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Relative Permeability
Module 10
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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
Relative Permeability
ratio of effective !ermeability to a base 'often absolute(!ermeability
e.g. *o/*a or *o/*o+ at )wi
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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
+
=
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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(
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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(
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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
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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
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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
Water Saturation (-)
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
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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
Water Saturation (-)
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
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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
Water Saturation (-)
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
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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
Water Saturation (-)
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
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8 - 12
Relative Permeability
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
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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
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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
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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
Water Saturation (-)
C a p i l l a r y P r e s s
u r e ( p s i )
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8 - 1=
Residual 3il )aturation
10µ 100
µ
Pore GcastsHof residual oil
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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
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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
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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
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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
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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
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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
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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
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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
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8 - 27
Ba!illary $nd $ffects
Ra!a!ort and eas )caling BoefficientFµw L 1'cm2/min.c!( A minimal end effect
3vercome by
flooding at %ig% rate
using longer core
difficult for reservoir core 'limited by core geometry(
GbuttH several cores toget%er
Reservoir frontal advance rateabout 1 ft/day
y!ical laboratory rates
about 1700 ft/day for 1.7H core sam!les
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8 - 2=
low Parameters
Nck
vLend
o
≈ σ φ
µ Nc
v w=
µ
σ
RateRateNNcendcend
(ml/h)(ml/h)
44 2!2!
"2#"2# ##$##$
!%#!%# ##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 $ffect Ba!illary umber lood Ba!illary umber
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8 - 2;
?um! lood
0.0
0.1
0.2
0.,
0.
0.7
0.=
0.;
0.8
0.:
1.0
0.0 0.1 0.2 0., 0. 0.7 0.= 0.; 0.8 0.: 1.0
Water Saturation (-)
R e l a t i v e P e r m e a
b i l i t y ( - )
ow Rate &rwO
?um! /lood &rwO
Ni % Rate &rw PPP
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8 - 28
Bom!osite Bore Plug
Ba!illary end effects adsorbed by Bores 1 and
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8 - 2:
Bom!osite Bore Plug ProblemsA
)am!le %eterogeneitydifferences in !orosity and !ermeability
Poor ca!illary contact between !lugs
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8 - ,0
)am!le )election
Bore )electionall significant reservoir flow units
often constrained by !reserved core availability
core B scanning to select !lugs
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8 - ,1
)am!le )election
)am!le c%aracterisation)$M
%in )ection
QRD
MIBP !ore siJe distribution
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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
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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-$
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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
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8 - ,7
$6am!le )B Re!orts
Dynamic dis!lacement Porous Plate
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8 - ,=
ab Fariation in )wir ')P$2882=(
ab ab * ab C ab +
#
'
"#
"'
2#
2'
!#
i ( )
+ynamic +isplacement
Porous Plate
...
"/# psi
2## psi
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8 - ,;
Dynamic aterflood ests
est Met%odsaterflood '$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
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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
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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 '>?(
&w at )row 'Darcy analysis(
µ
µ
µ
µ
o
w lab
o
w res
>>
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8 - 0
)B Re!orts
20011:8
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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
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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
+
=
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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
Water Saturation (-)
" 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
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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 )
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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
&w at )row 'Darcy analysis(
relative !ermeability 'Darcy nalysis(
)t d )t t
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8 - =
)teady-)tate
2008 1:8
)t d )t t P d
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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
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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
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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 )
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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 )
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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 )
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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
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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
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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
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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
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8 - 7=
E)) lood )cans
)MQ $6am!le =%eterogeneous coarse sand
variation in )wir
)ro variation !arallels )wir
end effect mas&ed by
%eterogeneity '(very low recovery at low rate'Ut%ief+Jones in !lug(
bum! flood !roducessignificant oil from body of core
neutral-wet
)teady state tests 'I))M(
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8 - 7;
)teady-state tests 'I))M(
Bore lood )imulation
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8 - 78
Bore lood )imulation
Nig% Fiscosity Ratioviscous fingering invalidates 1D flow assum!tion
ow Rate
end effects invalidate >?
Most E)) tests viewed wit% caution
if cend significant
if c not re!resentative
if >? met%od usedEse coreflood simulation
)imulation Data In!ut
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8 - 7:
)imulation Data In!ut
lood data 'continuous(in4ection rates and volumes
!roduction rates
differential !ressure
luid !ro!ertiesviscosity# I# density
Imbibition Pc curve 'o!tion(
I))M )cans 'o!tion(?eware several non-uniue solutions !ossible
Nistory Matc%ing
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8 - =0
Nistory Matc%ing
Pressure and !roduction
1** cc$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
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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
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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
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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
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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
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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
Water Saturation (-)
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
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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
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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
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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
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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
$nd effectsstill !resent but reduced
accounted for by com!uter
simulation
aboratory ests
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8 - ;0
aboratory ests
Sou can c%oose fromAmatc%ed or %ig% oil-water viscosity ratio
cleaned state# fres% state# restored-state tests
ambient or reservoir condition
%ig% rate or low rateE)) versus ))
aboratory variation e6!ected
McP%ee and rt%ur ')P$ 2882=(
Bom!ared labs using identical test met%ods
3il Recovery
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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
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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
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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
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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
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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
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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
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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
Water Saturation (-)
R e l a t i v e P e r m e a b i l i t y ( - )
&ro
&rw
Relative Permeability Burves
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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
Water Saturation (-)
R e l a t i v e P e r m e a b i l i t y ( - )
&ro
&rw
I &ro
I &rw
Relative Permeability Burves
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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
Water Saturation (-)
R e l a t i v e P e r m e a b i l i t y ( - )
&ro
&rw
I &ro
I &rw
3 &ro
3 &rw
ractional low Burves
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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
Water Saturation (-)
" r a c t i o n a l " l o w # f w ( - )
fw
ater et
)3R 9 0.,,
Recovery 9 0.7:
ractional low Burves
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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
Water Saturation (-)
" 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
ractional low Burves
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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
Water Saturation (-)
" 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
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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
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8 - 8
Fiscosity Ratio
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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
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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
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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
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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
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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
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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
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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
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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
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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 (-)
R e l a t i v e P e r m e a b i l i t y ( - )
*ro Do 9
&rg Dg 9 1.,&ro Do 9 ;
&rg Dg 9 ,.0
)gc 9 0.0,
5as-ater Met%ods
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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
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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
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8 - :=
Ensteady-state test e6am!le
og-linear scale
)rg ty!ically 20" - ,0"
ide range of *rw+
aterflood 'imbibition( tests
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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
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8 - :8
)teady-)tatewater and gas in4ected simultaneously from )wir
incremental waterAgas in4ection ratios
&rw+ at )gr
reuires I))M
Bentrifuge ests
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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
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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(
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Re!eatability of BBI tests
ater-gas Borey e6!onents
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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
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&rgn
ormalised Burves
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&rwn
Relative Permeability )ummary
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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