Shell Norway Module10 Relative Permeability

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Relative Permeability

Module 10



8 - 2

Definitions

bsolute Permeability!ermeability at 100" saturation of single fluid

e.g. brine !ermeability# gas !ermeability

$ffective Permeability

!ermeability to one !%ase w%en 2 or more !%ases!resent

e.g. &o'eff( at )wi


ratio of effective !ermeability to a base 'often absolute(!ermeability

e.g. *o/*a or *o/*o+ at )wi



8 - , 1- ,

%y core analysis matters recovery factor

Recovery factor de!ends on tec%nical and

economic factorsor secondary recovery 'e.g. waterflood( recovery

factor is !artly defined by relative !ermeability

RF OIP RESERVES *=

o

w

rw

row

k

k f

µ

µ .1

1

+

=



8 -

y!ical Reuirements

ater-3il Relative Permeability'&w-&o(water in4ection

5as-3il Relative Permeability '&g-&o(

solution gas drive

gas ca! drive

ater - 5as Relative Permeability '&w-&g(

auifer influ6 into gas reservoir

5as-ater Relative Permeability '&g-&w(gas storage 'gas re-in4ection into gas reservoir(



8 - 7 2 - 7

Darcy+s aw

L

P P k

A

Q 21 −= µ

1 mD 9 0.:8; 610-17 m2

p A

LQk

δ

µ =

& 9 !ermeability 'D(

< 9 flow rate 'cm,/s(

9 core area 'cm2(

9 core lengt% 'cm(

µ 9 brine or oilviscosity 'c!(

δ! 9 differential

!ressure 'atm(



8 - =

>argon ?uster@

Relative !ermeability curves are&nown as rel !erms

$nd!oints are t%e '( !oints at

t%e ends of t%e curves

%e dis!lacing !%ase is alwaysfirst# i.e.A

&w-&o is water'w( dis!lacing oil 'o(

&g-&o is gas 'g( dis!lacing oil 'o(

&g-&w is gas dis!lacing water

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Water Saturation (-)

R e l a t i v e P e r m e a b i l i t y ( - )

kro

krw



8 - ;

$nd!oints and Burves

Measure air !ermeability)aturate core in water 'brine(

Desaturate to )wir

Bentrifuge or !orous !late

Measure oil !ermeability *o+ C )wir end!oint

aterflood collect oil

Measure water !ermeability &w C)ro end!oint

So = 1-Swir

Swirr

Oil = Sro

Sw = 1-Sro



8 - 8

$nd!oints referenced to *o+

0.0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1.0

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0



)wir 9 0.20 )ro 9 0.27



8 - :

Burves - 1

0.0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1.0

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0



)wir 9 0.20 )ro 9 0.27



8 - 10

Burves - 2

0.0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1.0

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0



)wir 9 0.20 )ro 9 0.27



8 - 11

Burves - ,

0.0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1.0

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0


R e l a t i v e P e r m e a b i l i t

y ( - )

)wir 9 0.20 )ro 9 0.27



8 - 12


on-linear function of )wetBom!eting forces

gravity forces

minimised in lab tests

water in4ected from bottom

to to!

viscous forces

Darcy+s aw

ca!illary forces

flood rateswettability



8 - 1,

Relative Permeability Burves *ey

eatures

ater-3il Burvesirreducible water saturation ')wir( end!oint

&ro 9 1.0 &rw 9 0.0

residual oil saturation ')ro( end!oint

&ro 9 0.0 &rw 9 ma6imum

relative !ermeability curve s%a!e

Ensteady-state tests ?uc&ley-everett# elge# >?

)teady-state tests Darcy

Borey e6!onentsA o and w

)ome use *a or *l as &ro reference



8 - 1

Residual 3ilA Definitions

Residual 3il )aturation# )roAfinal oil saturation in lab flood tests

de!ends on flow rate# !ermeability# end effects# )wir

Remaining 3il )aturation 'R3)(minimum )o ac%ieved at end of field life

de!ends on viscous# gravity# ca!illary forces and t%enumber of PF of water t%at %ave !assed

different areas of reservoir may drain to different R3)

rue 'Eltimate( Residual 3il )aturation ')rot(function only of roc&/fluid system

saturation at w%ic% imbibition Pc becomes asym!totic



8 - 17

)aturation DistributionA aterflood

Prior to Waterflood

During Waterflood

After Waterflood

100

90

80

70

60

50

40

30

20

10

0

0 0.2 0.4 0.6 0.8 1


C a p i l l a r y P r e s s

u r e ( p s i )



8 - 1=

Residual 3il )aturation

10µ 100

µ

Pore GcastsHof residual oil



8 - 1;

aterflood Inter!retation

elge

A!erage "aturation

#e$ind flood front

"w at %&

o

w

rw

row

k

k f

µ

µ .1

1

+

=

f w onl' after %&

1"or "w(

f w)1

"w

S w

S f wf w S wf

* +

f w



8 - 18

Relative Permeability Inter!retation

elge/?uc&ley-everett fraction flowgives ratioA &ro/&rw

Decou!le &ro and &rw from &ro/&rw

>?# >ones and RosJelle# etc

o

w

rw

row

k

k f

µ

µ .1

1

+

=

w

o

ro

rw

k

k M

µ

µ .=

MK 1A !iston-li&e

M L 1A unstable



8 - 1:

>? Met%od 3utline

>o%nson# ?ossler# auman '>?(?ased on ?uc&ley-everett/elge

9 PF water in4ected

)wa 9 average '!lug( )w

fw2 9 1-fo2

o

w

rw

row

k

k f

µ

µ .1

1

+

=

2

2

,1

-

,1

-

ro

or

k

f

W d

WI d

=

2owa f

dW dS =

it

t

r p

p

I =

=

∆

∆=

0 n/e(ti!it' atio

Waterflood rate



8 - 20

?uc&ley everett ssum!tions

luids are immiscibleluids are incom!ressible

low is linear '1 Dimensional(

low is uni-directionalPorous medium is %omogeneous

Ba!illary effects are negligible

Most are not met in most core floods



8 - 21

Ba!illary $nd $ffect

If viscous force large '%ig% rate(Pc effects negligible

If viscous force small 'low rate(

Pc effects dominate flood be%aviour

everett

ca!illary boundary effects on s%ort cores

boundary effects negligible in reservoir



8 - 22

$nd $ffect

Pressure race for loodJero ∆! 'no in4ection(

start of in4ection

water nears e6it

∆! increases abru!tly until)w'e6it( 9 1-)ro and Pc nearsJero

su!!resses &rw?

)w'e6it( 9 1-)ro# Pc 0

fter ?

Rate of ∆! increase reduces as&rw increases



8 - 2,

$nd effects on s%ort core !lugs

?rea&t%roug% Recovery

ffected Pc end effects

t lengt%s L 27 cm

ittle effect on ?recovery

'Fmw L 1(

Nence com!osite

sam!les

or %ig% rates



8 - 2

$nd effects on s%ort core !lugs

Ra!a!ort and eas?rea&t%roug% recovery

oil volume recovered w%en

water brea&s t%roug%

affected by Pc end effects

t lengt%s L 27 cm

little effect on ? recovery

o/low end effects



8 - 27

Ba!illary $nd $ffects

Ra!a!ort and eas )caling BoefficientFµw L 1'cm2/min.c!( A minimal end effect

3vercome by

flooding at %ig% rate

using longer core

difficult for reservoir core 'limited by core geometry(

GbuttH several cores toget%er

Reservoir frontal advance rateabout 1 ft/day

y!ical laboratory rates

about 1700 ft/day for 1.7H core sam!les



8 - 2=

low Parameters

Nck

vLend

o

≈ σ φ

µ Nc

v w=

µ

σ

RateRateNNcendcend

(ml/h)(ml/h)

44 2!2!

"2#"2# ##$##$

!%#!%# ##2##2

4##4## ##2##2

ReservoirReservoir ##

RateRateNcNc

(ml/h)(ml/h)

44 "2 &"#"2 &"#-$-$

"2#"2# !% &!% & "#-%"#-%

!%#!%# "" &"" & "#-'"#-'

4##4## "2 &"2 & "#-'"#-'

ReservoirReservoir "#"#-$-$

or reservoir-a!!ro!riate data clab creservoir

If cend L 0.1 &ro and &rw decrease as cend increases

Relative Permeabilities are Rate-De!endent

$nd $ffect Ba!illary umber lood Ba!illary umber



8 - 2;

?um! lood

0.0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1.0

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0


R e l a t i v e P e r m e a

b i l i t y ( - )

ow Rate &rwO

?um! /lood &rwO

Ni % Rate &rw PPP



8 - 28

Bom!osite Bore Plug

Ba!illary end effects adsorbed by Bores 1 and



8 - 2:

Bom!osite Bore Plug ProblemsA

)am!le %eterogeneitydifferences in !orosity and !ermeability

Poor ca!illary contact between !lugs



8 - ,0

)am!le )election

Bore )electionall significant reservoir flow units

often constrained by !reserved core availability

core B scanning to select !lugs



8 - ,1

)am!le )election

)am!le c%aracterisation)$M

%in )ection

QRD

MIBP !ore siJe distribution



8 - ,2

est )tates

Gres%H or GPreservedH )tatetested Gas isH 'no cleaning(

often too oil wet 'e.g 3?M# long term storage(

GativeH state term also used 'defines GblandH mud(

GBleanedH )tatecleaned 'so6%let or miscible flus%(

water-wet e6!ected 'but could be oil-wet from so6%let(

GRestoredH )tate 'reservoir-a!!ro!riate wettability(native wettability restored

saturate in crude oil live oil or )3

if 53R low can use dead crude ageing 'c%ea!er(

if 53R %ig% must use live crude ageing 'e6!ensive(

age in oil at P to restore native wettability



8 - ,,

ettability

mott and E)?M tests reuiredettability !re-study 'can ta&e mont%s(

reservoir wettability

fres%-state# cleaned-state# restored-state wettabilities

?eware 3?M contamination in Gfres%-stateH tests

Reservoir condition tests most re!resentative

but e6!ensive and difficult

-1.0

0.0

1.0

-1.0 0.0 1.0

Amott

S ! M

3riginal )B8 !lugs

Not )o6 Bleaned

/lus% Bleaned

)R3D58S

$R-$

)R3D58S

3I8-$



8 - ,

Irreducible ater )aturation ')wir(

)wir essential for reliable waterflood data

Dynamic dis!lacement

flood wit% viscous oil t%en test oil

ra!id and can get !rimary drainage rel !erms

)wir too %ig% and can be non-uniform

Bentrifugefaster t%an ot%ers

)wir can be non-uniform

Porous Plate

slow# grain loss# loss of ca!illary contact

)wir uniform



8 - ,7

$6am!le )B Re!orts

Dynamic dis!lacement Porous Plate



8 - ,=

ab Fariation in )wir ')P$2882=(

ab ab * ab C ab +

#

'

"#

"'

2#

2'

!#

i ( )

+ynamic +isplacement

Porous Plate

...

"/# psi

2## psi



8 - ,;

Dynamic aterflood ests

est Met%odsaterflood '$nd-PointsA &o at )wi# &w at )row(

Ensteady-)tate 'relative !ermeability curves(

)teady-)tate 'relative !ermeability curves(

est Bonditions

fres% state

cleaned staterestored state

ambient or reservoir conditions



8 - ,8

Ensteady-)tate aterflood

)aturate in brineDesaturate to )wirr

3il !ermeability at )wirr 'Darcy analysis(

aterflood 'matc%ed viscosity(

otal 3il Recovery

&w at )row 'Darcy analysis(

labw

o

resw

o

=

µ

µ

µ

µ



8 - ,:

Ensteady-)tate Relative Permeability

)aturate in brineDesaturate to )wirr

3il !ermeability at )wirr 'Darcy analysis(

aterflood 'adverse viscosity ratio(

Incremental and total oil recovery

Intermediate relative !ermeability '>?(


µ

µ

µ

µ

o

w lab

o

w res

>>



8 - 0

)B Re!orts

20011:8



8 - 1

Ensteady-)tate Procedures

nl' oil rodu(ed

eaure oil !olue

ut After %reakt$roug$

eaure oil water !olue

Increasing ater Bollected

Bontinue until ::.6" water

Water Oil

3nly oil !roduced

Measure oil volume

>ust fter ?rea&t%roug%

Measure oil T water

volumes



8 - 2

Ensteady-)tate

Rel !erm calculations reuirefractional flow data at core outlet '>?(

!ressure data versus water in4ected

Many labs use %ig% oil/water viscosity ratio!romote viscous fingering

!rovide fractional flow data after ?

allow calculation of rel !erms

aterflood 'matc%ed viscosity ratio(

little or no oil after ?

little or no fractional flow 'no rel !erms(

or similar oil and water viscosity ratio - end !oints only

o

w

rw

row

k

k f

µ

µ .1

1

+

=



8 - ,

$ffect of dverse Fiscosity Ratio

0.0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1.0

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0


" r a c t i o n a l " l o w #

f w

o $ w = %&'1

Enstable flood front

$arly ?

Prolonged 2 !%ase flow

3il recovery lower

o $

w = %'1

)table flood front

? delayed

)u!!ressed 2 !%ase flow

3il recovery %ig%er



8 -

Ensteady-)tate ests

3nly !ost ? data are used for rel !ermcalculations

)w range restricted if matc%ed viscosities

dvantages

a!!ro!riate ?uc&ley-everett Gs%oc&-frontH

reservoir flow rates !ossible

fast and low t%roug%!ut 'fines(

Disadvantagesinlet and outlet boundary effects at lower rates

com!le6 inter!retation

) d )



8 - 7

)teady-)tate ests

Intermediate relative !ermeabilitycurves

desaturate to )wir

oil !ermeability at )wir 'Darcy

analysis(

in4ect oil and water simultaneously inste!s

determine )o and )w at steady state

conditions


relative !ermeability 'Darcy nalysis(

)t d )t t



8 - =

)teady-)tate

2008 1:8

)t d )t t P d



8 - ;

)teady-)tate Procedures

Summary

1&&( OilA &o at )wirr

Ratio 1A &o &w at )w'1(

Ratio 2AA &o &w at )w'2(

Ratio nA &o &w at )w'n(

1&&( Water A &w at )ro

)t d )t t E t d )t t



8 - 8

)teady-)tate versus Ensteady-)tate

5enerally %ig% flood rates '))(end effects minimised# !ossible fines damage

$asier analysisDarcy vs >?

)lower days versus %ours

$nd!oints may not be re!resentative

)aturation Measurementgravimetric 'volumetric often not reliable(

non-invasive 'I)M( or in situ 'I))M( saturation monitoring

E f I))M



8 - :

Ese of I))M

$6am!les from ort% )eaBore aboratories )MQ )ystem

low rate waterflood followed by bum! flood

Q-ray scanning along lengt% of core

end-!oints

some !lugs scanned during waterflood

res%-)tate ests

core drilled wit% oil-based mud

Q R )



8 - 70

Q-Ray )canner

)w'aI(

Q

- r a y a d s o r ! t i o n

0

" 100

"

Q-rays emittedQ-rays detected)canning

?ed

Bore%older

'invisible to Q-

rays(

Q-ray $mitter

'Detector

?e%ind(

E)) l d )



8 - 71

E)) lood )cans

)MQ $6am!le 1uniform )wir

oil-wet'( end effect

bum! flood removes end effect

some oil removed from body of

!lug

neutral-slig%tly oil-wet

E)) l d )



8 - 72

E)) lood )cans

)MQ $6am!le 2

s%ort sam!le

end effect e6tends t%roug%

entire sam!le lengt%

significant oil !roduced from

body of core on bum! flood

moderate-strongly oil-wet

data w%olly unreliable due to

!re-dominant end effect.

eed coreflood simulation

E)) lood )cans



8 - 7,

E)) lood )cans

)MQ $6am!le ,scanned during flood

minimal end effect

stable flood front until ?

vertical !rofile

bum! flood !roduces oil

from body of core

neutral wet

data reliable

E)) lood )cans



8 - 7

E)) lood )cans

)MQ $6am!le

)am!le 1;7 'fres%-state(

scanned during waterflood

unstable flood front

oil wetting effects

oil-wet end effectbum! !roduces incremental oil from

body of core but does not remove end

effect

neutral to oil-wet

data unreliable

E)) lood )cans



8 - 77

E)) lood )cans

)MQ $6am!le 7)am!le 1;7 re-run after

cleaning

increase in )wir

com!ared to fres%-state

test

no/minimal end effects

moderate-strongly

water-wet

E)) lood )cans



8 - 7=

E)) lood )cans

)MQ $6am!le =%eterogeneous coarse sand

variation in )wir

)ro variation !arallels )wir

end effect mas&ed by

%eterogeneity '(very low recovery at low rate'Ut%ief+Jones in !lug(

bum! flood !roducessignificant oil from body of core

neutral-wet

)teady state tests 'I))M(



8 - 7;

)teady-state tests 'I))M(

Bore lood )imulation



8 - 78

Bore lood )imulation

Nig% Fiscosity Ratioviscous fingering invalidates 1D flow assum!tion

ow Rate

end effects invalidate >?

Most E)) tests viewed wit% caution

if cend significant

if c not re!resentative

if >? met%od usedEse coreflood simulation

)imulation Data In!ut



8 - 7:

)imulation Data In!ut

lood data 'continuous(in4ection rates and volumes

!roduction rates

differential !ressure

luid !ro!ertiesviscosity# I# density

Imbibition Pc curve 'o!tion(

I))M )cans 'o!tion(?eware several non-uniue solutions !ossible

Nistory Matc%ing



8 - =0

Nistory Matc%ing

Pressure and !roduction

1** cc$min

0

100

200

,00

00

700

=00

;00

800

0#1 1#0 10#0 100#0 1000#0 10000#0 +ime (min)

,

i f f e r e n t i a l P r e s s u r e ( P a )

0#0

1#0

2#0

,#0

#0

7#0

=#0

O i l P r o d u c t i o n ( c c )

Measured differential !ressure )imulated differential !ressure Measured oil !roduction

)imulated oil !roduction

Nistory Matc%ing



8 - =1

Nistory Matc%ing

)aturation !rofiles

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.0 0.2 0. 0.= 0.8 1.0

.ormali/ed 0ore en2t3

W

a t e r S a t u r a t i o n

)imulation $6am!le >? Burves



8 - =2

)imulation $6am!le >? Burves

Relative Permeabilty 0urves

Pre-Simulation

0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1

0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1

Water saturation

R e l a t i v e P e r m e a b i l i t y

*rw

*ro

low rate end !oint

%ig% rate end !oint

)imulation $6am!le )imulated



8 - =,

!

Burves

Relative Permeabilty 0urves

Post Simulation

0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1

0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1

Water saturation

R e l a t i v e P e r m e a b i l i t y

*rw

*ro

low rate end !oint

%ig% rate end !oint

*rw )imulation

*ro )imulation

Borey $6!onents ater/3il )ystems



8 - =

Borey $6!onents ater/3il )ystems

Define relative !ermeability curve s%a!es?ased on normalised saturations

SwnS S S S Son

ror wi

row −=−− −−= 111

ror wi

wir w

S S S S Swn−− −=

1

k rw ) endoint krw

NoSonkro

krokron ==

:k ro ) endoint kro

NwSwnkrw

krwkrwn ==

:

ormalisation



8 - =7

ormalisation

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


W a t e r R e l a t i v e P e r m e a b i l i t y ( - )

"ale 1

"ale 2

krw at "rokrwn ) 1

)wn 9 1

&rwn 9 1

ater-3il Borey $6!onents



8 - ==

ater 3il Borey $6!onents

De!end on wettability

EsesA

inter!olate e6tra!olate data

lab data uality control

Wettability No (0

ro) N, (0

r,)

WaterWet 2 to 4 5 to 8

.nterediate Wet 3 to 6 3 to 5

ilWet 6 to 8 2 to 3

Bentrifuge ests



8 - =;

Bentrifuge ests

Dis!laced !%ase relative

!ermeability only

imbibition oil dis!laced &ro

drainage water dis!laced &rw

ests at ambient or elevated

!ressure tem!erature

synt%etic fluids or stoc& tan& oil

Bentrifuge s!un at single s!eed

!ressure differential across !lug

dis!laces oil

oil !roduction monitored versus

time

inter!retation based on Nagoort

( ) A !o"kro

ow

oo

ρ ρ

µ

−=

:1109

r 200001117.0 ω =

Bentrifuge tests



8 - =8

Bentrifuge tests

dvantages

arge !ressure difference

created wit%out creating

instability

arge »p reduces oil to

low saturationsKro at Sro “tail”

*ro ac%ieved ra!idly

imitations

*rw is not defined

*rw+ by flooding at )ro after

centrifuging

ettability may be an issue if

live fluids cannot be usedests can be !erformed on

restored-state core

Bentrifuge ests



8 - =:

Bentrifuge ests

Naugen '1::,(

&ro from centrifuge can define an

e6tension of waterflood curves

divergence at lower )o reflects

influence on ca!illary end effects

and flood instability in waterflood

tests

iev '1:88( )norre field

good agreement between steady-

state and centrifuge &ro

$nd effectsstill !resent but reduced

accounted for by com!uter

simulation

aboratory ests



8 - ;0

aboratory ests

Sou can c%oose fromAmatc%ed or %ig% oil-water viscosity ratio

cleaned state# fres% state# restored-state tests

ambient or reservoir condition

%ig% rate or low rateE)) versus ))

aboratory variation e6!ected

McP%ee and rt%ur ')P$ 2882=(

Bom!ared labs using identical test met%ods

3il Recovery



8 - ;1

3il Recovery

ab ab * ab C ab +

"#

2#

!#

4#

'#

%#

$#

i l e c e (

2

2

)

3i&ed - "2# ml/hour

Preerred

"2#

*ump

!%#

"2#

ettability



8 - ;2

ettability

ater wet

front moves at uniform rate

oil dis!laced into larger !ores

and !roduced

water moves along !ore

wallsoil tra!!ed at centre of large

!ores - Gsna!-offH

? delayed

oil !roduction essentially

com!lete at ?

ettability



8 - ;,

ettability

3il wet

water invades smaller !ores

earlier ?

oil remains continuous

oil !roduced at low rate after

?&rw %ig%er - fewer water

c%annels bloc&ed by oil

$ffects of ettability



8 - ;

$ffects of ettability

ater-etbetter &ro

lower &rw

&rw 9 &ro L 70"

better flood !erformance

3il-et

!oorer &ro

%ig%er &rw

&ro 9 &rw K 70"

!oorer flood !erformance

ettability $ffectsA ?rent ield



8 - ;7

y

Preserved Bore

eutral to oil-wet

low &ro - %ig% &rw

$6tracted Bore

ater wet

%ig% &ro - low &rw

Im!ortance of ettability - $6am!le



8 - ;=

! y !

ater et

o 9 2 w 9 8 )wir 9 0.20

)ro 9 0.,0# &rw+ 9 0.27# ultimate recovery 9 0.=27 3IIP

Intermediate et

o 9 w 9 )wir 9 0.17

)ro 9 0.27# &rw+ 9 0.7# ultimate recovery 9 0.;0= 3IIP

3il et

o 9 8 w 9 2 )wir 9 0.10

)ro 9 0.20# &rw+ 9 0.;7# ultimate recovery 9 0.;;8 3IIP

µo

/µw

9 ,A1

Relative Permeability Burves



8 - ;;

y

0.0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1.0

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0



&ro

&rw




8 - ;8

y

0.0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1.0

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0



&ro

&rw

I &ro

I &rw




8 - ;:

y

0.0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1.0

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0



&ro

&rw

I &ro

I &rw

3 &ro

3 &rw

ractional low Burves



8 - 80

0.0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1.0

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0


" r a c t i o n a l " l o w # f w ( - )

fw

ater et

)3R 9 0.,,

Recovery 9 0.7:




8 - 81

0.0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1.0

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0


" r a c t i o n a l "

l o w # f w ( - )

fw

I fw

I

)3R 9 0.

Recovery 9 0.82




8 - 82

0.0

0.1

0.2

0.,

0.

0.7

0.=

0.;

0.8

0.:

1.0

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0


" r a c t i o n a l " l o w # f w ( - )

fw

I fw

3 fw

3il et

)3R 9 0.=,

Recovery 9 0.,00

Bosts of ettability Encertainty



8 - 8,

It is really# really im!ortant to get wettability rig%t@@@

PF 120 MMbbls

3il Price ,0 E)V/bbls

Parameter Water-Wet 4W Oil wet

)wi 0.200 0.170 0.100Eltimate )ro 0.,00 0.270 0.200

Eltimate Recovery actor 0.=27 0.;0= 0.;;8)3R 0.,,0 0.0 0.=,0 ctual Recovery actor 0.788 0.82 0.,00)3IIP 'MMbbls( := 102 108Eltimate Recovery 'bbls( =0 ;2 8 ctual Recovery 'bbls( 7= : ,2

WossW 'MM E)V( 108 =8 178

Roc& e6ture



8 - 8

Fiscosity Ratio



8 - 87

$nd!oints de!endent on

viscosity ratio

use viscosity ratio matc%ed

to reservoir

$ffect on &ro and &rw

curves varyrelative !ermeability to t%e

non-wetting !%ase varies

wit% viscosity ratio for

sam!les K 1D '3de%# 1:7:(

&ro and &rw %ig%er for

viscous oil 'M 9 10.=(

5as-iuid Relative Permeability



8 - 8=

Drainage&g-&w and &g-&o

met%ods

unsteady-state

steady-state

centrifuge '&rw or &ro only(

Imbibition&w-&g

met%ods

unsteady-state 'including co-current imbibition(

steady-statecentrifuge 'water-decane(

residual gas saturation

counter current imbibition

centrifuge

5as-iuid Relative Permeability



8 - 8;

Ensteady-)tate

adverse mobility ratio 'µgKKµo or µw(

!rolonged two !%ase flow data after brea&t%roug%

)teady-)tate

&g-&o# &g-&w and &w-&g

saturation determination very uncertain wit%out I))M

muc% slower

Bentrifugeca!illary end effects reduced

5as %umidified to !revent mass transfer

else core dries out

5as-3il Met%ods



8 - 88

)teady-statesaturation determination uncertain wit%out I))M

)rog can be too %ig% on s%ort !lugsca!illary effects and unfavourable mobility ratio

Ensteady-stateca!illary effects and unfavourable mobility ratio on s%ortcores

early gas brea&t%roug%

reliable data using long com!osite core and at reservoir

conditions

Bentrifuge *ro 'gas dis!lacing oil(defines &ro curve only

&rg+ from end!oint gasflood test

5as-3il Relative Permeability



8 - 8:

est !erformed at )wir

5as is non wetting

ta&es easiest flow !at%

&ro dro!s ra!idly as )g

increases&rg %ig%er t%an &rw

)rog L )row in lab tests

end effects

)rog K )row in field)gc 2" - ="

Pore-)cale )aturation Distribution

y!ical 5as-3il BurvesA )emi-og



8 - :0

0.001

0.01

0.1

1

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0

5as Saturation (fractional)

R e l a t i v e P e r m

e a b i l i t y ( - )

&ro

&rg

1-')rogT)wi(

5as-3il Burves



8 - :1

Most lab data are artefacts

due to ca!illary end effects

tests best carried out on long

cores

insufficient flood !eriod

Real gas-oil curves)gc ,"

)rog is low and a!!roac%es Jero

Due to t%in film and gravity

drainage

&rg 9 1 at )rog 9 00.00001

0.0001

0.001

0.01

0.1

1

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0

Swi6S2 (fraction)

R e l a t i v e P e r m e a b i l i t y # r 2

Bom!osite 5as-3il Burves

Dg A 2.,

Do A .0

)gcA 0.0,

)rogA 0.10&rgO A 1.0

5as-3il Burves Borey Met%od



8 - :2

3il relative !ermeability

normalised oil saturation

5as relative !ermeability

normalised gas saturation)gcA critical gas saturation

No

Sonkro =

Sro Swir

Sro Swir S Son

−−−−−

=1

1

ScSro Swir

ScS Sn

−−−−

=1

N Snkr =

0orey 789onent :alues

Do to ;

Dg 1., to ,.0

Borey 5as-3il Burves



8 - :,

Swir &1;

ro 1&&r2< 1&&

Sro2 &&&&&

S2c &&%&&

0.00001

0.0001

0.001

0.01

0.1

1

0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0

5as Saturation (-)


*ro Do 9

&rg Dg 9 1.,&ro Do 9 ;

&rg Dg 9 ,.0

)gc 9 0.0,

5as-ater Met%ods



8 - :

Drainage '&g-&w(

unsteady-state 'waterflood and co-current imbibition test(steady-state

centrifuge '&rw only(

similar issues to gas-oil

Imbibition 'water-gas( !rocess is ca!illary dominated

unsteady-statevery stable dis!lacement and %ig% viscous force# )gr → 0

co-current test is !erformed on com!osite cores at low rate

steady-state

%ig% viscous force

saturation determination is uncertain wit%out I))M

Bentrifuge 'water-gas(

gas dissolution and com!ressibility issues

water-decane or water-!entane

Bounter-current imbibition

)gr only

Drainage 5as-ater Burves



8 - :7

)teady-state teste6am!le

og-linear scale

&rg+ L &rw+

5as saturationincreases

&rg increases to 1

&rw reduces to close to

Jero

Imbibition ater-5as Burves



8 - :=

Ensteady-state test e6am!le

og-linear scale

)rg ty!ically 20" - ,0"

ide range of *rw+

aterflood 'imbibition( tests



8 - :;

Bo-current imbibition 'low rate

waterflood(

vertically oriented sam!les

gravity stable

gas flood or centrifuge to )wir

&rg+ at )wir waterflood from bottom to to!

low rate so ca!illary forces

dominate

long com!osite core to minimise

end effects

*rw+ at )gr

aterflood 'imbibition( tests



8 - :8

)teady-)tatewater and gas in4ected simultaneously from )wir

incremental waterAgas in4ection ratios

&rw+ at )gr

reuires I))M

Bentrifuge ests



8 - ::

Imbibition

water-decane or water-

!entane

minimise gas

com!ressibility/diffusion

drainage Pc to )wir

*rg+ at )wir

imbibition Pc !ressure set to

ma6imum !ressure dro!

associated wit% auifer influ6

in reservoir

remove !lug and measure

*rw+ at )gr in core%older

Bounter-Burrent Imbibition ests



8 - 100

Dominated by ca!illary forces

Immerse sam!le in wetting

!%ase 'from controlled value of

)gi(

Monitor sam!le weig%t during

imbibition

Determine )gr from cross!lot

versus suare root time

ir-brine# decane-brine# or air-

toluene systems

o relative !ermeability data

)gr versus )gi relations%i!s

129.90 g129.90 g

BBIA Bom!osite Data 'and(



8 - 101

Re!eatability of BBI tests

ater-gas Borey e6!onents



8 - 102

ormalisation

5as relative !ermeability

ater relative !ermeability

ater saturation

w and gg %as narrow range as gas non-wettingA 2 to ,

w %as wider rangeA 2.7 to =

)imilar to o and g for gas-oil

( ) N Swnkr krn −== 1

ormalised Burves



8 - 10,

&rgn

ormalised Burves



8 - 10

&rwn

Relative Permeability )ummary



Muc% lab data are artefacted

ca!illary end effects on &rg# &ro and &rw)wir unre!resentative

ater-oil end!oint testsensure wettability conditioned

ensure re!resentative )wir

use matc%ed viscosity

use I)M and simulationuse Borey e6!onents for &r curves

use )) to verify &r curve s%a!es

consider centrifuge for ultimate end!oints

5as-3il tests

assume artefacted generate curves from Borey e6!onents and end!ointsater-gas testsuse centrifuge tests for end!oints and )wir

use )) tests wit% I))M

Documents

Shell Norway Module10 Relative Permeability