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Gas and Liquid Injection Rates 191
(2007) found that this chart can be replaced by the following correlation
with good accuracy:
ðCN L Þ = 10 Y (9.29)
where
2
Y = −2:69851 + 0:15841X 1 − 0:55100X
1
3 4 (9.30)
+ 0:54785X − 0:12195X
1 1
and
X 1 = logðN L Þ + 3 (9.31)
Once the value of parameter (CN L ) is determined, it is used for calcu-
0:1
lating the value of the group N vL p ðCN L Þ ,where p is the absolute pressure
N 0:575 0:1 N D
p
vG a
at the location where the pressure gradient is to be calculated, and p a is
the atmospheric pressure. The value of this group is then used as an entry
in the second chart in Hagedorn and Brown’s model to determine param-
eter ðy L /ψÞ. Guo and colleagues (2007) found that the second chart can
be represented by the following correlation with good accuracy:
y L 2
ψ =−0:10307+0:61777½logðX 2 Þ+6−0:63295½logðX 2 Þ+6 (9.32)
3 4
+0:29598½logðX 2 Þ+6 −0:0401½logðX 2 Þ+6
where
0:1
X 2 = N vL p ðCN L Þ (9.33)
N 0:575 0:1
vG p N D
a
According to Hagedorn and Brown, the value of parameter ψ can be
0:38
N vG N
L
determined from the third chart using a value of group 2:14 .
N
D
N vG N 0:38
Guo and colleagues (2007) found that for L > 0:01 the third chart
N 2:14
D
can be replaced by the following correlation with good accuracy:
ψ = 0:91163 − 4:82176X 3 + 1232:25X 2
3 (9.34)
3 4
− 22253:6X + 116174:3X
3 3
where
0:38
N vG N
X 3 = L (9.35)
N 2:14
D
