12.
Where qg is in MSCF/d, D46 is the choke diameter (bean size) in 64ths of inches,
Δp is in psi, T1 is the temperature upstream of the choke in °R, γ is the heat capacity ratio, Cp/ Cv, α
is the flow coefficient of the choke, γg is the gas gravity, psc is the standard pressure, and p1 and p2 are
the pressure upstream and downstream of the choke, respectively.
The Single‐Phase Gas Flow Equations apply when the pressure ratio is equal to or greater than the critical
pressure ratio, given by
( )
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −
1
2 1
1
2
γ
γ
γ
p
p
c
When the pressure ratio is less than the critical pressure ratio, p2/p1 should be set to (p2/p1) c
and the single gas flow equation is used, since the flow rate is insensitive to the downstream pressure whenever the flow
is critical. For air and other diatomic gases, γ is approximately 1.4, and the critical
pressure ratio is 0.53.
In petroleum engineering operations, it is commonly assumed that flow through a choke is critical
whenever the downstream pressure is less than about half of the upstream pressure.
Gas‐Liquid Flow
Two phase flow through a choke has not been described well theoretically. To determine the flow rate of two phases
through a choke, empirical correlations for critical flow are generally used. Some of these correlations for critical flow
are generally used. Some of these correlations are claimed to be valid up to pressure ratios of 0.7 (Gilbert, 1954).
One means of estimating the conditions for critical two‐phase flow through a choke is to compare the velocity in the
choke with the two‐phase sonic velocity, given by Wallis (1969) for homogeneous mixtures as
[ ]
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
++=
−
vv
v
lcl
l
gcg
g
llggc 22
2
1
ρ
λ
ρ
λ
ρλρλ
Where vc is the sonic velocity of the two‐phase mixture and vgc and v lc are the sonic velocities of the gas
and liquid, respectively.
The empirical correlations of Gilbert (1954) and Ros (1960) have the same form, namely,
( )
D
GLRqA
p C
B
l
64
1
=
12