Optimal determination of rheological parameters for Herschel-Bulkley drilling fluids and impact on pressure drop, velocity profiles and penetration rates during drilling

Fully developed laminar flow of purely viscous non-Newtonian liquids through annuli, including the effects of eccentricity and inner-cylinder rotation

Experimental study and predictions of pressure losses of fluids modeled as Herschel–Bulkley in concentric and eccentric annuli in laminar, transitional and turbulent flows

An integrated approach is presented for the flow of Herschel–Bulkley fluids in a concentric annulus, modelled as a slot, covering the full range of flow types, laminar, transitional, and turbulent flows. Prior analytical solutions for laminar flow are utilized. Turbulent flow solutions are developed using the Metzner–Reed Reynolds number after determining the local power law parameters as functions of flow geometry and the Herschel–Bulkley rheological parameters. The friction factor is estimated by modifying the pipe flow equation. Transitional flow is solved introducing transitional Reynolds numbers which are functions of the local power law index. Thus, an integrated, complete and consistent set, combining analytical, semi-analytical and empirical equations, is provided which describe fully the flow of Herschel–Bulkley fluids in concentric annuli, modelled as a slot. The comparison with experimental and simulator data from various sources shows very good agreement over the entire range of flow types.

Laminar, transitional and turbulent flow of Herschel–Bulkley fluids in concentric annulus

An analytical solution is given for the kinematic and stress variations across the radial gap of a concentric annular flow in fully developed conditions. The fluid is viscoelastic and obeys the non-linear rheological constitutive equation proposed by Phan-Thien and Tanner [1]. This constitutive model simulates well the material functions of many polymer melts and solutions and therefore, the present results are useful in a number of practical situations. The ratio of pressure drop to flow rate drop is found to be a complex mathematical function of the radial position of zero shear stress and this, in turn, depends weakly on the elasticity, based on the product of an elongational parameter by a Deborah number defined with an averaged velocity. There is thus a non-linear coupling which could not be solved in an explicit way for the inverse problem of an imposed flow rate, but an iterative procedure gives a ready result. For the direct problem of a given pressure drop the present results represent an exact explicit solution to the axial annular flow problem. Representative profiles of the solution are given and discussed. It is found that, for a given flow rate, the pressure drop scaled with the corresponding Newtonian value is independent of the diameter ratio. © 2000 Elsevier Science B.V. All rights reserved.

Richard W. Hanks

Papers

The Axial Laminar Flow of Yield-Pseudoplastic Fluids in a Concentric Annulus