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8/19/2019 2 Inflow Performance
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Infow PerormanceInfow Perormance
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Instructional ObjectivesInstructional Objectives
• Calculate the IPR or oil wellsCalculate the IPR or oil wells
• Calculate the IPR or gas wellsCalculate the IPR or gas wells
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Reservoir CapabilitiesReservoir Capabilities
• Darcy’s awDarcy’s aw! i"ui# fow in aminar $low through ai"ui# fow in aminar $low through a
permeable me#ium is #escribe# bypermeable me#ium is #escribe# byDarcy’s awDarcy’s aw
µ
=
s75.0r
r lnB
pphk10X08.7
q
w
eoo
wf 3
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Reservoir CapabilitiesReservoir Capabilities
• s % &'in $actor (#imensionless)s % &'in $actor (#imensionless)
w
a
a
r
r ln1
k
ks
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Pro#uctivity In#e*Pro#uctivity In#e*
• + common in#icator o li"ui#+ common in#icator o li"ui#reservoir behavior is PI orreservoir behavior is PI or
pro#uctivity in#e*pro#uctivity in#e*! Reerre# to as ,-. in &P/ nomenclatureReerre# to as ,-. in &P/ nomenclature
psi /D /STB
pp
qJ
wf
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Pro#uctivity In#e* in 0ermsPro#uctivity In#e* in 0erms
o Darcy’s awo Darcy’s aw
µ
=
s75.0r
r lnB
hk10X08.7J
w
eoo
3
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Calculating $lowrateCalculating $lowrate
• 1sing PI2 we can calculate fowrate21sing PI2 we can calculate fowrate2"2 "uic'ly an# easily rom"2 "uic'ly an# easily rom
)pp(Jq wf
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/*ercise 3/*ercise 3
• 4iven reservoir parameters54iven reservoir parameters5' %' %67 m#67 m#
h %h %87 t87 tµµoo % %79: cp79: cp
;;oo % % 39< R;=&0;39< R;=&0;
hole si>e %hole si>e % ? @ inches? @ inchess % 7s % 7
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ultiphase $lowultiphase $low
• ;ubblepoint pressure (p;ubblepoint pressure (pbb))! Pressure at which rst bubble o gas isPressure at which rst bubble o gas is
release# rom reservoir oilsrelease# rom reservoir oils
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ultiphase $lowultiphase $low
• Eogel’s ;ehaviorEogel’s ;ehavior! IPR Curve F Eogel plotte# the #ata usingIPR Curve F Eogel plotte# the #ata using
the ollowing #imensionless variablesthe ollowing #imensionless variables
and
p
pwf
maq
q
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Eogel CurveEogel Curve
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
q/qma
p w f / p r
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ultiphase $lowultiphase $low
• athematical mo#el or Eogel’sathematical mo#el or Eogel’scurvecurve
−
−=
2
8.02.01 p p
p p
qq wf wf
max
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ultiphase $lowultiphase $low
• athematical relationship betweenathematical relationship betweenEogel ("Eogel ("ma*ma*) an# Darcy (+O$)) an# Darcy (+O$)
8.1
pJ
8.1
!"#qma
×
=
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$in#ing Eogel "$in#ing Eogel "ma*ma*
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
q/qma
p w f / p r
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/*ercise
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/*ercise
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ultiphase $lowultiphase $low
• Combination Darcy=EogelCombination Darcy=Eogel
qma
J p%
1.8
q"
"
q%
&a'e
pwf
p%
( r e s s ) r e
p * o n s ' a n '
J
+ o , e l B e h a - i o r
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ultiphase $lowultiphase $low
• Gow to n#Gow to n# qqma*ma*::
( )
( )
( )
−−−+=≤
−=≥
−=
2
max 8.02.01:thenfor
:applieslawsDarcy',for
b
wf
b
wf bbb
wf b
bb
p
p
p
pqqqq p p
p pJ q p p
p pJ q
8.1
pJqq %%ma
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4as Reservoirs4as Reservoirs
• Pseu#ostea#y &tatePseu#ostea#y &tate! 0he behavior o gas fowing in laminar 0he behavior o gas fowing in laminar
fow through a porous me#iumfow through a porous me#ium(Darcy’s aw)(Darcy’s aw)
µ
=
s75.0r r lnT
pphk10X03.7q
w
e,
/wf
/
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q 2sf/4a
p w f s 1 p s i a
Calculation o IPR CurveCalculation o IPR Curve
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1sing the Real 4as1sing the Real 4as
Pseu#opressure (pPseu#opressure (ppp (p))(p))
]
=
s75.0r
r lnT
ppppkh1003.7
q
w
e
wf pp
an4
∫
µ
p
pp
o
4p
ppp
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/*ercise 6/*ercise 6
Plot the IPR CurvePlot the IPR Curve
4iven the ollowing #ata an# using the4iven the ollowing #ata an# using the
pressure s"uare# relationship5pressure s"uare# relationship5
'' % 377 m#% 377 m#
hh %
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IPR in 4as ReservoirsIPR in 4as Reservoirs
• -ones’ 4as IPR -ones’ 4as IPR! Problem FProblem F
•Darcy’s law vali# or laminar fow onlyDarcy’s law vali# or laminar fow only
•Gigh permeability gas wells pro#uce inGigh permeability gas wells pro#uce inturbulent fow near the wellboreturbulent fow near the wellbore
//
wf
/
%qaqpp
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DenitionsDenitions
γ
=
µ
=
wp
,1
w
e,
3
r h
T1016.3
%
hk
s75.0r
r lnT10.1
a
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hp
h
hp
h
Determination o hDetermination o h
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&olving -ones’ /"uation&olving -ones’ /"uation
• 0he fow rate is5 0he fow rate is5
%/
pp%aaq
/wf
//
=
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&olving -ones’ /"uation&olving -ones’ /"uation
• 0he value o the +O$ is then given 0he value o the +O$ is then givenby5by5
%
p%aa!"#
=
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&olving -ones’ /"uation&olving -ones’ /"uation
• &olve or the well fowing pressure5&olve or the well fowing pressure5
qaq%pp wf
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/*ercise 8/*ercise 8
• Calculate the IPR curve orCalculate the IPR curve or! hhpp %
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0ransient IPR Curves0ransient IPR Curves
• +ssumptions+ssumptions! Darcy’s an# -ones’ laws assume that theDarcy’s an# -ones’ laws assume that the
average pressure is constantaverage pressure is constant
! Drainage ra#ius2 rDrainage ra#ius2 ree2 is constant an# that2 is constant an# that
• 0hese assumptions are true in 0hese assumptions are true inpseu#oFstea#y state only2 i9e9 whenpseu#oFstea#y state only2 i9e9 when
all o the outer boun#aries o theall o the outer boun#aries o the
reservoir are reache#9reservoir are reache#9
p
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0ransient IPR Curves 0ransient IPR Curves
• 0he time to reach pseu#oFstea#y 0he time to reach pseu#oFstea#ystate (pss)2 tstate (pss)2 tstabstab2 can be calculate#2 can be calculate#
with the ollowing e"uationwith the ollowing e"uation
k
r 8
'
/e'
s'a%
µ
=
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/*ercise :/*ercise :
Oil Bell &tabili>ation 0imeOil Bell &tabili>ation 0ime• $in# t$in# tstabstab with the ollowing #atawith the ollowing #ata
! φφ % 793% 793
! µµoo % 79: cp % 79: cp! cctt % < J 37 % < J 37F:F: psipsiF3F3
! rree % 32:77 t % 32:77 t
$or the ollowing values o '5$or the ollowing values o '5
793 m#2 397 m#2 37 m#2 an# 377 m#793 m#2 397 m#2 37 m#2 an# 377 m#
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/*ercise H/*ercise H
4as Bell &tabili>ation 0ime4as Bell &tabili>ation 0ime• $in# t$in# tstabstab with the ollowing #atawith the ollowing #ata
! φφ % 793% 793
! µµgg % 797< cp % 797< cp! cctt % < J 37 % < J 37F8F8 psipsiF3F3
! rree % 32:77 t % 32:77 t
$or the ollowing values o '5$or the ollowing values o '5
793 m#2 397 m#2 37 m#2 an# 377 m#793 m#2 397 m#2 37 m#2 an# 377 m#
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0ransient $low 0ransient $low
'1
'
'3
's'a%
q
pwf
p 's'a% '3 ' '1
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0ransient IPR Curves0ransient IPR Curves
• 0ransient $low /"uation 0ransient $low /"uation! or oil wellsor oil wells
! or gas wells (low pressure only)or gas wells (low pressure only)
µ
µ
=
s87.03.3r
'klo,B6.16
pphkq
w'o
oo
wf
o
µ
µ
=
s87.0/3.3r
'klo,T1638
pphkq
w',
,
wf
,