Multiphase Flow As in the multiphase flow in vertical pipe, in horizontal pipe there are distinct flow regimes. In horizontal flow there are divided up into 3 main types, Segregated Flow, Intermittent Flow and Distributive Flow. Segregated Flow is divided up into Stratified, Wavy and Annular Flow. Intermittent Flow is divided up in to Plug and Slug Flow. Distributive Flow is divided up in to Bubble and Mist Flow. These regimes are predicted by using flow regime maps such as Baker’s shown here.

Horizontal Flow Regimes

Dukler Method It is based on empirical correlations of friction factor and liquid holdup. Like vertical flow, will assume kinetic energy contribution to be negligible. And there will be no potential energy contribution.

gDuf

dLdp mk

2

2ρ= (2-33)

where

g

gg

l

llk yy

22 λρλρρ += (2-34)

The friction factor is obtained from the no-slip friction factor, fn, defined by (2-35) 32.0

Re )(5.0056.0 −+= kn Nf

m

mkk

DuNμρ1488

Re = (2-36)

The 2 phase friction factor is given by the correlation

( ) ( ) ( )432 ln00843.ln094.ln444.ln478.281.1ln1

llll

l

nff

λλλλλ

++++−= (2-37)

In the fig 2-8 the liquid holdup, yl, is a function of input liquid fraction, λl with NRek as a parameter. Since holdup is needed to figure NRek, determining the liquid holdup in an iterative process. Example of Dukler

qo = 2000 bpd qg = 1 mmcfpd Temp = 175 oF μo = 2 cp μg = .0131 Pipe = 2.5” ρo = 49.9 lb/ft3 ρg = 2.6 lb/ft3 Pressure = 800 psi Find the liquid holdup

1) find the velocities ul = qo/A = 2000*5.614 / .034*86400 = 3.81 ft/sec ug = qg * z * T * psc / A *Tsc * p

= 1E6*.935*635*14.7 / .034*520*800*86400 = 7.12 ft/sec um = ul + ug = 10.94 ft/sec 2) find λl

λl = ul / um = 3.81 / 10.94 = .35

2) find liquid holup, yl This is an iterative process Assume yl = λl and solve for ρk.

3

2222

/19.1965.

656.235.

35.9.49 ftlbyy g

gg

l

llk =

×+

×=+=

λρλρρ

916007085.

1488208.94.1019.19Re =

×××==

m

mkk

DuN

μρ .

This gives a value of .44 for yl, use this value to calculate a ρk

32222

/86.1556.

656.244.

35.9.49 ftlbyy g

gg

l

llk =

×+

×=+=

λρλρρ

758007085.

1488208.94.1086.15Re =

×××==

m

mkk

DuN

μρ

yl = .46 Calculate fn 019.758005.0056.)(5.0056.0 32.32.0

Re =×+=+= −−kn Nf

Find f/fn

( ) ( ) ( )432 ln00843.ln094.ln444.ln478.281.1ln1

llll

l

nff

λλλλλ

++++−=

( ) ( ) ( )432 35.ln00843.35.ln094.35.ln444.35.ln478.281.135.ln1

019. ++++−=

f

f = .036 Find the gradient

ftpsiftlbgDuf

dLdp mk /035./08.5

208.17.32292.1086.15036.

23

22

==××××

==ρ

Fig 2-8