Three-dimensional numerical simulation, sensitivity analysis, and practical implications for crude oil pipeline flow

Sarah Khaindi Wandabwa; David Angwenyi; Frankline Tireito

doi:10.51867/scimundi.maths.6.2.22

Authors

Sarah Khaindi Wandabwa Department of Mathematics, Masinde Muliro University of Science and Technology, Kakamega, Kenya
David Angwenyi Department of Mathematics, Masinde Muliro University of Science and Technology, Kakamega, Kenya https://orcid.org/0000-0002-6958-2817
Frankline Tireito Department of Mathematics, Masinde Muliro University of Science and Technology, Kakamega, Kenya https://orcid.org/0000-0002-4106-4022

DOI:

https://doi.org/10.51867/scimundi.maths.6.2.22

Keywords:

Bend losses, crude oil pipeline, finite element method

Abstract

This paper presents comprehensive three-dimensional numerical simulations of crude oil flow in pipelines using the finite element method to investigate the effects of inlet velocity, fluid viscosity, pipe diameter, and bend curvature on flow behavior and energy consumption. The validated Navier–Stokes solver with k-epsilon turbulence model is employed. Results show that pressure drop increases linearly with velocity in laminar flow and as U^1.75 in turbulent flow; doubling velocity increases pumping power by a factor of 6.4. Bitumen (μ = 0.5 Pa·s) experiences 43 times higher pressure drop than light crude (μ = 0.001 Pa·s) at the same flow rate. Pressure drop scales as D^-5 at constant flow rate; increasing diameter from 0.5 m to 0.8 m reduces annual energy costs by 94%. Long-radius bends (Rc/D ≥ 3) reduce bend losses by 50–60% compared to short-radius bends, following the correlation K = 0.21(Rc/D)^-0.5. Sensitivity analysis identifies inlet velocity as the most influential parameter (SU = 1.78), and uncertainty quantification yields a combined uncertainty of ±15.3% in pressure drop predictions. These findings provide quantitative guidance for pipeline design, operation, and cost optimization.

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