Numerical modeling of laminar and turbulent annular flows of power-law fluids in partially blocked geometries

Abstract

The presence of cuttings bed in deviated wellbores has an undesirable effect on wellbore hydraulics by reducing the open flow area. In addition, pipe eccentricity affects the annular frictional pressure gradient under such configurations. The lack of practical correlations to account for the combined effects of cuttings bed and eccentricity on frictional pressure gradient of power-law fluids is the major motivation of this study. Thus, the effect of partially blocked eccentric annuli on frictional pressure gradient of power-law fluids is investigated. A numerical model is first developed to realize the laminar and turbulent annular flow of power-law fluids in eccentric configurations. The numerical solution of the governing equations is pursued using the finite difference method. The results of our numerical model are verified through comparisons with the published results of frictional pressure gradients in the literature. The numerical results indicate that with an increase in cuttings bed height the frictional pressure gradient can increase exponentially. Numerous simulation scenarios are considered for the flow of power-law fluids in partially blocked eccentric annuli. Then, the simulation results are fitted using regression analysis to obtain explicit correlations for the prediction of laminar and turbulent frictional pressure losses. The proposed correlations are essential for an accurate estimation of the annular frictional pressure gradient and equivalent circulating density, which ensures safe and optimized drilling operations.