multivariate production systems optimization - Stanford University

The hydrostatic head component of the total pressure gradient is then
dP g
=
dZ HH gC ρL HL + ρG HG = g
gC ρS
To determine the friction component, they proposed to use
dP =
dZ F
fM
2
ρS VM 2 gC D
where the Moody friction factor is obtained using a Reynold’s number of
Re = ρL VM D
μL
The acceleration component was considered to be negligible in the bubble flow regime.
Therefore, the total pressure gradient for the bubble flow regime is given by
3.4.2 Slug Flow Regime
dP =
dZ BUB
dP +
dZ HH
dP
dZ F
30
(3.54)
(3.55)
(3.56)
(3.57)
The density component in the slug flow regime uses the same definition for liquid holdup
and V BF employed in the bubble flow regime. However, V BS is defined as
where
VBS = C g D ρL - ρG
ρL
1 2
C = 0.345 1 - exp -0.029 NV 1 - exp
NE = g D ρL - ρG
σL
NV = g D3 ρL ρL - ρG 1 2
μL
where m in Equation 3.59 is evaluated as follows:
N V
m
3.37 - NE
m
(3.58)
(3.59)
(3.60)
(3.61)