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Mud Hydraulics Fundamentals 43

Power Law Fluids
For Power Law fluids, the pressure loss under laminar flow inside the drill
string and in the annulus can be estimated using the following equations
respectively:
h 96v 3n + 1 i n K
Δp f = ΔL (2.62)
d 4n 300d
and
n

Δp f = 144v 2n + 1 K ΔL (2.63)
d 2 − d 1 3n 300ðd 2 − d 1 Þ
Equations (2.62) and (2.63) are valid in U.S. field units. When expressed
in SI units, they take the following form:
8v 3n + 1 K
h i n
Δp f = 0:0019152 ΔL (2.64)
d 4n d
and
n

12v 2n + 1 K
Δp f = 0:0019152 ΔL (2.65)
d 2 − d 1 3n ðd 2 − d 1 Þ
There is no simple correlation found to estimate the friction factor for
pressure loss under turbulent flow of Power Law fluids. Therefore, the
original form of the friction loss equation has to be used. The following
equations are employed for pipe flow and annular flow respectively:
2
f ρv
Δp f = ΔL (2.66)
25:8d
and
2
f ρv
Δp f = ΔL (2.67)
21:1ðd 2 − d 1 Þ

Illustrative Example 2.6
Determine the system pressure loss for the well in Illustrative Example 2.5
assuming Power Law fluids with a consistency index of 20 cp equivalent and
a blow behavior index of 0.8.
Solution
According to Table 2.2, the pressure loss through the surface equipment is
equivalent to that through 479 ft of 4½-in, 16.6-lb/ft drill pipe.
(Continued )