Slot Flow Approximation for Herschel-Bulkley Drilling Fluid through Eccentric Annuli

The studies of fluid flow through eccentric annulus has been started since early
1940’s and numbers of solution in order to enhance the efficiency of the cutting
transport to the surface have been developed. The solution developed so far by many
investigators is either analytical or numerical and mostly involving parameters such as
velocity distribution, shear stress, shear rates and pressure drop.
The aim of this study is to develop and analyze the numerical solution of fluid
flow through eccentric annuli which is represented by slot of variable height with the
use of Herschel-Bulkley drilling fluid. Developed numerical solution is then used to
estimate the Velocity distribution in the eccentric annuli as well as to determine flow
rate for a given drilling condition. In addition, the rheology of non-Newtonian fluid
(Bingham, Power and Herschel-Bulkley) will be discussed.
By applying the correct assumption of eccentricity ratio (k=0.3) on the
numerical solution developed earlier, velocity distribution were obtained. Apart from
that, by representing the eccentric annuli as slot of variable height the accuracy of the
solution obtained can be improved and no iterative computation needed.