Helical Flow of Yield-Viscoplastic Fluids in Concentric Annuli

Abstract Helical flow in an annulus is a case of both practical and theoretical relevance. Such flows occur for example in separation processes, journal bearings of rotating machinery and when drilling wells for accessing sub-surface geological structures. Most drilling hydraulic models are designed for purely axial flow due to the added complexity of flow with a rotating drill string. Rotation is either accounted for using some empirical correlations or tackled using CFD models. However, when the annulus is concentric, the problem simplifies considerably, and a relatively simple numerical solution is available, valid both for Newtonian and for inelastic non-Newtonian fluids. In addition to the effect of the string rotation rate on the axial pressure drop, the solution also gives the resulting string torque as well as the cross-sectional profiles of axial and tangential velocities and any presence of an unsheared plug region. Here we revisit this solution, with a specific focus on Herschel-Bulkley type fluids where the shear thinning properties result in a reduction of pressure loss with increasing rotational speed. The novelty of this work will be an empirical correlation for the pressure loss reduction as function of rotational speed, based on the numerical model. Results will be presented in terms of dimensionless quantities like Reynolds number and Taylor number, within the range of hydrodynamically stable flow.