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Shell Norway Module10 Relative Permeability

Feb 21, 2018

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    www.senergyworld.com/training

    Relative Permeability

    Module 10

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    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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    %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

    RFOIPRESERVES *=

    o

    w

    rw

    row

    k

    kf

    .1

    1

    +

    =

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    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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    Darcy+s aw

    L

    PPk

    A

    Q 21=

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

    pA

    LQk

    =

    & 9 !ermeability 'D(

    < 9 flow rate 'cm,/s(

    9 core area 'cm2(

    9 core lengt% 'cm(

    9 brine or oilviscosity 'c!(

    ! 9 differential!ressure 'atm(

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    >argon [email protected]

    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 (-)

    RelativePermeability(-)

    kro

    krw

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    $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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    $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 (-)

    RelativePermeability(-)

    )wir 9 0.20 )ro 9 0.27

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    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 (-)

    RelativePermeability(-)

    )wir 9 0.20 )ro 9 0.27

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    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 (-)

    RelativePermeability(-)

    )wir 9 0.20 )ro 9 0.27

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    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 (-)

    RelativePermeabilit

    y(-)

    )wir 9 0.20 )ro 9 0.27

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    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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    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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    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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    )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 (-)

    CapillaryPress

    ure(psi)

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    Residual 3il )aturation

    10 100

    Pore GcastsHof residual oil

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    aterflood Inter!retation

    elge

    A!erage "aturation

    #e$ind flood front

    "w at %&

    o

    w

    rw

    row

    k

    kf

    .1

    1

    +

    =

    fwonl' after %&

    1"or"w(

    fw)1

    "w

    Sw

    S fwf w S wf

    * +

    fw

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    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

    kf

    .1

    1

    +

    =

    w

    o

    ro

    rw

    k

    kM

    .=

    MK 1A !iston-li&e

    M L 1A unstable

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    >? Met%od 3utline

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

    9 PF water in4ected

    )wa 9 average '!lug( )w

    fw29 1-fo2

    o

    w

    rw

    row

    k

    kf

    .1

    1

    +

    =

    2

    2

    ,1

    -

    ,1

    -

    ro

    or

    k

    f

    Wd

    WId

    =

    2owa f

    dWdS =

    it

    t

    r p

    p

    I=

    =

    =

    0 n/e(ti!it' atio

    Waterflood rate

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    ?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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    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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    $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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    $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

    'FmwL 1(

    Nence com!osite

    sam!les

    or %ig% rates

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    $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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