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The 2D nuclear magnetic resonance diffusion-relaxation experiment (NMR DT2) has proven to be a powerful method to characterize complex fluids. Molecular components with distinct diffusion coefficients are shown on DT2 maps as separate peaks. In porous media such as reservoir rocks, molecular diffusion is restricted such that the apparent diffusion coefficient is time dependent and the diffusion behavior is non-Gaussian. Such restricted diffusion effects can manifest on the DT2 maps and complicate the interpretation of the results, but so far, they have not been systematically investigated. We used controlled laboratory experiments to demonstrate the influence of non-Gaussian restricted diffusion on NMR DT2 maps under various conditions and to show how restricted diffusion effects on DT2 maps can be distinguished from multiphase fluids. NMR DT2 experiments were carried out on a series of water-saturated packs of glass beads and two rock cores. The results revealed the important role of two critical length scales controlling the restricted diffusion effects on NMR DT2 maps: the molecular diffusion length lD during the NMR diffusion encoding time and the characteristic pore size dpore. For lDdpore, the effect of non-Gaussian diffusion was negligible and the NMR DT2 map showed only one peak. As lD approaches dpore, an additional peak with a smaller diffusion coefficient emerged (resembling the DT2 map of an unrestricted two molecular components fluid), and its relative intensity was maximized (to 17%), when lDdpore. As lD further increased, the relative intensity of the additional peak started decreasing, in contrast to the scenario of DT2 maps of multiphase fluids. We determined the extent and influence of restricted diffusion on NMR DT2 maps, and we informed the interpretation of NMR DT2 measurements, which are commonly used to quantify gas, water, and oil signals in reservoir rocks.


  • Callaghan, P. T., 2011, Translational dynamics and magnetic resonance: Principles of pulsed gradient spin echo NMR: Oxford University Press.CrossrefGoogle Scholar
  • Callaghan, P. T., A. Coy, D. MacGowan, K. J. Packer, and F. O. Zelaya, 1991, Diffraction-like effects in NMR diffusion studies of fluids in porous solids, Nature, 351, 467–469, doi: 10.1038/351467a0.CrossrefWeb of ScienceGoogle Scholar
  • Freedman, R., S. Lo, M. Flaum, G. Hirasaki, A. Matteson, and A. Sezginer, 2001, A new NMR method of fluid characterization in reservoir rocks: Experimental confirmation and simulation results: SPE Journal, 6, 452–464, doi: 10.2118/75325-PA.SPEJAC0036-1844CrossrefWeb of ScienceGoogle Scholar
  • Gallegos, D. P., and D. M. Smith, 1988, A NMR technique for the analysis of pore structure: Determination of continuous pore size distributions: Journal of Colloid and Interface Science, 122, 143–153, doi: 10.1016/0021-9797(88)90297-4.JCISA50021-9797CrossrefWeb of ScienceGoogle Scholar
  • Hürlimann, M., and L. Venkataramanan, 2002, Quantitative measurement of two-dimensional distribution functions of diffusion and relaxation in grossly inhomogeneous fields: Journal of Magnetic Resonance, 157, 31–42, doi: 10.1006/jmre.2002.2567.JMARF31090-7807CrossrefWeb of ScienceGoogle Scholar
  • Hürlimann, M., L. Venkataramanan, and C. Flaum, 2002, The diffusion-spin relaxation time distribution function as an experimental probe to characterize fluid mixtures in porous media: The Journal of Chemical Physics, 117, 10223, doi: 10.1063/1.1518959.CrossrefWeb of ScienceGoogle Scholar
  • Hürlimann, M., L. Venkataramanan, C. Flaum, P. Speier, C. Karmonik, R. Freedman, and N. Heaton, 2002, Diffusion-editing: New NMR measurement of saturation and pore geometry: Presented at Society of Petrophysicists and Well-Log Analysts 43rd Annual Logging Symposium, SPWLA-2002-FFF.Google Scholar
  • Keating, K., and R. Knight, 2007, A laboratory study to determine the effect of iron oxides on proton NMR measurements: Geophysics, 72, no. 1, E27–E32, doi: 10.1190/1.2399445.GPYSA70016-8033AbstractWeb of ScienceGoogle Scholar
  • Kleinberg, R., W. Kenyon, and P. Mitra, 1994, Mechanism of NMR relaxation of fluids in rock: Journal of Magnetic Resonance, Series A, 108, 206–214, doi: 10.1006/jmra.1994.1112.JMRAE21064-1858CrossrefGoogle Scholar
  • Latour, L. L., P. P. Mitra, R. L. Kleinberg, and C. H. Sotak, 1993, Time-dependent diffusion coefficient of fluids in porous media as a probe of surface-to-volume ratio: Journal of Magnetic Resonance, Series A, 101, 342–346, doi: 10.1006/jmra.1993.1056.JMRAE21064-1858CrossrefGoogle Scholar
  • Marinelli, L., M. Hürlimann, and P. Sen, 2003, Modal analysis of q-space–relaxation correlation experiments: The Journal of Chemical Physics, 118, 8927, doi: 10.1063/1.1567259.CrossrefWeb of ScienceGoogle Scholar
  • Mitra, P. P., P. N. Sen, and L. M. Schwartz, 1993, Short-time behavior of the diffusion coefficient as a geometrical probe of porous media: Physical Review B, 47, 8565–8574, doi: 10.1103/PhysRevB.47.8565.PRBMDO1098-0121CrossrefWeb of ScienceGoogle Scholar
  • Mitra, P. P., P. N. Sen, L. M. Schwartz, and P. Le Doussal, 1992, Diffusion propagator as a probe of the structure of porous media: Physical Review Letters, 68, 3555–3558, doi: 10.1103/PhysRevLett.68.3555.PRLTAO0031-9007CrossrefWeb of ScienceGoogle Scholar
  • Price, W. S., 1998, Pulsed‐field gradient nuclear magnetic resonance as a tool for studying translational diffusion. Part II: Experimental aspects: Concepts in Magnetic Resonance, 10, 197–237, doi: 10.1002/(SICI)1099-0534(1998)10:4<197::AID-CMR1>3.0.CO;2-S.CMAEEM1099-0534CrossrefGoogle Scholar
  • Rémond, S., J. Gallias, and A. Mizrahi, 2008, Characterization of voids in spherical particle systems by Delaunay empty spheres: Granular Matter, 10, 329–334, doi: 10.1007/s10035-008-0092-4.GRMAFE1434-5021CrossrefWeb of ScienceGoogle Scholar
  • Sen, P. N., M. D. Hürlimann, and T. M. de Swiet, 1995, Debye-Porod law of diffraction for diffusion in porous media: Physical Review B, 51, 601–604, doi: 10.1103/PhysRevB.51.601.PRBMDO1098-0121CrossrefWeb of ScienceGoogle Scholar
  • Slijkerman, W., W. Looyestijn, P. Hofstra, and J. Hofman, 2000, Processing of multi-acquisition NMR data: SPE Reservoir Evaluation and Engineering, 3, 492–497, doi: 10.2118/68408-PA.SREEFG1094-6470CrossrefWeb of ScienceGoogle Scholar
  • Song, Y.-Q., L. Venkataramanan, M. Hürlimann, M. Flaum, P. Frulla, and C. Straley, 2002, T1-T2 correlation spectra obtained using a fast two-dimensional Laplace inversion: Journal of Magnetic Resonance, 154, 261–268, doi: 10.1006/jmre.2001.2474.CrossrefWeb of ScienceGoogle Scholar
  • Tanner, J., 1970, Use of the stimulated echo in NMR diffusion studies: The Journal of Chemical Physics, 52, 2523–2526, doi: 10.1063/1.1673336.CrossrefWeb of ScienceGoogle Scholar
  • Venkataramanan, L., Y.-Q. Song, and M. D. Hurlimann, 2002, Solving Fredholm integrals of the first kind with tensor product structure in 2 and 2.5 dimensions: IEEE Transactions on Signal Processing, 50, 1017–1026, doi: 10.1109/78.995059.ITPRED1053-587XCrossrefWeb of ScienceGoogle Scholar
  • Zielinski, L., R. Ramamoorthy, C. Cao Minh, K. Al Daghar, R. H. Sayed, and A. F. Abdelaal, 2010, Restricted diffusion effects in saturation estimates from 2D diffusion-relaxation NMR maps: Presented at Society of Petroleum Engineers Annual Technical Conference and Exhibition, doi: 10.2118/134841-MS.CrossrefGoogle Scholar