Stepwise mathematical derivation of the Herschel–Bulkley laminar fluid flow equations—in pipes
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T1 - Stepwise mathematical derivation of the Herschel–Bulkley laminar fluid flow equations—in pipes
AU - Ashena, Rahman
AU - Elmgerbi, Asad
AU - Badrouchi, Foued
AU - Mishani, Siamak
AU - Sotoudeh, Fatemeh
AU - Nekoeian, Sahand
PY - 2022/8/26
Y1 - 2022/8/26
N2 - Stepwise derivation of flow equations of the Herschel–Bulkley (HB) model is not available in the literature. Theseequations are crucial for mechanical, chemical and petroleum engineering academia and industries where fundamentalworks on non-Newtonian fluids may be done to reach future models and estimation methods. Therefore, this work focuseson derivation of laminar flow equations and estimation methods of HB fluids through pipes. In this work, first, stepwisederivation of the HB fluid flow parameters consisting of fluid velocity, flow rate, average velocity and relative velocityequations is presented, followed by a straightforward mathematical model for use in numerical solution. Next, stepwisemathematical derivation of the laminar pressure drop equations by Merlo et al. (An innovative model for drilling fluidhydraulics. Paper presented at the SPE Asia Pacific oil and gas conference, Kuala Lumpur, Malaysia, 1995) and Gjerstadand Time (SPE J 20:1–18, 2014) is presented, and finally practical and user-friendly calculation procedures for differentestimation methods are presented. The step-by-step derivation procedures presented in this work contribute to effectivelearning for engineering students and practitioners in addition to providing a clear example derivation guideline for futureresearchers to reach other more accurate non-Newtonian hydraulics models and estimation methods.
AB - Stepwise derivation of flow equations of the Herschel–Bulkley (HB) model is not available in the literature. Theseequations are crucial for mechanical, chemical and petroleum engineering academia and industries where fundamentalworks on non-Newtonian fluids may be done to reach future models and estimation methods. Therefore, this work focuseson derivation of laminar flow equations and estimation methods of HB fluids through pipes. In this work, first, stepwisederivation of the HB fluid flow parameters consisting of fluid velocity, flow rate, average velocity and relative velocityequations is presented, followed by a straightforward mathematical model for use in numerical solution. Next, stepwisemathematical derivation of the laminar pressure drop equations by Merlo et al. (An innovative model for drilling fluidhydraulics. Paper presented at the SPE Asia Pacific oil and gas conference, Kuala Lumpur, Malaysia, 1995) and Gjerstadand Time (SPE J 20:1–18, 2014) is presented, and finally practical and user-friendly calculation procedures for differentestimation methods are presented. The step-by-step derivation procedures presented in this work contribute to effectivelearning for engineering students and practitioners in addition to providing a clear example derivation guideline for futureresearchers to reach other more accurate non-Newtonian hydraulics models and estimation methods.
UR - https://doi.org/10.1007/s13202-022-01566-2
M3 - Paper
ER -
