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<p>The Herschel-Bulkley (HB) model is considered one of the most accurate non-Newtonian fluid flow models, useful in vari­ous disciplines, including chemical, mechanical and petroleum engineering. Past literature has presented clear derivations and validation of Bingham Plastic and Power Law models, but the HB model’s equations as well as pressure estimation methods were not covered adequately. Such a derivation and validation are important for showing the methodology for future development of more accurate non-Newtonian rheological models by future researchers and students. This work addresses this shortcoming by investigating the HB modelling methodology for the annular flow. Therefore, a methodol­ogy flowchart is presented for finding equations for HB fluid’s velocity, flow rate, average velocity and relative velocity equations as well as their validation and comparison using experimental data, with 6.34 % average absolute percent error between the numerical model and the experimental pressure loss measurements. The errors can be attributed to inaccurate measurements or readings, as well as HB’s imprecise estimations. Next, the methodology of finding equations of two main estimation methods for pressure drop is presented. This research represents a significant foundational contribution, establishing a basis for advancing future studies in non-Newtonian fluids. It offers a methodology, presented in the form of a flowchart, that enhances the clarity of the process for future researchers. This approach paves the way for developing models that could achieve greater accuracy.</p>

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Stepwise derivation and comparison of the Herschel–Bulkley Laminar Fluid Flow equations—in Annulus

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月29日

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  • Rahman Ashena

摘要

The Herschel-Bulkley (HB) model is considered one of the most accurate non-Newtonian fluid flow models, useful in vari­ous disciplines, including chemical, mechanical and petroleum engineering. Past literature has presented clear derivations and validation of Bingham Plastic and Power Law models, but the HB model’s equations as well as pressure estimation methods were not covered adequately. Such a derivation and validation are important for showing the methodology for future development of more accurate non-Newtonian rheological models by future researchers and students. This work addresses this shortcoming by investigating the HB modelling methodology for the annular flow. Therefore, a methodol­ogy flowchart is presented for finding equations for HB fluid’s velocity, flow rate, average velocity and relative velocity equations as well as their validation and comparison using experimental data, with 6.34 % average absolute percent error between the numerical model and the experimental pressure loss measurements. The errors can be attributed to inaccurate measurements or readings, as well as HB’s imprecise estimations. Next, the methodology of finding equations of two main estimation methods for pressure drop is presented. This research represents a significant foundational contribution, establishing a basis for advancing future studies in non-Newtonian fluids. It offers a methodology, presented in the form of a flowchart, that enhances the clarity of the process for future researchers. This approach paves the way for developing models that could achieve greater accuracy.