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Transport in Porous Media

, Volume 12, Issue 2, pp 107–123 | Cite as

Nuclear magnetic resonance imaging of miscible fingering in porous media

  • Zeev Pearl
  • Mordeckai Magaritz
  • Peter Bendel
Article

Abstract

Nuclear Magnetic Resonance Imaging (MRI) can noninvasively map the spatial distribution of Nuclear Magnetic Resonance (NMR)-sensitive nuclei. This can be utilized to investigate the transport of fluids (and solute molecules) in three-dimensional model systems. In this study, MRI was applied to the buoyancy-driven transport of aqueous solutions, across an unstable interface in a three-dimensional box model in the limit of a small Péclet number (Pe<0.4). It is demonstrated that MRI is capable of distinguishing between convective transport (‘fingering’) and molecular diffusion and is able to quantify these processes. The results indicate that for homogeneous porous media, the total fluid volume displaced through the interface and the amplitude of the fastest growing finger are linearly correlated with time. These linear relations yielded mean and maximal displacement velocities which are related by a constant dimensionless value (2.4±0.1). The mean displacement velocity (U) allows us to calculate the media permeability which was consistent between experiments (1.4±0.1×10−7cm2).U is linearly correlated with the initial density gradient, as predicted by theory. An extrapolation of the density gradient to zero velocity enables an approximate determination of the critical density gradient for the onset of instability in our system (0.9±0.3×10−3 g/cm3), a value consistent with the value predicted by a calculation based upon the modified Rayleigh number. These results suggest that MRI can be used to study complex fluid patterns in three-dimensional box models, offering a greater flexibility for the simulation of natural conditions than conventional experimental modelling methods.

Key-words

Nuclear magnetic resonance imaging (MRI) miscible displacement buoyancy three-dimensional diffusion permeability 

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References

  1. Baldwin, B. A. and Yamanashi, W. S., 1988, NMR imaging of fluid dynamics in reservoir core,Magn. Reson. Imag. 6, 493–500.Google Scholar
  2. Bear, J., 1972,Dynamics of Fluid in Porous Media, Elsevier, New York.Google Scholar
  3. Bear, J., 1979,Hydraulics of Groundwater, McGraw Hill, New York.Google Scholar
  4. Bendel, P., 1990, Spin-Echo attenuation by diffusion in nonuniform field gradients,J. Magn. Reson. 86, 509–515.Google Scholar
  5. Budinger, T. F. and Lauterbur, P. C., 1984, Nuclear magnetic resonance technology for medical studies,Science 226, 288–298.Google Scholar
  6. Carrington, A. and McLachlan, A. D., 1979,Introduction to Magnetic Resonance, Chapman and Hall, London, Ch. 13.Google Scholar
  7. Chen, J. D., Dias, M. M., Patz, S., and Schwartz, L. M., 1988, Magnetic resonance imaging of immiscible-fluid displacement in porous media,Phys. Rev. Lett. 61, 1489–1492.Google Scholar
  8. Coskuner, G. and Bentsen, R. G., 1990, An extended theory to predict the onset of viscous instabilities for miscible displacements in porous media,Transport in Porous Media 5, 473–490.Google Scholar
  9. Edelstein, W. A., Vinegar, H. J., Tutunjian, P. N., Roemer, P. B., and Mueller, D. M., 1979, NMR imaging for core analysis, SPE 18272; presented at the 63rd Ann. Technical Conference and Exhibition of the SPE, Houston, Tx, 1988.Google Scholar
  10. Freeze, R. A. and Cherry, J. A., 1979,Groundwater, Prentice-Hall, New Jersey.Google Scholar
  11. Gaigalas, A. K., Van Orden, A. C., Mareci, T. H., and Lewis L. A., 1989, Application of magnetic resonance imaging to visualization of flow in porous media,Nucl. Technol. 84, 113–118.Google Scholar
  12. Guillot, G., Trokiner, A., Darasse, L., and Saint-Jalmes, H., 1989, Drying of a porous rock monitored by NMR imaging,J. Phys. D: Appl. Phys. 22, 1846–1849.Google Scholar
  13. Guillot, G., Kassab G., Hulin, J. P., and Rigord, P., 1991, Monitoring of trace dispersion in porous media by NMR imaging,J. Phys. D: Appl. Phys. 24, 763–773.Google Scholar
  14. Gummerson, R. G., Hall, C., Hoff, W. D., Hawkes, R., Holland, G. N., and Moore W. S., 1979, Unsaturated water flow within porous materials observed by NMR imaging,Nature 281, 56–57.Google Scholar
  15. Hall, L. D. and Rajanayagam, V., 1987, Thin-slice, chemical shift imaging of oil and water in sandstone rock at 80 Mhz,J. Magn. Reson. 74, 139–146.Google Scholar
  16. Hellstrom, G., Tsang, C. F., and Claesson, J., 1988, Buoyancy flow at a two fluid interface in a porous medium: Analytical studies,Water Resour. Res. 24, 493–506.Google Scholar
  17. Homsy, G. M., 1987, Viscous fingering in porous media,Ann. Rev. Fluid Mech. 19, 271–311.Google Scholar
  18. Imnhoff, P. T. and Green, T., 1988, Experimental investigation of double-diffusive groundwater fingers,J. Fluid Mech. 188, 363–382.Google Scholar
  19. Jezzard, P., Attarrd, J. J., Carpenter, T. A., and Hall, L. D., 1991, Nuclear magnetic resonance imaging in the solid state,Progr. NMR Spectrosc. 23, 1–14.Google Scholar
  20. Kyle, C. R. and Perrine, R. L., 1965, Experimental studies of miscible displacement instability,Soc. Pet. Eng. J. 5, 189–195.Google Scholar
  21. Lapwood, E. R., 1948, Convection of a fluid in a porous medium,Proc. Cambridge Phil. Soc. 44, 508–521.Google Scholar
  22. Molz, F. G., Melville, J. G., Parr, A. D., King, D. A., and Hopf, M. T., 1983, Aquifer thermal energy storage: A well doublet experiment at increased temperatures,Water Resour. Res. 19, 149–160.Google Scholar
  23. Morris, P. G., 1986,Nuclear Magnetic Resonance Imaging in Medicine and Biology. Clarendon Press, Oxford.Google Scholar
  24. Oger, L., Guyon, E., and Wilkinson, D., 1987, Permeability variation due to spherical impurities in a disordered packing of equal spheres,Europhys. Lett. 4, 301–305.Google Scholar
  25. Pearl, Z., Magaritz, M. and Bendel, P., 1991, Measuring diffusion coefficients of solutes in porous media by NMR imaging,J. Magn. Reson. 95, 597–602.Google Scholar
  26. Ronen, D., Magaritz, M., and Paldor, N., 1988, Microscale haline convection — A proposed mechanism for transport and mixing at the water table region,Water Resour. Res. 24, 1111–1117.Google Scholar
  27. Wooding, R. A., 1963, Convection in a saturated porous medium at a large Rayleigh number or Péclet number,J. Fluid Mech. 15, 527–545.Google Scholar
  28. Wooding, R. A., 1964, Mixing layer flows in a saturated porous medium,J. Fluid Mech. 19, 103–112.Google Scholar
  29. Wooding, R. A., 1969, Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell,J. Fluid Mech. 39, 477–495.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Zeev Pearl
    • 1
  • Mordeckai Magaritz
    • 1
  • Peter Bendel
    • 2
  1. 1.Department of Environmental Sciences and Energy Research (ESER)Weizmann Institute of ScienceRehovotIsrael
  2. 2.Department of Chemical PhysicsWeizmann Institute of ScienceRehovotIsrael

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