Introduction to Relative PermeabilityIntroduction to Relative Permeability

AFES MeetingAFES Meeting

Aberdeen 28Aberdeen 28thth March 2007March 2007

Dave Mogford

ResLab UK Limited

Outline

1.1. IntroductionIntroduction2.2. Basic ConceptsBasic Concepts3.3. Overview of Test MethodsOverview of Test Methods4.4. InterpretationInterpretation

Introduction –What is Relative Permeability?

Relative Permeability is a concept used toRelative Permeability is a concept used todescribe the movement of more than onedescribe the movement of more than onefluid in a porous medium.fluid in a porous medium.

Introduction –Why Measure?

•• Important in many reservoir engineeringImportant in many reservoir engineeringcalculationscalculations

•• Provides a basic description of how fluidsProvides a basic description of how fluidsmove through the reservoirmove through the reservoir

•• Assists in determining many aspects ofAssists in determining many aspects ofreservoir economics and influences topreservoir economics and influences toplevel decision making by allowinglevel decision making by allowingprediction ofprediction of—hydrocarbon recovery rate—total recoverable reserves—water cut

Introduction –Why Measure?

Production profiles and ultimate recoveryProduction profiles and ultimate recoverydetermined by:determined by:

1.1. static reservoir descriptionstatic reservoir description— volumetrics— reservoir architecture

2.2. dynamics of multiphase flowdynamics of multiphase flow— relative permeabilities— capillary pressure

Outline

1.1. IntroductionIntroduction2.2. Basic ConceptsBasic Concepts3.3. Overview of Test MethodsOverview of Test Methods4.4. InterpretationInterpretation

Basic Concepts

General Expression for Fluid Flow DevelopedGeneral Expression for Fluid Flow Developedby Darcy in 1856.by Darcy in 1856.

K is a constant when:• the flow is laminar and

Newtonian• the fluid does not interact with

the rock• the rock is completely saturated

and fluid is continuous.

where:q = the rate of fluid flow (mL/s)A = cross-sectional area (cm2)µ = viscosity of the flowing fluid (cp)∆P = pressure drop across the sample (atm)L = length core (cm)K = constant of proportionality - absolutepermeability (Darcies)

LPKA

q

Basic Concepts

Relative Permeability is defined by setting upRelative Permeability is defined by setting upthe Darcy Equation individually for each phase ithe Darcy Equation individually for each phase ithat flows through the pore space:that flows through the pore space:

where:qi = flow rate of phase iµi = viscosity of phase i∆Pi = pressure drop within phase iA = cross-sectional areaL = length coreKkri = total permeability of phase i

L

PA

Kkq

i

i

rii

)(

Primary Drainage kro,krw...

• Measured primary drainage kro (orkrg) krw is normalised kr usuallyreferenced to Kabs brine

• Note: imbibition kr and secondarydrainage kr is referenced to ke at Swi

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Sw (PV)

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ativ

ep

erm

eab

ility

,kr

krw

kro (or krg)

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Water Saturation,Sw

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ativ

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erm

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,kr

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Oil

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Water Saturation,Sw

Rel

ativ

eP

erm

eab

ility

,kr

Water

Oil

Outline

1.1. IntroductionIntroduction2.2. Basic ConceptsBasic Concepts3.3. Overview of Test MethodsOverview of Test Methods4.4. InterpretationInterpretation

Overview of Test Methods

••Unsteady stateUnsteady state

••Steady stateSteady state

••CentrifugeCentrifuge

The basic methods used to measure relativeThe basic methods used to measure relativepermeability are:permeability are:

Overview of Test Methods: USS

•• Displacing phase injected into a core at initial conditionsDisplacing phase injected into a core at initial conditions

•• Injection Rate SelectionInjection Rate Selection

•• Either carried out at constant pressure drop or constant flowratEither carried out at constant pressure drop or constant flowratee— Constant pressure drop sometime used in gas floods due to difficulties in

maintaining constant flowrate with compressible gases— Constant flow rate normally used in oil or water floods

•• Pressure drop across the core measuredPressure drop across the core measured

•• Produced fluids of both phases monitoredProduced fluids of both phases monitored

•• Bump floods are normally carried out end of initial displacementBump floods are normally carried out end of initial displacement totoproduce further oilproduce further oil

USS (also termed as displacement or dynamic method)USS (also termed as displacement or dynamic method)

Overview of Test Methods: USS

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•W

ater

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ctio

n(P

V)

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Breakthrough

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•P

ress

ure

(psi

)

Main Flood

Bumped Flood

Overview of Test Methods: USS

•• Relatively quick to performRelatively quick to perform•• Reproduces correct poreReproduces correct pore

level displacementlevel displacementmechanismsmechanisms

•• BreakBreak--through recoverythrough recovery•• Post breakPost break--through data andthrough data and

endend--point recoverypoint recovery

AdvantagesAdvantages DisadvantagesDisadvantages

•• Rel perm data only collectedRel perm data only collectedin 2 phase flow regionin 2 phase flow region

•• Complex interpretationComplex interpretationprocedures to calculate relprocedures to calculate relperm (JBN, CFS)perm (JBN, CFS)

•• Capillary pressure effectsCapillary pressure effectscan distort recovery andcan distort recovery andpressure drop datapressure drop data

•• High flowrates required toHigh flowrates required toreduce capillary effectsreduce capillary effects

•• High flowrates may not beHigh flowrates may not besupported by critical velocitysupported by critical velocityissuesissues

•• True residual oil is notTrue residual oil is notalways reachedalways reached

Overview of Test Methods: SS

•• Simultaneous injection of 2 phases at a fixed ratioSimultaneous injection of 2 phases at a fixed ratio(fractional flow) of known individual flow rate(fractional flow) of known individual flow rate

•• System is allowed to reach steady state a givenSystem is allowed to reach steady state a givenfractional flow.fractional flow.— Steady state achieved when the injected fractional flow

equals the effluent fractional flow (saturation constant) andpressure drop across the core remains constant

•• Relative permeability calculated directly from theRelative permeability calculated directly from theDarcy equationDarcy equation— Assumes that the capillary pressure between phases is zero,

i.e. Pw = Po— Pressure drop across the core is used to calculate the

relative permeabilities of the two phases

Steady State methodSteady State method

orw

wro

w

kk

f

..

1

1

SS Imbibition Relative Permeability kro,krw...

•• Imbibition in this case as theImbibition in this case as thewetting phase (brine) is increasingwetting phase (brine) is increasing

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Brine Saturation, PV

Rel

ativ

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erm

eab

ility

S/S krw (fw 5%, 10%, 20%, 50%, 70%, 90% and 100%)

S/S kro (fw 5%, 10%, 20%, 50%, 70%, 90% and 100%)

Overview of Test Methods: SS

•• Data is easy to interpretData is easy to interpret•• Large saturation range of theLarge saturation range of the

relative permeability curverelative permeability curve(if not the complete range)(if not the complete range)can be measuredcan be measured

•• Process controlled byProcess controlled byfractional flow equationfractional flow equation

AdvantagesAdvantages DisadvantagesDisadvantages

•• Relatively long time toRelatively long time toachieve SS at each fachieve SS at each fww (1 to 2(1 to 2days or weeks at extremes )days or weeks at extremes )

•• Uncertainty as to whetherUncertainty as to whetherfluid displacement is trulyfluid displacement is trulyrepresentative of therepresentative of thereservoir process.reservoir process.

•• Possible fines mobilisationPossible fines mobilisationdue to large volumedue to large volumethroughputsthroughputs

•• Application of DarcyApplication of Darcy’’s Law iss Law isonly valid if the saturation inonly valid if the saturation inthe core is uniformthe core is uniform

Overview of Test Methods: Centrifuge

••Centrifuge permits gravity displacementCentrifuge permits gravity displacement(under centrifugal forces) to be the major(under centrifugal forces) to be the majorforce for displacementforce for displacement

••Negates viscous and capillary forces forNegates viscous and capillary forces foroptimal conditions to be appliedoptimal conditions to be applied

Centrifuge methodCentrifuge method

Overview of Test Methods: Centrifuge

•• Gravity stable displacement, notGravity stable displacement, notaffected by high mobility ratiosaffected by high mobility ratios(no viscous fingering)(no viscous fingering)

•• Flood not controlled by capillaryFlood not controlled by capillaryforces (Capillary end effectsforces (Capillary end effectsmay be lower than by flooding)may be lower than by flooding)

•• Automated data captureAutomated data capture•• Allows early data acquisition,Allows early data acquisition,

hence early curve definitionhence early curve definition•• Provides large data set for widerProvides large data set for wider

curve definitioncurve definition

•• Performed with attention toPerformed with attention tobond number (Nbond number (NBB)) -- to ensureto ensurenot overly denot overly de--saturatedsaturated

•• Produced valid data at trueProduced valid data at trueendpoint saturations where Relendpoint saturations where RelPerms are small (<0.0001)Perms are small (<0.0001)

AdvantagesAdvantages DisadvantagesDisadvantages•• Only a single relativeOnly a single relative

permeability is measuredpermeability is measured(displaced phase)(displaced phase)

•• Uncontrolled imbibition at SwiUncontrolled imbibition at Swicompared to SS and USS as thecompared to SS and USS as thesample is bathed in thesample is bathed in thedisplacing fluid at startdisplacing fluid at start

•• High pressure and temperatureHigh pressure and temperatureconditions are difficult toconditions are difficult torealiserealise

•• Tests using gas, oil, water areTests using gas, oil, water areconfined to the drainage modeconfined to the drainage mode(i.e. increasing saturation)(i.e. increasing saturation)

•• Samples may be altered by highSamples may be altered by highforces applied, esp. poorlyforces applied, esp. poorlyconsolidated. Calls for properconsolidated. Calls for properencapsulation before testing.encapsulation before testing.

Outline

1.1. IntroductionIntroduction2.2. Basic ConceptsBasic Concepts3.3. Overview of Test MethodsOverview of Test Methods4.4. InterpretationInterpretation

Interpretation

Key link of laboratory data (S,Key link of laboratory data (S, ΔΔP) to reservoirP) to reservoirengineering data (Kr, Pc)engineering data (Kr, Pc)

••JBN analysis of USS dataJBN analysis of USS data••Corey exponent representationCorey exponent representation••Core Flood SimulationCore Flood Simulation

Interpretation

•• JBN analysis method is based on BuckleyJBN analysis method is based on Buckley--Leverett theoryLeverett theoryand is used to analyse USS data to calculate relativeand is used to analyse USS data to calculate relativepermeabilities.permeabilities.

•• The method calculates the relative permeability of eachThe method calculates the relative permeability of eachphase at the outlet end of the core.phase at the outlet end of the core.

•• 2 phase range only2 phase range only ––ie from breakthrough to end point.ie from breakthrough to end point.•• It is only valid for tests carried out using immiscible,It is only valid for tests carried out using immiscible,

incompressible fluids in homegenous media with stableincompressible fluids in homegenous media with stableflood front with negilible capillary pressureflood front with negilible capillary pressure

•• In most cases capillary effects are present and using thisIn most cases capillary effects are present and using thismethod in such circumstance can lead to:method in such circumstance can lead to:

—Apparent low Kr data (suppressed mobility of phases)—Artifically early breakthrough—Apparent high ROS

Interpretation

•• Corey exponent representation is often used toCorey exponent representation is often used tomodel oil and water relative permeabilitymodel oil and water relative permeabilityfunctions.functions.

1.1. Water wetWater wet1. Sor ~30% +; no = 2 to 3; kro 0.6 to 0.82. Swi ~10% +; nw = 4 to 6; krw 0.1 to 0.4

2.2. Oil WetOil WetWater and oil exchange places

3.3. Intermediate WetIntermediate WetSor, Swi ~20%; no, nw 3 to 5; kro, krw ~0.5

o

orwi

orwwiro

nSSSS

kkro

11

,

w

orwi

wiworrwrw

nSS

SSkk

1

,

Interpretation

••Simulation is used as a validation tool for both USS and SS testSimulation is used as a validation tool for both USS and SS testss

••Can account for the effects of capillary pressure to deriveCan account for the effects of capillary pressure to deriverelative permeabilities that are free from artifacts that arerelative permeabilities that are free from artifacts that aregenerated in the laboratory.generated in the laboratory.

••Simulated production and pressure drop data is compared toSimulated production and pressure drop data is compared tomeasured data and relative permeability data is iterativelymeasured data and relative permeability data is iterativelyadjusted until a good match to measured data is obtained.adjusted until a good match to measured data is obtained.

••Simulated saturation profiles can also be used to refine theSimulated saturation profiles can also be used to refine thesolution furthersolution further

••Limitations to CFS is validity of measured Pc function and theLimitations to CFS is validity of measured Pc function and thecorrect Pc function should be used (ie imbibition or drainage)correct Pc function should be used (ie imbibition or drainage)

Core Flood Simulation: Production and Pressure data

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simulated water recovery

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Simulated dataProduction data

•Pressure drop data

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Gas Saturation

Rel

ativ

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data: Low Krdue to endeffects

Simulated data:curves corrected foreffects of capillarypressure

Gas Displacing Water Flood: Simulated Kr data

ENDEND