Pore-Scale Simulation of NMR Response in Porous Media

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

• OUTLINE
• Pore-scale modeling Overview
• Modelling NMR response
• Simulation of NMR response in micro-CT images
• Simulation of NMR response of single-phase fluids
  in networks
• Simulation of NMR response of two-phase fluids in
  networks
• Single-phase NMR simulation results
• Two-phase NMR simulation results
• Conclusions and recommendations for future work

3
Pore Scale Modelling Overview
Network
Core
Micro CT
Rock Properties
Porosity Permeability Formation Factor Capillary
Pressure Relative Permeability NMR Response
Porosity Permeability Formation Factor NMR
Response
Porosity Permeability Formation Factor Capillary
Pressure Relative Permeability NMR Response
Capillary Pressure
Relative Permeability (Valvatne and Blunt, 2004)
Pore-scale modeling complementary to SCAL, for
the determination of single and multiphase flow
properties.
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Modelling NMR Response Basics
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

Relaxation mechanisms above all act in parallel
and as such their rates add up.
NMR response provides information on pore size
distribution and wettability.
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Modelling NMR Response Surface Relaxation
Analytical solution (sphere)
(Crank, 1975)
Killing probability
(Bergman et al. 1995)
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Modelling NMR Response Validation
Comparison
Analytical Solution (sphere)
Random Walk Solution
Fig 1 Comparison of the magnetization decay for
a spherical pore obtained by random walk
solution with the analytical solution.
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Modelling NMR Response Bulk relaxation
Bulk Relaxation
(Surface Bulk) Relaxations
From Surface Relaxation
T2 (Pore Size) Distributions
Inversion
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Simulation of NMR response in Micro-CT images
convert to binary
z lt 0 0 lt
z lt Length z gt Length
Reference voxel X is surrounded by 26
neighbouring voxels
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NMR response of Single-Phase fluids in Networks
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?
no
is z lt0 or zgtL
Walker enters one of connected throats.
yes
yes
no
contact with any surface?
is z lt0 or zgtL
no
no
yes
yes
Walker enters new pore
is walker killed?
no
yes
Generate new x, y values
return to previous position
retain x, y and z values
Nd Nd 1
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NMR response of Two-Phase fluids in Networks
At a given fluid saturation (Drainage)
Oil
Water
Assign walkers
3D displacement, t -gt
Diffusion Coefficient
(Vinegar, 1995)
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NMR response of Two-Phase fluids in Networks
At a given fluid saturation (Imbibition)
Oil layers
Bulk Relaxation
(Vinegar, 1995)
(Looyestijn and Hofman, 2005)
Surface Relaxation
(Surface Bulk) Relaxation
Dominant Bulk
Dominant Surface
Total Relaxation (Oil Water)
(Toumelin, 2005)
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Single-phase simulation results

• 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)

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Sand packs
Rock and fluid properties
Grain Size Distribution
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
2-D Sections of Micro CT Images of Sandpacks
Simulation Parameters
Diffusion Coefficient
(Vinegar, 1995)
Bulk Relaxivity
1mm
Surface Relaxivity
41µm/s
LV60A
F42C
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Sand packs
Experimental results
Magnetization Decay
T2 - Distribution
Micro CT Image
LV60
F42
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Sand packs
Simulation vs. Experimental
LV60A
LV60B
LV60C
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Sand packs
Simulation vs. Experimental
F42A
F42B
F42C
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Sand packs
Simulation Results vs. Experimental Data
Single-phase properties
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Sandstones
Fontainebleau
Network Dilation Method Maximal 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)
16µm/s
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).
Surface Relaxivity
(Liaw et al., 1996)
Number of walkers 2,000,000
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Sandstones
Poorly consolidated sandstone, S
Network
Pores 3,127
Throats 7,508

Simulation Parameters
Diffusion Coefficient 2.07x10-9m2/s
(Vinegar, 1995)
Bulk Relaxivity 3.1s
(Vinegar, 1995)
15µm/s
Surface Relaxivity
Micro-CT image ( resolution 9.1µm) and extracted
network of the poorly consolidated sandstone, S.
The network was extracted using the maximal ball
method.
Number of walkers 2,000,000
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Sandstones
Berea sandstone
Network Dilation Method Maximal Ball
Pores 12,349
3,212 Throats
26,146 5,669
Simulation Parameters
Diffusion Coefficient 2.07x10-9m2/s
(Vinegar, 1995)
Bulk Relaxivity 3.1s
(Vinegar, 1995)
15µm/s
Surface Relaxivity
3D micro-CT image ( resolution 5.345µm) of the
Berea sandstone and networks extracted using the
maximal ball method and dilation method.
Number of walkers 2,000,000
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Sandstones
Bentheimer sandstone
Network Tuned Berea
Pores 12,349 Throats
26,146
Simulation Parameters
Diffusion Coefficient 1.9x10-9m2/s
(Vinegar, 1995)
Bulk Relaxivity 2.84s
(Vinegar, 1995)
9.3µm/s
(Liaw et al., 1996)
Surface Relaxivity
Number of walkers 2,000,000
Comparison of the experimental capillary
pressures of Bentheimer sandstone with simulation
results from a tuned Berea network.
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Carbonates
Carbonate (C)
Network
Pores 3,574 Throats
4,198
Simulation Parameters
Diffusion Coefficient 2.07x10-9m2/s
(Vinegar, 1995)
Bulk Relaxivity 3.1s
(Vinegar, 1995)
5.0µm/s
(Chang et al., 1997)
Surface Relaxivity
Number of walkers 2,000,000
Micro-CT image and extracted network
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Carbonates
Carbonate (C22)
Network Tuned Berea
Pores 12,349 Throats
26,146
Simulation Parameters
Diffusion Coefficient 2.07x10-9m2/s
(Vinegar, 1995)
Bulk Relaxivity 3.1s
(Vinegar, 1995)
2.8µm/s
Surface Relaxivity
Number of walkers 2,000,000
Comparison of the experimental capillary
pressures of carbonate C22 with simulation
results from a tuned Berea network.
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Carbonates
Carbonate (C32)
Network Tuned Berea
Pores 12,349 Throats
26,146
Simulation Parameters
Diffusion Coefficient 2.07x10-9m2/s
(Vinegar, 1995)
Bulk Relaxivity 3.1s
(Vinegar, 1995)
2.1µm/s
Surface Relaxivity
Number of walkers 2,000,000
Comparison of the experimental capillary
pressures of carbonate C32 with simulation
results from a tuned Berea network.
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Carbonates
Edward limestone (MB03)
Network Tuned Berea
Pores 12,349 Throats
26,146
Simulation Parameters
Diffusion Coefficient 1.9x10-9m2/s
(Vinegar, 1995)
Bulk Relaxivity 2.84s
(Vinegar, 1995)
3.0µm/s
Surface Relaxivity
Number of walkers 2,000,000
Comparison of the experimental capillary
pressures of Edward limestone MB03 with
simulation results from a tuned Berea network.
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Carbonates
Edward limestone (MB11)
Network Tuned Berea
Pores 12,349 Throats
26,146
Simulation Parameters
Diffusion Coefficient 1.9x10-9m2/s
(Vinegar, 1995)
Bulk Relaxivity 2.84s
(Vinegar, 1995)
4.5µm/s
Surface Relaxivity
Number of walkers 2,000,000
Comparison of the experimental capillary
pressures of Edward limestone MB11 with
simulation results from a tuned Berea network.
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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.

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Two-phase simulation results
Simulation Parameters
Diffusion Coefficient (Oil)
0.67x10-9m2/s
Diffusion Coefficient (Brine)
2.07x10-9m2/s
Bulk Relaxivity (Oil) 0.62s
Bulk Relaxivity (Brine) 3.1s
Surface Relaxivity
Drainage Intermediate water saturations
Waterflooding Water saturation (Sw
0.5) Moderately water-wet (300
400) Intermediate-wet (700 800) Oil-wet (1100
1200)
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Two-phase simulation results
Sand pack (F42A)
Drainage
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.
Waterflooding
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.
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Two-phase simulation results
Berea sandstone
Drainage
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.
Waterflooding
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.
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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.

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Recommendations for future work

• 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.
• The maximal ball network extraction algorithm can
  be further developed to be suitable for
  consolidated media.
• 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.
• 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.
• A detailed and extensive experimental programme
  is necessary to test the ability of network
  modelling to give reliable predictions in these
  cases.

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Acknowledgements

• Department of Earth Science and Engineering.
• UniversitiesUK
• Petroleum Technology Development Fund of Nigeria
  (PTDF).
• 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)
• Reslab, UAE
• Department of Physics and Technology, University
  of Bergen, Norway
• Numerical Rocks AS
• Contributors Saif AlSayari, Stefan Iglauer,
  Saleh Al-Mansoori, Martin Fernø and Haldis
  Riskedal
• Members of the PERM research group

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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