Numerical simulation of nuclear magnetic resonance in saturated porous media with consideration of phase motion

Authors

  • K.L. Klimenok Moscow Institute of Physics and Technology
  • A.Yu. Demianov Schlumberger Moscow Research Center

DOI:

https://doi.org/10.26089/NumMet.v18r317

Keywords:

numerical simulation,, nuclear magnetic resonance, nuclear magnetic relaxation, flow propagator, passive admixture transport

Abstract

A method to perform the numerical simulation of Nuclear Magnetic Resonance (NMR) for porous media saturated with a multicomponent fluid with consideration of phase motion is proposed. This method is applied to numerical models of porous media whose fluid component distribution is determined by the direct hydrodynamic simulation using the density functional method. Numerical results for NMR signals obtained for various pulse sequences and their usage for the transport description of fluid in porous media are discussed. Flow propagators for various flows are calculated. The flow propagators and the results obtained during passive admixture simulation are compared.

Author Biographies

K.L. Klimenok

A.Yu. Demianov

Schlumberger Moscow Research Center
• Senior Researcher

References

  1. C. P. Slichter, Principles of Magnetic Resonance (Springer, Heidelberg, 1990), Vol. 1.
  2. A. Timur, “Pulsed Nuclear Magnetic Resonance Studies of Porosity, Movable Fluid, and Permeability of Sandstones,” J. Pet. Technol. 21 (6), 775-786 (1969).
  3. J. D. Loren, J. D. Robinson, “Relations between Pore Size Fluid and Matrix Properties, and NML Measurements,” Soc. Pet. Eng. J. 10 (3), 268-278 (1970).
  4. W. J. Looyestijn, “Wettability Index Determination from NMR Logs,” Soc. Petrophys. Well-Log Anal. 49 (2), 130-145 (2008).
  5. J. K854rger and W. Heink, “The Propagator Representation of Molecular Transport in Microporous Crystallites,” J. Magn. Reson. 51 (1), 1-7 (1983).
  6. L. Lebon, J. Leblond, J.-P. Hulin, et al., “Pulsed Field Gradient NMR Measurements of Probability Distribution of Displacement under Flow in Sphere Packings,” Magn. Reson. Imaging 14 (7-8), 989-991 (1996).
  7. K. J. Packer, S. Stapf, J. J. Tessier, and R. A. Damion, “The Characterisation of Fluid Transport in Porous Solids by Means of Pulsed Magnetic Field Gradient NMR,” Magn. Reson. Imaging 16 (5-6), 463-469 (1998).
  8. J. J. Tessier, K. J. Packer, J. F. Thovert, and P. M. Adler, “NMR Measurements and Numerical Simulation of Fluid Transport in Porous Solids,” AIChE J. 43 (7), 1653-1661 (1997).
  9. J. J. Tessier and K. J. Packer, “The Characterization of Multiphase Fluid Transport in a Porous Solid by Pulsed Gradient Stimulated Echo Nuclear Magnetic Resonance,” Phys. Fluids. 10 (1), 75-85 (1998).
  10. B. Bijeljic, A. Raeini, P. Mostaghimi, and M. J. Blunt, “Predictions of Non-Fickian Solute Transport in Different Classes of Porous Media Using Direct Simulation on Pore-Scale Images,” Phys. Rev. E 87 (2013).
    doi 10.1103/PhysRevE.87.013011
  11. N. K. Karadimitriou, V. Joekar-Niasar, M. Babaei, and C. A. Shore, “Critical Role of the Immobile Zone in Non-Fickian Two-Phase Transport: A New Paradigm,” Environ. Sci. Technol. 50 (8), 4384-4392 (2016).
  12. Z. Zhang, D. L. Johnson, and L. M. Schwartz, “Simulating the Time-Dependent Diffusion Coefficient in Mixed-Pore-Size Materials,” Phys. Rev. E 84 (2011).
    doi 10.1103/PhysRevE.84.031129
  13. J. Yang and E. S. Boek, “Pore Scale Simulation of Flow in Porous Media Using the Lattice-Boltzmann Method,” in Proc. SPE Annual Tech. Conf. and Exhibition, Denver, USA, October 30-November 2, 2011 (SPE Press, Richardson, 2011), pp. 1-13.
  14. J. Yang, J. Crawshaw, and E. S. Boek, “Quantitative Determination of Molecular Propagator Distributions for Solute Transport in Homogeneous and Heterogeneous Porous Media Using Lattice Boltzmann Simulations,” Water Resour. Res. 49 (12), 8531-8538 (2013).
  15. E. S. Boek and M. Venturoli, “Lattice-Boltzmann Studies of Fluid Flow in Porous Media with Realistic Rock Geometries,” Comput. Math. Appl. 59 (7), 2305-2314 (2010).
  16. B. Manz, L. F. Gladden, and P. B. Warren, “Flow and Dispersion in Porous Media: Lattice-Boltzmann and NMR Studies,” AIChE J. 45 (9), С. 1845-1854 (1999).
  17. M. Ferrari, J-P. Mérel, S. Leclerc, et al., “Study of Dispersion by NMR: Comparison between NMR Measurements and Stochastic Simulation,” Diffus. Fundam. 18 (11), 1-4 (2013).
  18. D. S. Grebenkov, “A Fast Random Walk Algorithm for Computing the Pulsed-Gradient Spin-Echo Signal in Multiscale Porous Media,” J. Magn. Reson. 208 (2), 243-255 (2011).
  19. R. A. Damion, K. J. Packer, K. S. Sorbie, and S. R. McDougall, “Pore-Scale Network Modelling of Flow Propagators Derived from Pulsed Magnetic Field Gradient Spin Echo NMR Measurements in Porous Media,” Chem. Eng. Sci. 55 (24), 5981-5998 (2000).
  20. W. Zhao, G. Picard, G. Leu, and P. M. Singer, “Characterization of Single-Phase Flow through Carbonate Rocks: Quantitative Comparison of NMR Flow Propagator Measurements with a Realistic Pore Network Model,” Transp. Porous Media 81 (2), 305-315 (2010).
  21. F. Mees, R. Swennen, M. van Geet, and P. Jacobs, “Applications of X-Ray Computed Tomography in the Geosciences,” in Applications of X-Ray Computed Tomography in the Geosciences (Geological Society Press, London, 2003), Vol. 215, pp. 1-6.
  22. A. Yu. Dem’yanov, O. Yu. Dinariev, and N. V. Evseev, Foundations of the Density Functional Method in Hydrodynamics (Fizmatlit, Moscow, 2009) [in Russian].
  23. H. C. Torrey, “Bloch Equations with Diffusion Terms,” Phys. Rev. 104 (3), 563-565 (1956).
  24. K. R. Brownstein and C. E. Tarr, “Importance of Classical Diffusion in NMR Studies of Water in Biological Cells,” Phys. Rev. A 19 (6), 2446-2453 (1979).
  25. K. R. Brownstein and C. E. Tarr, “Spin-Lattice Relaxation in a System Governed by Diffusion,” J. Magn. Reson. 26 (1), 17-24 (1977).
  26. R. W. MacCormack, “A Numerical Method for Solving the Equations of Compressible Viscous Flow,” AIAA J. 20 (9), 1275-1281 (1982).
  27. S. V. Patankar, Numerical Heat Transfer and Fluid Flow: Computational Methods in Mechanics and Thermal Science (CRC Press, Boca Raton, 1980).
  28. E. L. Hahn, “Spin Echoes,” Phys. Rev. 80 (4), 580-594 (1950).
  29. E. O. Stejskal and J. E. Tanner, “Spin Diffusion Measurements: Spin Echoes in the Presence of a Time-Dependent Field Gradient,” J. Chem. Phys. 42 (1), 288-292 (1965).
  30. R. I. Nigmatulin, Foundations of Mechanics of Heterogeneous Media (Nauka, Moscow, 1978) [in Russian].

Published

25-05-2017

How to Cite

Клименок К., Демьянов А. Numerical Simulation of Nuclear Magnetic Resonance in Saturated Porous Media With Consideration of Phase Motion // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2017. 18. 192-203. doi 10.26089/NumMet.v18r317

Issue

Section

Section 1. Numerical methods and applications