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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.9

ISSN Imprimir: 2152-5102
ISSN En Línea: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.2019027635
pages 99-119


Mohammad Reza Khorsand Movaghar
Department of Petroleum Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, 1591634311, P.O. Box 15875-4413, Tehran, Iran


During the well-drilling operation, it is common practice to circulate non-Newtonian fluids as drilling mud through the annular spaces between the (rock) formation and the drill string. To have an efficient operation, it is crucial to predict the stress and velocity fields in this space precisely. Hence, to simulate the flow pattern of the drilling mud, a numerical study employing a finite volume method is performed for a laminar, steady state, and axial flow of non-Newtonian fluids through an annulus. The rheological behavior of fluid is interpreted by using the viscoelastic single extended pom-pom (XPP) model. To run the simulation, the integration operator is used on a staggered grid to discretize the governing equations in the control volume. In addition, an iterative solution algorithm that decouples the computation of momentum from that of the XPP differential equations is used to solve the discrete equations. In this study, the axial velocity; shear stress; all relevant normal stresses; and stretch, axial, and radial pressure gradients are presented. This study also refers to the influence of all rheological parameters on the solution as well as on the flow behavior. The outcome shows that despite the other differential viscoelastic models, the XPP model can predict the third normal stress tensor for viscoelastic fluid in two-dimensional axial annular flows; this eventuates in the precise prediction of the second normal stress difference, as well as the first normal stress difference. Finally, the results are compared with the analytical solution of the Giesekus viscoelastic model (implemented) in an annulus, which shows good agreement.


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