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Vertical Multiphase Flow
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(ressure Loss in Incline! (ipe
∆ Z
∆ P
θ
h
After Brown, Technology of Artificial Lift Methods, Vol 4, p. 71
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(ressure Loss )omponents
dZ
dv
g
v
d g
v f
g
g
dZ
dP m
c
mm
c
mmmm
ctot
ρ ρ θ ρ ++=
2sin
2
"levation
Friction
*cceleration
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Liui! +ol!up
V$
VL
g L
L L
V V
V H
+≡
( ) g L L Lm H H ρ ρ ρ −+= 1
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,ubin$ )urve
0
500
1000
1500
2000
2500
3000
3500
0 500 1000 1500 2000 2500 3000 3500 4000 4500
(ro!uction rate- &,/D
F l o w
i n $ b o t t o m h o l e p
r e s s u r e - p s i
,ubin$ )urve
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0ellbore )orrelations for Oil
"arl "mpirical Mo!els• Develope! primaril from !ata on hi$h flow
rate wells
• *ssume eual $as an! oil velocities• Mo!if Fannin$ friction factor to a$ree with
multiphase flow !ata
• (oettman an! )arpenter 1'24• a#en!ell an! ,homas 1514
• Fancher an! rown 1534
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(oettman an! )arpenter
• (ublishe! in 1'2
• ase! on fiel! !ata from % wells
– 3% flowin$ wells- 1' $as6lift wells
• ,ubin$ si7e8 2 3/9: an! 2 ;/9: OD
• ,otal liui! rate8 3
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a#en!ell an! ,homas
• (ublishe! in 151
• "#ten!e! (>) to hi$her flow rates
• ase! on !ata from li$ht6oil test well in
Vene7uela
• ,ubin$ si7e8 2 ;/9: an! 3 1/2: OD
• Flow rates8 1;5 6 '
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Fancher an! rown
• (ublishe! in 153
• "#ten!e! (>) to lower flow rates an!
hi$her =L?@s• ase! on !ata from 9
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0ellbore )orrelations for Oil
=enerali7e! "mpirical Mo!els• ase! on !imensional analsis b Duns
an! ?os
• Duns an! ?os 1534
• +a$e!orn an! rown 1534
• OrAis7ewsAi 15;4
• e$$s an! rill 1;34
• MuAherjee an! rill 1934
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Duns an! ?os
• (ublishe! in 153
• I!entifie! 1< !imensionless $roups
• &electe! % as important in multiphase
flow base! on e#tensive e#perimental
!ata
• Define! Bliui! hol!up:
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+a$e!orn an! rown
• (ublishe! in 153
• 0i!el accepte! throu$hout in!ustr
• ase! on !ata from 1'
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e$$s an! rill
• (ublishe! in 1;3
• ase! on e#perimental !ata from
incline!
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MuAherjee an! rill
• (ublishe! in 193
• ase! on !ata from 1 1/2: ID incline!
pipe• Develope! three separate correlations
– Ephill an! hori7ontal flow
– Downhill stratifie! flow
– Other !ownhill flow re$imes
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0ellbore )orrelations for Oil
Mechanistic Mo!els• *ttempt to pre!ict pressure !rop b
incorporatin$ all important variables an!
ri$orous !escription of phsicalprocesses
• MO* 1954
• &lvester > Gao 19;4• *nsari 19;4
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0ellbore )orrelations
Low =L? =as 0ells• =ra 1;%4
– 0et $ases- $as con!ensates
• ?os an! =ra 1514
• Oil well correlations ma also be useful
– Duns an! ?os 1534
– +a$e!orn an! rown 1534
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)ritical ?ate ,o Lift Liui!
• Most $as wells pro!uce some liui!s
• Liui!s ma be
– Vapori7e! in reservoir $as
– Free liui! in reservoir
• Liui!s will accumulate if not lifte! to surface
• *ccumulate! liui!s will re!uce pro!uctivit
• For a $iven set of con!itions- there is a
minimum flow rate to lift liui!s
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)ritical Velocit
( )[ ]
−= 21
4141
912.1
g
g Lt v
ρ ρ ρ σ
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)ritical ?ate
Tz A pvq t c !"!=
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