The combined effect of fluid rheology, inner pipe rotation and eccentricity on the flow of Newtonian and non-Newtonian fluid through the annuli

Abstract

The accurate prediction of the fluid dynamics and hydraulics of the axial or helical flow of non-Newtonian drilling fluids in the annuli is essential for the determination and effective management of wellbore pressure during drilling operations. Previous studies have shown that the pressure losses and fluid velocity distributions in the annuli are highly influenced by the rheological properties of the fluid, inner pipe rotary speed and eccentricity. However, many studies in literature have developed or applied theoretical models that were either only valid for Newtonian annuli flows or have not considered the combined effect of the fluid rheological parameters with the inner pipe rotary speed and eccentricity when calculating the frictional annuli pressure losses for non-Newtonian shear thinning fluids. Furthermore, there have been inconsistencies in the description of the effect of inner pipe rotation on the pressure losses experienced for both Newtonian and non-Newtonian flows in concentric and eccentric annuli. In this study, an analytical and numerical approach were carried out to investigate and evaluate the hydrodynamic behaviour of the axial and helical isothermal flow of Newtonian and non-Newtonian fluids through the annuli. Techniques of computational fluid dynamics for fully developed steady-state fluid flow were applied to obtain detailed information of the flow field in the annuli. New analytical and numerical models were developed to obtain the fluid velocity and viscosity field distribution and determine the frictional pressure gradient for laminar and turbulent flows in the concentric and eccentric annuli with and without inner pipe rotation and were compared and validated favourably with models previously presented in literature. Results showed that for a fully developed flow of non-Newtonian shear thinning fluids, if the fluid flowrate is kept constant, an increase in inner pipe rotation leads to a decrease in the axial frictional pressure gradient when the pipe is rotating on its axis. For annuli flows of non-Newtonian fluids, the effect of inner pipe rotation on the axial pressure gradient is dependent on the fluid flowrate and at high fluid flowrates, the influence of the inner pipe rotation on the fluid hydraulics decreases. In general, for shear thinning non-Newtonian fluids, pipe rotation can improve the fluid flow in the region of lower flow in the eccentric annuli. Unlike the flow of Newtonian fluids through the annuli, the friction geometry parameter and thus the friction factor is highly influenced by the rheological parameters of the fluid, the fluid flowrate, inner pipe rotary speed and eccentricity.