Page 90 - Handbook Of Multiphase Flow Assurance

Flow modeling 85

TABLE 4.4 Application of correlations to flow in cylindrical pipes
Correlation Geometry Development Observation
Beggs-Brill (Beggs and Brill, 1973) Inclined Empirical
Duns-Ross (Duns Jr. and Ros, 1963) Vertical Empirical
Hagedorn-Brown (Hagedorn and Brown, 1965) Vertical Empirical Small diameter
Mukherjee-Brill (Mukherjee and Brill, 1985) Inclined Empirical
Dukler (Dukler et al., 1964) Vertical Mechanistic Holdup model issues
Aziz (Aziz et al., 1972) Vertical Mechanistic

the flow modeling today is performed using software. Discussion and review of various flow
correlations is available in literature such as (Brill and Mukherjee, 1999).
To name a few correlations as in Table 4.4 and their typical application to flow in cylindri-
cal pipes,
A more detailed information on flow correlation is in the chapter on reference information.
Although each correlation had been fit to best accuracy to data available at the time,
broader application of two-phase flow correlations may provide ±50% accuracy in system
with different conditions.
At present both engineering firms and academia aim to use computational power to val-
idate three-phase correlations against ever larger data sets, including tens of thousands of
flow cases (Roullier et al., 2017). This results in a more reliable predictive capability of soft-
ware tools and more cost-effective production system design.

Dimensionless numbers
The dimensionless numbers more commonly used in flow assurance as in multiphase flow,
fluid interfaces or solids deposition modeling include:

ρvD inertialforce
Reynolds Re = =
µ viscousforce

µ momentum diffusion
Prandtl Pr = =
/
kC P thermal diffusion

v inertialforce
Froude Fr = =
( gD) 05 . gravitationalforce

v compressible fluid velocity
Mach Ma = =
v speed of inncompressible fluid
sound
Sound
∆ P pressure o frce
Euler Eu = = = energydissipatioon in fluid flow

ρ v 2 inertialforce