relative permeability
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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
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0.00.51.0
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0.60.00.10.20.30.40.50.60.70.80.91.0Water Saturation (-)Relative Permeability (-)Swir = 0.20Sro = 0.25Page 10Curves - 10.4
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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
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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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0.60.00.10.20.30.40.50.60.70.80.91.0Water 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
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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
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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
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