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

Pore-Scale Simulation of NMR Response in Porous Media Olumide Talabi Supervisor : Prof Martin Blunt Contributors: Saif AlSayari, Stefan Iglauer, Saleh Al-Mansoori, Martin Fern ø and Haldis Riskedal. OUTLINE Pore-scale modeling: Overview Modelling NMR response

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

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  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.

  4. Modelling NMR Response: Basics (transverse relaxation) 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.

  5. Modelling NMR Response: Surface Relaxation Random walk solution: (Ramakrishnan et al. 1998). Analytical solution (sphere): (Crank, 1975) Killing probability; (Bergman et al. 1995)

  6. Modelling NMR Response: Validation D - 2.5x10-9m2/s r - 5μm, - 20μm/s. - 10,000 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.

  7. Modelling NMR Response: Bulk relaxation Bulk Relaxation: (Surface + Bulk) Relaxations: From Surface Relaxation T2 (Pore Size) Distributions: Inversion

  8. Simulation of NMR response in Micro-CT images 18 19 20 1 2 3 9 10 11 X 21 22 23 4 5 12 13 14 y 16 17 24 25 26 15 6 7 8 z x convert to binary z < 0 0 < z < Length z > Length Reference voxel X is surrounded by 26 neighbouring voxels

  9. 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 enters one of connected throats. yes is z <0 or z>L no walker in a throat? yes no no contact with any surface? is z <0 or z>L no yes yes no is walker killed? Walker enters new pore yes Generate new x, y values return to previous position retain x, y and z values Nd = Nd + 1

  10. NMR response of Two-Phase fluids in Networks Oil Water Oil Pores Throats At a given fluid saturation:(Drainage) Oil Water Assign walkers: 3D displacement, t -> : Diffusion Coefficient: (Vinegar, 1995)

  11. 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)

  12. 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)

  13. Sand packs Rock and fluid properties Grain Size Distribution LV60F42 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

  14. Sand packs Experimental results Magnetization Decay T2 - Distribution Micro CT Image LV60 F42

  15. Sand packs Simulation vs. Experimental LV60A LV60B LV60C

  16. Sand packs Simulation vs. Experimental F42A F42B F42C

  17. Sand packs Mean T2 (ms) Permeability (D) Formation Factor Sample Experiment Micro CT Network Experiment Micro CT Network Experiment Micro CT Network F42A 668 677 756 42.0 59.0 61.5 5.2 5.8 3.6 F42C 668 647 694 42.0 50.4 44.8 5.2 5.6 3.7 LV60A 496 512 565 32.2 35.3 27.2 4.8 4.9 3.8 LV60C 496 471 530 32.2 19.4 23.2 4.8 5.0 3.9 Simulation Results vs. Experimental Data Single-phase properties

  18. 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

  19. 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

  20. 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

  21. 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.

  22. 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

  23. 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.

  24. 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.

  25. 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.

  26. 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.

  27. Discussion • 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. • For sandstones, magnetization decays faster in networks extracted using the maximal ball algorithm – inability to capture the correct surface areas. • For Bentheimer sandstone, consistent results were obtained with experimental data thereby validating the algorithm developed to simulate NMR response in networks. • 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. 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)

  29. 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.

  30. 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.

  31. Conclusions • Successful comparisons of the simulated magnetization decays were made with experimental data for sand packs. • The maximal ball extraction algorithm can be used to extract networks from which single-phase transport properties in unconsolidated media can be predicted successfully. • 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. • 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. • We simulated magnetization decay during multiphase flow in both drainage and waterflooding for different rock wettabilities. • 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 • 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.

  33. 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

  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

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