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26 Part I Liquid Drilling Systems

If the rotary speed of the Fann VG meter is chosen to be N =300 rpm,
Eq. (2.10) degenerates to

K = 510 θ 300 (2.11)
n
ð511Þ

Herschel-Bulkley Fluids
The fluid yield stress τ y is normally taken as the 3 rpm reading, with the
flow behavior index n and the consistency index K then calculated from
the 600 or 300 rpm values or graphically. The approximate yield stress
τ y , commonly known as the low-shear-rate yield point, should be deter-
mined by

(2.12)
τ y = 2 θ 3 − θ 6
The fluid flow index n is given by

θ 600 − τ y
n = 3:322 log (2.13)
θ 300 − τ y
The fluid consistency index K is calculated by

ðθ 300 − τ y Þ
K = 500 n (2.14)
ð511Þ
For water-based drilling fluids containing large amounts of viscous poly-
mers and thus high θ 600 values, Eq. (2.12) can yield overstated values of τ y .
At high shear rates, it is acceptable to treat Herschel-Bulkley fluids as
Power Law fluids. The assumption is that the log-log slope of the
Herschel-Bulkley flow equation is numerically close to that of the Power
Law flow equation.

2.3 HYDRAULICS MODELS
The flow behavior of drilling mud can be described using mathe-
matical models called hydraulics models. These models define the rela-
tionship between flow rate and pressure drop for a given geometry of
flow conduit and fluid properties. The relationship also depends on flow
regime.