No Slide Title

Module 8: Relative PermeabilitySynopsisWhat is water-oil relative permeability and why does it matter?

endpoints and curves, fractional flow, what curve shapes mean

Understand the jargon (and impress reservoir engineers)

Wettability

water-wet, oil-wet and intermediate

How do we measure it (in the lab)?

How do we quality control and refine data?Page 2ApplicationsTo predict movement of fluid in the reservoir

e.g velocity of water and oil fronts

To predict and bound ultimate recovery factor

Application depends on reservoir type

gas-oil

water-oil

gas-waterPage 2DefinitionsAbsolute Permeability

permeability at 100% saturation of single fluid

e.g. brine permeability, gas permeability

Effective Permeability

permeability to one phase when 2 or more phases present

e.g. ko(eff) at Swi

Relative Permeability

ratio of effective permeability to a base (often absolute) permeability

e.g. ko/ka or ko/ko at SwiPage 2RequirementsGas-Oil Relative Permeability (kg-ko)

solution gas drive

gas cap drive

Water-Oil Relative Permeability(kw-ko)

water injection

Water - Gas Relative Permeability (kw-kg)

aquifer influx into gas reservoir

Gas-Water Relative Permeability (kg-kw)

gas storage (gas re-injection into gas reservoir)Page 2Jargon Buster!Relative permeability curves are known as rel perms

Endpoints are the (4) points at the ends of the curves

The displacing phase is always first, i.e.:

kw-ko is water(w) displacing oil (o)

kg-ko is gas (g) displacing oil (o)

kg-kw is gas displacing waterPage 2Why shape is importantMeasure air permeability

Saturate core in water (brine)

Desaturate to Swir

Centrifuge or porous plateka = 100 mDSwir = 0.20 (20%Measure oil permeability ko @ Swir endpoint

Ko = 80 mD

Waterflood collect water volumeSro = 0.25

Swr = 1-0.25 = 0.75

Measure water permeability kw @Sro endpointSo = 1-SwirSwirrOil = SroKw = 24 mDPage 7Sw = 1-SroEndpoints0.00.10.20.30.40.50.60.70.80.91.00.00.10.20.30.70.80.91.0Relative Permeability (-)Endpoint - water krw = kw/ko @ Swir

= 24/80

= 0.30

0.40.50.6

Water Saturation (-)Page 10Swir = 0.20Sro = 0.25Endpoint- oil

kro = ko/ko @ Swir

= 80/80

= 1Endpoints0.4

0.3

0.2

0.1

0.00.51.0

0.9

0.8

0.7

0.60.00.10.20.30.40.50.60.70.80.91.0Water Saturation (-)Relative Permeability (-)Swir = 0.20Sro = 0.25Page 10Curves - 10.4

0.3

0.2

0.1

0.00.51.0

0.9

0.8

0.7

0.60.00.10.20.30.40.50.60.70.80.91.0Water Saturation (-)Relative Permeability (-)Swir = 0.20Sro = 0.25Page 10Curves - 20.4

0.3

0.2

0.1

0.00.51.0

0.9

0.8

0.7

0.60.00.10.20.30.40.50.60.70.80.91.0Water Saturation (-)Relative Permeability (-)Swir = 0.20Sro = 0.25Page 10Curves - 30.4

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0.2

0.1

0.00.51.0

0.9

0.8

0.7

0.60.00.10.20.30.40.50.60.70.80.91.0Water Saturation (-)Relative Permeability (-)Swir = 0.20Sro = 0.25Page 10Relative PermeabilityNon-linear function of Swet

Competing forces

gravity forcesminimised in lab tests

e.g.water injected from bottom to topviscous forces

Darcys Law

capillary forceslow flood rates0Page 100.10.20.30.40.50.60.70.80.9100.20.40.6Water Saturation (-)0.81Relative Permeability (-)kro krwRelative Permeability Curves Key FeaturesWater-Oil Curves

irreducible water saturation (Swir) endpoint

kro = 1.0krw = 0.0

residual oil saturation (Sro) endpoint

kro = 0.0krw = maximum

relative permeability curve shapePage 10Unsteady-state

Steady-state

Corey exponents:Buckley-Leverett, Welge, JBN Darcy

No and NwWaterflood InterpretationWelgeok rw1-SorSwcSwAverage Saturation behind flood front

fw

Sw at BT ro . w f w=k1 +1fw only after BTfw=1SwS, f|wfwSwfPage 10Relative Permeability InterpretationWelge/Buckley-Leverett fraction flow

gives ratio:kro/krwDecouple kro and krw from kro/krw

JBN, Jones and Roszelle, etcwM= krw . okrooPage 10 ro . w k rwf w=k1 +1M< 1: piston-like M > 1: unstableJBN Method OutlineJohnson, Bossler, Nauman (JBN)

Based on Buckley-Leverett/WelgeW = PV water injected

Swa = average (plug) Sw

fw2 = 1-fo2o ro . w k rwf w=k1 +1o 2wa=fdWdSk ro 2f o 2d ( 1))1d (rWWI=t = iPage 10= pt = 0rpIInjectivity Ratio Waterflood rate, qBuckley Leverett AssumptionsFluids are immiscible

Fluids are incompressible

Flow is linear (1 Dimensional)

Flow is uni-directional

Porous medium is homogeneous

Capillary effects are negligible

Most are not met in most core floodsPage 10Capillary End EffectIf viscous force large (high rate)

Pc effects negligible

If viscous force small (low rate)

Pc effects dominate flood behaviour

Leverett

capillary boundary effects on short cores

boundary effects negligible in reservoirPage 10End EffectPressure Trace for Flood

zero p (no injection)start of injectionwater nears exitp increases abruptly until Sw(exit) = 1-Sro and Pc nears zero

suppresses krwBT

Sw(exit) = 1-Sro, Pc ~0After BT

rate of p increase reduces as krw increasesPage 10Scaling CoefficientBreakthrough Recovery (Rappaport & Leas) Affected by Pc end effects At lengths > 25 cmLittle effect on BT recovery (LVw > 1)

Hence composite samples

or high ratesPage 10Capillary End EffectsRapaport and Leas Scaling CoefficientLVw > 1(cm2/min.cp) :minimal end effect

Overcome by:flooding at high rate300 ml/hour +

using longer cores

difficult for reservoir core (limited by core geometry)butt several cores togetherusing capillary mixing sectionsend-point saturations only in USS tests (weigh sample)Page 10Composite Core PlugCapillary end effects adsorbed by Cores 1 and 4Page 10Corey Exponents Water/Oil SystemsDefine relative permeability curve shapes

Based on normalised saturations

No guarantee that real rock curves obey Coreykro = SonNok= k(Srwrwwn)Nwkrw = end-point krwSwnwiro= 1 Sw Sroon1 S SS= 1 Sw Swiwn1 S SwiroPage 24S=Normalisation0.1

00.20.5

0.4

0.30.61

0.9

0.8

0.700.10.20.30.40.50.60.70.80.91Water Saturation (-)Water Relative Permeability (-)krw at Sro krwn = 1Swn = 1krwn = 1Page 25Sample 1Sample 2Corey ExponentsDepend on wettabilityPage 25Uses:

interpolate & extrapolate data

lab data quality controlWettabilityNo (kro)Nw (krw)Water-Wet2 to 45 to 8Intermediate Wet3 to 63 to 5Oil-Wet6 to 82 to 3Gas-Oil Relative PermeabilityTest performed at Swir

Gas is non wetting

takes easiest flow path

kro drops rapidly as Sg increases

krg higher than krw

Srog > Srow in lab tests

end effects

Srog < Srow in field

Sgc ~ 2% - 6%Pore-Scale Saturation DistributionPage 25Typical Gas-Oil Curves:Linear0.3

0.2

0.1

0.00.40.50.61.0

0.9

0.8

0.70.00.10.20.30.40.50.6

Gas Saturation (fractional)0.70.80.91.0Relative Permeability (-)kro krg1-(Srog+Swi)SgcPage 28Labs plot kr vs liquid saturation (So+Swi)Typical Gas-Oil Curves:Semi-Log0.0010.010.1

1-(Srog+Swi)

kro krg10.00.10.20.30.40.50.6Gas Saturation (fractional)0.70.80.91.0Relative Permeability (-)Page 29Gas-Oil CurvesMost lab data are artefacts

due to capillary end effects

Tests should be carried out on long cores

insufficient flood period

Real gas-oil curves

Sgc ~ 3%

Srog is low and approaches zero

Due to thin film and gravity drainage

krg = 1 at Srog = 0

well defined Corey exponentsPage 29Gas-Oil Curves Corey Methodkro = SonNoOil relative permeability

normalised oil saturationGas relative permeability

normalised gas saturationSgc:critical gas saturation1 Swir SrogSon = 1 Sg Swir Srog1 Swir Srog SgcPage 29Sg SgcSgn =krg = SgnNgCorey ExponentValuesNo4 to 7Ng1.3 to 3.0Corey Gas-Oil Curves0.000010.00010.0010.10.20.30.40.50.60.70.80.91.0Gas Saturation (-)Relative Permeability (-)0.01Kro No = 4 krg Ng = 1.3 kro No = 7 krg Ng = 3.00.110.0Sgc = 0.03Page 29Swir0.15kro1.00krg'1.00Srog0.0000Sgc0.0300Typical Lab Data - krg0.000010.00010.0010.010.110.00.10.20.30.40.50.6Swi+Sg (fraction)0.70.80.91.0Relative Permeability, krgNg = 2.3; Swir = 0.15Ng = 2.3; Swir = 0.2011a-5 # 411a-5 # 3111a-5 # 3411a-5 #3911a-7 BEA511a-7 BEA711a-7 BEB511a-7 BEC5Composite Gas-Oil CurvesNg : 2.3No : 4.0Sgc: 0.03Srog: 0.10krg' : 1.0Krg too low Srog too highPage 29Laboratory MethodsCore Selection

all significant reservoir flow units

often constrained by preserved core availability

core CT scanning to select plugs

Core Size

at least 25 cm long to overcome end effects

butt samples (but several end effects?)

flood at high rate to overcome end effects?Page 29Test StatesFresh or Preserved Statetested as is (no cleaning)probably too oil wet (e.g OBM, long term storage)Native state term also used (defines bland mud)Some labs fresh state is other labs restored state

Cleaned StateCleaned (soxhlet or miscible flush)water-wet by definition (but could be oil-wet!!!!!!)

Restored State (reservoir-appropriate wettability)saturate in crude oil (live or dead)age in oil at P & T to restore native wettabilityPage 29Test StateFresh-State Teststoo oil wet

Cleaned-State Teststoo water wet (or oil-wet)

Restored-State Testsnative wettability restoredPage 29data unreliabledata unreliabledata reliable (?)if GOR low can use dead crude ageing (cheaper)if GOR high must use live crude ageing (expensive)if wettability restored - use synthetic fluids at ambientensure cores water-wet prior to restoration

Compare methods - are there differences?Irreducible Water Saturation (Swir)Swir essential for reliable waterflood data

Dynamic displacement

flood with viscous oil then test oil

rapid and can get primary drainage rel perms

Swir too high and can be non-uniform

Centrifuge

faster than others

Swir can be non-uniform

Porous Plate

slow, grain loss, loss of capillary contactPage 37Swir uniformLab Variation in Swir (SPE28826)Lab ALab BLab CLab D05???

1015202530Swi (%)Dynamic DisplacementPorous Plate180 psi200 psiPage 38Centrifuge TestsDisplaced phase relative permeability onlyoil-displacing-brine :krw drainagebrine-displacing-oil :kro imbibitionassume no hysteresis for krw imbibitionoil-wet or neutral wet rocks?Good for low kro data (near Sro)e.g. for gravity drainageComputer simulation usedProblemsuncontrolled imbibition at Swirrmobilisation of trapped oilsample fracturing0.00.10.20.30.40.50.60.70.80.91.00.00.10.20.30.40.50.60.70.80.91.0Water Saturation (-)Relative Permeability (-)Page 38Dynamic Displacement TestsTest Methods

Waterflood (End-Points: ko at Swi, kw at Srow)

Unsteady-State (relative permeability curves)

Steady-State (relative permeability curves)

Test Conditions

fresh state

cleaned state

restored state ambient or reservoir conditionsPage 40Unsteady-State WaterfloodSaturate in brine

Desaturate to Swirr

Oil permeability at Swirr (Darcy analysis)

Waterflood (matched viscosity)Total Oil Recoverylabw oresw o = kw at Srow (Darcy analysis)Page 41Unsteady-State Relative PermeabilitySaturate in brineDesaturate to SwirrOil permeability at Swirr (Darcy analysis)Waterflood (adverse viscosity)Incremental oil recovery measuredkw at Srow (Darcy analysis)Relative permeability (JBN Analysis) o o w lab w res>> Page 57Unsteady-State ProceduresWaterOilOnly oil produced Measure oil volumeJust After Breakthrough Measure oil + water volumesIncreasing Water Collected Continue until 99.x% waterPage 57Unsteady-StateRel perm calculations requirefractional flow data at core outlet (JBN)pressure data versus water injected

Labs use high oil/water viscosity ratiopromote viscous fingeringprovide fractional flow data after BTallow calculation of rel perms

Waterflood (matched viscosity ratio)little or no oil after BTlittle or no fractional flow (no rel perms)end points onlyPage 57Effect of Adverse Viscosity Ratio0.2

0.1

0.00.30.40.50.60.70.80.91.00.00.10.20.30.40.5Water Saturation (-)0.60.70.80.91.0Fractional Flow, fwo/w = 30:1 Unstable flood front Early BTProlonged 2 phase flow Oil recovery lowero/w = 3:1Stable flood front BT delayedSuppressed 2 phase flowOil recovery higherPage 57Unsteady-State TestsOnly post BT data are used for rel perm calculations

Sw range restricted if matched viscosities

Advantages

appropriate Buckley-Leverett shock-front

reservoir flow rates possible

fast and low throughput (fines)

Disadvantages

inlet and outlet boundary effects at lower rates

complex interpretationPage 57Steady-State TestsIntermediate relative permeability curves

Saturate in brine

Desaturate to Swir

Oil permeability at Swir (Darcy analysis)

Inject oil and water simultaneously in steps

Determine So and Sw at steady state conditions

kw at Srow (Darcy analysis)

Relative Permeability (Darcy Analysis)Page 57Steady-State Test EquipmentOil and water outpCoreholderOil inWater inMixing SectionsPage 57Steady-State ProceduresSummary

ko at Swirr

ko & kw at Sw(1)

ko & kw at Sw(2)Page 57100% Oil:Ratio 1: Ratio 2:

.. Ratio n:

100% Water:ko & kw at Sw(n) kw at SroSteady-State versus Unsteady-StateConstant rate (SS) vs constant pressure (USS)fluids usually re-circulatedGenerally high flood rates (SS)

end effects minimised, possible fines damageEasier analysis

Darcy vs JBNSlower

days versus hoursEndpoints may not be representativeSaturation Measurementgravimetric (volumetric often not reliable)NISMPage 57Laboratory TestsYou can choose from:

matched or high oil-water viscosity ratio

cleaned state, fresh state, restored-state tests

ambient or reservoir condition

high rate or low rate

USS versus SS

Laboratory variation expected

McPhee and Arthur (SPE 28826)

Compared 4 labs using identical test methodsPage 57Oil RecoveryLab ALab BLab CLab D10203040506070Oil Recovery (% OIIP)Fixed - 120 ml/hourPreferred120Bump360120Page 57Gas-Oil and Gas-Water Relative PermeabilityUnsteady-State

adverse mobility ratio (g 50%better flood performance

Oil-Wetpoorer krohigher krwkro = krw < 50%poorer flood performancePage 60Wettability Effects: Brent FieldPreserved Core Neutral to oil-wet low kro - high krw Extracted Core Water wet

high kro - low krwPage 60Importance of Wettability - ExampleWater Wet

No = 2Nw = 8Swir = 0.20

Sro = 0.30, krw = 0.25, ultimate recovery = 0.625 OIIP

Intermediate Wet

No = 4Nw = 4Swir = 0.15

Sro = 0.25, krw = 0.5,ultimate recovery = 0.706 OIIP

Oil Wet

No = 8Nw = 2Swir = 0.10

Sro = 0.20, krw = 0.75, ultimate recovery = 0.778 OIIPo/w = 3:1Page 66Relative Permeability Curves0.4

0.3

0.2

0.1

0.00.51.0

0.9

0.8

0.7

0.60.00.10.20.30.40.50.60.70.80.91.0Water Saturation (-)Relative Permeability (-)WW kro WW krwPage 67Relative Permeability Curves1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.00.00.10.20.30.40.50.60.70.80.91.0Water Saturation (-)Relative Permeability (-)Page 67WW kro WW krw IW kro IW krwRelative Permeability Curves0.00.10.20.30.40.50.60.70.80.91.00.00.10.20.30.40.50.60.70.80.91.0Water Saturation (-)Relative Permeability (-)WW kro WW krw IW kro IW krw OW kro OW krwPage 67Fractional Flow Curves0.00.10.20.30.40.50.60.70.80.91.00.00.10.20.30.40.50.60.70.80.91.0Water Saturation (-)Fractional Flow, fw (-)WW fwWater Wet SOR = 0.33Recovery = 0.59Page 67Fractional Flow Curves0.00.10.20.30.40.50.60.70.80.91.00.00.10.20.30.40.50.60.70.80.91.0Water Saturation (-)Fractional Flow, fw (-)WW fw IW fwIWSOR = 0.44Recovery = 0.482Page 67Fractional Flow Curves0.00.10.20.30.40.50.60.70.80.91.00.00.10.20.30.40.50.60.70.80.91.0Water Saturation (-)Fractional Flow, fw (-)WW fw IW fw OW fwOil Wet SOR = 0.63Recovery = 0.300Page 67Costs of Wettability UncertaintyPVOil PricePage 67120 MMbbls30 US$/bblsIt is really, really important to get wettability right!!!ParameterWater-WetIWOil wetSwi0.2000.1500.100Ultimate Sro0.3000.2500.200Ultimate Recovery Factor0.6250.7060.778SOR0.3300.4400.630Actual Recovery Factor0.5880.4820.300STOIIP (MMbbls)96102108Ultimate Recovery (bbls)607284Actual Recovery (bbls)564932"Loss" (MM US$)1086841548Rock TexturePage 67Viscosity Ratiokrw and kro - no effect ?End-Points - viscosity dependent Hence:use high viscosity ratio for curves use matched for end-points

Not valid for neutral-wet rocks (?)Page 67Saturation HistoryPrimary DrainagePrimary Imbibition100 %0 %kr0 %100 %Sw0 %kr0 %100 %SwSwiSroNWWNo hysteresis in wettingphaseNWPage 67WFlow RateReservoir Frontal Advance Rate

about 1 ft/day

Typical Laboratory Rates

about 1500 ft/day for 1.5 core samples

Why not use reservoir rates ?

slow and time consuming

capillary end effects

capillary forces become significant c.f. viscous forces

Buckley-Leverett (and JBN) invalidatedPage 67Flow ParametersNc k vLendoNc=

Rate (ml/h) 4120360400ReservoirPage 78Relative Permeabilities are Rate-Dependentv wRate (ml/h) 4120360400ReservoirNcend 2.30.070.020.020Nc1.2 x10-73.6 x 10-6x 10-5x 10-510-7For reservoir-appropriate data Nclab ~ NcreservoirIf Ncend > 0.1kro and krw decrease as Ncend increasesEnd Effect Capillary NumberFlood Capillary NumberBump Flood0.00.10.20.30.00.10.20.30.40.50.60.70.80.91.0Water Saturation (-)Relative Permeability (-)Low Rate krw'1.0

0.9

0.8

0.7

0.6

0.5High Rate krw ??? 0.4Bump Flood krw'Page 79Flow Rate ConsiderationsImbibition (waterflood of water-wet rock)

Sro function of Soi:Sro is rate dependentoil production essentially complete at BTkrw suppressed by Pcend and rate dependent

bump flood does not produce much oil but removes Pcend and krw increases significantly

high rates acceptable but only if rock is homogeneous at pore levelConsiderationsensure Swi is representativelow rate floods for Sro:bump for krwsteady-state testsPage 79Flow Rate ConsiderationsDrainage (Waterflood of Oil-Wet Rock)

end effects present at low rateSro, krw dependent on capillary/viscous force ratiohigh rate:significant production after BTreduced recovery at BT compared with water-wet

Considerations

high rate floods (minimum Dp = 50 psid) to minimise end effectssteady-state tests with ISSMlow rates with ISSM and simulationPage 79Flow Rate ConsiderationsNeutral/Intermediate

Sro and kro & krw are rate dependent

bump flood produces oil from throughout sample, not just from ends

ISSM necessary to distinguish between end effects and sweep

Recommendations

data acquired at representative rates

(e.g. near wellbore, grid block rates)Page 79JBN ValidityHigh Viscosity Ratio

viscous fingering invalidates 1D flow assumption

Low Rate

end effects invalidate JBN

Most USS tests viewed with caution

if Ncend significant

if Nc not representative

if JBN method used

Use coreflood simulationPage 79Test RecommendationsWettability Conditioning

flood rate selected on basis of wettability

Amott and USBM tests required

Wettability pre-study

reservoir wettability?

fresh-state, cleaned-state, restored-state wettabilities

beware fresh-state tests (often waste of time)

reservoir condition tests most representative

but expensive and difficultPage 79Wettability RestorationHot soxhlet does not make cores water wet!

Restored-state cores too oil wet

Lose 10% OIIP potential recoverylugs d

-1.00.01.0-1.00.0Amott1.0USBMPage 79STRONGLY WATER-WETSTRONGLY OIL-WETOriginal SCAL p Hot Sox Cleane Flush CleanedKey Steps in Test DesignEstablishing Swi

must be representative

use capillary desaturation if at all possible

remember many labs cant do this correctly

fresh-state Swirr is fixed

Viscosity Ratio

matched viscosity ratio for end-points

investigate viscosity dependency for rel perms

normalise then denormalise to matched end-pointsPage 79Key Steps In Test DesignFlood Rate

depends on wettability

determine rate-appropriate end-points

steady-state or Corey exponents for rel perm curves

Saturation Determination

conventional

grain loss, flow processes unknown

NISM

can reveal heterogeneity, end effects, etcPage 79Use of NISMExamples from North Sea

Core Laboratories SMAX System

low rate waterflood followed by bump flood

X-ray scanning along length of core

end-points

some plugs scanned during waterflood

Fresh-State Tests

core drilled with oil-based mudPage 79X-Ray ScannerSw(NaI)X-ray adsorption0%100%X-rays emittedX-rays detectedScanning BedCoreholder(invisible to X- rays)X-ray Emitter (DetectorBehind)Page 79NISM Flood ScansSMAX Example 1

uniform Swirr

oil-wet(?) end effect

bump flood removes end effect

some oil removed from body of plug

neutral-slightly oil-wetPage 79NISM Flood ScansSMAX Example 2

short sample

end effect extends through entire sample length

significant oil produced from body of core on bump flood

moderate-strongly oil-wet

data wholly unreliable due to pre-dominant end effect. Need coreflood simulationPage 79NISM Flood ScansSMAX Example 3

scanned during flood

minimal end effect

stable flood front until BT

vertical profile

bump flood produces oil from body of core

neutral wet

data reliablePage 79NISM Flood ScansSMAX Example 4

Sample 175 (fresh-state)

scanned during waterflood

unstable flood front

oil wetting effects

oil-wet end effect

bump produces incremental oil from body of core but does not remove end effect

neutral to oil-wet data unreliablePage 93NISM Flood ScansSMAX Example 5

Sample 175 re-run after cleaning

increase in Swirr compared to fresh-state test

no/minimal end effects

moderate-strongly water- wetPage 94NISM Flood ScansSMAX Example 6heterogeneous coarse sandvariation in SwirrSro variation parallels Swirr

end effect masked by heterogeneity (?)

very low recovery at low rate (thiefzones in plug?)

bump flood produces significant oil from body of coreneutral-wetPage 94Key Steps in Test DesignRelative Permeability Interpretation

key Buckley-Leverett assumptions invalidated by most short corefloods

Interpretation Model must allow for:

capillarity

viscous instability

wettability

Simulation required

e.g. SENDRA, SCORESPage 94Simulation Data InputFlood data (continuous)

injection rates and volumes

production rates

differential pressure

Fluid properties

viscosity, IFT, density

Imbibition Pc curve (option)

ISSM or NISM Scans (option)

Beware several non-unique solutions possiblePage 94History MatchingPressure and production1.66 cc/min01002003004005006007008000,11,010,0100,01000,010000,0Time (min)Differential Pressure (kPa)0,01,02,03,04,05,06,0Oil Production (cc)Measured differential pressure Simulated differential pressure Measured oil production Simulated oil productionPage 94History MatchingSaturation profiles0.8

0.7

0.6

0.5

0.4

0.3

0.2Normalized Core LengthPage 990.00.20.40.60.81.0Water SaturationSimulation Example JBN CurvesRelative Permeabilty Curves Pre-Simulation1

0.9

0.8

0.70.3

0.2

0.1

00.40.50.6Relative PermeabilityKrw Krolow rate end point high rate end point00.10.20.30.40.50.60.70.80.91Water saturationPage 100Simulation Example Simulated CurvesRelative Permeabilty Curves Post Simulation1

0.9

0.8

0.70.3

0.2

0.1

00.40.50.6Relative PermeabilityKrw Krolow rate end point high rate end point Krw Simulation Kro Simulation00.10.20.30.40.50.60.70.80.91Water saturationPage 100Quality ControlMost abused measurement in core analysis

Wide and unacceptable laboratory variation

Quality Control essentialtest designdetailed test specifications and milestonescontractor supervisionmodify test programme if required

Benefitsbetter datamore cost effectivePage 107Water-Oil Relative Permeability RefiningKey Steps

curve shapes

Sro determination and refinement

refine krw

determine Corey exponents

refine measured curves

normalise and average

Uses Corey approach

rock curves may not obey Corey behaviourPage 107Curve ShapesWater-Oil Rel. Perms.0.00010.0010.010.1100.20.40.60.81SwKr KroKrw00.10.20.30.40.50.60.70.80.9100.20.40.60.81SwKr KroKrwPage 107Cartesian

Good data convex upwardsSemi-log

Good data concave downSro DeterminationCompute Son

high, medium and low Srolow rate, bump, centrifuge SroPlot Son vs kro (log-log)

Sro too low

curves down

Sro too high

curves up

Sro just right

straight line0.00010.0010.010.110.0100.100Son = (1-Sw-Sor)/(1-Swi-Sor)1.000KroSor = 0.40Sor = 0.20Sor = 0.35Page 107Refine krwRefined krwUse refined Sro

Plot krw versus Swn

Fit line to last few pointsDetermine refined krw0.010.110.11Swn = 1-SonKrwPage 107Determine Best Fit CoreysUse refined Sro and krw

Determine instantaneous CoreysNw* = log(krw' ) log(krw) log(1.0) log(Swn )

No* = log(kro)log(Son )

Plot vs Sw

Take No and Nw from flat sections

Least influenced by end effects1

0.5

01.53.5

3

2.5

200.20.40.60.81SwNo' & Nw'No NwPage 107Refine Measured DataEndpointsRefined krw and Sro

Corey Exponents

No and Nw (stable)

Corey Curves0.00.10.20.30.40.60.70.80.91.000.10.20.30.40.5Sw0.60.70.80.91Relative PermeabilityRefined Kro Refined Krw Original Kro Original KrwPage 107Nokro( refined ) = SonNwkrw( refined ) = krw' SwnNormalisation EquationsWater-Oil DataGas - Oil Datarwendkrwrwnkk=ro endkroro nkk=rowwiSw SwiSwn = 1 S SwiroggcSg Sgcgn1SSSS=kro endkroro nk=rgendPage 107krgkrgn =kExample - kro NormalisationSwn = 00

0.3

0.2

0.1

0.5

.401

0.9

0.8

0.7

0.600.10.20.30.40.50.60.70.80.91Water Saturation (-)Oil Relative Permeability (-)Sample 1Sample 2SwirrSw = 1-Sro Swn = 1Page 107Example - krw Normalisation0.5

0.4

0.3

0.2

0.1

00.61

0.9

0.8

0.700.10.20.30.40.50.60.70.80.91Water Saturation (-)Water Relative Permeability (-)krw at Sro krwn = 1Page 107Sample 1Sample 2Normalise and Compare Data - kron0.1

0.00.20.30.40.50.60.70.81.0

0.90.00.10.20.30.40.50.6

Normalised Water Saturation (-)0.70.80.91.0Normalised Oil Relative Permeability (-)123456789101112131415Different Rock Types ? Different Wettabilities?Steady StatePage 107Normalise and Compare Data - krwn0.2

0.1

0.00.30.40.50.60.71.0

0.9

0.80.00.10.20.30.40.50.6

Normalised Water Saturation (-)0.70.80.91.0Normalised Water Relative Permeability (-)1234567891112131415Page 107DenormalisationGroup data by zone, HU, lithology etc

Determine Swir (e.g. logs, saturation-height model)

Determine ultimate Sroe.g. from centrifuge core tests

Determine krw at ultimate Sroe.g. from centrifuge core tests

Denormalise to these end-points

Truncate denormalised curves at ROSdepends on location in reservoirPage 107Denormalisation EquationsWater Oil

Sw dn

krodnPage 107Gas-Oil SDenormalised Endpoints Water-Oil

Swi

kro (@Swi)

krw (@1-Srow)

From correlations & average datarwnrwendrwdn= Swn (1 Swi Sro ) + Swi

= kro end .kronk= k.kkrodn = koend .kron

krgdn = krg end .krgngcgcrog= Sgn (1 Swi Sg dn S) + SSummary Getting the Best Rel PermsEnsure samples are representative of poro-perm distribution

Ensure Swir representative (e.g. porous plate, centrifuge)

Ensure representative wettability (restored-state?)

Use ISSM (at least for a few tests)

Ensure matched viscosity ratio

Low rate then bump flood

Centrifuge ultimate Sro and maximum krw

Tail ok kro curve if gravity drainage significant

Use coreflood simulation or Coreys for intermediate krPage 107