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Mud Hydraulics Fundamentals 45

In the open-hole/drill pipe annulus:
v = 300 = 2:36 ft/s
2 2
2:448 × ð8:5 − 4:5 Þ
0:8
N Re = 109,000 × 10:5 × 2:36 ð2−0:8Þ × 0:0208 × ð8:5 − 4:5Þ
20 2 + 1/0:8
= 8,544 > 3,174 turbulent flow
f = 0:0791 = 0:00823
8,544 0:25
Δp f = 0:00823 × 10:5 × 2:36 2 × 3,000 = 17 psi
21:1 × ð8:5 − 4:5Þ
In the open-hole/drill collar annulus:

v = 300 = 4:59 ft/s
2 2
2:448 × ð8:5 − 6:75 Þ
0:8
N Re = 109,000 × 10:5 × 4:59 ð2−0:8Þ × 0:0208 × ð8:5 − 6:75Þ
20 2 + 1/0:8
= 9,798 > 3,174 turbulent flow
f = 0:0791 = 0:00795
9,798 0:25

Δp f = 0:00795 × 10:5 × 4:59 2 × 450 = 21 psi
21:1 × ð8:5 − 6:75Þ
The total system pressure loss is
Δp d = 408 + 211 + 30 + 17 + 21 = 687 psi = 4,737 kPa

Herschel-Bulkley Fluids
For Herschel-Bulkley fluids, the pressure loss under laminar flow can be
calculated in U.S. field units using the following equations.
Inside the drill pipe:
n
8q
Δp f = 4K τ y + 3n + 1 ΔL (2.68)
14400d K nC c πd 3
In the annulus:
n

Δp f = 4K τ y + 16ð2n + 1Þ q ΔL
K 2 2
1
2
a
14400ðd 2 − d 1 Þ n × C ðd 2 − d 1 Þ πðd − d Þ
(2.69)