Page 515 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

Flow of Fluids 471

where the gravitational pressure gradient is still the same as in Equation 6-833
and the frictional pressure gradient can be determined by subtraction from
Equation 6-84a or 6-843.

Annular Flow Regime

In the annular flow regime, the extent of liquid entrainment must first be
estimated, then the liquid holdup and the pressure gradient can be calculated.

Liquld Entrainment E,,
Calculation methods in this area have not been validated and may be poor.
First, calculation ve (critical gas velocity on set of entrainment) is made as follows:
v, = 0.00025(~] (3 (6-85)
0.5

If the value of the v, < v,, then there is no entrainment E, = 0. If vsg ve, then
the entrainment fraction should be estimated by
[ r v;y 11
E, =1-exp 0.23 3 (6-86)

where E, = mass fraction or volume fraction of the total liquid flow that is in
the form of entrained droplets

Equation 6-86 is an empirical correlation without experimental basis. Figure 654
graphically shows the liquid entrainment fraction far various values of the critical
entrainment velocity, ve.

Liquid Holdup H,

After E, fraction is calculated, the liquid holdup can be estimated. To
determine H,, dimensionless specific weight ratio f has to be known:

(6-87)

density of a Wdroplet mixture in the core of the annular flow
r: =
density of the gas phase
with this density ratio, other dimensionless parameters could be defined

X
x, = - (6-88a)
(Y:)o.6