Page 53 -

30 Part I Liquid Drilling Systems

Thus, for Bingham plastic fluids, Eqs. (2.15), (2.17), (2.19), and (2.21),
respectively, become
N Re = ρvd (2.25)
μ a

N Re = 0:816 × ρvðd 2 − d 1 Þ (2.26)
μ a

ρvd
N Re = 928 × (2.27)
μ a

N Re = 757 × ρvðd 2 − d 1 Þ (2.28)
μ
a

Illustrative Example 2.2
A 10.5-ppg Bingham plastic fluid with a plastic viscosity of 20 cp and yield
2
point of 5 lb/100 ft is circulating at 250 gpm in an 8¾-inch-diameter wellbore.
Determine the flow regime inside a 4½-in OD, 16.60-lb/ft drill pipe (3.826-in
ID), and in the drill pipe/hole annulus.

Solution
Inside the drill pipe:

v = 250 = 6:98 ft/s
2
2:448 × ð3:826Þ
μ = 20 + 6:66 × 5 × 3:826 = 38:25 cp
a
6:98
N Re = 928 × 10:5 × 6:98 × 3:826 = 6,803
38:25
Since N Re > 4,000, turbulent flow exists inside the drill pipe.
In the annulus:

v = 250 = 1:81 ft/s
2 2
2:448 × ð8:75 − 4:5 Þ
μ = 20 + 5 × 5 × ð8:75 − 4:5Þ = 78:70 cp
a
1:81
N Re = 757 × 10:5 × 1:81 × ð8:75 − 4:5Þ = 777
78:70
Since N Re < 2,100, laminar flow exists in the annular space.