Talisman Energy, capillary pressure, saturation, permeability and NMR Malay Basin Example.pdf

Capillary Pressure, Saturation,

Permeability and NMR: Malay

Basin Example

Andrew Logan – Talisman Malaysia Limited

FESM November 2008

Summary

• Compare methods of modeling capillary pressure (Saturation Height Functions) and demonstrate similarity of Sw results in generic models for the Malay Basin.– Parameters for J-Function, Power Function, Lambda Functions

and Thomeer Method are derived and results compared.

• Use Capillary Pressure data to derive a generic permeability equation based on porosity and irreducible water saturation– Coates Parameters are derived from capillary pressure data.

• Application of NMR in the above models– Some preliminary results

• These three closely related topics gain from being discussed together rather than individually.

• Wetting fluid (usually water) is held in the pore space by capillary forces.

• The wetting fluid is displaced only when the capillary forces are exceeded. Pc arises from density difference between water and hydrocarbon.

• Sw may be estimated by computing the pressure difference due to the “height-above-free water”combined with knowledge of the capillary pressure curve.

– Suitable conversions for fluid types must be applied.

• Fluid contact (i.e. the height above free water) is a key parameter since it impacts Pc.

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 60 70 80 90 100

Water Saturation, % pore volume

Pre

ss

ure

, b

ar

Review of Capillary Pressure

Well XXXXXX

Fluids Air-Water

Method HS Centrifuge

NOB 800 psi

Klinkenberg Capillary End face

Sample Depth Permeability Porosity Pressure Sw

No. (m) (mD) (frac) (psi) (frac)

XXXX XXXX.XX 1050.00 0.2550 0.00 1.00

1.00 0.57

2.00 0.44

5.00 0.33

10.00 0.26

25.00 0.23

50.00 0.20

100.00 0.20

200.00 0.18

500.00 0.16

750.00 0.16

• It is necessary to make a conversion between Laboratory Conditions,

(fluids used for Pc measurement) and Reservoir conditions with

different fluids. Different fluids have different wettability (surface

tension) properties.

• Typical values for usual reservoir fluids are shown in the table below.

)cos(

)cos(

RESRES

LABLABcREScLAB PP

θσθσ

=

260.86630º30Oil/Water/Solid

-370-0.755140º480Air/Mercury/Solid

7210º72Air/Water/Solid

σσσσcos(θθθθ)cos(θθθθ)θθθθσσσσSystem

Fluid System Conversion

hP oilbrinec )( ρρ −=

• In the reservoir, the

capillary pressure may

be estimated by

computing the pressure

difference due to

different fluid densities

and the “height-above-

free-water”, h.

0

10

20

30

40

50

60

70

80

90

100

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0

Water Saturation ( % PV)

He

igh

t A

bo

ve

Fre

e W

ate

r (m

)

Capillary Pressure and Saturation Height Functions

Capillary Pressure Modeling

λc

wirrwP

CSS =−

φθσkP

JJSIS cw

cos

2166.0:)log(* =+=

b

c

wP

aS =

−=

−

dP

cP

G

eSwlog

1

Lambda

Function

J-Function

Power

Function

Thomeer

Parameters

• Capillary pressure curves usually have differing relationships

between Pc and Sw.

– Usually one Cap-pressure curve does not adequately describe a

reservoir.

• Several methods are available to describe Capillary Pressure

Measurements

– J-Function

– Lambda Function

– Thomeer Parameters

– Power Function

• All methods are based on curve fitting with little or no physical

modeling behind them.

– Relationships hint at some underlying physical principles.

• Each may be used to describe capillary pressure, but differ in

implementation.

Modeling Capillary Pressure Data

Fitting of Capillary Pressure Models

Well XXXXXX Lab Sigma 72 Sum of all fitting error 0.74478

Fluids Air-Water Lab Theta 0

Method HS Centrifuge Norm Sigma 72

NOB 800 psi Norm Theta 0

Scaling 1

Lambda 0.410836781

Normalized J-Slope -0.20243357 C 0.416837169 G 1.252286835 a 0.500002723

Klinkenberg Capillary End face Capillary J-Function J-Inter -1.02527047 Swirr 0.122185501 Pd 0.223069737 b 0.202254711

Sample Depth Permeability Porosity Pressure Sw Pressure

No. (m) (mD) (frac) (psi) (frac) (psi)

XXXX XXXX.XX 1050.00 0.2550 0.00 1.00 0.00 0.00 J(Sw) J-Error Lam(Sw) Lam Error BV Thom(BV) Thom(Sw) Thom. Err PF(Sw) PF. Error

1.00 0.57 1.00 0.19 0.5004 0.0656 0.53902267 0.0270 0.1107 0.1107 0.5660 0.0000 0.5000 0.0660

RQI 64.17 2.00 0.44 2.00 0.39 0.4349 0.0001 0.435724988 0.0007 0.1441 0.1441 0.4350 0.0000 0.4346 0.0004

5.00 0.33 5.00 0.97 0.3613 0.0363 0.337366466 0.0124 0.1721 0.1705 0.3315 0.0065 0.3611 0.0361

10.00 0.26 10.00 1.93 0.3140 0.0550 0.284041819 0.0250 0.1890 0.1835 0.2806 0.0216 0.3138 0.0548

25.00 0.23 25.00 4.83 0.2608 0.0328 0.23326688 0.0053 0.1969 0.1956 0.2331 0.0051 0.2608 0.0328

50.00 0.20 50.00 9.65 0.2267 0.0237 0.205739467 0.0027 0.2032 0.2023 0.2066 0.0036 0.2266 0.0236

100.00 0.20 100.00 19.30 0.1970 0.0000 0.185033705 0.0120 0.2048 0.2077 0.1854 0.0116 0.1970 0.0000

200.00 0.18 200.00 38.61 0.1712 0.0108 0.169459101 0.0125 0.2086 0.2121 0.1682 0.0138 0.1712 0.0108

500.00 0.16 500.00 96.52 0.1422 0.0208 0.154629194 0.0084 0.2134 0.2168 0.1498 0.0132 0.1423 0.0207

750.00 0.16 750.00 144.78 0.1310 0.0260 0.149650875 0.0073 0.2150 0.2186 0.1429 0.0141 0.1311 0.0259

Error 0.27098 Error 0.11334 Error 0.08928 Error 0.271172469

Normalized

Power Function Parms.

Normalized

Lambda Function Parms.

Normalized

J-Function Parms.

Normalized

Thomeer Parms

Air-Brine Capillary Pressure

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

0.00 0.20 0.40 0.60 0.80 1.00

Water Saturation

Air

Bri

ne C

apilla

ry P

ressure

(P

si)

Measured

J-Function

Lambda

Thomeer

Power Function


0.10

1.00

10.00

100.00

1000.00

0.10 1.00

Water Saturation

Air

Bri

ne C

apilla

ry P

ressure

(P

si)

Measured

Lambda

Thomeer

Power Function

J-Function - Water Saturation

0.10

1.00

10.00

100.00

1000.00

10000.00

0.10 1.00

Water Saturation

J-F

unction

J-Function

J(Sw)

Parameters

a,b,λλλλ,C� etc.

Table of Fitting Results

Well Sample Depth Lab Sigma Lab Theta Porosity Permeability Swirr C Lamda At 50 psi BVI Error

XXXXXX XXXX XXXX.XX 72 0 0.2160 46.00 0.21 0.78557 0.410837 0.371895 0.080329 0.2029


































Lambda Function Parameters

J-Function Model

RQIPkP

J cc

)cos(

2166.0

)cos(

2166.0

θσφθσ==

Porosityφφφφ

Permeabilityk

Contact Angleθθθθ

Interfacial tensionσσσσ

Capillary pressure from FWL

– convert to/from

Air/Brine

Pc

SaturationSw

• The J-Function is one of the oldest, and a standard method of implementing Capillary Pressure measurements into reservoir modeling. The use of the Reservoir Quality Indicator (RQI) is intended to accommodate variable rock types.

J-Function

)log(* JSlopeInterceptSw +=

• For each J-Function, a fit may be computed between the J-Function and Sw. Where the slope and intercept can be used to describe Sw as a function of J.

J-Function - Water Saturation

0.10

1.00

10.00

100.00

1000.00

10000.00

0.10 1.00

Water Saturation

J-F

unction

J-Function

J(Sw)

J-Function Slope and Intercepts

as Functions of Permeability

J-Function Slope and Intercept - Permeability

-2

-1.9

-1.8

-1.7

-1.6

-1.5

-1.4

-1.3

-1.2

-1.1

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.10 10.00 1000.00

Permeability (mD)

J-F

unction S

lope a

nd Inte

rcept

J-Function Intercept

J-Function Slope

Model Intercept

Model Slope

Best Fit Intercept

Best Fit Slope

• Best fit of ln(k) to parameters compared to least squares fit of Sw

prediction.

• Parameters between two methods are close but not exactly the same.

• Since the objective is to predict Sw, the least squares approach is preferred.

)ln(* kslopeconstParameter +=

Least Squares Fit on all Capillary Pressure Data

to Optimize Model fit – J-Function

Measured Sw vs. Modeled Sw

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000

Permeability Predicted Sw

Capilla

ry P

ressure

Sw

J-Function

• Optimize 4 J-Function Parameters over the entire Capillary Pressure data set.

• Average Error = 0.069

Power Function Model

• The Power Function is a very simple model (few parameters) which is similar to the Lambda Function

• Fitting is done to laboratory conditions conversions must be done from Pc at reservoir conditions to Pc at laboratory conditions.

b

c

wP

aS =

Fitting Constanta

Fitting exponentb

Capillary pressure from

FWL – convert to/from

Air/Brine

Pc

SaturationSw

Power Function Parameters


Power Function a,b - Permeability

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

0.10 10.00 1000.00

Permeability (mD)

Pow

er Function a

, b

Power Function a

Power Function b

Model a

Model b

Best fit a

Best fit b



prediction.




to Optimize Model fit – Power Function


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000


Capilla

ry P

ressure

Sw

Power Function

• Optimize 4 Power-Function Parameters over the entire Capillary Pressure data set.


Thomeer Parameter Model

• The Thomeer Equation was developed for the analysis of Mercury Injection data to very high pressures. Sb∞∞∞∞ is the maximum pore volume that can be injected at extremely high pressures (e.g. 60,000 psi) and represents the total interconnected pore space. In these spreadsheets it is assumed that the measured porosity is equal to Sb∞∞∞∞. As such the methods used here are suitable for clastics but not for carbonates which may have unconnected vugs.

−

∞= dP

cP

G

eSS bb

log

Pore Geometrical factor – or shape of the cap

pressure curve

G

Air-mercury extrapolated Displacement pressurePd

Air mercury capillary pressurePc

Bulk Volume occupied by Hg at infinite pressure or

the total interconnected pore volume

Sb

∞∞∞∞

Bulk Volume occupied by Hg at pressure PcSb

Thomeer Parameter Model

−=

−

dP

cP

G

eSwlog

1

• Expressing in terms of Sw

and assuming Sb∞∞∞∞ = φφφφe


Assume Sb∞∞∞∞= φe

Parameter to correlate to logsG

Parameter to correlate to logsPd

Capillary pressure from FWL –

convert to/from Air/Brine

Pc

SaturationSw

Thomeer Parameters


Thomeer Pd - Permeability

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0.10 10.00 1000.00

Permeability (mD)

Thom

eer

G, P

d Thomeer G

Thomeer PD

Model G

Model Pd

Best Fit G

Best Fit Pd



prediction.




to Optimize Model fit – Thomeer Parameters


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000


Capilla

ry P

ressure

Sw

Thomeer

• Optimize 4 J-Function Parameters over the entire Capillary Pressure data set.


– Fitting error low in part due to limits put on computation at high permeabilies to remove irrational results.

Lambda-Function Model

• The Lambda function is similar to the Power Function except that it is controlled asymptotically to the Swirr


λc

wirrwP

CSS =−

Fitting ConstantC

Fitting exponentλλλλ

Capillary pressure from

FWL – convert to/from

Air/Brine

Pc

SaturationSw



Lambda Swirr,C

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

0.10 10.00 1000.00

Permeability (mD)

Lam

bda P

ara

mete

rs (Sw

irr, C

)

Lamda Swirr

Lamda C

Modeled Swirr

Modeled C

Best Fit Swirr

Best Fit C



prediction.




to Optimize Model fit – Lambda Function


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000


Capilla

ry P

ressure

Sw

Lambda Function

• Optimize 5 Lambda Function Parameters over the entire Capillary Pressure data set.


Saturation Height Functions

Malay Basin Core Calibrated Models

λc

wirrwP

CSS =−

)ln(03302.0306447.0 kSwirr −=

)ln(07664.00645.1 kC −=

41084.0=λ

)log(* JSlopeInterceptSw +=

b

c

wP

aS =

−=

−

dP

cP

G

eSwlog

1

)ln(06043.063807.0 kIntercept −−=

)ln(02357.015885.0 kSlope −−=

)ln(10018.0275117.1 ka −=)ln(015192.0192164.0 kb −=

)ln(10612.0048778.1 kPd −=

)ln(24418.0751447.2 kG −=

Lambda

Function

J-Function

Power

Function

Thomeer

Parameters

Model Comparison – Prediction of Sw


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000


Capilla

ry P

ressure

Sw

J-Function

Lambda Function

Thomeer

Power Function

• Fitting error comparable between methods

• Thomeer and Lambda have physical interpretation (Swirrand Entry Pressure)

• J-Function is a variation on a “standard” method

• Thomeer and Power have problems at low and high permeabilities in poorly calibrated models.

• J-Function is conservative at high permeabilities

Model Comparison

Swirr vs. Permeability (50psi)

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

0.10 1.00 10.00 100.00 1000.00 10000.00

Permeability

Sw

irr

Measured

J-Function

Lambda Model

Thomeer

Power Function

• Comparison of methods as function of Permeability.

• Lambda and Thomeer have physical interpretation (Swirr and Entry Pressure, Pd)

• J-Function is a variation on a “standard” method

• Thomeer and Power have problems at low and high permeabilities in poorly calibrated models.

• J-Function is conservative at high permeabilities

Example Comparing Different Methods.

2365

2370

2375

2385

2390

2395

2360

2380

2353.7

2400.0

2303.5

2310

2315

2320

2325

2330

2335

2340

2345.4

Clastic Permeability Review

• Permeability is a complex phenomena in rocks.

• Permeability is closely related to pore throat size.

• In clastics there is a loose relationship between pore throat size and grain size.

• There is a loose relationship between grain size and sorting.

• There is a loose relationship between porosity, sorting and grain size.

• Logs measure bulk properties and have little response to grain size and texture.

• These simplifications may be appropriate for clastics, but do not always work and are not necessarily applicable to carbonates or fractured reservoirs

(after Chilingar, 1969)(after Chilingar, 1969)

104

103

102

101

100

K in m

d

10-11

10-13

10-14

10-15

10-12

K in m

2

1 - coarse & very

coarse grained

2 - coarse & medium

coarse grained

3 - fine grained

4 - silty

5 - clayey

0 0.30.20.1 φ

Porosity - Permeability Relationships in Clastics

(Chilingar, 1969)(Chilingar, 1969)


104

103

102

101

100

K in m

d

10-11

10-13

10-14

10-15

10-12

K in m

2

1 - coarse & very

coarse grained

2 - coarse & medium

coarse grained

3 - fine grained

4 - silty

5 - clayey

0 0.30.20.1 φ

Porosity - Permeability Relationships in Clastics

Observations

(Chilingar, 1969)(Chilingar, 1969)

Permeability decreases with decreasing

grain size.

Permeability increases with increasing

porosity.

Permeability does not increase infinitely

with porosity.

k = 2301 mD

φ φ φ φ = 24.9%

10.16 mm

Permeability and Grain Size

10.16 mm

k = 212 mD

φ φ φ φ = 23.1%

Common Permeability Models

2,4.4,136.0 === mnC

2,4,10 === mnC

Log - Fit

Timur

Coates

φbak +=10

m

wirr

n

SCk

φ=

m

e

e

n

e BVI

Ck

−

=φ

φφ*100

No standard values for the parameters. User derives parameters from

an appropriate fit of the core data.

Timur derived this equation in the 1960’s and assigned nominal

values. The user may adjust the fitting parameters to their data

Coates created this variation of the Timur equation, using

Bulk Volume of Immovable (BVI) fluid instead of Swirr for

use with NMR data. The model premise is that since

immovable water (Swirr) does not contribute to flow, there

should be a permeability control based on BVI.

Standard Values

Standard Values

Malay Basin Core Data – Log Fit

22 wells

Malay Basic Core Data

1 14

Color: FREQUENCY

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

0.01

0.1

1

10

100

1000

10000

100000

CORE.KAIR (MD)

CORE.PHI (V/V)

1091

9900

96

5 5

φ8.2170.210 +−=k

• Log-fit typical method often selected to “engineer” a good solution in a short period of time.

• Requires sufficient core for each reservoir or facies to be modeled to a desired accuracy.

• Simple (empirical) fits have minimal interpretive meaning.

• Single parameter input limits use when permeability is more complex.

• Tend to be limited to a certain porosity range.

Basic Inputs for Coates Equation

Well Sample Depth Lab Sigma Lab Theta Porosity Permeability Swirr C Lamda At 50 psi BVI Error




































BVI from Capillary Pressure

• Capillary Pressure data can be

used to estimate BVI via Swirr

of the Lambda fitting.

Well XXXXXX

Fluids Air-Water

Method HS Centrifuge

NOB 800 psi

Klinkenberg Capillary End face

Sample Depth Permeability Porosity Pressure Sw

No. (m) (mD) (frac) (psi) (frac)

XXXX XXXX.XX 1050.00 0.2550 0.00 1.00

1.00 0.57

2.00 0.44

5.00 0.33

10.00 0.26

25.00 0.23

50.00 0.20

100.00 0.20

200.00 0.18

500.00 0.16

750.00 0.16


0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

0.00 0.20 0.40 0.60 0.80 1.00

Water Saturation

Air B

rine C

apilla

ry P

ressure

(Psi)

wirrSBVI φ=

Coates Equation Fit of Malay Basin Capillary

Pressure Data

Core Air Permeability - Modeled Pemeability

Capillary Pressure Data Only

0.10

1.00

10.00

100.00

1000.00

10000.00

0.1 1 10 100 1000 10000

Modeled Permeability

Core

Air P

erm

eability (m

D)

Coates

Unity

• Create Least squares fit of Capillary Pressure/Core Data (Swirr, φφφφ k) to Coates Parameters using capillary pressure 59 samples.

57.358.6036.0

23.9

*100

−

=e

eekφ

φφ

Coates: Permeability - Porosity

Capillary Pressure Data Only

0.10

1.00

10.00

100.00

1000.00

10000.00

0.0000 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000 0.3500

Core Porosity

Core

Air

Perm

eability (m

D)

Poro-Perm

BVI=0.01

BVI=0.036

BVI=0.07

Coates Equation Fit of Malay Basin Capillary Pressure

• Fit of Coates model for BVI = 0.01, 0.036 and 0.07 for coarse grained, medium grained and fine grained (increasing surface to volume ratio resulting in increasing BVI.

• Model behaves as we would expect rocks to behave (i.e. decreasing permeability with increasing bound water.

• Similar behavior to known rock behavior

• Core calibrated Coates model with constant BVI of 0.01, 0.036 and 0.07.

• Coates model seeks to model permeability variations with grain-size though surface to volume relationships.

Core Calibrated Coates Model

18 WellsMalay Basin Core Data

Core Air Permeability vs. Core Porosity

1 12

Color: FREQUENCY

0.000

0.000

0.050

0.050

0.100

0.100

0.150

0.150

0.200

0.200

0.250

0.250

0.300

0.300

0.350

0.350

0.400

0.400

0.01 0.01

0.1 0.1

1 1

10 10

100 100

1000 1000

10000 1000020000 20000

Core Air Perm

eability (mD)

Core Porosity

943

8460

96

5 1


104

103

102

101

100

K in m

d

10-11

10-13

10-14

10-15

10-12

K in m

2

1 - coarse & very

coarse grained

2 - coarse & medium

coarse grained

3 - fine grained

4 - silty

5 - clayey

0 0.30.20.1 φ

Permeability As a Function of

Porosity and Grain Size

• Core calibrated Coates model with constant BVI of 0.01, 0.036 and 0.07.

• Note how average BVI of 0.036 does not fit well over the entire range of porosity.

• This is because BVI changes with porosity (probably sorting of grains)

Core Calibrated Coates Model



1 12

Color: FREQUENCY

0.000

0.000

0.050

0.050

0.100

0.100

0.150

0.150

0.200

0.200

0.250

0.250

0.300

0.300

0.350

0.350

0.400

0.400

0.01 0.01

0.1 0.1

1 1

10 10

100 100

1000 1000

10000 1000020000 20000

Core Air Perm

eability (mD)

Core Porosity

943

8460

96

5 1

Capilliary Pressure BVI vs. Core Porosity

0.0000

0.0200

0.0400

0.0600

0.0800

0.1000

0.1200

0.1400

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

Core Porosity

Capilliary

Pre

ssure

BV

I

BVI

Fit

• Simple model of BVI vs. φφφφ to capture variable of BVI due to rock quality.

φφ

≤≤

−=

BVI

BVI

01.0

29.010.0

Variation of BVI with Porosity

φφ

≤≤

−=

BVI

BVI

01.0

29.010.0

• Final Coates Model with variable BVI achieves better fit with all the core data.

• Honors core calibration parameters.

• If BVI data is available from NMR or other sources it may be used in place of the Simple BVI to φφφφrelationship.

57.358.6

23.9

*100

−

=e

ee BVIk

φφφ

Core Calibrated Coates Model with Variable

BVM – Generic Malay Basin Model



1 12

Color: FREQUENCY

0.000

0.000

0.050

0.050

0.100

0.100

0.150

0.150

0.200

0.200

0.250

0.250

0.300

0.300

0.350

0.350

0.400

0.400

0.01 0.01

0.1 0.1

1 1

10 10

100 100

1000 1000

10000 1000020000 20000

Core Air Perm

eability (mD)

Core Porosity

943

8460

96

5 1

• Core Air Permeability compared to Log Estimated Permeability– Demonstrates good

relationship.

– Data scatter in part due to depth matching and measurement resolution differences.

Comparison of Core Permeability to Log based model


Core Air Permeability vs. Log Estimated Permeability

1 14

0.01

0.01

0.1

0.1

11

10

10

100

100

1000

1000

10000

10000

20000

20000

0.01 0.01

0.1 0.1

1 1

10 10

100 100

1000 1000

10000 1000020000 20000

Core Air Perm

eability (mD)

Log Estimated Permeabiltlity (mD)

944

6970

102

238

0

Pore Volume Definition Review

Bulk Volume MovableBVM

Bound Water Irreducible – also known as Capillary bound

Water

BVI

Clay Bound Water – water hydrated on clay surface.CBW

Effective Porosityφφφφe

Total Porosityφφφφt

φφφφeVq Vsh

Silt

Clay Bound W

ater

Bulk Volume

Movable (BVM)

Capillary Bound

Water (B

VI)BVIBVM

CBW

e

et

+=

+=

φ

φφ

Humidity dried core is expected to relate to

Effective Porosity, φe, since humidity drying

cannot remove the Clay Bound Water.

When relating to logs and log derived effective

porosity there are some differences which

become more pronounced as shaliness

increases because log analysis tends to define

capillary bound water in shale as CBW. While it

is non-effective, technically it is not the water of

hydration.

Clay

MatrixMatrixDryDryClayClay

Clay-Clay-BoundBoundWaterWater

MobileMobileWaterWater

CapillaryCapillaryBoundBoundWaterWater

HydrocarbonHydrocarbon

Echo A

mplitu

de

0 15 1501351201059075604530

Time (ms)

20

15

10

5

T2 Decay

NMR Porosity

Transform

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

Incre

menta

l P

oro

sity (pu)

CBW

T2 Decay (ms)

T2 Cutoffs

ECHO TRAIN T2 SPECTRUM

25

NMR Basics

0

1

2

3

4

5

6

0 10 20 30 40 50 60 70 80 90 100

Water Saturation, % pore volume

Pressure, bar

Simple (Undisturbed) Reservoir States

Above the transition zone, pressure difference due to the density difference

between hydrocarbon and water force water to drain from the reservoir. This

volume of hydrocarbon can be approximated by Swirr or BVI

Silt

Clay Bound

Water

Hydrocarbon

Capillary Bound

Water (BVI)

Clay

Silt

Clay Bound

Water

Transition

Capillary Bound

Water (BVI)

Clay

Silt

Clay Bound

Water

Wet

Capillary Bound

Water (BVI)

Clay

Within the transition zone pressure is insufficient to displace all the water and

“free” water may be produced. The length of the transition zone is determined by

the fluid density differences and the capillary properties. In general high

permeability means short transition zones.

Below the OWC the formation is 100% wet.

Rule of “Thumb” reservoir

is either “wet” or near Swirr.

I-Gas Sand Analysis using Generic Models

2080

2085

2090

2095

2105

2110

2115

2120

2130

2135

2140

2145

2100

2125

2050

2055

2060

2065

2070

2075

2080

2085

2090

2095

2100

2105

2110

2115

I8014.9

2090.9I90

2093.1

I90 SAND25.9

2119.0

I90 SHALE13.1

2132.1

I10025.0

I8014.9

2090.9I90

2093.1

I90 SAND25.9

2119.0

I90 SHALE13.1

2132.1

I10025.0

2080

2085

2090

2095

2105

2110

2115

2120

2130

2135

2140

2145

2100

2125

2050

2055

2060

2065

2070

2075

2080

2085

2090

2095

2100

2105

2110

2115

I8014.9

2090.9I90

2093.1

I90 SAND25.9

2119.0

I90 SHALE13.1

2132.1

I10025.0

I8014.9

2090.9I90

2093.1

I90 SAND25.9

2119.0

I90 SHALE13.1

2132.1

I10025.0

I-Gas Sand with NMR data

2330

2335

2340

2345

2355

2360

2365

2370

2380

2385

2390

2395

2405

2410

2415

2420

2430

2435

2350

2375

2400

2425

2280

2285

2290

2295

2300

2305

2310

2315

2320

2325

2330

2335

2340

2345

2350

2355

2360

2365

2370

2375

2380

2331.7

J509.1

2340.9

J50 SHALE12.8

2353.7

J5518.6

2372.3

J6027.7

2400.0

J7023.2

2423.2

K520.1

2331.7

J509.1

2340.9

J50 SHALE12.8

2353.7

J5518.6

2372.3

J6027.7

2400.0

J7023.2

2423.2

K520.1

J-Sand Standard Analysis

2330

2335

2340

2345

2355

2360

2365

2370

2380

2385

2390

2395

2405

2410

2415

2420

2430

2435

2350

2375

2400

2425

2280

2285

2290

2295

2300

2305

2310

2315

2320

2325

2330

2335

2340

2345

2350

2355

2360

2365

2370

2375

2380

2331.7

J509.1

2340.9

J50 SHALE12.8

2353.7

J5518.6

2372.3

J6027.7

2400.0

J7023.2

2423.2

K520.1

2331.7

J509.1

2340.9

J50 SHALE12.8

2353.7

J5518.6

2372.3

J6027.7

2400.0

J7023.2

2423.2

K520.1

J-Sand with NMR Data

2330

2335

2340

2345

2355

2360

2365

2370

2380

2385

2390

2395

2405

2410

2415

2420

2430

2435

2350

2375

2400

2425

2280

2285

2290

2295

2300

2305

2310

2315

2320

2325

2330

2335

2340

2345

2350

2355

2360

2365

2370

2375

2380

2331.7

J509.1

2340.9

J50 SHALE12.8

2353.7

J5518.6

2372.3

J6027.7

2400.0

J7023.2

2423.2

K520.1

2331.7

J509.1

2340.9

J50 SHALE12.8

2353.7

J5518.6

2372.3

J6027.7

2400.0

J7023.2

2423.2

K520.1

J-Sand SHF Analysis

2330

2335

2340

2345

2355

2360

2365

2370

2380

2385

2390

2395

2405

2410

2415

2420

2430

2435

2350

2375

2400

2425

2280

2285

2290

2295

2300

2305

2310

2315

2320

2325

2330

2335

2340

2345

2350

2355

2360

2365

2370

2375

2380

2331.7

J509.1

2340.9

J50 SHALE12.8

2353.7

J5518.6

2372.3

J6027.7

2400.0

J7023.2

2423.2

K520.1

2331.7

J509.1

2340.9

J50 SHALE12.8

2353.7

J5518.6

2372.3

J6027.7

2400.0

J7023.2

2423.2

K520.1

J-Sand SHF Analysis using NMR BVI

I-Sand Example

Permeability estimate

both with and without

NMR BVI have good

agreement. Also fair

agreement with RCI

mobilities

Hydrocarbon volume

increases in the

transition zone to

match BVI at the top.

Hydrocarbon volume

matches BVI in the

interval because above

transition. Good match

indicates resistivity

modeling is robust

Good match at the top.

Indications of potential free

water at the bottom.

-Possible shoulder bed

effect.

-Possible near GWC

-NOT due to decreasing

reservoir quality.

Resistivity model does

not match NMR data.

Almost certainly due to

should bed effects. Can

reliably upgrade

hydrocarbon volumes.

J-Sands with NMR

Fair match of

resistivity with BVI.

Suggests slightly

pessimistic resistivity

Sw model

BVI of J20 is higher

than J18 indicating

poorer quality

reservoir.

I Sands – Resistivity Mismatch?

Poor match between Resistivity

model and NMR BVI. Highlights poor

understanding we have of some

potential reservoirs, but NMR helps

by improving our assessment of

reservoir quality and potential.

Log Based Permeability Estimate

Compared to Measured Mobility

0.1 1

10

100

1000

10000

0.1

1

10

100

1000

10000

0.1 1

10

100

1000

10000

0.1

1

10

100

1000

10000

Without NMR With NMR

Log Derived Permeability

RCI Mobility

Impact of NMR on Analysis during Pilot

Program

35 %30 %34 %38 %No

Change

25 %45 %21 %15 %Low

Change

19 %10 %21 %23 %Medium

Change

21%15 %24 %23 %High

Change

7520 / 27%29 / 39%26 / 35%Number

TotalLow

Res. Qual.

Medium

Res. Qual.

High

Res. Qual.

45% of high and medium quality reservoir had significant changes of interpretation

NMR Application

• Three Principle Observations– Confirmation of Core based permeability and saturation height

models. This confirmation is good over the formations to which the core data is biased but start to deviate where core data hasbeen sparse.

– Highlights deviations from BVI correlations

• SHF and permeability models still appear to apply but fail due to assumptions about BVI.

– Highlights where resistivity based saturation is struggling by imposing more reasonable bounds and values for Sw through reasonable height functions.

• Cautions– Interpreted BVI from NMR does not necessarily match

definitions derived from core

– Signal to noise of in-situ NMR may not be robust enough for fluid classification at an accuracy required for computation. Separation of BVI and BVM may not be accurate enough

Conclusions

• Several different Saturation Height functions give similar results when implemented as correlations to permeability– Use which ever model you feel comfortable with or that fits your

modeling work flow.

• Capillary pressure may be used to derive the parameters of the Coates equation providing a non-log and non-NMR method of verifying/calibrating the Coates permeability model.

• Used appropriately, NMR BVI measurements are compatible with the methods above and provide guidance on permeability and saturation.– Caution must be exercised in the interpretation of the NMR data.

• Using these methods, log derived permeability achieves greater consistency with mobility from pressure measurements.

Acknowledgements

PVEP

For permission to present the data

and results I would like to thank:

PETRONAS

PETRONAS – Carigali

Petro-Vietnam Production Corporation

Talisman Energy, capillary pressure, saturation, permeability and NMR Malay Basin Example.pdf

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