multivariate production systems optimization - Stanford University

Moreover, the Sachdeva et al. (1986) model makes no attempt to distinguish between free
gas and solution gas, nor does it take into account the effect of different mixtures of
liquids. Despite all of its apparent shortcomings, the Sachdeva et al. (1986) model is,
relatively speaking, one the best available.
The first step of the Sachdeva et al. (1986) approach is to locate the criticalsubcritical
flow boundary. This is done by iterating and converging on YC in the
expression
YC =
K
K - 1 + 1 - X1 VL 1 - YC
X1 VG1
K
K - 1 + N 2 + N 1 - X1 VL
+
X1 VG2
N 2 1 - X1 VL
X1 VG2
Use the critical pressure ratio to determine the critical mass flux
2 1 - X1 1 - YC
GC = CD 2 gC 144 P1 ρM2 ρL
47
2
+ X1 K
K - 1 VG1 - YC VG2
K
K - 1
and use the upstream parameters to determine the mass flux at upstream conditions as
G1 = ρG QG + 5.615 ρL QL
2
150 π DCH 0.5
(4.5)
(4.6)
(4.7)
Compare the upstream mass flux with the critical mass flux. If the mass flux is greater than
the critical mass flux, G1 ≥ GC, then we are in the critical flow region and the maximum
downstream pressure is
P2 = YC P1
(4.8)
If the calculated mass flux is less than the critical mass flux, G1 < GC, then we are in the
subcritical flow region. The downstream pressure may be found by solving for the root of
the expression (G1 - G2 ), where G2 is found with the equations
Y = P2
P1
VG2 = VG1 Y
- 1
K
ρM2 = X1 VG2 + 1 - X1 VL -1
(4.9)
(4.10)
(4.11)