Post on 05-Jan-2016
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
0.4
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)(
0
0.2
0.4
0.6
0.8
1
0 1000 2000 3000 4000
Time (ms)
Nor
mal
ized
Am
plitu
de
0
0.05
0.1
0.15
0.2
0.25
10 100 1000 10000
T2 (ms)
Nor
mal
ized
Am
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
0.2
0.3
10 100 1000 10000T2 (ms)
Fre
qu
ency
F42X
F42Y
15
Simulation vs. Experimental
LV60A
LV60C
LV60A
0.01
0.1
1
0 1000 2000 3000Time (ms)
Nor
mal
ized
Am
plitu
de
Experimental
Micro-CT
Network
LV60A
0
0.1
0.2
0.3
0.4
10 100 1000 10000T2 (ms)
Fre
quen
cy
Experimental
Micro-CTNetwork
LV60B
0.01
0.1
1
0 1000 2000 3000Time (ms)
Nor
mal
ized
Am
plitu
de
Experimental
Micro-CT
Network
Sand packs
LV60B
0
0.1
0.2
0.3
0.4
0.5
10 100 1000 10000T2 (ms)
Fre
quen
cy
Experimental
Micro-CTNetwork
LV60C
0.01
0.1
1
0 1000 2000 3000Time (ms)
Nor
mal
ized
Am
plitu
de
Experimental
Micro-CT
Network
LV60C
0
0.1
0.2
0.3
0.4
0.5
10 100 1000 10000T2 (ms)
Fre
quen
cy
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
0.1
0.2
0.3
0.4
10 100 1000 10000T2 (ms)
Fre
quen
cy
Experimental
Micro-CTNetwork
F42B
0.01
0.1
1
0 1000 2000 3000Time (ms)
Nor
mal
ized
Am
plitu
de
Experimental
Micro-CT
Network
F42B
0
0.1
0.2
0.3
0.4
10 100 1000 10000T2 (ms)
Fre
quen
cy
Experimental
Micro-CTNetwork
F42C
0.01
0.1
1
0 1000 2000 3000Time (ms)
Nor
mal
ized
Am
plitu
de
Experimental
Micro-CT
Network
F42C
0
0.1
0.2
0.3
0.4
10 100 1000 10000T2 (ms)
Fre
quen
cy
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
0.1
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
0.1
0.2
0.3
0.4
0.5
100 1000 10000T2 (ms)
Fre
quen
cy
MicrostructureDilation MethodMaximal Ball
Pores: 4,997 3,101 Throats: 8,192 6,112
Simulation Parameters
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
0.1
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
Simulation Parameters
Diffusion Coefficient: 2.07x10-9m2/s (Vinegar, 1995)
Bulk Relaxivity: 3.1s (Vinegar, 1995)
Surface Relaxivity: 15μm/s
Network:
Number of walkers: 2,000,000
0
0.1
0.2
0.3
0.4
0.5
10 100 1000 10000T2 (ms)
Fre
quen
cy
Micro-CT
Network
20
Berea sandstone
Sandstones
Berea
0.01
0.1
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.
Simulation Parameters
Diffusion Coefficient: 2.07x10-9m2/s (Vinegar, 1995)
Bulk Relaxivity: 3.1s (Vinegar, 1995)
Surface Relaxivity: 15μm/s
Number of walkers: 2,000,000
Pores: 12,349 3,212 Throats: 26,146 5,669
Network: Dilation Method Maximal Ball
0
0.1
0.2
0.3
0.4
0.5
10 100 1000 10000T2 (ms)
Fre
quen
cy
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.
Simulation Parameters
Diffusion Coefficient: 1.9x10-9m2/s (Vinegar, 1995)
Bulk Relaxivity: 2.84s (Vinegar, 1995)
Surface Relaxivity: 9.3μm/s
Number of walkers: 2,000,000
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
cy
Experimental
Simulation
Bentheimer
0.01
0.1
1
0 1000 2000 3000Time (ms)
Nor
mal
ized
Am
plit
ud
e
Experimental
Simulation
22
Carbonate (C)
Carbonates
Micro-CT image and extracted network
Simulation Parameters
Diffusion Coefficient: 2.07x10-9m2/s (Vinegar, 1995)
Bulk Relaxivity: 3.1s (Vinegar, 1995)
Surface Relaxivity: 5.0μm/s
Number of walkers: 2,000,000
Pores: 3,574Throats: 4,198
Network:
(Chang et al., 1997)
Carbonate C
0.01
0.1
1
0 1000 2000 3000 4000Time (ms)
Nor
mal
ized
Am
plit
ud
e
Micro-CT
Network
Carbonate C
0
0.1
0.2
0.3
0.4
0.5
100 1000 10000T2 (ms)
Fre
quen
cy
Micro-CT
Network
23
Carbonate (C22)
Carbonates
Comparison of the experimental capillary pressures of carbonate C22 with simulation results from a tuned Berea network.
Simulation Parameters
Diffusion Coefficient: 2.07x10-9m2/s (Vinegar, 1995)
Bulk Relaxivity: 3.1s (Vinegar, 1995)
Surface Relaxivity: 2.8μm/s
Number of walkers: 2,000,000
Pores: 12,349Throats: 26,146
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)
Nor
mal
ized
Am
plit
ud
e
Experimental
SimulationC22
0
0.05
0.1
0.15
0.2
0.25
10 100 1000 10000T2 (ms)
Fre
quen
cy
Experimental
Simulation
24
Carbonate (C32)
Carbonates
Comparison of the experimental capillary pressures of carbonate C32 with simulation results from a tuned Berea network.
Simulation Parameters
Diffusion Coefficient: 2.07x10-9m2/s (Vinegar, 1995)
Bulk Relaxivity: 3.1s (Vinegar, 1995)
Surface Relaxivity: 2.1μm/s
Number of walkers: 2,000,000
Pores: 12,349Throats: 26,146
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
0.1
1
0 500 1000 1500 2000Time (ms)
Nor
mal
ized
Am
plit
ud
e
Experimental
Simulation
C32
0
0.1
0.2
0.3
0.4
0.5
10 100 1000 10000T2 (ms)
Fre
quen
cy
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.
Simulation Parameters
Diffusion Coefficient: 1.9x10-9m2/s (Vinegar, 1995)
Bulk Relaxivity: 2.84s (Vinegar, 1995)
Surface Relaxivity: 3.0μm/s
Number of walkers: 2,000,000
Pores: 12,349Throats: 26,146
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
0.01
0.1
1
0 500 1000 1500 2000Time (ms)
Nor
mal
ized
Am
plit
ud
e
Experimental
Simulation
MB03
0
0.05
0.1
0.15
0.2
10 100 1000 10000T2 (ms)
Fre
quen
cy
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.
Simulation Parameters
Diffusion Coefficient: 1.9x10-9m2/s (Vinegar, 1995)
Bulk Relaxivity: 2.84s (Vinegar, 1995)
Surface Relaxivity: 4.5μm/s
Number of walkers: 2,000,000
Pores: 12,349Throats: 26,146
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
0.01
0.1
1
0 500 1000 1500 2000Time (ms)
Nor
mal
ized
Am
plit
ud
e
Experimental
SimulationMB11
0
0.05
0.1
0.15
0.2
0.25
10 100 1000 10000T2 (ms)
Fre
qu
ency
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
Simulation Parameters
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)
Two-phase simulation results
Drainage
F42A
0.01
0.1
1
0 1000 2000 3000Time (ms)
Nor
mal
ized
Am
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
Two-phase simulation results
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
0.3
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