BAKER HUGHES - Drilling Fluids Reference Manual

Hydraulics
The Bingham Plastic Model includes a simple yield stress, but does not accurately describe the fluid
behavior at low shear rates. The Power Law Model more accurately describes the behavior at low
shear rates, but does not include a yield stress and therefore can give poor results at extremely low
shear rates. A typical drilling fluid actually exhibits behavior between the Bingham Plastic Model
and the Power Law Model. This sort of behavior approximates the Herschel Bulkley model which is
described below.
Determination of n and K
The Power Law constants n and K can be determined from any two sets of shear stress-shear rate data.
Baker Hughes Drilling Fluids has chosen to follow API Bulletin 13D in developing n and K values
from 300 rpm and three rpm V-G meter readings (initial gel shear rate is approximately equal to three
rpm) for the low shear rate region, and 600 rpm and 300 rpm readings for the high shear rate range.
The low shear rate region corresponds roughly to the shear rate existing in the annulus, while the high
shear rate region corresponds to the shear rate existing in the drill pipe. This may be written in
logarithmic form as,
log τ = logK + n( log γ)
A plot of shear stress versus shear rate on log-log paper is linear for a pseudo plastic fluid. As shown
in Figure 1–13, the slope of the curve is equal to n, and the intercept on the shear stress axis at γ = 1 is
equal to K (since log 1 = 0).
Log Θ 600
Log Θ 300
n p
Log Θ 600
–Log Θ 300
LOG DIAL READING, Θ
Log K
Log Θ 300
–log Θ 3
Log Θ 3
n a
n
3 rpm
Log 511 – log 5.11
Log Θ 300
–n a
log 511
300 rpm
Log 1022 – log 511
600 rpm
n p
log 1022
Log Θ 600
–n p
log 1022
n a
log 511
1
10 100 1000
SHEAR RATE, Ў
Figure 1-13
Determination of n and K
Reference Manual
Baker Hughes Drilling Fluids
1-18 Revised 2006