NMR Petrophysics

8/12/2019 NMR Petrophysics

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Lecture Presentation

PGE368Fall 2001 Semester

December 5 and 7

Fundamentals of Nuclear Magnetic Resonance

Logging

Carlos Torres-Verdn, Ph.D. Assistant Professor


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Bedding scale Well logs

Stratum scale

Core plug scalePore scale


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SPIN MAGNETIZATION

N

S Proton

H

Hydrogen


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PRECESSION

B

Parallel

Antiparallel

100,006

100,000

oBo

Larmor Precession

freq. = 4258 HGauss

z B o


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ELEMENTAL NMR RESPONSE

Nucleus[most common

applications in log &core analysis]

2ss

Naturalabundance

(%)

Relativesensitivity I (Hz/Gau )

4257.591H[core and log]

2

H[aqueous phase]13 C

[need high freq.]19

F[nonwetting phase]

1/2 99.99 1.000

653.57 1 0.015 0.0097

1070.5 1/2 1.10 0.0159

4005.5 1/2 100.00 0.83323 Na

[salinity]11.26 3/2 100.00 0.0925


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TRANSVERSAL TIPPING


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TRANSVERSAL TIPPING and PROTON PRECESSION


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BASIC NMR INSTRUMENTATION COMPONENTS

B1

B0N

S

A time-constant magneticfield used to polarize thespins

A time-varying RFmagnetic field to excitethe spins

A magnetic receptor tomeasured the spinresponse


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COMMERCIAL NMR WIRELINE TOOLS

MRIL CMR

B 0

Magnet

B1

vs. Homogeneous B 0Gradient field


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LONGITUDINAL AND TRANSVERSE RELAXATION

TW

T2 T1

TETw= wait timeTE= inter-echo timeT1= Longitudinal magnetization build upT2= Transverse magnetization decay


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T1 BUILD-UP OF OILS

T1 Buildup

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0

. 5 1 1

. 5 2 2

. 5 3 3

. 5 4 4

. 5 5 5

. 5 6 6

. 5 7 7

. 5 8 8

. 5 9 9

. 5 1 0

1 0

. 5 1 1

1 1

. 5 1 2

1 2

. 5 1 3

1 3

. 5 1 4

1 4

. 5 1 5

Time (sec.)

% P

o l a r i z a

t i o n

0.2 cP

0.4 cP0.6 cP

0.8 cP

1 cP

2 cP

4 cP

Water (512 m)

Water (256 ms)

Water (64 ms)

Water (16 ms)


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TRANSVERSE RELAXATIONAmplitude Decay Explanation


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Gradient Field and DiffusionGradient Field and Diffusion

TT11

TT22

BB 00 BB 00 BB 00 BB 00BB 00

f f f f f f f f --f f Diffusion during the pulse sequence causes a reductionDiffusion during the pulse sequence causes a reduction

in signal amplitude with time and decreases T2.in signal amplitude with time and decreases T2.

MM

TimeTime


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Elements of T2 DecayElements of T2 Decay

(Wetting Phase Saturation = 100%)(Wetting Phase Saturation = 100%)

1

2T

= + + 1T 2D

S

V

1T 2b

Bulk Fluid Relaxivity

Surface Relaxivity Pore Surface Area to Volume RatioPore Surface Area to Volume Ratio

Diffusion DecayDiffusion Decay

lP i C l T2 D


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Primary Controls on T2 DecayPrimary Controls on T2 Decay


1122

T T == ++ ++S S

V V 11

T T 2b2b

Pore Fluid Viscosity

Pore Fluid Diffusivity

Magnetic Field GradientInter-Echo Spacing (TE)

11T T 2D2D

Pore Size & Geometry

M a g n e t i c

s

Pore Mineralogy

Wettability


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TT22 Decay and Pore SizeDecay and Pore Size(Wetting Phase Saturation = 100%)(Wetting Phase Saturation = 100%)

0

20

40

60

80

100

0 50 100 150 200 250 300 350 400 450 500

Time (ms)

E c h

o A m p

l i t u d e

( p u

) Small Pore Size = Rapid Decay RateLarge Pore Size = Slow Decay Rate


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M ltiM lti ti l Dti l D


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MultiMulti --exponential Decayexponential Decay

== por por .. ee -- t / Tt / T 22

16 64 25616 64 256

TT22 (ms)(ms)

I n c r e m e n

t a l

I n c r e m e n

t a l

( ( p u p u

) )

1010

151564 ms64 ms

16 ms16 ms

256256

msms

55

= 30p.u.= 30p.u.

tt

y = 5y = 5 .. ee --t/t/ 1616 + 10+ 10 .. ee --t/t/ 6464 + 15+ 15 .. ee --t/t/ 256256


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T2 RELAXATION AND PORE SIZE

0.5 100101.0 1,000

T2 ms

Clay Silt Fine Coarse

Clay Domain

2 = 1 m/sSand Domain

2 = 5 m/s

d b k


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Water-Wet Hydrocarbon-Bearing Rock Formation

Clay

Wilcox SandOklahoma City

1 cm

Close-Up

Effect of Pore Size on T2 SpectraEffect of Pore Size on T2 Spectra


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I n c r e m e n

t a l P o r o s

i t y

[ p u

]

T2 [msec]

0.00

0.50

1.00

1.50

2.00

0.1 1. 10. 100. 1000. 10000.

T2 Spectra @ Sw = 1.0

Formation AFormation B

T2 Cut-off

Small Pores Large PoresMicro-Pores

NMR = 25 pu

Formation B (high-k)

Formation A (Low-k)

BVI = 10 pu BVM = 15 pu




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SurfaceSurface RelaxivityRelaxivity and Tand T 22 DecayDecay

Controls on SurfaceControls on Surface Relaxivity Relaxivity

Pore surface mineralogyPara, ferri, and ferro-magnetic ions (e.g., Fe 3+ , Mn 2+)

Wettability

Effects ofEffects of VariationsVariations (Wetting Phase Only)(Wetting Phase Only)

Higher results in faster T 2 Decay

Lower results in slower T 2 Decay

SurfaceSurface RelaxivityRelaxivity and Tand T DecayDecay


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Low (Carbonates)High (Clastics)

E c

h o

A m p

l i t u d e

[ p u

]

I n c r e m e n t a

l P o r o s

i t y

[ p u

]

T2 [ms]

0.00

0.50

1.00

1.50

2.00

0.1 1.0 10. 100. 1000. 10000.

NMR porosity

Time [ms]



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Low (Carbonates)High (Clastics)

22 --phase Fluid System, Wetting Phasephase Fluid System, Wetting Phase@ Irreducible Saturation@ Irreducible Saturation

E c

h o

A m p

l i t u d e

[ p u

]

I n c r e m e n t a

l P o r o s

i t y [ p u

]

T2 [ms]

0.00

0.50

1.00

1.50

2.00

0.1 1.0 10. 100. 1000. 10000.

NMR porosity

Time [ms]


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Effect of Magnetic Ions on TEffect of Magnetic Ions on T 22 DecayDecay

The presence of Para, ferri, and ferro-magnetic ions (e.g., Fe 3+ , Mn 2+

will increase and produce internal magnetic field gradients which

attenuate echo amplitudes due to accelerated diffusion decay (T 2D).Mineral Constituents with Low Magnetic SusceptibilitMineral Constituents with Low Magnetic Susceptibilit

Mineral Constituents with High Magnetic SusceptibilitMineral Constituents with High Magnetic Susceptibilit

NMR porosity

Time [ms]

E c

h o

A m p

l i t u d e

[ p u ]

I n c r .

P o r o s

i t y

[ p u

]

T2 [ms]0.00

0.50

1.00

1.50

2.00

0.1 1. 10. 100. 1000. 10000.

Basic NMR Field DeliverableBasic NMR Field Deliverable


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Basic NMR Field DeliverableBasic NMR Field Deliverable

GR T 2 Spectra Resistivity &Permeability Pore Volumetrics

Formation Tester Data and NMR Data


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Formation Tester Data and NMR Data

Patagonia Example


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g p


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Patagonia

Example


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PatagoniaExample


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China Example


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VenezuelaExample

Petrophysical Applications of NMR DataPetrophysical Applications of NMR Data


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Mineralogically-Independent Porosities ( Total & Effective )

Clay-Bound Water Volume

Capillary-Bound Water & Free Fluid Volumes

Pore Size Distribution ( Single Phase Fluid Saturation )

Permeability ( With calibration to core or test data )Shale Volume & Distribution

Flushed Zone Fluid Saturations ( DTW analysis )

Hydrocarbon Viscosity ( DTE analysis )

Electrical Properties & Water Saturation ( Integrated Products )

Basic MRIL Field DeliverableBasic MRIL Field Deliverable


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Basic MRIL Field Deliverable

GR T 2 Spectra Resistivity &Permeability Pore Volumetrics

Basic NMR DataBasic NMR Data


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Basic NMR DataBasic NMR Data

NMR measurements provideNMR measurements provide ::Echo Amplitudes

Echo Decay RatesCalibrated transforms provide:

Mineralogically Independent Porosities.

Clay Bound Water

Capillary Bound Water & Free Fluid Volumes

Permeability

Echo Train Inversion ProcessingEcho Train Inversion Processing


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C u m u

l a t i v e

P o r o s i t y

[ p u

]

I n c r e m e n

t a l P o r o s i t y

[ p u

]

T2 [msec]

0.00

0.50

1.00

1.50

2.00

0.1 1. 10. 100. 1000. 10000.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

multi-exponential fit

to spin-echo amplitudes

NMR porosity

Time [msec]

E c

h o A m p

l i t u d e

[ p u

]

Acquisition Time Domain T2 Relaxation Time DomainInversion

Processing

NMR Porosity DefinitionsNMR Porosity Definitions


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yy

Effective - Pore volume excluding clay bound water.

Total - Pore volume including clay bound water.CBW - Clay bound water, which represents anion-freewater adsorbed within clay inter-layers.

BVI - Bulk volume irreducible water which includeswater retained by capillary forces in small pores, andwater wetting pore surfaces.

BVM - Free-fluid volume which is available forhydrocarbon storage and fluid flow.

MRIL PorosityMRIL Porosity -- Test Pit VerificationTest Pit Verification


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Echo Spacing of 1.75 ms

E c

h o

A m

p l i t u d e

1500 15 1351201059075604530

BVM = 20.30 puMRIL = 26.25 pu

BVI = 5.95 pu

Time ( ms )

25

20

15

10

5

Limestone Block

core = 25.5%

E c

h o

A m p

l i t u d e

0 15 1501351201059075604530

MRIL = 19.82 pu

BVM = 15.61 pu

BVI = 4.21 puEcho Spacing of 1.5 ms

Time (ms)

20

15

10

5

Berea Sandstone Block

core = 20.3%

BVM Fit ResultsEcho Amplitude Complete Echo Fit Results

MineralogyMineralogy --Independent PorosityIndependent Porosity


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Gulf of Mexico SandstoneGulf of Mexico Sandstone Middle East CarbonateMiddle East Carbonate

20

Core Porosity (%)

M R I L P o r o s

i t y

( % )

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12 14 16 180

0.05

0.1

0.15

0.2

0.25

0.3

0 0.05 0.1 0.15 0.2 0.25 0.3

Core Porosity (frac.)

M R I L P o r o s i t y

( f r a c . )

Porosity ConsiderationsPorosity Considerations


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y

Although NMR porosity isAlthough NMR porosity is mineralogicallymineralogicallyIndependent, it is not fluid independent.Independent, it is not fluid independent.

NMR porosity can be too low whenNMR porosity can be too low when :: Hydrogen Index of reservoir fluids < 1.0Hydrogen Index of reservoir fluids < 1.0 Reservoir fluids with long T1 are only partiallyReservoir fluids with long T1 are only partially

polarized due to insufficient acquisition wait time (TW)polarized due to insufficient acquisition wait time (TW) Solid hydrocarbons (tar) are present with relaxationSolid hydrocarbons (tar) are present with relaxation

rates faster than the measurement time windowrates faster than the measurement time window

Internal gradients caused from magnetic mineralsInternal gradients caused from magnetic mineralsaccelerate NMR echo decay to below measurementaccelerate NMR echo decay to below measurementtime windowtime window

T2 Decay and Pore SizeT2 Decay and Pore Size


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y


Pore Volumetric DistributionPore Volumetric Distribution


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E c h o

A m p

l i t u

d e

0 15 1501351201059075604530

Time (ms)

20

15

10

5

0.00

1.00

2.00

3.00

4.00

0.1 1 10 100 1000 10000

BVI BVM

4.00

0.00

1.00

2.00

3.00

I n c r e m e n

t a l P o r o s

i t y

( p u )

CBW

MatrixMatrix DryDryClayClay

Clay-Clay-BoundBoundWater Water

MobileMobileWater Water

CapillaryCapillaryBoundBoundWater Water

HydrocarbonHydrocarbon

T2 Decay

NMR Porosity

T2 Decay (ms)

T2 Cutoffs

Transform

BulkBulk VolumetricsVolumetrics -- Light HCLight HC


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Matrix DryClay

Clay-BoundWater

MobileWater

MobileHC

Capillary-BoundWater

Res.HC

MBVM

MPHS

MPHE

MBVIMCBW

Effect of Oil Saturation & TEffect of Oil Saturation & T 22 SpectraSpectra


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Adapted fromAdapted from StraleyStraley et al, Log Analyst (Jan. 1995)et al, Log Analyst (Jan. 1995)

OilOil

Water Water

SwSw = 100%= 100%

SwSw = 76%= 76%

SwSw = 57%= 57%

SwSw = 34%= 34%

SwSw = 0%= 0%

Bulk OilBulk Oil

TT22

T2 Decay in a 2T2 Decay in a 2 --Phase SystemPhase System


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Wetting Phase Relaxivity

++ 11T T 2D2D water water

11T T 2b2b water water

11T T

== ++ S S V V 2b2b water water

((SwSw ))S S V V

Non-Wetting Phase Relaxivity

11

22hchcT T

== ++ 11T T 2D2D hchc

11T T 2b2b hchc

T2 Spectra for Various Fluid TypesT2 Spectra for Various Fluid Types


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Water Water

OilOil

GasGas



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Small Pores Large PoresMicro-Pores

NMR = 25 pu

Formation B (high-k)

Formation A (Low-k)



I n c r e m e n

t a l P o

r o s

i t y

[ p u ]

T2 [msec]

0.00

0.50

1.00

1.50

2.00

0.1 1. 10. 100. 1000. 10000.

T2 Spectra @ Sw = Swir

Formation AFormation B

T2 Cut-off

(2(2 --Phases with Wetting Phase Saturation @ Irreducible)Phases with Wetting Phase Saturation @ Irreducible)

Default TDefault T 22 CutCut --off Valuesoff Values


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T 2 [msec]

Carbonates : 92 msecSandstones : 33 msec

0.00

1.00

2.00

3.00

4.00

0.1 1 10 100 1000 10000

BVI BVM

4.00

0.00

1.00

2.00

3.00T2 Cut-off

I n c r e m e n

t a l P o r o s

i t y

( p u

)

CBW

CoreCore -- Calibration ProcessCalibration Process


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Capillary Pressure DataCore NMR Data

Calibrate BVI Model

Core Perm DataCalibrate Permeability Model

TT22 CutCut --off from Core NMRoff from Core NMR


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-- Obtain two core NMR measurements at:Obtain two core NMR measurements at:

SwSw = 1.0= 1.0SwSw == Swir Swir (obtained with centrifuging)(obtained with centrifuging)

-- Determine TDetermine T 22 cutcut --off where the terminaloff where the terminalcumulative porosity @cumulative porosity @ SwSw == SwirSwir is equalis equalto the cumulative porosity @to the cumulative porosity @ SwSw = 1.0.= 1.0.

T2 Cut-offs from Core NMR


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T2 (ms)10 10 100 2 4

0

5

10

15

C

u m u

l a t i v e

( p u )

T2 cut-off (Sxo = Swi)

S w = 1.0

S w (air-brine) = S wir

BVI

T2 cut-off(Sxo = 1.0)

S w (oil-brine) = S wir


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TT22 CutCut --off from Pc & Log NMR Dataoff from Pc & Log NMR Data


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0 100

Sw (%)

Pc

T2 cutoff Capillary Pressure Data

Swir core

BVIcore

NMR Post-Processing

Cumulative LogNMR Porosity

10 0 10 3T2 (ms)

4 8 16 32 64 128 256 512

T2 (ms)

BVI BVM

Integrated Petrophysical Analysis ResultsIntegrated Petrophysical Analysis Results


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Resistivity &Permeability

RockVolume

FluidSaturation

PoreVolume

T2Spectra


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Permeability from NMRPermeability from NMR


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k k

aa

S S wir wir

11 -- S S wir wir

C C

bb

=

Generalized CoatesGeneralized Coates --Timur Timur Model:Model:

This model is designed to compute the effective (nonThis model is designed to compute the effective (non --wettingwettingphase) permeability model based on the lower permeabilityphase) permeability model based on the lower permeabilityboundary condition which is controlled by the ratio of nonboundary condition which is controlled by the ratio of non --wetting phase (1wetting phase (1 --Swir Swir ) to wetting phase () to wetting phase ( Swir Swir ) saturation .) saturation .

Permeability from NMRPermeability from NMR


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Coates-Timur Model ( NMR version ):

NMR NMR

BVI BVI

BVM BVM

C C k k

bb

= aa

Where default parameters are: C =10 , a = 4 & b = 2


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BVI Dependence on CapillaryBVI Dependence on CapillaryPressure/Height above FWLPressure/Height above FWL


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0

2

4

6

8

10

12

14

16

18

0 50 100 150 200 250 300 350 400 450

Capillary Pressure (psi)

N M R P r e d

i c t e d B V I ( % )

Calibration Pc

BVI at calibration Pc

Capillary Drainage Curve

CoatesCoates --Timur Timur Permeability vs. Column HeightPermeability vs. Column Height

24


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Coates-Timur Permeability

k = (20 / 10) 4 (15.7 / 4.3) 2 = 213 md

NMR = 20 pu

2

k

= BVI

BVI NMR 4

10

NMR

P c

( p s

i )

1 10 100 10000 20 40 60 80 100

Sw (%)

0

250

100

150

200

50

T2 (ms)

T2 Cut-off @ Reference Pc

Capillary Pressure T2 Spectra

BVI = 4 pu

BVI = 4.3 pu

BVI = 6 pu

BVI = 5 pu

k = (20 / 10) 4 (16 / 4)2 = 256 md

k = (20 / 10) 4 (15 / 5)2 = 144 md

k = (20 /10) 4 (14 /6)2 = 87 md

k absolute = 256 md

Limitations of CoatesLimitations of Coates --TimurTimurPermeability ModelPermeability Model


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Application of the model is predicated on assumption thatApplication of the model is predicated on assumption that

the porosity is all interconnected, and that pore throatthe porosity is all interconnected, and that pore throatdiameterdiameter sytematicallysytematically increases proportional to an increaseincreases proportional to an increasein the magnitude of the bulk free fluid volume (BVM).in the magnitude of the bulk free fluid volume (BVM).

Computed permeability may systematically increase as afunction of increasing height above free water level. Thiseffect is most likely to occur for lower quality reservoirs withhighly sloped capillary pressure curves, but should not bean issue for very high permeability reservoirs wherecapillary presure curves are near-asymptotic.

Model Losses sensitivity at very high permeabilities whereirreducible water saturation is on the asymptote of thecapillary pressure curve, and porosity doesnt increaserelative to increased pore size and/or pore throat size.

Calibration of Coates-Timur Permeability Model


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Local calibration of model fitting parameters (C, a & b) arenecessary to account for variations in the complexity andconnectivity of the pore system, which control thepermeability and its correlation to the bulk pore volumetric

elements of which model is strictly comprised.

Multi-linear regression can be employed to solve for the theformation-specific fitting parameters (C, m & n) whenreference permeability data from core or formation tests areavailable.

Minimum error analysis can also be employed to solve foran optimum value of the porosity denominator C whileholding parameters a and b constant at default values.

Multiple Water SaturationMultiple Water Saturation ModelsModels


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ShaleShale --Free Conductance ModelFree Conductance Model

ArchieArchie

Laminated Shale Conductance ModelLaminated Shale Conductance Model

PouponPoupon --LeveauxLeveaux (Indonesian)(Indonesian)

DoubleDouble --Layer Dispersed Clay Conductance ModelsLayer Dispersed Clay Conductance Models

WaxmanWaxman --SmitsSmits

DualDual --WaterWater

Mixed DispersedMixed Dispersed --Clay / Laminar Clay / Laminar --Shale Conductance ModelShale Conductance Model

PatchettPatchett --HerrickHerrick

WaxmanWaxman -- SmitsSmits Water Saturation ModelWater Saturation Model


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C t C w

F* S wn* =

F* S w

B Q v

WaxmanWaxman --SmitsSmits Model:Model:

Where, F* is the Total Formation ResistivityFactor, and Q v = Total Q v

PatchettPatchett --Herrick Water Saturation ModelHerrick Water Saturation Model


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PatchettPatchett --Herrick Model:Herrick Model:

C t = (1 - V sh ) C w

F* S wn*

F* S w

B Q v (V sh C sh )

Where, V sh = Laminar Shale Volume, F* is theFormation Resistivity Factor of the Sand layers,and Q v = Q v of Dispersed Shale in Sand Layers

CoreCore --Calibrated Analyses ResultsCalibrated Analyses Results

Permeability & T2Rock Fluid Porosity


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Permeability &

Resistivity

T2

Spectra

Rock

Volumetrics

Fluid

Saturations

Porosity

Volumetrics


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NMR Petrophysics