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Ex Situ Measurement of One- and Two-Dimensional Distribution Functions

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Single-Sided NMR

Abstract

Measurements of diffusion [1–4], relaxation [5–7], and distribution functions between relaxation and diffusion [8–10] by nuclear magnetic resonance have become important techniques to study the structure of materials and porous media ranging from biological systems to hydrocarbon bearing sedimentary rocks. These measurements probe the dynamics of molecules on the molecular level and are sensitive to the local environment. The techniques are also particularly well suited for the characterization of heterogeneous systems.

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Notes

  1. 1.

    In fields of higher homogeneity, the second and third terms typically contribute to many echoes and often interfere with the relaxation measurement [35]. In this rare instance, large-field inhomogeneities improve the lives of NMR practitioners!

References

  1. Cory DG, Garroway AN (1990) Measurement of translational displacement probabilities by NMR: an indicator of compartmentation. Magn Reson Med 14:435–444

    Article  CAS  Google Scholar 

  2. Callaghan PT, Coy A, MacGowan D, Packer KJ, Zelaya FO (1991)Diffraction-like effects in NMR diffusion studies of fluids in porous solids. Nature 351:467–469

    Article  CAS  Google Scholar 

  3. Callaghan PT (1991) Principles of nuclear magnetic resonance microscopy. Clarendon Press, Oxford

    Google Scholar 

  4. Mitra PP, Sen PN, Schwartz LM, and Le Doussal P (1992) Diffusion propagator as a probe of the structure of porous media. Phys Rev Lett 68:3555–3558

    Article  CAS  Google Scholar 

  5. Brownstein KR, Tarr CE (1979) Importance of classical diffusion in NMR studies of water in biological cells. Phys Rev A 19:2446

    Article  Google Scholar 

  6. Kenyon WE, Day PI, Straley C, Willemsen JF (1988) A three-part study of NMR longitudinal relaxation properties of water-saturated sandstones. Soc Petrol Eng Form Eval 3:622–636; Erratum: Soc Petrol Eng Form Eval 4:8 (1989)

    CAS  Google Scholar 

  7. D’Orazio F, Tarczon JC, Halperin WP, Eguchi K, Mizusaki T (1989) Application of nuclear magnetic resonance pore structure analysis to porous silica glass. J Appl Phys 65:742–751

    Article  Google Scholar 

  8. English AE, Whittal KP, Joy MLG, Henkelman RM (1991) Quantitative two-dimensional time correlation relaxometry. Magn Reson Med 22:425–434

    Article  CAS  Google Scholar 

  9. Song Y-Q, Venkatarmanan L, Hürlimann MD, Flaum M, Frulla P, Straley C (2002) \(T_1 - T_2\) correlation spectra obtained using a fast two-dimensional Laplace inversion. J Magn Reson 154:261–268

    Article  CAS  Google Scholar 

  10. Hürlimann MD, Venkataramanan L (2002) Quantitative measurement of two dimensional distribution functions of diffusion and relaxation in grossly inhomogeneous fields. J Magn Reson 157:31–42

    Article  Google Scholar 

  11. Kleinberg RL (1996) Well logging. In: Encyclopedia of nuclear magnetic resonance, vol 8. John Wiley & Sons, Chichester, pp 4960–4969

    Google Scholar 

  12. Eidmann G, Savelsberg R, Blümler P, Blümich B (1996) The NMR MOUSE, a mobile universal surface explorer. J Magn Reson A 122:104–109

    Article  CAS  Google Scholar 

  13. Kimmich R, Fischer E (1994) One- and two-dimensional pulse sequences for diffusion experiments in the fringe field of superconducting magnets. J Magn Reson A 106:229–235

    Article  CAS  Google Scholar 

  14. McDonald PJ (1997) Stray field magnetic resonance imaging. Prog Nucl Magn Reson Spect 30:69–99

    Article  CAS  Google Scholar 

  15. Bloembergen N, Purcell EM, Pound RV (1948) Relaxation effects in nuclear magnetic resonance absorption. Phys Rev 73:679–712

    Article  CAS  Google Scholar 

  16. Zega A, House WV, Kobayshi R (1989) A corresponding-states correlation of spin relaxation in normal alkanes. Physica A 156:277–293

    Article  CAS  Google Scholar 

  17. Brown RJS (2001) The Earth’s-field NML development at Chevron. Concepts Magn Reson 13:344–366

    Article  CAS  Google Scholar 

  18. Belton PS, Jackson RR, Packer KJ (1972) Pulsed NMR studies of water in striated muscle. Transverse nuclear spin relaxation times and freezing effects. Biochim Biophys Acta 286: 16–25

    Article  CAS  Google Scholar 

  19. Hazelwood CF, Chang DC, Nichols BL, Woessner DE (1974) Nuclear magnetic resonance transverse relaxation times of water proton in skeletal muscle. Biophys J 14:583–606

    Article  Google Scholar 

  20. Araujo CD, MacKay AL, Whittall KP, Hailey JRT (1993) A diffusion model for spin-spin relaxation of compartmentalized water in wood. J Magn Reson B 101:248–261

    Article  CAS  Google Scholar 

  21. Halperin WP, Jehng JY, Song YQ (1994) Application of spin-spin relaxation to measurement of surface area and pore size distributions in a hydrating cement paste. Magn Reson Imaging 12:169–173

    Article  CAS  Google Scholar 

  22. Hahn EL (1950) Spin echoes. Phys Rev 80:580–594

    Article  Google Scholar 

  23. Einstein A (1906) Eine neue Bestimmung der Moleküldimensionen. Annalen der Physik 19:289–306

    Article  CAS  Google Scholar 

  24. Douglass DC, McCall DW (1958) Diffusion in paraffin hydrocarbons. J Phys Chem 62:1102–1107

    Article  CAS  Google Scholar 

  25. Freed DE, Burcaw L, Song Y-Q (2005) Scaling laws for diffusion coefficients in mixtures of alkanes. Phys Rev Lett 94:067602

    Article  Google Scholar 

  26. Bloembergen N (1966) Paramagnetic resonance precession method and apparatus for well logging. United States Patent No. 3,242,422A. Filed 1954, issued 1966.

    Google Scholar 

  27. Woessner DE (1963) NMR spin-echo self-diffusion measurements on fluids undergoing restricted diffusion. J Phys Chem 67:1365–1367

    Article  CAS  Google Scholar 

  28. Ernst RR, Bodenhausen G, Wokaun A (1987) Principles of nuclear magnetic resonance in one and two dimensions. Clarendon Press, Oxford

    Google Scholar 

  29. Carr HY, Purcell EM (1954) Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys Rev 94:630–638

    Article  CAS  Google Scholar 

  30. Meiboom S, Gill D (1958) Modified spin-echo method for measuring nuclear relaxation times. Rev Sci Instrum 29:688–691

    Article  CAS  Google Scholar 

  31. Goelman G, Prammer MG (1995) The CPMG pulse sequence in strong magnetic field gradients with applications to oil-well logging. J Magn Reson A 113:11–18

    Article  CAS  Google Scholar 

  32. Hürlimann MD, Griffin DD (2000) Spin dynamics of Carr – Purcell – Meiboom – Gill – like sequences in grossly inhomogeneous B o and B 1 fields and application to NMR well logging. J Magn Reson 143:120–135

    Article  Google Scholar 

  33. Bãlibanu F, Hailu K, Eymael R, Demco DE, Blümich B. (2000) Nuclear magnetic resonance in inhomogeneous magnetic fields. J Magn Reson 145:246–258

    Article  Google Scholar 

  34. Jaynes ET (1955) Matrix treatment of nuclear induction. Phys Rev 98:1099–1105

    Article  CAS  Google Scholar 

  35. Bull TE (1974) Effect of RF field inhomogeneities on spin-echo measurements. Rev Sci Instrum 45:232–242

    Article  CAS  Google Scholar 

  36. Hürlimann MD (2001) Diffusion and relaxation effects in general stray field NMR experiments. J Magn Reson 148:367–378

    Article  Google Scholar 

  37. Song Y-Q (2002) Categories of coherence pathways for the CPMG sequence. J Magn Reson 157:82–91

    Article  CAS  Google Scholar 

  38. Stejskal EO, Tanner JE (1965) Spin diffusion measurements: spin echoes in the presence of a time-dependendent field gradient. J Chem Phys 42:288–292

    Article  CAS  Google Scholar 

  39. Cotts RM, Hoch MJR, Sun T, Markert JT (1989) Pulsed field gradient stimulated echo methods for improved NMR diffusion measurements in heterogeneous systems. J Magn Reson 83:252–266

    CAS  Google Scholar 

  40. Kimmich R, Unrath W, Schnur G, Rommel E (1991) NMR measurement of small self-diffusion coefficients in the fringe field of superconducting magnets. J Magn Reson 91: 136–140

    CAS  Google Scholar 

  41. Rata DG, Casanova F, Perlo J, Demco DE, Blümich B (2006) Self-diffusion measurements by a mobile single-sided NMR sensor with improved magnetic field gradient. J Magn Reson 180:229–235

    Article  CAS  Google Scholar 

  42. Woessner DE (1961) Effects of diffusion in nuclear magnetic resonance spin-echo experiments. J Chem Phys 34:2057–2061

    Article  CAS  Google Scholar 

  43. Fischer E, Kimmich R (2004) Constant time steady gradient NMR diffusometry using the secondary stimulated echo. J Magn Reson 166:273–279

    Article  CAS  Google Scholar 

  44. Hürlimann MD, Venkataramanan L, Flaum C (2002) The diffusion – spin relaxation time distribution function as an experimental probe to characterize fluid mixtures in porous media. J Chem Phys 117:10223–10232

    Article  Google Scholar 

  45. Hürlimann MD (2007) Encoding of diffusion and T 1 in the CPMG echo shape: single-shot D and T 1 measurements in grossly inhomogeneous fields. J Magn Reson 184:114–129

    Article  Google Scholar 

  46. Kenyon WE (1992) Nuclear magnetic resonance as a petrophysical measurement. Nucl Geophys 6:153

    CAS  Google Scholar 

  47. Provencher SW (1982) A constrained regularization method for inverting data represented by linear algebraic or integral equations. Comput Phys Commun 27:213–227

    Article  Google Scholar 

  48. Kroeker RM, Henkelman RM (1986) Analysis of biological NMR relaxation data with continuous distributions of relaxation times. J Magn Reson 69:218–235

    CAS  Google Scholar 

  49. Whittall KP, MacKay AL (1989) Quantitative interpretation of NMR relaxation data. J Magn Reson, 84:134–152

    CAS  Google Scholar 

  50. Fordham EJ, Sezginer A, Hall LD (1995) Imaging multiexponential relaxation in the (y, log e T1) plane, with application to clay filtration in rock cores. J Magn Reson A 113: 139–150

    Article  CAS  Google Scholar 

  51. Borgia GC, Brown RJS, Fantazzini P (1998) Uniform-penalty inversion of multiexponential decay data. J Magn Reson 132:65–77

    Article  CAS  Google Scholar 

  52. Brown RJS (1989) Information available and unavailable from multiexponential relaxation data. J Magn Reson 82:539–561

    Google Scholar 

  53. Borgia GC, Brown RJS, Fantazzini P (2000) Uniform-penalty inversion of multiexponential decay data II. Data spacing, T 2 data, systematic data errors, and diagnostics. J Magn Reson 147:273–285

    Article  CAS  Google Scholar 

  54. Parker RL, Song YQ (2005) Assigning uncertainties in the inversion of NMR relaxation data. J Magn Reson 174:314–324

    Article  CAS  Google Scholar 

  55. Britton MM, Graham RG, Packer KJ (2001) Relationships between flow and NMR relaxation of fluids in porous solids. Magn Reson Imaging 19:325–331

    Article  CAS  Google Scholar 

  56. Scheven UM (2005) Stray field measurements of flow displacement distributions without pulsed field gradients. J Magn Reson 174:338–342

    Article  CAS  Google Scholar 

  57. Callaghan PT, Furó I (2004) Diffusion–diffusion correlation and exchange as a signature for local order and dynamics. J Chem Phys 120:4032–4038

    Article  CAS  Google Scholar 

  58. McDonald PJ, Korb JP, Mitchell J, Monteilhet L (2005) Surface relaxation and chemical exchange in hydrating cement pastes: a two-dimensional NMR relaxation study. Phys Rev E 72:011409

    Article  CAS  Google Scholar 

  59. Hürlimann MD, Venkataramanan L, Flaum C, Speier P, Karmonik C, Freedman R, Heaton N (2002) Diffusion-editing: new NMR measurement of saturation and pore geometry. In: Transactions of the SPWLA 43rd Annual Logging Symposium, Oiso, Japan, Paper FFF

    Google Scholar 

  60. Venkataramanan L, Song Y-Q, Hürlimann MD (2002) Solving Fredholm integrals of the first kind with tensor product structure in 2 and 2.5 dimensions. IEEE Trans. Signal Process 50:1017–1026

    Google Scholar 

  61. Butler JP, Reeds JA, V.Dawson S (1981) Estimating solutions of first kind integral equations with nonnegative constraints and optimal smoothing. SIAM J Numer Anal 18:381–397

    Article  Google Scholar 

  62. de Swiet TM, Tomaselli M, Hürlimann MD, Pines A (1998) In situ NMR analysis of fluids contained in sedimentary rock. J Magn Reson 133:385–387

    Article  Google Scholar 

  63. Freedman R, Heaton N (2004) Fluid characterization using nuclear magnetic resonance logging. Petrophysics 45:241–250

    Google Scholar 

  64. Seland J, Bruvold M, Anthonsen H, Brurok H, Nordhøy W, Jynge P, Krane J (2005) Determination of water compartments in rat myocardium using combined \(D - T_1\) and \(T_1 - T_2\) experiments. Magn Reson Imaging 23:353–354

    Article  CAS  Google Scholar 

  65. Godefroy S, Creamer LK, Watkinson PJ, Callaghan PT (2003) The use of 2d Laplace inversion in food materials. In: Webb GA, Belton PS, Gil AM, Delgadillo I (eds) Magnetic resonance in food science: a view to the future. Royal Society of Chemistry, Cambridge

    Google Scholar 

  66. Hürlimann MD, Burcaw L, Song YQ (2006) Quantitative characterization of food products by two-dimensional \(D - T_2\) and \(T_1 - T_2\) distribution functions in a static gradient. J Colloid Interface Sci 297:303–311

    Article  Google Scholar 

  67. Hürlimann MD, Flaum M, Venkataramanan L, Flaum C, Freedman R, Hirasaki GJ (2003) Diffusion–relaxation distribution functions of sedimentary rocks in different saturation states. Magn Reson Imaging 21:305–310

    Article  Google Scholar 

  68. Mutina AR, Hürlimann MD (2008)Correlation of transverse and rotational diffusion coefficient: a probe of chemical composition in hydrocarbon oils. J Phys Chem A112:3291–3301

    Article  Google Scholar 

  69. Windt CW, Vergeldt FJ, Van As H (2007) Correlated displacement – T 2 MRI by means of a pulsed field gradient-multi spin echo method. J Magn Reson 185:230–239

    Article  CAS  Google Scholar 

  70. Hills B, Benamira S, Marigheto N, Wright K (2004) \(T_1 - T_2\) correlation analysis of complex foods. Appl Magn Reson 26:543–560

    Article  CAS  Google Scholar 

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Acknowledgements

I would like to thank all my colleagues at Schlumberger–Doll Research who have contributed to the development of this field, in particular Lalitha Venkataramanan and Yi-Qiao Song.

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Authors and Affiliations

  1. Schlumberger-Doll Research, Cambridge, MA, 02141, USA

    Martin D. Hürlimann

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  1. Martin D. Hürlimann
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Correspondence to Martin D. Hürlimann .

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Editors and Affiliations

  1. Inst. Technische und, Makromolekulare Chemie, RWTH Aachen, Worringerweg 1, Aachen, 52074, Germany

    Federico Casanova

  2. Inst. Technische und, Makromolekulare Chemie, RWTH Aachen, Worringerweg 1, Aachen, 52074, Germany

    Juan Perlo

  3. Inst. Technische und, Makromolekulare Chemie, RWTH Aachen, Worringerweg 1, Aachen, 52074, Germany

    Bernhard Blümich

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Hürlimann, M.D. (2011). Ex Situ Measurement of One- and Two-Dimensional Distribution Functions. In: Casanova, F., Perlo, J., Blümich, B. (eds) Single-Sided NMR. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16307-4_3

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