911530129), Sichuan Science and Technology Program (Grant No. 2019YJ0350), China Postdoctoral Science Foundation funded project (Grant No. 2019M653483), and State Key Laboratory of Heavy Oil Processing (Grant No. SKLOP201901002).


  1. Al-Wahaibi, T. 2012. Pressure gradient correlation for oil–water separated flow in horizontal pipes. Exp Therm Fluid Sci, 42: 196–203.Google Scholar
  2. Al-Wahaibi, T., Al-Wahaibi, Y., Al-Ajmi, A., Al-Hajri, R., Yusuf, N., Olawale, A. S., Mohammed, I. A. 2014. Experimental investigation on flow patterns and pressure gradient through two pipe diameters in horizontal oil–water flows. J Petrol Sci Eng, 122: 266–273.Google Scholar
  3. Angeli, P., Hewitt, G. F. 1999. Pressure gradient in horizontal liquid–liquid flows. Int J Multiphase Flow, 24: 1183–1203.zbMATHGoogle Scholar
  4. Arney, M. S., Bai, R., Guevara, E., Joseph, D. D., Liu, K. 1993. Friction factor and holdup studies for lubricated pipelining—I. Experiments and correlations. Int J Multiphase Flow, 19: 1061–1076.zbMATHGoogle Scholar
  5. Bai, R. Y., Chen, K. P., Joseph, D. D. 1992. Lubricated pipelining: Stability of core–annular flow. Part 5. Experiments and comparison with theory. J Fluid Mech, 240: 97–132.Google Scholar
  6. Bannwart, A. C. 1999. A simple model for pressure drop in horizontal core annular flow. J Braz Soc Mech Sci, 21: 233–244.Google Scholar
  7. Bannwart, A. C. 2001. Modeling aspects of oil–water core–annular flows. J Petrol Sci Eng, 32: 127–143.Google Scholar
  8. Bannwart, A. C., Rodriguez, O. M. H., de Carvalho, C. H. M., Wang, I. S., Vara, R. M. O. 2004. Flow patterns in heavy crude oil–water flow. J Energ Resour Technol, 126: 184–189.Google Scholar
  9. Bensakhria, A., Peysson, Y., Antonini, G. 2004. Experimental study of the pipeline lubrication for heavy oil transport. Oil Gas Sci Technol, 59: 523–533.Google Scholar
  10. Brauner, N. 1991. Two-phase liquid–liquid annular flow. Int J Multiphase Flow, 17: 59–76.zbMATHGoogle Scholar
  11. Brauner, N. 1998. 2.3.5 Multiphase fluid flow and pressure drop: Liquid–liquid two-phase flow. Heat Exchanger Design Updates, 5.Google Scholar
  12. Brauner, N., Moalem Maron, D. 1992. Stability analysis of stratfied liquid–liquid flow. Int J Multiphase Flow, 18: 103–121.zbMATHGoogle Scholar
  13. Brauner, N., Moalem Maron, D. 1999. Classification of liquid–liquid two-phase flow systems and the prediction of flow pattern maps. In: Proceedings of the 2nd International Symposium on Two-Phase Flow Modeling and Experimentation, 9: 747–754.Google Scholar
  14. Charles, M. E., Govier, G. W., Hodgson, G. W. 1961. The horizontal pipeline flow of equal density oil–water mixtures. Can J Chem Eng, 39: 27–36.Google Scholar
  15. Chen, N. H. 1979. An explicit equation for friction factor in pipe. Ind Eng Chem Fundamen, 18: 296–297.Google Scholar
  16. Georgiou, E., Maldarelli, C., Papageorgiou, D. T., Rumschitzki, D. S. 1992. An asymptotic theory for the linear stability of a core–annular flow in the thin annular limit. J Fluid Mech, 243: 653–677.MathSciNetzbMATHGoogle Scholar
  17. Ghosh, S., Mandal, T. K., Das, G., Das, P. K. 2009. Review of oil water core annular flow. Renew Sust Energ Rev, 13: 1957–1965.Google Scholar
  18. Grassi, B., Strazza, D., Poesio, P. 2008. Experimental validation of theoretical models in two-phase high-viscosity ratio liquid–liquid flows in horizontal and slightly inclined pipes. Int J Multiphase Flow, 34: 950–965.Google Scholar
  19. Isaac, J. D., Speed, J. B. 1904. Method of piping fluids. U.S. Patent 759,374.Google Scholar
  20. Jain, A. K. 1976. Accurate explicit equation for friction factor. J Hydr Eng Div, 102: 674–677.Google Scholar
  21. Joseph, D. D., Bai, R. Y., Mata, C., Sury, K., Grant, C. H. R. I. S. 1999. Self-lubricated transport of bitumen froth. J Fluid Mech, 386: 127–148.zbMATHGoogle Scholar
  22. Joseph, D. D., Renardy, M., Renardy, Y. 1984. Instability of the flow of two immiscible liquids with different viscosities in a pipe. J Fluid Mech, 141: 309–317.zbMATHGoogle Scholar
  23. Lanier, D. 1998. Heavy oil: A major energy source for the 21st century. In: Proceedings of the 7th UNITAR International Conference on Heavy Crude and Tar Sands, 1: 361.Google Scholar
  24. Li, H. W., Wong, T. N., Skote, M., Duan, F. 2013. A simple model for predicting the pressure drop and film thickness of non-Newtonian annular flows in horizontal pipes. Chem Eng Sci, 102: 121–128.Google Scholar
  25. Marinescu, I. D., Rowe, W. B., Dimitrov, B., Ohmori, H. 2012. Tribology of Abrasive Machining Processes. William Andrew.Google Scholar
  26. Martínez-Palou, R., de Lourdes Mosqueira, M., Zapata-Rendón, B., Mar-Juárez, E., Bernal-Huicochea, C., de la Cruz Clavel-López, J., Aburto, J. 2011. Transportation of heavy and extra-heavy crude oil by pipeline: A review. J Petrol Sci Eng, 75: 274–282.Google Scholar
  27. McKibben, M. J., Gillies, R. G., Shook, C. A. 2000. Predicting pressure gradients in heavy oil–water pipelines. Can J Chem Eng, 78: 752–756.Google Scholar
  28. Moody, L. F. 1947. An approximate formula for pipe friction factors. Trans ASME, 69: 1005–1011.Google Scholar
  29. Oliemans, R. V. A., Ooms, G., Wu, H. L., Duijvestijn, A. 1987. Core–annular oil/water flow: The turbulent-lubricating-film model and measurements in a 5 cm pipe loop. Int J Multiphase Flow, 13: 23–31.Google Scholar
  30. Oliemans, R., Ooms, G., Wu, H., Duijvestijn, A. 1985. Core–annular oil/water flow: The turbulent-lubricating-film model and measurements in a 2-in pipe loop. In: Proceedings of the Middle East Oil Technical Conference and Exhibition, SPE-13725-MS.Google Scholar
  31. Ooms, G., Segal, A., van der Wees, A. J., Meerhoff, R., Oliemans, R. V. A. 1983. A theoretical model for core–annular flow of a very viscous oil core and a water annulus through a horizontal pipe. Int J Multiphase Flow, 10: 41–60.zbMATHGoogle Scholar
  32. Prada, J. W. V., Bannwart, A. C. 2001. Modeling of vertical core-annular flows and application to heavy oil production. J Energ Resour Technol, 123: 194–199.Google Scholar
  33. Rodriguez, O. M. H., Bannwart, A. C. 2008. Stability analysis of core-annular flow and neutral stability wave number. AIChE J, 54: 20–31.Google Scholar
  34. Rodriguez, O. M. H., Bannwart, A. C., de Carvalho, C. H. M. 2009. Pressure loss in core–annular flow: Modeling, experimental investigation and full-scale experiments. J Petrol Sci Eng, 65: 67–75.Google Scholar
  35. Russell, T. W. F., Charles, M. E. 1959. The effect of the less viscous liquid in the laminar flow of two immiscible liquids. Can J Chem Eng, 37: 18–24.Google Scholar
  36. Saniere, A., Hénaut, I., Argillier, J. F. 2004. Pipeline transportation of heavy oils, a strategic, economic and technological challenge. Oil Gas Sci Technol, 59: 455–466.Google Scholar
  37. Schorle, B. J., Churchill, S. W., Shacham, M. 1980. Comments on: “An explicit equation for friction factor in pipe”. Ind Eng Chem Fundamen, 19: 228.Google Scholar
  38. Serghides, T. 1984. Estimate friction factor accurately. Chem Eng, 91: 63–64.Google Scholar
  39. Shi, J. 2015. A study on high-viscosity oil–water two-phase flow in horizontal pipes. Ph.D. Thesis. Cranfield University.Google Scholar
  40. Shi, J., Yeung, H. 2017. Characterization of liquid–liquid flows in horizontal pipes. AIChE J, 63: 1132–1143.Google Scholar
  41. Singh, V., Lo, S. 2010. Predicting pressure drop in pneumatic conveying using the discrete element modelling approach. Prog Comput Fluid Dy, 10: 334.zbMATHGoogle Scholar
  42. Sotgia, G., Tartarini, P., Stalio, E. 2008. Experimental analysis of flow regimes and pressure drop reduction in oil–water mixtures. Int J Multiphase Flow, 34: 1161–1174.Google Scholar
  43. Strazza, D., Grassi, B., Demori, M., Ferrari, V., Poesio, P. 2011. Core–annular flow in horizontal and slightly inclined pipes: Existence, pressure drops, and hold-up. Chem Eng Sci, 66: 2853–2863.Google Scholar
  44. Tan, J. T., Jing, J. Q., Hu, H. L., You, X. Y. 2018. Experimental study of the factors affecting the flow pattern transition in horizontal oil–water flow. Exp Therm Fluid Sci, 98: 534–545.Google Scholar
  45. Tripathi, S., Bhattacharya, A., Singh, R., Tabor, R. F. 2015. Lubricated transport of highly viscous non-Newtonian fluid as core-annular flow: A CFD study. Procedia IUTAM, 15: 278–285.Google Scholar
  46. Zigrang, D. J., Sylvester, N. D. 1982. Explicit approximations to the solution of Colebrook’s friction factor equation. AIChE J, 28: 514–515.Google Scholar

Copyright information

© Tsinghua University Press 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Oil and Gas Reservoir Geology and ExploitationSouthwest Petroleum UniversityChengduChina
  2. 2.School of Mechanical and Manufacturing EngineeringUniversity of New South WalesSydneyAustralia
  3. 3.Oil & Gas Fire Protection Key Laboratory of Sichuan ProvinceChengduChina

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