TITLE : LAMINAR FLOW OF NON-NEWTONIAN FLUIDS IN CONCENTRIC ANNULI
BY : CHAM Development Team - G.Garnier
FOR : Validation of Non-Newtonian Models
DATE : 1997 PHOENICS Version : 3.0
PURPOSE OF THE CALCULATIONS:
PHOENICS calculations are performed for the laminar flow of viscous
non-Newtonian fluids in concentric annuli.
The main objective is to validate the PHOENICS implementation of
the Herschel-Bulkley (HB) rheological model against analytical and
The problem has practical relevance in the flow of drilling muds
in the annular space between the drillstring and the rock.
Numerical predictions can help the drilling engineer to adapt
fluid rheology and flow rate to the specific well geometry, so
that transport is efficient, while annular pressures
remain below the formation fracturation pressure.
The HB model relates the shear stress tau to the strain rate
Gamma via the consistency index K, the power law index n and the
yield stress tauy, i.e. tau= tauy + K*(Gamma**n).
The HB model simplifies to the power-law model when tauy=0. For
values of n<1, the fluid is pseudoplastic (shear thinning),
and for values of n>1, it is dilitant (shear thickening).
The motion only commences when the yield stress is exceeded.
The HB model reduces to the Bingham plastic model when n=1.
When tauy=0 and n=1, the fluid is Newtonian.
Calculations are made for fully-developed laminar flow of both
power-law and Herschel-Bulkley fluids so as to calculate the
frictional resistance, and hence pressure drop, by use of the
The parameters are: the Fanning friction factor f and the
Generalized Reynolds number, GRE based on the effective
diameter (see Reed & Pilehvari ).
The effective diameter is a function of both the annular geometry
and the rheology of the fluid, as defined by Reed & Pilhvari .
The experimental data on the friction factor f are given by f=16/GRE,
a result which is reproduced by PHOENICS.
PHOENICS calculations are also performed to produce the pressure-drop
versus flow-rate curve for the power-law data of Quigley et al