Soluções analíticas e numéricas para o escoamento laminar desenvolvido de fluído viscoplástico em dutos e anulares elípticos

Abstract

During the oil well drilling operations, the oscillations and the advancement of the drill makes the well takes an oval shape. This work presents an analytical and numerical study of the viscoplastic fluid flow of a Herschel-Bulkley fluid, through three types of elliptical cross sections ducts: elliptical, concentric and eccentric elliptical annulus. The objective is to analyze the effects of the pipe geometrical parameters, the kinematics of the flow and the fluid rheology over the pressure drop. The mathematical model was based on the mass and momentum balance equations and a constitutive equation expressing the stress tensor of the fluid. The analytical solutions employed were an analytical transformation of coordinates and other one based on in the slot flow model and the fluid flow was modeled as parallel plates in narrow annuli. For the numerical solution of the balance equations the finite volume method was used. The numerical simulations were carried out with PHOENICS-CFD. For validation of the results, comparisons with numerical and analytical results available in literature were done. Relevant engineering parameters were obtained, like velocity profiles, volumetric flow rate, shear stress profiles and an expression for the friction factor. The results for the concentric and eccentric circular annulus are adequately reproduced when the elliptical cross section tends towards unitary aspect ratio.