Pore-Scale Simulation of NMR Response in Porous Media Olumide Talabi

1

Pore-Scale Simulation of NMR Response in Porous Media

Olumide Talabi

Supervisor: Prof Martin Blunt

Contributors: Saif AlSayari, Stefan Iglauer, Saleh Al-Mansoori, Martin Fernø and Haldis Riskedal

2

OUTLINE1. Pore-scale modeling: Overview

2. Modelling NMR response

3. Simulation of NMR response in micro-CT images

4. Simulation of NMR response of single-phase fluids in networks

5. Simulation of NMR response of two-phase fluids in networks

6. Single-phase NMR simulation results

7. Two-phase NMR simulation results

8. Conclusions and recommendations for future work

3

Pore Scale Modelling: Overview

Core Micro CT Network

Rock Properties PorosityPermeabilityFormation FactorCapillary PressureRelative PermeabilityNMR Response**

PorosityPermeabilityFormation FactorNMR Response**

PorosityPermeabilityFormation FactorCapillary PressureRelative PermeabilityNMR Response**

Relative Permeability (Valvatne and Blunt, 2004) Capillary Pressure

Pore-scale modeling: complementary to SCAL, for the determination of single and multiphase flow properties.

4

NMR is a phenomenon that occurs when the nuclei of certain atoms are immersed in a static magnetic field and then exposed to a second oscillating magnetic field.

Relaxation Mechanisms:

Bulk Relaxation:

Surface Relaxation: Diffusive Relaxation:

V

A

TS

1

BT

DT

Relaxation mechanisms above all act in parallel and as such their rates add up.

DSB TTTT 2222

1111 (transverse relaxation)

Modelling NMR Response: Basics

NMR response provides information on pore size distribution and wettability.

5

Modelling NMR Response: Surface Relaxation

Analytical solution (sphere):(Crank, 1975)

rt

M

M t 3exp

0

Random walk solution: (Ramakrishnan et al. 1998).

ttt zyx ,, tttttt zyx ,,

Dt

6

2

cossin)( ttt xx

sinsin)( ttt yy

cos)( ttt zz

(Bergman et al. 1995)Killing probability;

D3

2

00

)(N

NtP

M

tM t

6

Analytical Solution (sphere) Random Walk Solution

00

)(N

NtP

M

tM t

rt

M

tM 3exp

0

Fig 1: Comparison of the magnetization decay for a spherical pore obtained by random walk solution with the analytical solution.

D - 2.5x10-9m2/sr - 5μm, - 20μm/s. - 10,000

0N

Comparison:

Modelling NMR Response: Validation

0

0.2

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0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5

Time (s)

No

rma

lize

d A

mp

litu

de

Analytical

Random Walk

7

Bulk Relaxation:

B2

expT

ttb

(Surface + Bulk) Relaxations: tbtPM

M t 0

T2 (Pore Size) Distributions:

n

i ii T

tF

M

tM

1 20

exp)(

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0.8

1

0 1000 2000 3000 4000

Time (ms)

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mal

ized

Am

plitu

de

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10 100 1000 10000

T2 (ms)

Nor

mal

ized

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plitu

de

Inversion

V

A

TS

1From Surface Relaxation

Modelling NMR Response: Bulk relaxation

Time (s)

Mag

net

izat

ion

Time (s)

Mag

net

izat

ion

Time (s)

Mag

net

izat

ion

Time (s)

Mag

net

izat

ion

8

Reference voxel X is surrounded by 26 neighbouring voxels

z < 0 0 < z < Length z > Length

Time (ms)

Nor

mal

ized

Am

plitu

de

T2 (ms)

Nor

mal

ized

Fre

quen

cy

Simulation of NMR response in Micro-CT images

convert to binary

X7

1 2 3

4 5

6 8

9 10 11

12 13 14

15 16 17

18 19 20

21 22 23

24 25 26

x

y

z

9

START

Place N walkers randomly in network

Spherical 3D displacement of walkers

For all walkers; i = 1,2,3,4………(N - Nd)

walker in a throat?

yes

nois z <0 or z>L

Walker enters one of connected throats.

contact with any surface?

yes

no

is z <0 or z>L

yes

Walker enters new pore

no

is walker killed?

yes

no

yes

no

Generate new x, y values

return to previous position

retain x, y and z values

Nd = Nd + 1

Time (ms)

Norm

aliz

ed A

mplit

ude

T2 (ms)

Nor

mal

ized

Fre

quen

cy

NMR response of Single-Phase fluids in Networks

10

NMR response of Two-Phase fluids in Networks

Oil Oil Water

At a given fluid saturation: (Drainage)

Oil Water

Assign walkers: wNoN

3D displacement, t -> : tDR ww 6tDR oo 6tt

(Vinegar, 1995))298(

2TDw )298(

3.1 TDo Diffusion Coefficient:

Throats

Pores

11

NMR response of Two-Phase fluids in Networks

At a given fluid saturation:: (Imbibition)

Oil layers

Bulk Relaxation: )298(

2.12

TT bo

)298(

32

TT bw

w 3.00 w

boo

oto T

t

N

NM

2

exp

bww

wtw T

t

N

NM

2

exp

oow

ooowwt SHS

MSHMSM

(Vinegar, 1995)

(Looyestijn and Hofman, 2005)

(Toumelin, 2005)

Surface Relaxation:

(Surface + Bulk) Relaxation:

Dominant: Bulk Dominant: Surface

Total Relaxation (Oil + Water):

WaterWater WaterWater

12

Sand packs LV60 – (LV60A, LV60B and LV60C)

F42 – (F42A, F42B and F42C)

Sandstones Fontainebleau

Poorly consolidated sandstone, S.

Berea

Bentheimer

Carbonates Carbonates: (C, C22 and C32) Edward limestone: (MB03 and MB11)

Single-phase simulation results

13

LV60 F42

Porosity: 37% ± 0.2% 35.4 ±1.3% Permeability (D): 32.2D ± 0.3D 41.8D ± 4D Density (kg/m3): 2630 2635

Sand Plugs: 3cm (diameter) 9cm (length)Fluid: Brine Density: 1035 (kg/m3): Viscosity: 1.04cp

LV60A F42C1mm

0

0.1

0.2

0.3

0.4

0.5

90 150 180 250 355 500 710Sieve size (mm)

Ma

ss

Fra

cti

on

F42

LV60

Simulation Parameters

298

20

TD brine Diffusion Coefficient:

Bulk Relaxivity: 298

32

TT brineB

Surface Relaxivity: 41μm/s

(Vinegar, 1995)

Sand packs

Grain Size Distribution

2-D Sections of Micro – CT Images of Sandpacks

Rock and fluid properties

14

Experimental results

Magnetization Decay T2 - Distribution

0.01

0.1

1

0 1000 2000 3000Time (ms)

Nor

mal

ized

Am

plit

ude LV60X

LV60Y

0.01

0.1

1

0 1000 2000 3000Time (ms)

Nor

mal

ized

Am

plit

ude

F42XF42Y

Micro CT Image

LV60

F42

Sand packs

0

0.1

0.2

0.3

10 100 1000 10000T2 (ms)

Fre

qu

ency

LV60X

LV60Y

0

0.1

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0.3

10 100 1000 10000T2 (ms)

Fre

qu

ency

F42X

F42Y

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Simulation vs. Experimental

LV60A

LV60C

LV60A

0.01

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1

0 1000 2000 3000Time (ms)

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mal

ized

Am

plitu

de

Experimental

Micro-CT

Network

LV60A

0

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0.4

10 100 1000 10000T2 (ms)

Fre

quen

cy

Experimental

Micro-CTNetwork

LV60B

0.01

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1

0 1000 2000 3000Time (ms)

Nor

mal

ized

Am

plitu

de

Experimental

Micro-CT

Network

Sand packs

LV60B

0

0.1

0.2

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0.5

10 100 1000 10000T2 (ms)

Fre

quen

cy

Experimental

Micro-CTNetwork

LV60C

0.01

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1

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mal

ized

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plitu

de

Experimental

Micro-CT

Network

LV60C

0

0.1

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10 100 1000 10000T2 (ms)

Fre

quen

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Experimental

Micro-CTNetwork

LV60B

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Simulation vs. Experimental

F42A

F42C

Sand packs

F42B

F42A

0.01

0.1

1

0 1000 2000 3000Time (ms)

Nor

mal

ized

Am

plitu

de

Experimental

Micro-CT

Network

F42A

0

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10 100 1000 10000T2 (ms)

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quen

cy

Experimental

Micro-CTNetwork

F42B

0.01

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1

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mal

ized

Am

plitu

de

Experimental

Micro-CT

Network

F42B

0

0.1

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0.4

10 100 1000 10000T2 (ms)

Fre

quen

cy

Experimental

Micro-CTNetwork

F42C

0.01

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1

0 1000 2000 3000Time (ms)

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mal

ized

Am

plitu

de

Experimental

Micro-CT

Network

F42C

0

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10 100 1000 10000T2 (ms)

Fre

quen

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Experimental

Micro-CTNetwork

17

Simulation Results vs. Experimental DataSand packs

Sample Experiment Micro CT Network

F42A

F42C

LV60A

LV60C

677 756

668 647 694

668

512

471

565

530

496

496

Mean T2 (ms) Permeability (D)

Experiment Micro CT Network

Formation Factor

Experiment Micro CT Network

59.0 61.5

42.0 50.4 44.8

42.0

35.3

19.4

27.2

23.2

32.2

32.2

5.8 3.6

5.2 5.6 3.7

5.2

4.9

5.0

3.8

3.9

4.8

4.8

Single-phase properties

18

Fontainebleau

Sandstones

Fontainebleau

0.01

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1

0 1000 2000 3000Time (ms)

Nor

mal

ized

Am

plit

ud

e

Microstructure

Dilation Method

Maximal Ball

The pore spaces in a sub region of a reconstructed Fontainebleau sandstone (right) of porosity 0.18 and a micro-CT image of an actual Fontainebleau sandstone (left) (Øren et. al., 2002).

0

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MicrostructureDilation MethodMaximal Ball

Pores: 4,997 3,101 Throats: 8,192 6,112


Diffusion Coefficient: 2.07x10-9m2/s (Vinegar, 1995)

Bulk Relaxivity: 3.1s (Vinegar, 1995)

Surface Relaxivity: 16μm/s (Liaw et al., 1996)

Network: Dilation Method Maximal Ball

Number of walkers: 2,000,000

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Poorly consolidated sandstone, S

Sandstones

Sandstone, S

0.01

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1

0 1000 2000 3000Time (ms)

Nor

mal

ized

Am

plit

ud

e Micro-CT

Network

Micro-CT image ( resolution 9.1μm) and extracted network of the poorly consolidated sandstone, S. The network was extracted using the maximal ball method.

Pores: 3,127 Throats: 7,508





Network:


0

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10 100 1000 10000T2 (ms)

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quen

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Micro-CT

Network

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Berea sandstone

Sandstones

Berea

0.01

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1

0 1000 2000 3000Time (ms)

Nor

mal

ized

Am

plit

ud

e

Micro-CT

PBM Network

MB Network

3D micro-CT image ( resolution 5.345μm) of the Berea sandstone and networks extracted using the maximal ball method and dilation method.






Pores: 12,349 3,212 Throats: 26,146 5,669

Network: Dilation Method Maximal Ball

0

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Micro-CTPBM NetworkMB Network

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Bentheimer sandstone

Sandstones

Comparison of the experimental capillary pressures of Bentheimer sandstone with simulation results from a tuned Berea network.




Surface Relaxivity: 9.3μm/s


Pores: 12,349Throats: 26,146

Network: Tuned Berea

(Liaw et al., 1996)

Capillary Pressure

0

10

20

30

40

50

0 0.2 0.4 0.6 0.8 1S w

Cap

illar

y P

ress

ure

(K

Pa)

Experimental

Tuned Network

0

0.05

0.1

0.15

0.2

100 1000 10000T2 (ms)

Fre

quen

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Experimental

Simulation

Bentheimer

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Experimental

Simulation

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Carbonate (C)

Carbonates

Micro-CT image and extracted network







Network:

(Chang et al., 1997)

Carbonate C

0.01

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mal

ized

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plit

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Micro-CT

Network

Carbonate C

0

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Micro-CT

Network

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Carbonate (C22)

Carbonates

Comparison of the experimental capillary pressures of carbonate C22 with simulation results from a tuned Berea network.







Network: Tuned BereaCapillary Pressure (C22)

0

200

400

600

800

1000

0.0 0.2 0.4 0.6 0.8 1.0S w

Cap

illar

y P

ress

ure

(K

Pa)

Experimental

Tuned Network

C22

0.01

0.1

1

0 500 1000 1500 2000Time (ms)

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mal

ized

Am

plit

ud

e

Experimental

SimulationC22

0

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10 100 1000 10000T2 (ms)

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Experimental

Simulation

24

Carbonate (C32)

Carbonates

Comparison of the experimental capillary pressures of carbonate C32 with simulation results from a tuned Berea network.







Network: Tuned BereaCapillary Pressure (C32)

0

200

400

600

800

1000

0.0 0.2 0.4 0.6 0.8 1.0S w

Cap

illar

y P

ress

ure

(K

Pa)

Experimental

Tuned Network

C32

0.01

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mal

ized

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plit

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Experimental

Simulation

C32

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quen

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Experimental

Simulation

25

Edward limestone (MB03)

Carbonates

Comparison of the experimental capillary pressures of Edward limestone MB03 with simulation results from a tuned Berea network.







Network: Tuned BereaCapillary Pressure (MB03)

0

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1S w

Cap

illar

y P

ress

ure

(K

Pa)

Experimental

Tuned Network

MB03

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plit

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Experimental

Simulation

MB03

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Experimental

Simulation

26

Edward limestone (MB11)

Carbonates

Comparison of the experimental capillary pressures of Edward limestone MB11 with simulation results from a tuned Berea network.







Network: Tuned BereaCapillary Pressure (MB11)

0

100

200

300

400

500

0 0.2 0.4 0.6 0.8 1S w

Cap

illar

y P

ress

ure

(K

Pa)

Experimental

Tuned Network

MB11

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Experimental

SimulationMB11

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ExperimentalSimulation

27

Discussion

1. Successfully comparison of magnetization decays and T2 distributions of brine in networks extracted using the maximal ball method and micro-CT images of sand packs.

2. For sandstones, magnetization decays faster in networks extracted using the maximal ball algorithm – inability to capture the correct surface areas.

3. For Bentheimer sandstone, consistent results were obtained with experimental data thereby validating the algorithm developed to simulate NMR response in networks.

4. For carbonates, tuning elements’ properties of a known network to match experimental capillary pressure resulted in differences in the comparison of the simulated magnetization decays and T2 distributions with experimental data.

28


Diffusion Coefficient (Oil): 0.67x10-9m2/s

Bulk Relaxivity (Oil): 0.62s

Surface Relaxivity:

Two-phase simulation results

Diffusion Coefficient (Brine): 2.07x10-9m2/s

Bulk Relaxivity (Brine): 3.1s

w 33.00

Drainage

Intermediate water saturations

Waterflooding

Water saturation (Sw = 0.5)

Moderately water-wet (300 – 400)

Intermediate-wet (700 – 800)

Oil-wet (1100 – 1200)

0.01

0.1

1

0 1 2 3 4Time (s)

Nor

mal

ized

Am

plit

ud

e

Surface R. (Oil)Bulk R. (Oil)Surface R. (Water)Bulk R. (Water)

29

Sand pack (F42A)


Drainage

F42A

0.01

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mal

ized

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plit

ud

e

Sw_0.3Sw_0.5Sw_0.7Sw_0.8

F42A

0

0.1

0.2

0.3

0.4

0.5

100 1000 10000

T2 (ms)

Fre

qu

ency

Sw_0.3Sw_0.5Sw_0.7Sw_0.8

F42A

0.01

0.1

1

0 1000 2000 3000Time (ms)

Nor

mal

ized

Am

plit

ud

e

Con_30_40

Con_70_80

Con_110_120

Waterflooding

F42A

0

0.1

0.2

0.3

0.4

100 1000 10000

T2 (ms)

Freq

uenc

y

Con_30_40

Con_70_80

Con_110_120

As oil saturation increases, magnetization decays very fast as a result of the dominant bulk relaxivity of the oil, correspondingly the T2 distribution becomes narrower approaching the bulk relaxivity value of oil.

As the network becomes more oil-wet, the magnetization decays slowly, this is because the oil in contact with most of the grain surfaces, thereby leaving the water to decay at its bulk rate. Similarly the mean T2 increases as the network becomes more oil-wet.

30

Berea sandstone


Drainage

Waterflooding

Berea

0.01

0.1

1

0 1000 2000 3000Time (ms)

Nor

mal

ized

Am

plit

ud

e

Sw_0.2

Sw_0.4

Sw_0.7

Berea

0

0.1

0.2

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0.4

0.5

100 1000 10000

T2 (ms)

Fre

qu

ency

Sw_0.2

Sw_0.4

Sw_0.7

Berea

0.01

0.1

1

0 1000 2000 3000Time (ms)

Nor

mal

ized

Am

plit

ud

e

Con_30_40

Con_70_80

Con_110_120

Berea

0

0.1

0.2

0.3

0.4

0.5

100 1000 10000

T2 (ms)

Freq

uenc

y

Con_30_40

Con_70_80

Con_110_120

As oil saturation increases, magnetization decays very fast as a result of the dominant bulk relaxivity of the oil, correspondingly the T2 distribution becomes narrower approaching the bulk relaxivity value of oil.

As the network becomes more oil-wet, the magnetization decays slowly, this is because the oil in contact with most of the grain surfaces, thereby leaving the water to decay at its bulk rate. Similarly the mean T2 increases as the network becomes more oil-wet.

31

Conclusions

1. Successful comparisons of the simulated magnetization decays were made with experimental data for sand packs.

2. The maximal ball extraction algorithm can be used to extract networks from which single-phase transport properties in unconsolidated media can be predicted successfully.

3. For all the networks extracted using the maximal ball method, comparison of the simulated T2 distributions of these networks are narrower than those of the corresponding micro-CT images.

4. Overall, in single-phase flow we were able to predict permeability, formation factor and NMR response with reasonable accuracy in most cases, which serves to validate the network extraction algorithm and to serve as the starting point for the prediction of multiphase properties.

5. We simulated magnetization decay during multiphase flow in both drainage and waterflooding for different rock wettabilities.

6. In oil-wet media, we predict a slow decay and a broad distribution of T2, this is because water in the centres of the pores has a low bulk relaxivity, since the grain surface is covered by oil layers, this suggests a straightforward technique to indicate oil wettability.

32

Recommendations for future work

1. In order to further validate the simulation results, further experiments should be conducted on consolidated media which can be compared with simulation results on both micro-CT images and extracted networks.

2. The maximal ball network extraction algorithm can be further developed to be suitable for consolidated media.

3. The two-phase NMR simulations in networks can be validated by performing simulations directly on 3D images. The respective fluid configurations can be mapped to the appropriate pore voxels in the 3D image,

since we know the voxels that define a given network element.

4. Our results suggests that oil-wet conditions are readily identified in NMR experiments, indicated by a slow magnetization decay from water in the centres of the pore space, protected from the grain surface by oil layers. This prediction needs to be tested directly by experiments.

5. A detailed and extensive experimental programme is necessary to test the ability of network modelling to give reliable predictions in these cases.

33

Acknowledgements

1. Department of Earth Science and Engineering.

2. UniversitiesUK

3. Petroleum Technology Development Fund of Nigeria (PTDF).

4. Imperial college consortium on pore-scale modelling (BHP, Eni, JOGMEC, Saudi Aramco, Schlumberger, Shell, Statoil, Total, the U.K. Department of Trade and Industry and the EPSRC)

5. Reslab, UAE

6. Department of Physics and Technology, University of Bergen, Norway

7. Numerical Rocks AS

8. Contributors: Saif AlSayari, Stefan Iglauer, Saleh Al-Mansoori, Martin Fernø and Haldis Riskedal

9. Members of the PERM research group

34

Pore Scale Simulation of NMR Response in Porous Media

Olumide Talabi

Supervisor: Prof Martin Blunt

Contributors: Saif AlSayari, Stefan Iglauer, Saleh Al-Mansoori, Martin Fernø and Haldis Riskedal

Documents

Pore-Scale Simulation of NMR Response in Porous Media Olumide Talabi