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46 Part I Liquid Drilling Systems

For turbulent flow, the pressure loss inside the drill pipe and in the annulus
are estimated respectively as
f c q ρ
2
Δp f = ΔL (2.70)
1421:22d 5

and
f a q ρ
2
Δp f = ΔL (2.71)
2 2 2
2 1
1421:22ðd 2 − d 1 Þðd − d Þ
The friction factors f c inside the drill pipe and f a in the annulus are calcu-
lated respectively as
− z
(2.72)
f c = yðC c N Re Þ
and
− z
(2.73)
a
f a = yðC N Re Þ

Illustrative Example 2.7
Determine the system pressure loss for the following well:
Total depth: 9,950 ft (3,036 m)
Casing: 9⅝ in, 43.5 lb/ft (8.755-in ID), set at 6,500 ft (1,982 m)
Open hole: 8½ in from 6,500 ft to 9,950 ft
Drill pipe: 9,500 ft of 4½ in, 16.6 lb/ft (3.826-in ID)
Drill collar: 450 ft of 6¾-in OD and 2¼-in ID
Surface equipment: Combination 3
Mud weight: 10.5 ppg
Yield point: 6 lb/100 ft 2
Consistency index: 20 eq. cp
Flow behavior index: 0.8
Mud flow rate: 300 gpm
Solution
According to Table 2.2 shown earlier, the pressure loss through the surface
equipment is equivalent to that through 479 ft of 4½ in, 16.6-lb/ft drill pipe.
Inside the drill pipe:

v = 300 = 8:37 ft/s
2
2:448ð3:826Þ