2 Inflow Performance

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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• 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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• 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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• 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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• 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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• 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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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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• 0he value o the +O$ is then given 0he value o the +O$ is then givenby5by5

%

p%aa!"#

=


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• &olve or the well fowing pressure5&olve or the well fowing pressure5

qaq%pp wf


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• 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

,

2 Inflow Performance

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