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Gas and Liquid Injection Rates 189

ECD (ppg)
0 5 10 15 20
0

1000
2000
3000
Depth (ft) 4000

5000
6000

7000
Annular profile
8000
In-pipe profile
9000
Figure 9.11 Calculated ECD profile along the flow path.

The Hagedorn‒Brown Separated Flow Model
The Hagedorn‒Brown (1965) correlation is widely used in petroleum pro-
duction engineering for tubing performance calculations. It was proposed
by Lyons and colleagues (2009) for aerated liquid drilling operations. The
Hagedorn‒Brown correlation takes the following form in U.S. field units:

2 2
dp fW t Δðu Þ
m
144 = γ mix + + γ mix (9.23)
11
5
dz 2:97 × 10 D γ 2g c Δz
H mix
where
W t = total weight flow rate, lbf/day
γ mix = in situ mixture specific weight, lbf/ft 3
u m = mixture velocity, ft/s
and
(9.24)
u m = u SL + u SG
where
u SL = superficial velocity of liquid phase, ft/s
u SG = superficial velocity of gas phase, ft/s