Investigation on laminar pipe flow of a non-Newtonian Carreau-Extended fluid

Jie Sun, Liejin Guo*, Jiaqiang Jing, Chao Tang, Yingda Lu, Jiqiang Fu, Amos Ullmann, Neima Brauner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Many fluids used in petroleum and chemical industries are generally described as complex systems that exhibit time-independent non-Newtonian behavior. To adequately represent the rheological behavior of an oil-tolerant and salt-resistant aqueous foam system, a Carreau-Extended (Carreau-E) rheological model, which includes a yield stress, a shear-thinning parameter and a time constant, has been established based on Carreau and Herschel-Bulkley models. In the present study, generalized Reynolds number definitions are proposed for laminar and fully developed pipe flow of non-Newtonian fluids (Carreau-E, Carreau, Herschel-Bulkley and Bingham fluids). Perturbation solutions for pipe flow of a Carreau-E fluid are obtained and their ranges of validity in the problem parameter space are identified. The quantitative effects of rheological parameters (e.g., yield stress, time constant, shear-thinning parameter) and flow parameters, (e.g., pressure gradient, pipe radius) on the velocity profile and flow rate in pipe flow of a Carreau-E fluid are explored. The results obtained for the flow characteristics can be applied or extended for other types of non-Newtonian fluid flow encountered in practical applications.

Original languageEnglish
Article number108915
JournalJournal of Petroleum Science and Engineering
StatePublished - Oct 2021


  • Carreau-extended fluid
  • Flow characteristics
  • Laminar pipe flow
  • Non-Newtonian fluid
  • Yield stress


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