BAKER HUGHES - Drilling Fluids Reference Manual

HYDRAULICS
Figure 9 - 9 Flow in an Eccentric Annulus with Inner Cylinder Rotation
Power Law Constants, n and K
As described above, the consistency factor, K, describes the thickness of the fluid and is somewhat
analogous to the effective viscosity. The flow behavior index, n, indicates the degree of non-
Newtonian behavior. These two constants can be calculated from any two values of shear rate/shear
stress relationships. When readings are obtained from a V-G meter at 600 rpm, 300 rpm, and 3
rpm, two sets of n and K can be developed corresponding with fluid flow inside the drill pipe and
fluid flow in the annulus. This is done to improve the accuracy of hydraulic calculations in the drill
pipe or annulus since the Power Law Model does not exactly describe the behavior of drilling
fluids.
To obtain the power law constants corresponding to fluid flow inside the drill pipe, the 600 rpm
and 300 rpm readings are used.
n
p
⎛ θ
= 3.32log
⎜
⎝ θ
5.11×
θ
=
1022
n p
600
600
300
⎞
⎟
⎠
To obtain the power law constants corresponding to fluid flow in the annulus, the 300 rpm and
3 rpm (or initial gel strength) readings are used.
n a
⎛ θ
= 0.5 log
⎜
⎝ θ
5.11×
θ
K
a
=
n
5.11 a
300
300
3
⎞
⎟
⎠
where,
n = flow behavior index, dimensionless
K = consistency factor, poise.
Effective Viscosity
Since all drilling fluids are shear-thinning to some degree, the viscosity of the fluid changes with a
change in the shear rate. In order to calculate other hydraulic parameters, the effective viscosity at a
given rate of shear must be known. By definition, effective viscosity is the viscosity of a
Newtonian fluid that exhibits the same shear stress at the same rate of shear.
The equation for effective viscosity in pipe is:
96V
n p – 1
μe p
= 100K p
p ------------
D
where,
BAKER HUGHES DRILLING FLUIDS
REFERENCE MANUAL
REVISION 2006 9-11