relative permeability presentation
TRANSCRIPT
Relative Permeability Display VersionRelative Permeability Display Version
Relative Relative PermeabilityPermeability
April 2005April 2005
Presentation OverviewPresentation Overview What is relative permeability & UsesWhat is relative permeability & Uses Factors that affect relative permeabilityFactors that affect relative permeability How does relative permeability impact How does relative permeability impact
reservoir performance?reservoir performance? Proper design and interpretation of relative Proper design and interpretation of relative
permeability testspermeability tests Optimizing reservoir performance by Optimizing reservoir performance by
understanding relative permeability issuesunderstanding relative permeability issues Summary and conclusionsSummary and conclusions
Common Uses of Relative Common Uses of Relative Permeability DataPermeability Data
Evaluation of residual saturations and Evaluation of residual saturations and displacement efficiency for waterflood, gasflood displacement efficiency for waterflood, gasflood and various EOR processesand various EOR processes
Evaluation of flow characteristics in multiphase Evaluation of flow characteristics in multiphase reservoir situationsreservoir situations
Prediction of reservoir performance and Prediction of reservoir performance and recoverable reservesrecoverable reserves
Reservoir optimization for primary, secondary Reservoir optimization for primary, secondary and tertiary depletion operationsand tertiary depletion operations
Absolute Permeability – is defined Absolute Permeability – is defined asas
The Resistance to Fluid Flow Existing in a The Resistance to Fluid Flow Existing in a Porous Media When it is the Only Phase Porous Media When it is the Only Phase PresentPresent
Darcy’s Law for SINGLE Phase Darcy’s Law for SINGLE Phase Flow in Porous Media Can be Flow in Porous Media Can be
Expressed asExpressed as
K = Q x L x uA x DP
Relative Permeability – is defined Relative Permeability – is defined asas
The Resistance to Fluid Flow Existing in a The Resistance to Fluid Flow Existing in a Porous Media When it is in the presence Porous Media When it is in the presence of other mobile or immobile, immiscible of other mobile or immobile, immiscible fluidsfluids
Relative Permeability DefinitionRelative Permeability Definition
Kri = Ki(Si)Kabs
Measured Permeability to a SpecificPhase at a Given Saturation of that Phase
Absolute (single phase) Permeability of thePorous Media Under Consideration
Relative Permeability toA Given Phase at SaturationLevel ‘I’ Value of ThatPhase
ExampleExampleAbsolute Permeability = 100 mDPerm to Oil = 85 mDPerm to water = 21 mDPerm to gas = 14 mD
Kro = 85/100 = 0.85Krw = 21/100 = 0.21Krg = 14/100 = 0.14
‘‘Normalized’ Relative PermeabilityNormalized’ Relative Permeability
1.0
0.00.0 1.0SATURATION
KRO @ Swi = 1.00
‘‘Absolute’ Relative Perm BasisAbsolute’ Relative Perm Basis
1.0
0.00.0 1.0SATURATION
KRO @ Swi = KoKabs
Which Method of Representation is Which Method of Representation is the Bestthe Best
Either method is accurate as long as the Either method is accurate as long as the correct value of the reference ‘initial’ correct value of the reference ‘initial’ permeability is usedpermeability is used
Normalized basis is useful in many cases Normalized basis is useful in many cases where ‘absolute’ permeability is unknown where ‘absolute’ permeability is unknown (e.g. – preserved state core material)(e.g. – preserved state core material)
Saturation ConceptsSaturation Concepts
Sinit Scr it Sir r SmaxSinitial
Initial Saturation (Swi)Represents the initial water
Saturation present in the Reservoir before any man induced
External influences
Critical (Swcrit) Saturation refersTo the water saturation at
Which the water phase firstIs able to move – note in manyReservoirs than Swi is NOT the
Same as Swcrit (dehydratedOr undersaturated reservoir)
The maximum saturation (Swmax) is theMaximum water saturation present under
Floodout conditions (a residual oil or trappedGas saturation would comprise the
Remainder of the pore system)
The Irreducible or Trapped water saturation (Swirr) represents the water saturation
Present after the saturation has been increasedBeyond the critical value and then
Subsequently reduced – it is often (almost Always) greater than Scrit
Major Factors Impacting Relative Major Factors Impacting Relative PermeabilityPermeability
Fluid SaturationsFluid SaturationsRock PropertiesRock PropertiesWettabilityWettabilitySaturation HistorySaturation History
Other Factors Which Also Influence Other Factors Which Also Influence Relative PermeabilityRelative Permeability
Overburden PressureOverburden Pressure In-Situ Stresses and HydrationIn-Situ Stresses and Hydration TemperatureTemperature IFTIFT ViscosityViscosity Initial Fluid SaturationsInitial Fluid Saturations Immobile PhasesImmobile Phases Displacement RatesDisplacement Rates Core handling and PreservationCore handling and Preservation
Saturation Effects on Relative Saturation Effects on Relative PermeabilityPermeability
Water Saturation Gas Saturation Liquid Saturation
Saturation Effects on Relative Saturation Effects on Relative PermeabilityPermeability
Strongly dependant function of saturationStrongly dependant function of saturationRel perm is always expressed as a Rel perm is always expressed as a
saturation functionsaturation function
Pore GeometryPore GeometryRelative permeability is strongly impacted Relative permeability is strongly impacted
by the specific geometry/tortuosity of the by the specific geometry/tortuosity of the pore system under considerationpore system under considerationGrain sizeGrain sizePore size Pore size Aspect ratioAspect ratioPresence of vugs/natural fracturesPresence of vugs/natural fracturesWormholesWormholesHorizontal laminationsHorizontal laminations
Example of Rel Perm Curves for a Example of Rel Perm Curves for a System Dominated by System Dominated by
Macroporosity (e.g. – fractures)Macroporosity (e.g. – fractures)
More Uniform Intergranular/Matrix More Uniform Intergranular/Matrix Type Porosity SystemType Porosity System
Macroporous Flow System With Macroporous Flow System With MicroporosityMicroporosity
Anisotropic FlowAnisotropic Flow
Flow Parallel to Bedding PlanesFlow Parallel to Bedding Planes
Flow Perpendicular to Bedding Flow Perpendicular to Bedding PlanesPlanes
WettabilityWettabilityThe fluid that coats the rock poresAlso describes the wettability Nature of that reservoir
Wettability TypesWettability TypesWater WetWater WetOil WetOil WetNeutral WetNeutral WetMixed WetMixed WetSpotted/Dalmation WetSpotted/Dalmation Wet
Relative PermeabilityRelative Permeability
Water Saturation - Fraction
Rel
ativ
e P
erm
eabi
lity
- Fra
ctio
n
Swi 10%Crossover 22% SwKrw = 0.88
Swi approx 25%Crossover approx 68% Krw = 0.08
Typical Relative Typical Relative Permeability Curve Permeability Curve
Configurations for Other Configurations for Other Wettability TypesWettability Types
Neutral Wet FormationsNeutral Wet Formations
Swi 10-20%Crossover around 50%Krw = 0.45
Mixed WettabilityMixed WettabilityA fairly common wettability type in which A fairly common wettability type in which
tight microporosity is water saturated and tight microporosity is water saturated and water wet, while oil saturated macropores water wet, while oil saturated macropores are oil wetare oil wet
Typical Mixed Wettability Relative Typical Mixed Wettability Relative Permeability CurvesPermeability Curves
Swi = 40%Crossover approx 55%Krw = 0.70
Spotted/Dalmation WettabilitySpotted/Dalmation WettabilitySwi = 22%Crossover = 59%Krw = 0.28
Mobility & Mobility & Waterflood Waterflood
PerformancePerformance
Concept of ‘Mobility Ratio’Concept of ‘Mobility Ratio’
M = x Krw
w x K roMobility Ratio
Viscosity ofDisplaced Phase
Rel Perm ofDisplacingPhase
Viscosity ofDisplacing Phase
Rel Perm ofDisplaced Phase
Factors Improving MobilityFactors Improving Mobility
M = x Krw
w x K ro
Low Oil ViscosityLow Krw/Krg Value
High Displacing Phase ViscosityHigh Kro Value
Example – Waterflood in a Example – Waterflood in a Favorable Mobility System (M=0.5)Favorable Mobility System (M=0.5)
Example – Waterflood in a Example – Waterflood in a Unfavorable Mobility System Unfavorable Mobility System
(M=20)(M=20)
Residual Oil Saturations in Residual Oil Saturations in WaterfloodsWaterfloods
BREAKTHROUGH BREAKTHROUGH SorSorECONOMICECONOMIC Sor SorULTIMATEULTIMATE Sor Sor
Breakthrough SorBreakthrough SorRefers to residual oil saturation in the Refers to residual oil saturation in the
swept pattern at the time of swept pattern at the time of firstfirst water water productionproduction
INJ PROD
Economic SorEconomic SorRefers to residual oil saturation in the Refers to residual oil saturation in the
swept pattern at the time of swept pattern at the time of Maximum Maximum EconomicEconomic water cut water cut
INJ PROD
Ultimate (True) SorUltimate (True) SorRefers to residual oil saturation in the Refers to residual oil saturation in the
swept pattern if a near swept pattern if a near Infinite Infinite volume of volume of water were displaced to near zero oil cutwater were displaced to near zero oil cut
INJ PROD
Lab Measurements of SorLab Measurements of SorLab measurements of Sor generally give a Lab measurements of Sor generally give a
reasonable approximation of the reasonable approximation of the ULTIMATE Sor since usually a very large ULTIMATE Sor since usually a very large number of pore volumes of displacement number of pore volumes of displacement are conducted (10-100 typical)are conducted (10-100 typical)
Waterflooding in Differing Waterflooding in Differing Wettability ReservoirsWettability Reservoirs
Cumulative Pore Volumes of Injection
Per
cent
Rec
over
y O
OIP Breakthrough Sor
Economic Sor
Ultimate Sor
Waterflooding in Differing Waterflooding in Differing Wettability ReservoirsWettability Reservoirs
Cumulative Pore Volumes of Injection
Per
cent
Rec
over
y O
OIP
Waterflooding in Differing Waterflooding in Differing Wettability ReservoirsWettability Reservoirs
Cumulative Pore Volumes of Injection
Per
cent
Rec
over
y O
OIP
Waterflooding in Differing Waterflooding in Differing Wettability ReservoirsWettability Reservoirs
Cumulative Pore Volumes of Injection
Per
cent
Rec
over
y O
OIP
Relative Permeability HysteresisRelative Permeability HysteresisRelative Permeability is not a unique Relative Permeability is not a unique
function of saturationfunction of saturationThe relative permeability value depends The relative permeability value depends
on the direction of saturation changeon the direction of saturation change
Example – Primary Drainage – Example – Primary Drainage – Initial Reservoir SaturationInitial Reservoir Saturation
Water Saturation – Fraction of Pore Space
Rel
ativ
e Pe
rmea
bilit
y
0 1.00
1.0WATER
OIL
Example – Primary Imbitition – Example – Primary Imbitition – (Waterflood)(Waterflood)
Water Saturation – Fraction of Pore Space
Rel
ativ
e Pe
rmea
bilit
y
0 1.00
1.0
WATER
OIL
Example – Primary Imbitition – Example – Primary Imbitition – (Waterflood)(Waterflood)
Water Saturation – Fraction of Pore Space
Rel
ativ
e Pe
rmea
bilit
y
0 1.00
1.0
WATER
OIL
Example –Secondary Drainage – Example –Secondary Drainage – (ie Gas flood)(ie Gas flood)
Water Saturation – Fraction of Pore Space
Rel
ativ
e Pe
rmea
bilit
y
0 1.00
1.0
WATER
OIL
Effect of Confining (Overburden) Effect of Confining (Overburden) Pressure on Relative PermeabilityPressure on Relative Permeability
Increased overburden pressure causes Increased overburden pressure causes compaction and compaction and a reductiona reduction in absolute in absolute permeabilitypermeability
Changes in Changes in pore geometrypore geometry may also affect may also affect relative permeabilityrelative permeability
Proper net overburden pressure should be Proper net overburden pressure should be used in all determinationsused in all determinations
Effect of Temperature on Relative Effect of Temperature on Relative PermeabilityPermeability
Modifies WettabilityModifies WettabilityChanges Viscosity RatioChanges Viscosity RatioChanges IFTChanges IFTMay Alter Rel PermMay Alter Rel PermTests Should be Run At Temp Of InterestTests Should be Run At Temp Of Interest
Effect of Interfacial Tension (IFT)Effect of Interfacial Tension (IFT)
IFT is a IFT is a very strong factorvery strong factor in controlling in controlling residual saturations and relative residual saturations and relative permeability curve endpoints and permeability curve endpoints and configurationsconfigurations
Proper IFT conditions are essential to a Proper IFT conditions are essential to a proper relative permeability determinationproper relative permeability determination
IFT EffectsIFT EffectsThe level of the IFT controls both the The level of the IFT controls both the
magnitude of the residual saturations in magnitude of the residual saturations in accessible pore spaceaccessible pore space and the degree of and the degree of ‘interference’ between phases‘interference’ between phases
Residual saturation is controlled by Residual saturation is controlled by capillary pressure, the lower the IFT, the capillary pressure, the lower the IFT, the lower the capillary pressurelower the capillary pressure
Effect of IFT on Rel Perm and SorEffect of IFT on Rel Perm and Sor
Is highly dependant on wettability, pore Is highly dependant on wettability, pore geometry and pore system accessibilitygeometry and pore system accessibility
Not all low/zero IFT systems give high Not all low/zero IFT systems give high recoveryrecovery
Concept of IFT vs. Mobility dominated Concept of IFT vs. Mobility dominated displacements in porous mediadisplacements in porous media
‘‘Classic’ IFT Effects on Relative Classic’ IFT Effects on Relative PermeabilityPermeability
Gas or Water Saturation - Fraction
Rel
ativ
e Pe
rmea
bilit
y
‘‘Classic’ IFT Effects on Relative Classic’ IFT Effects on Relative PermeabilityPermeability
Gas or Water Saturation - Fraction
Rel
ativ
e Pe
rmea
bilit
y
‘‘Classic’ IFT Effects on Relative Classic’ IFT Effects on Relative PermeabilityPermeability
Gas or Water Saturation - Fraction
Rel
ativ
e Pe
rmea
bilit
y
Using Proper IFTUsing Proper IFTAvoid treated fluidsAvoid treated fluidsAvoid surfactants and de-emulsifiersAvoid surfactants and de-emulsifiersLive reservoir fluids should be usedLive reservoir fluids should be used
Viscosity IssuesViscosity Issues
Viscosity IssuesViscosity Issues
Viscosity EffectsViscosity EffectsConsiderably controversy in the pastConsiderably controversy in the pastClassically rel perm considered to be Classically rel perm considered to be
purely a rock functionpurely a rock functionResearch has indicated that viscosity ratio Research has indicated that viscosity ratio
can strongly affect rel perm curve can strongly affect rel perm curve configuration and location of endpointsconfiguration and location of endpoints
Use of proper live reservoir fluids is Use of proper live reservoir fluids is required to mimic proper viscosity ratiorequired to mimic proper viscosity ratio
Favorable Viscosity Ratio (Favorable Viscosity Ratio (d d >>>>insitu)insitu)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Unit Viscosity Ratio (Unit Viscosity Ratio (d = d = insitu)insitu)R
elat
ive
Per
mea
bilit
y
Water Saturation
Unfavorable Viscosity Ratio (Unfavorable Viscosity Ratio (d d <<<<insitu)insitu)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Initial SaturationsInitial SaturationsProper level of initial water saturation in Proper level of initial water saturation in
the matrix for testing is essential for the matrix for testing is essential for accurate relative permeability accurate relative permeability measurementsmeasurements
Value of Swi can strongly effect original Ko Value of Swi can strongly effect original Ko or Kg endpoint permeabilityor Kg endpoint permeability
Incorrect values of Swi can have a laterally Incorrect values of Swi can have a laterally shifting effect on the entire relative shifting effect on the entire relative permeability curvepermeability curve
Example – Effect of Swi on Ko/KgExample – Effect of Swi on Ko/KgR
elat
ive
Per
mea
bilit
y
Water Saturation
Example – Effect of Swi on Rel Example – Effect of Swi on Rel Perm Curve ConfigurationPerm Curve Configuration
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Presence of a Mobile or Immobile Presence of a Mobile or Immobile Third PhaseThird Phase
Generally free or trapped gas in a water-oil Generally free or trapped gas in a water-oil situationsituation
Trapped oil saturation may exist in some Trapped oil saturation may exist in some water-gas systemswater-gas systems
Trapped saturations generally reduce Trapped saturations generally reduce perm to both phasesperm to both phases
Mobile third saturations may selectively Mobile third saturations may selectively reduce perm more to one phase than reduce perm more to one phase than anotheranother
Example – Presence of Trapped Example – Presence of Trapped Initial Gas SaturationInitial Gas Saturation
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Example – Presence of Trapped Example – Presence of Trapped Initial Gas SaturationInitial Gas Saturation
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Example – Presence of Trapped Example – Presence of Trapped Initial Gas SaturationInitial Gas Saturation
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Capillary End EffectsCapillary End EffectsCaused by a discontinuity in capillary Caused by a discontinuity in capillary
pressure at the outlet face of the core pressure at the outlet face of the core samplesample
Consequences of an End EffectConsequences of an End Effect
Commence WaterInjection
Delayed Production of Water& Dp due to End Effect
Consequences of an End EffectConsequences of an End EffectDelayed water breakthrough timesDelayed water breakthrough timesZone of ‘Stagnant’ fluid at end of sampleZone of ‘Stagnant’ fluid at end of sampleReduced apparent perm to water at lower Reduced apparent perm to water at lower
displacement ratesdisplacement rates
Mitigation of End EffectsMitigation of End EffectsHigh rates and delta PHigh rates and delta PLong coresLong coresPressure tapped coresPressure tapped coresSemi permeable membranesSemi permeable membranesNumerical simulation methodsNumerical simulation methods ‘‘Bump’ floodsBump’ floods
Measurement of Measurement of Relative Relative
Permeability DataPermeability Data
Common Determination MethodsCommon Determination Methods
Steady StateSteady StateUnsteady StateUnsteady StateCentrifugeCentrifugeAmbient vs. Reservoir Condition TestingAmbient vs. Reservoir Condition Testing
Sample SelectionSample SelectionRock typing and classificationRock typing and classificationSingle plug vs. composite stacksSingle plug vs. composite stacksPlug vs. full diameter testingPlug vs. full diameter testingVertical vs. horizontal flooding methodsVertical vs. horizontal flooding methods
Steady State Steady State MethodMethod
The Steady State Determination The Steady State Determination Method for Relative Permeability (2 Method for Relative Permeability (2
Phase)Phase)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Sample at Initial Conditions ofWater (Irreducible) and Oil(Maximum) Saturation
The Steady State Determination The Steady State Determination Method for Relative Permeability (2 Method for Relative Permeability (2
Phase)Phase)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Commence Injection of 100%Oil at Swi, Measure Ko atSwi
The Steady State Determination The Steady State Determination Method for Relative Permeability (2 Method for Relative Permeability (2
Phase)Phase)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Commence Injection of 90%Oil and 10% water, Measure Ko And Kw at New StabilizedHigher Sw
The Steady State Determination The Steady State Determination Method for Relative Permeability (2 Method for Relative Permeability (2
Phase)Phase)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Commence Injection of 70%Oil and 30% water, Measure Ko And Kw at New StabilizedHigher Sw
The Steady State Determination The Steady State Determination Method for Relative Permeability (2 Method for Relative Permeability (2
Phase)Phase)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Commence Injection of 30%Oil and 70% water, Measure Ko And Kw at New StabilizedHigher Sw
The Steady State Determination The Steady State Determination Method for Relative Permeability (2 Method for Relative Permeability (2
Phase)Phase)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Commence Injection of 10%Oil and 90% water, Measure Ko And Kw at New StabilizedHigher Sw
The Steady State Determination The Steady State Determination Method for Relative Permeability (2 Method for Relative Permeability (2
Phase)Phase)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Commence Injection of 0%Oil and 100% water, Measure Kw at Sorw
The Steady State Determination The Steady State Determination Method for Relative Permeability (2 Method for Relative Permeability (2
Phase)Phase)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Advantages of the Steady State Advantages of the Steady State MethodMethod
Computationally very simpleComputationally very simple Inherently stable (no viscous effects)Inherently stable (no viscous effects)Test modifications can reduce or eliminate Test modifications can reduce or eliminate
impact of capillary end effectsimpact of capillary end effects ‘‘Classic’ method of relative permeability Classic’ method of relative permeability
determinationdetermination
Disadvantages of the Steady State Disadvantages of the Steady State MethodMethod
Complex and expensive method, very time Complex and expensive method, very time consumingconsuming
Difficult and expensive for full reservoir Difficult and expensive for full reservoir conditionsconditions
Large volumes of reservoir fluids requiredLarge volumes of reservoir fluids required In-situ saturation monitoring essential for In-situ saturation monitoring essential for
accuracyaccuracyMore of a research method in many cases More of a research method in many cases
than a viable commercial techniquethan a viable commercial technique
Typical Steady State ApparatusTypical Steady State Apparatus
Capillary Contact Paper
Inlet Section Outlet Section
Typical Steady State ApparatusTypical Steady State ApparatusPressure Taps
External Core SleeveFlow Head Flow Head
Steady State ApparatusSteady State Apparatus
Water Inj Pump
Oil Inj PumpInjection Pumps
Coreholder
In-Situ SaturationMonitoring
Three PhaseSeparator
BPR
PistonCylinders
Pressure Transducers
Core Sample
OVEN
Common In-situ Saturation Common In-situ Saturation Determination MethodsDetermination Methods
GravimetricGravimetricElectrical resistivityElectrical resistivityX-rayX-rayMRIMRIGamma rayGamma rayMicrowave attenuationMicrowave attenuation
X-Ray SaturationX-Ray Saturation
Mannville Samples 13A, 14B, 16, 19, 24A
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 50 100 150 200 250 300 350
Distance, mm
X-R
ay c
ount
s
Typical Steady State Lab Typical Steady State Lab ApparatusApparatus
Displacement PumpsDisplacement Pumps
Unsteady Unsteady State MethodState Method
Unsteady State Method for Relative Unsteady State Method for Relative Permeability (2 Phase)Permeability (2 Phase)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Sample at Initial Conditions ofWater (Irreducible) and Oil(Maximum) Saturation
Unsteady Steady State Method for Unsteady Steady State Method for Relative Permeability (2 Phase)Relative Permeability (2 Phase)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Commence Injection of 100%Oil at Swi, Measure Ko atSwi
Unsteady Steady State Method for Unsteady Steady State Method for Relative Permeability (2 Phase)Relative Permeability (2 Phase)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Switch to Injection of 100%Water at Swi, Measure TransientPressure and Production History
Transient Pressure and Production Transient Pressure and Production HistoryHistory
Diff
eren
tial P
ress
ure
Cumulative Run Time
BreakthroughPoint
Transient Pressure and Production Transient Pressure and Production HistoryHistory
Prod
uctio
n R
ate
Cumulative Run Time
BreakthroughPoint
Transient Pressure and Production Transient Pressure and Production HistoryHistory
Prod
uctio
n Vo
lum
e
Cumulative Run Time
BreakthroughPoint
The Unsteady State Determination The Unsteady State Determination Method for Relative Permeability (2 Method for Relative Permeability (2
Phase)Phase)
Rel
ativ
e P
erm
eabi
lity
Water Saturation
Advantages of the Unsteady State Advantages of the Unsteady State MethodMethod
RapidRapidRelatively inexpensive, even for full Relatively inexpensive, even for full
reservoir condition HTHP testsreservoir condition HTHP testsLimited reservoir fluid requirementsLimited reservoir fluid requirementsEasy to run at full reservoir conditionsEasy to run at full reservoir conditionsSimpler equipment and procedures than Simpler equipment and procedures than
steady statesteady state
Disadvantages of the Unsteady Disadvantages of the Unsteady State MethodState Method
Unstable flow possibleUnstable flow possibleCapillary end effects possibleCapillary end effects possibleMore complex data reduction proceduresMore complex data reduction proceduresData may be poorly conditioned Data may be poorly conditioned
depending on computational method used depending on computational method used to regress transient lab resultsto regress transient lab results
Typical Unsteady State ApparatusTypical Unsteady State Apparatus
Injection Pump
Coreholder
Three PhaseSeparator
BPR
PistonCylinders
Pressure Transducers
Core Sample
OVEN
Typical Unsteady State ApparatusTypical Unsteady State Apparatus
Centrifuge MethodsCentrifuge Methods Use transient production vs. capillary pressure Use transient production vs. capillary pressure
history to generate psuedo rel perm curvehistory to generate psuedo rel perm curve Limited to very small samples and higher perm Limited to very small samples and higher perm
mediamedia Reservoir condition tests can not be easily Reservoir condition tests can not be easily
conductedconducted Common requirement to augment SS or USS rel Common requirement to augment SS or USS rel
perm experiments for evaluation of near Sor & perm experiments for evaluation of near Sor & Swir rel perm effects – always history matched Swir rel perm effects – always history matched for integration of the two methodsfor integration of the two methods
What is the Best Method to Use?What is the Best Method to Use?
What is the Best Method to UseWhat is the Best Method to UseMany of the limitations of the unsteady Many of the limitations of the unsteady
state method have been overcome in state method have been overcome in recent years by experimental and recent years by experimental and numerical modificationsnumerical modifications
95% plus of all commercial rel perm 95% plus of all commercial rel perm measurements are conducted using measurements are conducted using variants of the unsteady state methodvariants of the unsteady state method
Requirement for Two Phase FlowRequirement for Two Phase Flow
Fw
Average Sw
Water Saturation
Rel
ativ
e P
erm
eabi
lity
Results in HighlyCompressed SaturationRange
Requirement for Two Phase FlowRequirement for Two Phase Flow
Fw
Average Sw
Water Saturation
Rel
ativ
e P
erm
eabi
lity
Requirement for Two Phase FlowRequirement for Two Phase Flow
Fw
Average Sw
Water Saturation
Rel
ativ
e P
erm
eabi
lity Results in a More
Dispersed SaturationRange
Requirement for Two Phase FlowRequirement for Two Phase Flow
Fw
Average Sw
Water Saturation
Rel
ativ
e P
erm
eabi
lity
Common Techniques Used in the Common Techniques Used in the Past to Disperse FlowPast to Disperse Flow
Viscous refines oils used instead of Viscous refines oils used instead of reservoir oil to ‘smear’ production profilereservoir oil to ‘smear’ production profile
Problem – wrong viscosity, IFT and Problem – wrong viscosity, IFT and possibly wettabilitypossibly wettability
High rate displacementsHigh rate displacementsProblem – unstable flowProblem – unstable flow
Overcoming These Overcoming These Deficiencies Using Deficiencies Using Modern Simulation Modern Simulation
MethodsMethods
Simulation or ‘History Matching’ Simulation or ‘History Matching’ Generation of Rel Perm DataGeneration of Rel Perm Data
Most common current techniqueMost common current techniqueBasically a numerical simulation study in Basically a numerical simulation study in
reversereverse
History Matching TechniqueHistory Matching Technique In a normal simulation we know the rel In a normal simulation we know the rel
perm curves and we use this, along with perm curves and we use this, along with other input data, to predict the reservoir other input data, to predict the reservoir pressure and production historypressure and production history
In the history matching method we know In the history matching method we know the pressure and production history from the pressure and production history from the lab tests, and we use this data in an the lab tests, and we use this data in an iterative fashion to generate the rel perm iterative fashion to generate the rel perm curvescurves
Typical History Match ModelTypical History Match ModelInput Physical Parameters (L, A, Kabs, Porosity, Pore Volume, # Blocks
Input Fluid Properties – Viscosity, Density, Rate, Initial Saturations
Input Test Properties – Endpoint Perms and Saturations, PressureHistory, Production History
Input Cap Pressureand OutletBoundary Cond-ition to ModelCapillary Effects
The History The History Matching Matching ProcessProcess
Time Time Saturation
Cum
ulat
ive
Pro
duct
ion
Diff
eren
tial P
ress
ure
Rel
ativ
e P
erm
eabi
lity
Step 1 – Pick Functional FormFor Rel Perm Curve
Step 2 – Pick Initial ‘Guess’For Rel Perm Curve Configuration
Time Time Saturation
Cum
ulat
ive
Pro
duct
ion
Diff
eren
tial P
ress
ure
Rel
ativ
e P
erm
eabi
lity
Time Time Saturation
Cum
ulat
ive
Pro
duct
ion
Diff
eren
tial P
ress
ure
Rel
ativ
e P
erm
eabi
lity
Time Time Saturation
Cum
ulat
ive
Pro
duct
ion
Diff
eren
tial P
ress
ure
Rel
ativ
e P
erm
eabi
lity
Time Time Saturation
Cum
ulat
ive
Pro
duct
ion
Diff
eren
tial P
ress
ure
Rel
ativ
e P
erm
eabi
lity
Time Time Saturation
Cum
ulat
ive
Pro
duct
ion
Diff
eren
tial P
ress
ure
Rel
ativ
e P
erm
eabi
lity
History Matching ProcessHistory Matching ProcessContinue the iterative process until the Continue the iterative process until the
error between the stimulated and actual error between the stimulated and actual production and pressure data is as small production and pressure data is as small as possibleas possible
The resulting set of rel perm curves The resulting set of rel perm curves represent the best fit to the lab generated represent the best fit to the lab generated datadata
Algorithms to avoid localized or non-Algorithms to avoid localized or non-physical solutionsphysical solutions
Time Time Saturation
Cum
ulat
ive
Pro
duct
ion
Diff
eren
tial P
ress
ure
Rel
ativ
e P
erm
eabi
lity
Conventional Relative Permeability Conventional Relative Permeability TestsTests
Only provide data in the range of mobile Only provide data in the range of mobile fluid saturationsfluid saturations
Presence and effect of critical fluid Presence and effect of critical fluid saturations is essential in many processessaturations is essential in many processes
Special tests and procedures are required Special tests and procedures are required to precisely measure these saturations to precisely measure these saturations and their effect on relative permeabilityand their effect on relative permeability
Specialty Rel Perm ExperimentsSpecialty Rel Perm Experiments
Critical condensate floodsCritical condensate floodsConstant IFT floodsConstant IFT floodsAbove are two examples of super normal Above are two examples of super normal
relative permeability experimentsrelative permeability experiments
Critical condensate floodsCritical condensate floods Rich gas condensatesRich gas condensates
Produced below dew point at near wellboreProduced below dew point at near wellbore Two stage experimentTwo stage experiment Stage 1: establish critical condensate satStage 1: establish critical condensate sat
Incremental pressure decrements in pore spacesIncremental pressure decrements in pore spaces Flood with equilibrium gasFlood with equilibrium gas Stop at first sign of condensate productionStop at first sign of condensate production
Stage 2: Steady state gas & condensate floodStage 2: Steady state gas & condensate flood Equilibrium gas & condensateEquilibrium gas & condensate Gas saturation decreasingGas saturation decreasing Stop at trapped gas – residual gas saturation Stop at trapped gas – residual gas saturation
Typical critical condensate Typical critical condensate apparatusapparatus
Constant IFT FloodsConstant IFT FloodsCreate high IFT injection gas & oilCreate high IFT injection gas & oil
ie models the near well bore for vaporizing driveie models the near well bore for vaporizing driveCreate low IFT injection gas & oilCreate low IFT injection gas & oil
ie models deep reservoir for vaporizing driveie models deep reservoir for vaporizing driveRun two floods on matched core stacksRun two floods on matched core stacksCompare results to determine IFT Compare results to determine IFT
domination versus other controls of domination versus other controls of incremental oil recoveryincremental oil recovery
Ie mobility, pore geometry…Ie mobility, pore geometry…
Vaporizing MiscibilityVaporizing Miscibility Fluid Preparation Fluid Preparation
Rich GasLean Gas
Low IFT Oil
High IFT Oil
Flood #1Made From:
Flood #2Made From:
Condensing MiscibilityCondensing Miscibility Fluid Preparation Fluid Preparation
Leaner GasRich Gas
High IFT Oil
Low IFT Oil
Flood #1Made from:
Flood #2Made From:
Constant IFT Flood Constant IFT Flood Reservoir Dominated by Reservoir Dominated by IFTIFT
Gas Saturation - Fraction
Rel
ativ
e P
erm
eabi
lity
Constant IFT Flood Constant IFT Flood Reservoir Dominated by Reservoir Dominated by MobilityMobility
Gas Saturation - Fraction
Rel
ativ
e P
erm
eabi
lity
ConclusionsConclusionsMany controls / influences on relative Many controls / influences on relative
permeabilitypermeabilityLive oil & reservoir conditions necessaryLive oil & reservoir conditions necessarySpecialty floods for extension of routine Specialty floods for extension of routine
relative permeability applicationsrelative permeability applications
Thank you!Thank you!