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Solid state NMR imaging of irreducible water in reservoir cores for spatially resolved pore surface relaxation estimation
Magnetic Resonance Imaging, Vol. 12, No. 2, pp. 355-359, 1994 Copyright 0 1994 Elsevier Science Ltd Printed in the USA. All rights reserved 0730-725X194 $6.00 + .OO
Pergamon
0730-725X(93)EOO48-S
l
Contributed Paper
SOLID STATE NMR IMAGING OF IRREDUCIBLE WATER IN RESERVOIR CORES FOR SPATIALLY RESOLVED PORE SURFACE RELAXATION ESTIMATION J. J. ATTARD,*? P. J. MCDONALD,$ S.P. ROBERTS,$ AND T. TAYLOR* *British Gas Research and Technology Division, Michael Road, London, SW6 2AD, UK SDepartment of Physics, University of Surrey, Guildford, Surrey, GU2 SXH, UK The use of solid state NMR imaging in reservoir core applications has long been proposed. This paper describes the use of a simple, robust technique in the first such application. One- and two-dimensional images of the irreducible brine in a sandstone and carbonate reservoir core are demonstrated. The applicability of solid state NMR imaging to pore surface relaxation estimation is discussed. Keywords: Solid state MRI; Irreducible water; Surface relaxation; Reservoir cores.
magnet (Magnex Scientific Ltd., Abingdon, Oxon, UK). A purpose built 8 cm diameter bore (4 cm3 d.s.v) actively shielded Magnex gradient set generated gradients of up to 40 G/cm. A 2.5 cm diameter birdcage coil
INTRODUCTION NMR imaging (MRI) has evolved rapidly since its first
practical demonstration in the early 1970s.’ Despite one of the first papers in MRI dealing specifically with the imaging of solid materials,2 to this day solid state MRI remains a specialist area. The motion of atoms in solid (or very viscous) materials may be severely restricted, resulting in little time available for encoding spatial information into the NMR signal (typically lOs100s of I.LS).Numerous approaches have been proposed for overcoming the linewidth/encoding time difficulties, and these are extensively reviewed elsewhere? The aim of this paper is to establish solid state MRI in reservoir core studies, and to attempt to apply the technique to investigating pore surface relaxation (psr). Previous imaging experiments4-’ and studies of psr’-” involved having the porous regions fully saturated with a variety of fluids, the latter thereby indirectly probing pore surface phenomena. In this work, the brine content of the cores is reduced to 53% by volume, establishing a more “solid state” condition. METHOD
time
Field Gradient
T2* weighted profile
a!
AAA,
, time
Tl weighted profile
T2 weighted profile
Gradient echo FLASH variant
AND RESULTS
Fig. 1. Schematic of the variants of the basic oscillating gradient recalled echo techniques used. 7 represents the gradient
All experiments were performed at 30 MHz using a SMIS (SMIS Ltd., Guildford, Surrey, UK) imaging console modified for solid state, combined with a 20 cm diameter, horizontal bore Magnex superconducting fPresent address: SINTEFUNIMED, Trondheim, Norway.
oscillation period, 01represents a short flip angle pulse and T,,, represents the inversion delay between 180” pulse and an a! pulse.
MR-Centre, N-7034, 355
356
Magnetic Resonance Imaging 0 Volume 12, Number 2, 1994
was used for rf excitation. Profiles with approximately 0.2 mm pixel resolution were generated by a variety of gradient echo imaging techniques employing large oscillating gradients’*,‘2 (Pig. 1). Two dimensional images were generated by back-projection reconstruction employing two oscillating gradients. The mobile brine was removed from two cores, one sandstone and one carbonate with dimensions 2.5 cm x 3.8 cm, by standard
porous plate desaturation using humidified nitrogen gas at pressures up to 1.24 MPa. At this pressure it is known that the irreducible water condition was reached for these cores. Core integrity was maintained by subsequent saturation with a fluorinated hydrocarbon. Prior to imaging, whole core Tl and T2 data were obtained and fitted to stretched-exponential functions13 for sample characterisation. The sandstone
4oooo -5OOm.s
, 00 ms
30ms
-
30000
20000 p ;: ;
I
loooo 0
-10000
-20000
0.0
-2.5
5
CM
(4 -
200 ms. .-.
-2.5
looms.
2.5
W Fig. 2. Tr-weighted profiles (gradient echo time = 216 ps) of the carbonate (A) and sandstone (B) cores. The carbonate core exhibits a Tr gradient from the left (~51 ms) to the right (a37 ms) of the figure. The sandstone core exhibits spatially uniform growth in magnetisation (Tr = 17 ms).
Solid state NMR in reservoir cores 0 J.J. ATTARDET
core had a T,, (a) = 18 ms (0.29) and a Tza (CY)varying from 650 ps (0.36) to 80 ps (0.19) for CPMG 180” pulse gaps of 120-940 ~LS,indicating significant bulk diffusion behaviour. On the other hand, the carbonate core had a Tl, (a) = 55 ms(0.48) and a T,, (a) varying from 1300 ps (0.28) to 1150 ps (0.27), relatively independent of pulse gap, for the same pulse gap range
357
AL.
as above. The (Yvalues imply very broad distributions of relaxation. Tl -weighted profiles for the two cores can be seen in Fig. 2. Technical limitations meant that the shortest 180”~(1! pulse gap was 3 ms. Hence, fully inverted signals could not be obtained for either core. The first gradient echo (7 = 2 16 ps) was sampled in each case, and 12
60000 CARBONATE
-
-
-
50000
1st echo 3rd echo 7thecho 12th &lo
0.0 CM
-2.5
(A) 4oooo.o
r
-
lstecho ..__....3rd echo
-
7th echo
CM
(B) Fig. 3. T2-weighted profiles (spin echo time = 432 ps) of the carbonate (A) and sandstone (B) cores obtained with the CPMG variant. Both cores exhibit a uniform decay in magnetisation, with T2= 1040 ps for the carbonate core and T2= 360 ps for the sandstone core. The T2gradient observed for the sandstone is not real, and is due to the small amplitude of the 180” pulse field relative to the maximum gradient field occurring during the pulse at the ends of the sample.
Magnetic Resonance Imaging 0 Volume 12, Number 2, 1994
358
profiles were obtained with delays ranging from 3 to 700 ms taking over 15 h (2000 averages) for each complete data set. Fitting the data gave T,, ((;Y) = 40 f 5 ms (0.24 f 0.01) for the carbonate core and 17 + 2 ms (0.23 f 0.02) for the sandstone core. The carbonate core exhibits a reproducible gradient in T,, across the core (Fig. 2A). A 180” pulse gap of 432 1s was used for generating the TZ-weighted profiles seen in Fig. 3. Again 12 profiles were obtained, taking 5 h (2000 averages) for each data set. Fitting the data gave Tzcu (0.36 f 0.03) for the carbonate core (CY)= 1040 + 140 I.LS and 360 f 50 ps (0.32 + 0.03) for the sandstone core. It is worth noting that whole core CPMG (7 = 432 ps) data gave T,, (a) = 1190 ps (0.3 1) for the carbonate core and 330 ps (0.30) for the sandstone core, in very good agreement with the spatially resolved data. Interestingly, no Tla gradient comparable to the T,, gradient is observed for the carbonate core. Figure 4 shows longitudinal, 120 x 120, non slice selected images of the two cores. These were acquired with the flash variant technique using a gradient echo time of 216 ps, and 2000 averages were taken. PORE SURFACE RELAXATION AND DISCUSSION
,owhich has dimensions of length/time. As p is the scaling term for relating psr to pore geometry, its accurate determination is critical for pore size distribution calculations, which, in turn, are essential for modelling fluid flow properties.15 p is usually (but not only) determined by comparing NMR relaxation to pore geometry derived by other means such as petrographic image analysis and mercury porosimetry.8-10 Our whole core relaxation data give conflicting interpretations. The values for T,, and T,, agree very well with those obtained for a monolayer of water in porous silica glasses,” where average T, I 100 ms (27 MHz) and average T2 5 1 ms (CPMG, 7 = 500 ps). Assuming that we have a monolayer of brine over the pore surface, then 1/T,,Z = P~,~/X, where X is the thickness of the monolayer, of order 3 A. This gives p, =O.l6A/msandp 2 = 4.62 A/ms for the sandstone core, and p1 = 0.053 A/ms, p2 = 2.31 A/ms for the carbonate core. These are to be compared with p1 = 0.058 ,&/ms and p2 = 1.09 A/ms for the silica glasses.” Thus, the whole core relaxation data seems to suggest that we may be observing psr, and therefore may be able to estimate p. The observation of bulk diffusion, however, suggests that the irreducible brine is not present as a monolayer over the pore surfaces. The equation 1/T,,2 = ~,,~/h may therefore not be appli-
Brownstein and Tarr14 showed that surfaces play a dominant role in the NMR relaxation of saturating fluids in porous media. The effectiveness of the surface in relaxing nuclei is characterised by the psr strength
cable, and we may not be in a position to unambiguously estimate p. It should be noted that the values of p,.? reported here are orders of magnitude smaller
(A)
@I
than those reported previously for fully saturated res-
Fig. 4. T,*-weighted, 120 x 120 pixel images of the two reservoir cores. The gradient echo time = 216 ps, and 2000 averages were taken in each case. (A) Carbonate and (B) Sandstone.
Solid state NMR in reservoir cores 0 J .J. ervoir cores8 where l/T, = p x S/V is valid, inviting the conclusion that the pores are in an intermediate state of saturation (S/V is the pore surface to volume
ratio). Estimates of psr obtained from the profile data (assuming X = 3 A) are p1 = 0.18 A/ms and p2 = 8.26 A/ms for the sandstone core, and p, = 0.075 A/ms and p2 = 2.87 A/ms for the carbonate core, in good agreement with the values obtained from the bulk data. Future developments will include improving the imaging procedures with extensions to two dimensions (slice select) and three dimensions, while studying psr as a function of saturation. Acknowledgments- We would like to thank British Gas Exploration & Production for funding this work. PJM and SPR thank SMIS and MAGNEX for support, and the SERC for a studentship (SPR). JJA and TT thank J.J. Howard (Phillips Petroleum) and W.E. Kenyon (Schlumberger) for helpful discussions.
REFERENCES 1. Lauterbur, P.C. Image formation by induced local interactions: Examples employing nuclear magnetic resonance. Nature 242:190-191; 1973. 2. Mansfield, P.; Grannell, P.K. NMR diffraction in solids? J. Phys. C6:L426-L432; 1973. 3. Jezzard, P.; Attard, J. J.; Carpenter, T.A.; Hall, L.D. Nuclear magnetic resonance imaging in the solid state. JPNMRS 23:1-41; 1991. 4. Rothwell, W.P.; Vinegar, H.J. Petrophysical applications of NMR imaging. Appl. Optics 24:3969-3972; 1985. 5. Attard, J.J.; Doran, S.J.; Herrod, N.J.; Carpenter, T.E.; Hall, L.D. Quantitative NMR spin-lattice-relaxation imaging of brine in sandstone reservoir cores. J. Magn. Reson. 96:514-525; 1992.
ATTARD
ET AL.
359
6. Gibbs, S.J.; Attard, J.J.; Hall, L.D. Spatially determined water diffusivities in brine saturated reservoir cores obtained by NMR imaging. A. I. Ch. E. 39:689-694; 1993. 7. Gleeson, J.W.; Woessner, D.E. Three-dimensional and flow-weighted NMR imaging of pore connectivity in a limestone. Magn. Reson. Imaging 9:879-884; 1991. 8. Howard, J.J.; Kenyon, W.E. Determination of pore size distribution in sedimentary rocks by proton nuclear magnetic resonance. Marine and Petroleum Geology 9: 139145; 1992. 9. Halperin, W.P.; D’Orazio, F.; Bhattacharja, S.; Tarczon, J.C. Magnetic resonance relaxation analysis of porous media. In: J. Klafter, J.M. Drake (Eds). Molecular Dynamics in Restricted Geometries. New York: Wiley; 1989: pp. 311-349. 10. D’Orazio, F.; Tarczon, J.C.; Halperin, W.P.; Eguchi, K.; Mizusaki, T. Application of nuclear magnetic resonance pore structure analysis to porous silica. J. Appl. Phys. 65:742-75 1; 1989. 11. Cottrell, S.P.; Halse, M.R.; Strange, J.H. NMR imaging of solids using large oscillating gradients. Meas. Sci. Technol. 1:624-629; 1990. 12. McDonald, P.J.; Perry, K.L.; Roberts, S.P. A repetitive pulse variant of broad line gradient echo magnetic resonance imaging. Meas. Sci. Technol. 4:896-898; 1993. 13. Kenyon, W.E. ; Day, P.I.; Straley, C.; Willemsen, J.F. Compact and consistent representation of rock NMR data for permeability estimation. SPE 15643. 61st Annual SPE Conference; 1986. 14. Brownstein, K.R.; Tarr, C.E. Importance of classical diffusion in NMR studies of water in biological cells. Phys. Rev. A 19:2446-2453; 1979. 15. Kenyon, W.E. Nuclear magnetic resonance as a petrophysical measurement. Nucl. Geophys. 6: 153-171; 1992.
Pergamon
0730-725X(93)EOO48-S
l
Contributed Paper
SOLID STATE NMR IMAGING OF IRREDUCIBLE WATER IN RESERVOIR CORES FOR SPATIALLY RESOLVED PORE SURFACE RELAXATION ESTIMATION J. J. ATTARD,*? P. J. MCDONALD,$ S.P. ROBERTS,$ AND T. TAYLOR* *British Gas Research and Technology Division, Michael Road, London, SW6 2AD, UK SDepartment of Physics, University of Surrey, Guildford, Surrey, GU2 SXH, UK The use of solid state NMR imaging in reservoir core applications has long been proposed. This paper describes the use of a simple, robust technique in the first such application. One- and two-dimensional images of the irreducible brine in a sandstone and carbonate reservoir core are demonstrated. The applicability of solid state NMR imaging to pore surface relaxation estimation is discussed. Keywords: Solid state MRI; Irreducible water; Surface relaxation; Reservoir cores.
magnet (Magnex Scientific Ltd., Abingdon, Oxon, UK). A purpose built 8 cm diameter bore (4 cm3 d.s.v) actively shielded Magnex gradient set generated gradients of up to 40 G/cm. A 2.5 cm diameter birdcage coil
INTRODUCTION NMR imaging (MRI) has evolved rapidly since its first
practical demonstration in the early 1970s.’ Despite one of the first papers in MRI dealing specifically with the imaging of solid materials,2 to this day solid state MRI remains a specialist area. The motion of atoms in solid (or very viscous) materials may be severely restricted, resulting in little time available for encoding spatial information into the NMR signal (typically lOs100s of I.LS).Numerous approaches have been proposed for overcoming the linewidth/encoding time difficulties, and these are extensively reviewed elsewhere? The aim of this paper is to establish solid state MRI in reservoir core studies, and to attempt to apply the technique to investigating pore surface relaxation (psr). Previous imaging experiments4-’ and studies of psr’-” involved having the porous regions fully saturated with a variety of fluids, the latter thereby indirectly probing pore surface phenomena. In this work, the brine content of the cores is reduced to 53% by volume, establishing a more “solid state” condition. METHOD
time
Field Gradient
T2* weighted profile
a!
AAA,
, time
Tl weighted profile
T2 weighted profile
Gradient echo FLASH variant
AND RESULTS
Fig. 1. Schematic of the variants of the basic oscillating gradient recalled echo techniques used. 7 represents the gradient
All experiments were performed at 30 MHz using a SMIS (SMIS Ltd., Guildford, Surrey, UK) imaging console modified for solid state, combined with a 20 cm diameter, horizontal bore Magnex superconducting fPresent address: SINTEFUNIMED, Trondheim, Norway.
oscillation period, 01represents a short flip angle pulse and T,,, represents the inversion delay between 180” pulse and an a! pulse.
MR-Centre, N-7034, 355
356
Magnetic Resonance Imaging 0 Volume 12, Number 2, 1994
was used for rf excitation. Profiles with approximately 0.2 mm pixel resolution were generated by a variety of gradient echo imaging techniques employing large oscillating gradients’*,‘2 (Pig. 1). Two dimensional images were generated by back-projection reconstruction employing two oscillating gradients. The mobile brine was removed from two cores, one sandstone and one carbonate with dimensions 2.5 cm x 3.8 cm, by standard
porous plate desaturation using humidified nitrogen gas at pressures up to 1.24 MPa. At this pressure it is known that the irreducible water condition was reached for these cores. Core integrity was maintained by subsequent saturation with a fluorinated hydrocarbon. Prior to imaging, whole core Tl and T2 data were obtained and fitted to stretched-exponential functions13 for sample characterisation. The sandstone
4oooo -5OOm.s
, 00 ms
30ms
-
30000
20000 p ;: ;
I
loooo 0
-10000
-20000
0.0
-2.5
5
CM
(4 -
200 ms. .-.
-2.5
looms.
2.5
W Fig. 2. Tr-weighted profiles (gradient echo time = 216 ps) of the carbonate (A) and sandstone (B) cores. The carbonate core exhibits a Tr gradient from the left (~51 ms) to the right (a37 ms) of the figure. The sandstone core exhibits spatially uniform growth in magnetisation (Tr = 17 ms).
Solid state NMR in reservoir cores 0 J.J. ATTARDET
core had a T,, (a) = 18 ms (0.29) and a Tza (CY)varying from 650 ps (0.36) to 80 ps (0.19) for CPMG 180” pulse gaps of 120-940 ~LS,indicating significant bulk diffusion behaviour. On the other hand, the carbonate core had a Tl, (a) = 55 ms(0.48) and a T,, (a) varying from 1300 ps (0.28) to 1150 ps (0.27), relatively independent of pulse gap, for the same pulse gap range
357
AL.
as above. The (Yvalues imply very broad distributions of relaxation. Tl -weighted profiles for the two cores can be seen in Fig. 2. Technical limitations meant that the shortest 180”~(1! pulse gap was 3 ms. Hence, fully inverted signals could not be obtained for either core. The first gradient echo (7 = 2 16 ps) was sampled in each case, and 12
60000 CARBONATE
-
-
-
50000
1st echo 3rd echo 7thecho 12th &lo
0.0 CM
-2.5
(A) 4oooo.o
r
-
lstecho ..__....3rd echo
-
7th echo
CM
(B) Fig. 3. T2-weighted profiles (spin echo time = 432 ps) of the carbonate (A) and sandstone (B) cores obtained with the CPMG variant. Both cores exhibit a uniform decay in magnetisation, with T2= 1040 ps for the carbonate core and T2= 360 ps for the sandstone core. The T2gradient observed for the sandstone is not real, and is due to the small amplitude of the 180” pulse field relative to the maximum gradient field occurring during the pulse at the ends of the sample.
Magnetic Resonance Imaging 0 Volume 12, Number 2, 1994
358
profiles were obtained with delays ranging from 3 to 700 ms taking over 15 h (2000 averages) for each complete data set. Fitting the data gave T,, ((;Y) = 40 f 5 ms (0.24 f 0.01) for the carbonate core and 17 + 2 ms (0.23 f 0.02) for the sandstone core. The carbonate core exhibits a reproducible gradient in T,, across the core (Fig. 2A). A 180” pulse gap of 432 1s was used for generating the TZ-weighted profiles seen in Fig. 3. Again 12 profiles were obtained, taking 5 h (2000 averages) for each data set. Fitting the data gave Tzcu (0.36 f 0.03) for the carbonate core (CY)= 1040 + 140 I.LS and 360 f 50 ps (0.32 + 0.03) for the sandstone core. It is worth noting that whole core CPMG (7 = 432 ps) data gave T,, (a) = 1190 ps (0.3 1) for the carbonate core and 330 ps (0.30) for the sandstone core, in very good agreement with the spatially resolved data. Interestingly, no Tla gradient comparable to the T,, gradient is observed for the carbonate core. Figure 4 shows longitudinal, 120 x 120, non slice selected images of the two cores. These were acquired with the flash variant technique using a gradient echo time of 216 ps, and 2000 averages were taken. PORE SURFACE RELAXATION AND DISCUSSION
,owhich has dimensions of length/time. As p is the scaling term for relating psr to pore geometry, its accurate determination is critical for pore size distribution calculations, which, in turn, are essential for modelling fluid flow properties.15 p is usually (but not only) determined by comparing NMR relaxation to pore geometry derived by other means such as petrographic image analysis and mercury porosimetry.8-10 Our whole core relaxation data give conflicting interpretations. The values for T,, and T,, agree very well with those obtained for a monolayer of water in porous silica glasses,” where average T, I 100 ms (27 MHz) and average T2 5 1 ms (CPMG, 7 = 500 ps). Assuming that we have a monolayer of brine over the pore surface, then 1/T,,Z = P~,~/X, where X is the thickness of the monolayer, of order 3 A. This gives p, =O.l6A/msandp 2 = 4.62 A/ms for the sandstone core, and p1 = 0.053 A/ms, p2 = 2.31 A/ms for the carbonate core. These are to be compared with p1 = 0.058 ,&/ms and p2 = 1.09 A/ms for the silica glasses.” Thus, the whole core relaxation data seems to suggest that we may be observing psr, and therefore may be able to estimate p. The observation of bulk diffusion, however, suggests that the irreducible brine is not present as a monolayer over the pore surfaces. The equation 1/T,,2 = ~,,~/h may therefore not be appli-
Brownstein and Tarr14 showed that surfaces play a dominant role in the NMR relaxation of saturating fluids in porous media. The effectiveness of the surface in relaxing nuclei is characterised by the psr strength
cable, and we may not be in a position to unambiguously estimate p. It should be noted that the values of p,.? reported here are orders of magnitude smaller
(A)
@I
than those reported previously for fully saturated res-
Fig. 4. T,*-weighted, 120 x 120 pixel images of the two reservoir cores. The gradient echo time = 216 ps, and 2000 averages were taken in each case. (A) Carbonate and (B) Sandstone.
Solid state NMR in reservoir cores 0 J .J. ervoir cores8 where l/T, = p x S/V is valid, inviting the conclusion that the pores are in an intermediate state of saturation (S/V is the pore surface to volume
ratio). Estimates of psr obtained from the profile data (assuming X = 3 A) are p1 = 0.18 A/ms and p2 = 8.26 A/ms for the sandstone core, and p, = 0.075 A/ms and p2 = 2.87 A/ms for the carbonate core, in good agreement with the values obtained from the bulk data. Future developments will include improving the imaging procedures with extensions to two dimensions (slice select) and three dimensions, while studying psr as a function of saturation. Acknowledgments- We would like to thank British Gas Exploration & Production for funding this work. PJM and SPR thank SMIS and MAGNEX for support, and the SERC for a studentship (SPR). JJA and TT thank J.J. Howard (Phillips Petroleum) and W.E. Kenyon (Schlumberger) for helpful discussions.
REFERENCES 1. Lauterbur, P.C. Image formation by induced local interactions: Examples employing nuclear magnetic resonance. Nature 242:190-191; 1973. 2. Mansfield, P.; Grannell, P.K. NMR diffraction in solids? J. Phys. C6:L426-L432; 1973. 3. Jezzard, P.; Attard, J. J.; Carpenter, T.A.; Hall, L.D. Nuclear magnetic resonance imaging in the solid state. JPNMRS 23:1-41; 1991. 4. Rothwell, W.P.; Vinegar, H.J. Petrophysical applications of NMR imaging. Appl. Optics 24:3969-3972; 1985. 5. Attard, J.J.; Doran, S.J.; Herrod, N.J.; Carpenter, T.E.; Hall, L.D. Quantitative NMR spin-lattice-relaxation imaging of brine in sandstone reservoir cores. J. Magn. Reson. 96:514-525; 1992.
ATTARD
ET AL.
359
6. Gibbs, S.J.; Attard, J.J.; Hall, L.D. Spatially determined water diffusivities in brine saturated reservoir cores obtained by NMR imaging. A. I. Ch. E. 39:689-694; 1993. 7. Gleeson, J.W.; Woessner, D.E. Three-dimensional and flow-weighted NMR imaging of pore connectivity in a limestone. Magn. Reson. Imaging 9:879-884; 1991. 8. Howard, J.J.; Kenyon, W.E. Determination of pore size distribution in sedimentary rocks by proton nuclear magnetic resonance. Marine and Petroleum Geology 9: 139145; 1992. 9. Halperin, W.P.; D’Orazio, F.; Bhattacharja, S.; Tarczon, J.C. Magnetic resonance relaxation analysis of porous media. In: J. Klafter, J.M. Drake (Eds). Molecular Dynamics in Restricted Geometries. New York: Wiley; 1989: pp. 311-349. 10. D’Orazio, F.; Tarczon, J.C.; Halperin, W.P.; Eguchi, K.; Mizusaki, T. Application of nuclear magnetic resonance pore structure analysis to porous silica. J. Appl. Phys. 65:742-75 1; 1989. 11. Cottrell, S.P.; Halse, M.R.; Strange, J.H. NMR imaging of solids using large oscillating gradients. Meas. Sci. Technol. 1:624-629; 1990. 12. McDonald, P.J.; Perry, K.L.; Roberts, S.P. A repetitive pulse variant of broad line gradient echo magnetic resonance imaging. Meas. Sci. Technol. 4:896-898; 1993. 13. Kenyon, W.E. ; Day, P.I.; Straley, C.; Willemsen, J.F. Compact and consistent representation of rock NMR data for permeability estimation. SPE 15643. 61st Annual SPE Conference; 1986. 14. Brownstein, K.R.; Tarr, C.E. Importance of classical diffusion in NMR studies of water in biological cells. Phys. Rev. A 19:2446-2453; 1979. 15. Kenyon, W.E. Nuclear magnetic resonance as a petrophysical measurement. Nucl. Geophys. 6: 153-171; 1992.