1. 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. 2 OUTLINE 1.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. 3 Pore Scale Modelling: Overview CoreMicro CT Network 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** Relative Permeability (Valvatne and Blunt, 2004) Capillary Pressure Pore-scale modeling: complementary to SCAL, for the determination of single and multiphase flow properties.

4. 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: Relaxation mechanisms above all act in parallel and as such their rates add up. (transverse relaxation) Modelling NMR Response: Basics NMR response provides information on pore size distribution and wettability.

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

6. 6 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. D - 2.5x10 -9 m 2 /s r - 5μm, - 20μm/s. - 10,000 Comparison: Modelling NMR Response: Validation

7. 7 Bulk Relaxation: (Surface + Bulk) Relaxations: T 2 (Pore Size) Distributions: Inversion From Surface Relaxation Modelling NMR Response: Bulk relaxation

8. 8 Reference voxel X is surrounded by 26 neighbouring voxels z Length Simulation of NMR response in Micro-CT images convert to binary X 7 123 45 68 91011 121314 15 1617 1819 20 212223 242526 x y z

9. 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 no is z L Walker enters one of connected throats. contact with any surface? yes no is 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 NMR response of Single-Phase fluids in Networks

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

11. 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) (Toumelin, 2005) Surface Relaxation: (Surface + Bulk) Relaxation: Dominant : Bulk Dominant : Surface Total Relaxation (Oil + Water):

12. 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. 13 LV60 F42 Porosity: 37% ± 0.2% 35.4 ±1.3% Permeability (D): 32.2D ± 0.3D 41.8D ± 4D Density (kg/m 3 ): 2630 2635 Sand Plugs: 3cm (diameter) 9cm (length) Fluid: Brine Density: 1035 (kg/m 3 ): Viscosity: 1.04cp LV60AF42C 1mm Simulation Parameters Diffusion Coefficient: Bulk Relaxivity: 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. 14 Experimental results Magnetization Decay T 2 - DistributionMicro CT Image LV60 F42 Sand packs

15. 15 Simulation vs. Experimental LV60A LV60C Sand packs LV60B

16. 16 Simulation vs. Experimental F42A F42C Sand packs F42B

17. 17 Simulation Results vs. Experimental Data Sand packs Sample Experiment Micro CT Network F42A F42C LV60A LV60C 677756 668647694 668 512 471 565 530 496 Mean T 2 (ms) Permeability (D) Experiment Micro CT Network Formation Factor Experiment Micro CT Network 59.061.5 42.050.444.8 42.0 35.3 19.4 27.2 23.2 32.2 5.83.6 5.25.63.7 5.2 4.9 5.0 3.8 3.9 4.8 Single-phase properties

18. 18 Fontainebleau Sandstones 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). Pores: 4,997 3,101 Throats: 8,192 6,112 Simulation Parameters Diffusion Coefficient: 2.07x10 -9 m 2 /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

19. 19 Poorly consolidated sandstone, S Sandstones 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 -9 m 2 /s (Vinegar, 1995) Bulk Relaxivity: 3.1s (Vinegar, 1995) Surface Relaxivity: 15μm/s Network: Number of walkers: 2,000,000

20. 20 Berea sandstone Sandstones 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 -9 m 2 /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

21. 21 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 -9 m 2 /s (Vinegar, 1995) Bulk Relaxivity: 2.84s (Vinegar, 1995) Surface Relaxivity: 9.3μm/s Number of walkers: 2,000,000 Pores: 12,349 Throats: 26,146 Network: Tuned Berea (Liaw et al., 1996)

22. 22 Carbonate (C) Carbonates Micro-CT image and extracted network Simulation Parameters Diffusion Coefficient: 2.07x10 -9 m 2 /s (Vinegar, 1995) Bulk Relaxivity: 3.1s (Vinegar, 1995) Surface Relaxivity: 5.0μm/s Number of walkers: 2,000,000 Pores: 3,574 Throats: 4,198 Network: (Chang et al., 1997)

23. 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 -9 m 2 /s (Vinegar, 1995) Bulk Relaxivity: 3.1s (Vinegar, 1995) Surface Relaxivity: 2.8μm/s Number of walkers: 2,000,000 Pores: 12,349 Throats: 26,146 Network: Tuned Berea

24. 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 -9 m 2 /s (Vinegar, 1995) Bulk Relaxivity: 3.1s (Vinegar, 1995) Surface Relaxivity: 2.1μm/s Number of walkers: 2,000,000 Pores: 12,349 Throats: 26,146 Network: Tuned Berea

25. 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 -9 m 2 /s (Vinegar, 1995) Bulk Relaxivity: 2.84s (Vinegar, 1995) Surface Relaxivity: 3.0μm/s Number of walkers: 2,000,000 Pores: 12,349 Throats: 26,146 Network: Tuned Berea

26. 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 -9 m 2 /s (Vinegar, 1995) Bulk Relaxivity: 2.84s (Vinegar, 1995) Surface Relaxivity: 4.5μm/s Number of walkers: 2,000,000 Pores: 12,349 Throats: 26,146 Network: Tuned Berea

27. 27 Discussion 1.Successfully comparison of magnetization decays and T 2 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 T 2 distributions with experimental data.

28. 28 Simulation Parameters Diffusion Coefficient (Oil): 0.67x10 -9 m 2 /s Bulk Relaxivity (Oil): 0.62s Surface Relaxivity: Two-phase simulation results Diffusion Coefficient (Brine): 2.07x10 -9 m 2 /s Bulk Relaxivity (Brine): 3.1s Drainage Intermediate water saturations Waterflooding Water saturation (S w = 0.5) Moderately water-wet (30 0 – 40 0 ) Intermediate-wet (70 0 – 80 0 ) Oil-wet (110 0 – 120 0 )

29. 29 Sand pack (F42A) Two-phase simulation results Drainage Waterflooding As oil saturation increases, magnetization decays very fast as a result of the dominant bulk relaxivity of the oil, correspondingly the T 2 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 T 2 increases as the network becomes more oil-wet.

30. 30 Berea sandstone Two-phase simulation results Drainage Waterflooding As oil saturation increases, magnetization decays very fast as a result of the dominant bulk relaxivity of the oil, correspondingly the T 2 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 T 2 increases as the network becomes more oil-wet.

31. 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 T 2 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 T 2, 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. 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. 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. 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