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A study of formation damage of drilling mud invasion by NMR
Abstracts / Magnetic Resonance Imaging 19 (2001) 569 –589
A variable temperature-2H-NMR study of benzene-D6 confined in mesoporous silica SBA-15 Buntkowsky Ga, Gedat Ea, Albrecht Ja, Shenderovich Ia, Schreiber Ab, Findenegg Gb, Limbach HHa. a Freie Universita¨t Berlin, Institut fu¨r Chemie, Takustraße 3, 14195 Berlin, Germany bTechnische Universita¨t Berlin, Iwan-N.-StranskiInstitut fu¨r Physikalische und Theoretische Chemie, Straße des 17. Juni 112, 10623 Berlin, Germany. Benzene-d6 confined in the cylindrical pores of the mesoporous silica SBA-15 and as reference bulk benzene-d6 have been studied by 2H solid state NMR spectroscopy in the temperature range between 30K and 300K. The spectra of the benzene in the silica show the coexistence of two different phases, which can be attributed to an inner core phase and an inner surface phase. The relative amounts of the two phases are independent of the temperature. The bulk benzene-d6 exhibits three different rotational states, namely: liquid (isotropic motion), solid I (anisotropic rotation around the six-fold axis), and solid II (no rotation). The same three states with well defined, however different, phase transition temperatures are found for the benzene in the core phase of the pores. For the inner surface phase, however, no well defined phase transition temperatures exist and in general a coexistence of two different phases over a broad temperature range is observed, i.e. a more glassy behavior. From the pore diameter of 7.6 nm of the silica SBA-15 and the relative amount of the surface phase (60%) of the benzene the average range of the solid-liquid interaction is estimated as 1.4 nm, which corresponds to approximately 3 molecular layers of benzene. PII: S0730-725X(01)00313-7
Trabecular bone microstructure by means of multiples spin echo Capuani Sa, Alessandri F.M.a, Maraviglia Ba, Bifone Ab. a INFM UdR Roma 1 and Dpt. di Fisica Universita` “La Sapienza”, 00185 Roma, Italy. bCRC Clinical Magnetic Resonance Research Group, The Institute of Cancer Research, Sutton, Surrey SM2 5PT, UK. The most common NMR methods of assaying trabecular bone quality is based on the measurement of bone marrow T2 and T*2 relaxation times. During normal aging and disease processes such as osteoporosis, trabeculation is reduced with a concomitant loss in bone strength. However the sensitivity of these MR imaging techniques is not sufficient to detect small changes in trabecular density that are typical of the first stage of osteoporosis disease. Recently, a new contrast mechanism by means Multiple Spin Echo (MSE) sequence has been successfully applied [1–3] in human brain. The MSE sequence exploits the residual dipolar coupling between distant spins to give rise to the refocusing of a train of echoes. The second echo amplitude depends on T2 and on apparent diffusion coefficient more strongly than the first echo. Furthermore the MSE signals come primarily from spins separated by a distance d ⫽ /( ␥ G )-half a cycle of the magnetisation helix generated by gradient G4 and this distance can be much smaller than a conventional voxel size. We have used the MSE sequence to analyse calf bone samples characterised by small differences in trabecular density. The ratio between the second and the first echo amplitudes (A2/A1) shows, at delay time varying and at fixed field gradient G, some minima. We have observed that these minima appear when the size of the trabecular porous system is equal to the characteristic distance d. By using the imaging version of MSE method realised with the ⫽ * corresponding to the (A2/A1) minima, we can resolve different porous sizes in relation to the *, independently of image resolutions. These preliminary ex vivo results show that MSE is more sensitive than conventional NMR techniques to bone microstructure, and might provide a powerful means for improved diagnosis of osteoporosis at an early stage.
571
References [1] [2] [3] [4]
Bifone A, Payne GS, Leach MO. J Magn Reson 1998;135:30. Zhong J, Chen Z, Kwok E. Magn Reson Med 2000;43:335. Rizi RR, Ahn S, et al. Magn Reson Med 2000;43:627. Richter W, Lee S, Warren WS, He Q. Science 1995;267:654. PII: S0730-725X(01)00314-9
Multiple spin echoes technique as a tool for the evaluation of stone pore size Cauani S, Alesiani M, Alessandri FM, Maraviglia B. INFM UdR Roma 1 and Dpt. di Fisica Universita` “La Sapienza”, 00185 Roma, Italy. The most common NMR methods for the evaluation of stone pore size are based on the measurements of relaxation times and diffusion coefficient of water inside the porous system. Recently, it has been recognised that intermolecular residual dipolar couplings provide a novel contrast mechanism to study heterogeneity in tissues [1,2]. When the sample magnetisation is spatially modulated, typically by applying field gradients G that generate a magnetisation helix, dipolar couplings between distant nuclear spins affect the NMR signal. Most importantly, the intensity of the NMR signal depends on the sample heterogeneity over a distance d ⫽ /( ␥ G )-half a cycle of the magnetisation helix [1]. Multiple Spin Echoes (MSE) technique exploits this residual dipolar coupling between distant spins to give rise to the refocusing of a train of echoes. The second echo amplitude (A2) depends on T2 and on diffusion coefficient more strongly than the first echo (A1). We have observed, in trabecular bone samples, that it is possible to know the pore size of trabecular microstructure from the ratio between the second and the first echo amplitudes (A2/A1) obtained at a delay time varying. Where the ratio A2/A1 reaches a minimum, for *, we have verified that the characteristic distance d, calculated in *, becomes equal to the trabecular porous size. In this communication we present the first application of MSE technique for the pore size evaluation of stones. We have analysed travertine and Carrara marble samples characterised by a sufficiently long T2 to have a large domain for the ratio A2/A1 analysis. By using MSE method we have evaluated the pore size of our samples, which match with the results obtained with a mercury porosimeter. These preliminary results show that MSE can provide a new means for porosity investigation of stone and rocks.
References [1] Bifone A, Payne GS, Leach MO. J Magn Reson 1998;135:30. [2] Richter W, Lee S, Warren WS, He Q. Science 1995;267:654. PII: S0730-725X(01)00315-0
A study of formation damage of drilling mud invasion by NMR Quan Chena,b, Chaohui Yea, Yong Yue.a aLab. of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box 71010, Wuhan 430071, China. bInstitute of porous Flow, CNPC & Chinese Academy of Sciences, P.O. Box 44, Langfang, Hebei 065007, China. The invasion of drilling mud into a near well bore formation can reduce hydrocarbon production potential of a reservoir substantially. The research of formation damage of drilling mud invasion is very important for petroleum exploitation. Using nuclear magnetic resonance 2D and 3D imaging, and relaxation time spectrum measurement techniques, this paper researched the drilling (D2O based) mud invasion into the sandstone of formation during drilling of wells for petroleum exploitation. Invasion depth and velocity of drilling
572
Abstracts / Magnetic Resonance Imaging 19 (2001) 569 –589
mud, voxel porosity and pore size distribution of formation before and after drilling mud invasion were obtained by nuclear magnetic resonance. These parameters can not be obtained by traditional methods. The results indicated that the porosity, permeability, voxel porosity and pore size distribution decreased after invasion of drilling mud and recovered partly after backflooding with oil. The recovery ratio of porosity and permeability decreased with the decrease of the original formation permeability. As flow resistance increased and mud cake was gradually produced, the invasion velocity decreased with increasing invasion time. So the earlier a mud cake is produced the less drilling mud invades the formation. Compared with the horizontal permeability (in direction of the formation bedding), the vertical permeability was decreased to a much higher degree. This obviously reduced the degree of formation damage. Therefore the damage of formation occurred mainly in horizontal direction, parallel to the formation. PII: S0730-725X(01)00316-2
Investigation of perforation damage characteristics of Berea sandstone by MRI Quan Chena,b, Chaohui Yea, Yong Yuea. aLab. of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box 71010, Wuhan 430071, China. bInstitute of porous Flow, CNPC & Chinese Academy of Sciences, P.O. Box 44, Langfang, Hebei 065007, China. Shaped charge jet perforation is the most widely used method of establishing flow pathways from an oil or gas formation to the inside of a wellbore in oil and gas producing well. Perforation causes a reduction in permeability in a region around the perforation tunnel known as the “perforation damaged zone”. The amount of permeability reduction and its extent has an important impact on the productivity of the well. A combination of novel petro-physical methods has been used for an integrated investigation of perforation damage characteristics of Berea sandstone with diameter of 17.8 cm. After perforating, the distribution of porosity and permeability was measured by magnetic resonance imaging (MRI), the pore size distribution was detected by nuclear magnetic resonance (NMR) relaxation time distribution and mercury porosimetry, the pore microstructure and mine composition were examined by environment scanning electron microscopy (ESEM), thin sections, and energy spectrum. To the knowledge of authors, this paper was the first time to investigate perforation damage by MRI and NMR. Analysis of perforated Berea sandstone samples indicated that an average porosity reduction of 18% and an average permeability reduction of 76% occurred within a damage zone of an average thickness of 1.25 cm. The mechanisms of perforation damage are that large pores are compacted or destroyed as a result microfracturing on quartz grains or are filled by broken pieces of grains. This resulted in reduction of porosity, permeability and diameter of large pores within damage zone. PII: S0730-725X(01)00317-4
Studies of the dissolution of structured surfactant using spatially localised double quantum filter and J-cyclic-cross polarisation edited NMR Ciampi Ea, Goerke Ua, McDonald PJa, Chambers J.b, Newling Bb. a School of Physics and Chemistry, Department of Physics, University of Surrey, Guildford, GU2 7XH, UK. bUnilever Research Port Sunlight Laboratory, Quarry Road East, Bebington, Wirral, CH63 3JW, UK. Magnetic resonance microscopy techniques are well developed for the study of a wide range of problems in materials science. Advantages of the method include its non invasive nature and the availability of contrast based on spin relaxation time differences. However, often relaxation time based contrast alone is insufficient, or the number of components to be differentiated is too great to be practical. An example of such a system is the dissolution of structured surfactant, where liquid crystalline phases,
having a transverse spin relaxation time intermediate between those of bulk water and crystalline surfactant, form at the water/surfactant interface. It is the objective of this paper to explore the efficacy of spatially localised double quantum filter edited NMR [1] and J-cyclic-cross polarisation edited PFG diffusometry [2] to determine the spatial and temporal distribution of the different components in a developing model surfactant solution. In the former case, the anisotropic motion of deuterated water in the liquid crystalline phases offers a very selective visualisation of the surfactant/water interface. The quadrupolar splittings offer a quantitative measure of surfactant concentration independent of relaxation time. By comparison with completely dissolved samples at different water concentrations, the composition of the liquid crystalline phases is followed with time at different sample locations. In the latter case, the chemical selectivity of the J-cyclic-cross polarisation technique is used to specifically detect the hydrogen resonance of CH2 units in mobile surfactant molecules. This approach is used to explore the micellar region and is compared to standard 1 H PFG diffusometry.
References [1] Tsoref L, Shinar H, Seo Y, Eliav U, Navon G. Magn Res Med 1998;40:720. [2] McDonald PJ, Ciampi E, Keddie JL, Heidenreich M, Kimmich R. Phys Rev E 1999;59:874. PII: S0730-725X(01)00318-6
Structural characterisation of porous media using experimental and simulated Q-space imaging Colgan G, Johns ML, Sederman AJ, Gladden LF. Department of Chemical Engineering, University of Cambridge, Cambridge CB2 3RA, UK. The echo attenuation function E(q) has been used to probe pore scale geometry in a packed bed of spheres. It has previously been shown that diffraction peaks in E(q) yield important structural information characterising a porous medium in a manner analogous to X-Ray diffraction [1]. In this paper, we report the development of a numerical technique which predicts the experimentally-determined E(q) data for a given pore structure. A lattice-Boltzmann simulation of water flow through a sphere pack was performed to generate a 3-D velocity field; the 3-D simulation lattice was derived from an MRI visualisation of a water-saturated sphere pack. The displacement propagator, P(x,y,z,⌬), was then calculated from this predicted flow field. E(q) was then derived from the calculated P(z,⌬) by summing the incremental phase shifts corresponding to the displacements in P(z,⌬) to obtain an overall phase vector with real and imaginary points. The magnitude of this vector is the amplitude of E(q). E(q) is then compared with the experimentally-determined function recorded under the same flow conditions. Results will be presented for Pulsed Field Gradient NMR measurements of E(q) for water flowing in a 50 m sphere pack over a range of observation times (⌬). As expected, E(q) clearly shows a diffraction peak in reciprocal space at approximately the inverse of the sphere diameter [2]. This diffraction peak was strongest when the average displacement was between one and two times greater than the sphere diameter. The diffraction peaks observed in the derived E(q) appear at the same point in q-space as those acquired experimentally. These results illustrate that a simple phase vector method can be used to yield an E(q) which is in good agreement with that obtained from an MR experiment. This method is now being used to explore the extent to which the structural characteristics of a porous solid can be determined from an experimentally-determined E(q).
A variable temperature-2H-NMR study of benzene-D6 confined in mesoporous silica SBA-15 Buntkowsky Ga, Gedat Ea, Albrecht Ja, Shenderovich Ia, Schreiber Ab, Findenegg Gb, Limbach HHa. a Freie Universita¨t Berlin, Institut fu¨r Chemie, Takustraße 3, 14195 Berlin, Germany bTechnische Universita¨t Berlin, Iwan-N.-StranskiInstitut fu¨r Physikalische und Theoretische Chemie, Straße des 17. Juni 112, 10623 Berlin, Germany. Benzene-d6 confined in the cylindrical pores of the mesoporous silica SBA-15 and as reference bulk benzene-d6 have been studied by 2H solid state NMR spectroscopy in the temperature range between 30K and 300K. The spectra of the benzene in the silica show the coexistence of two different phases, which can be attributed to an inner core phase and an inner surface phase. The relative amounts of the two phases are independent of the temperature. The bulk benzene-d6 exhibits three different rotational states, namely: liquid (isotropic motion), solid I (anisotropic rotation around the six-fold axis), and solid II (no rotation). The same three states with well defined, however different, phase transition temperatures are found for the benzene in the core phase of the pores. For the inner surface phase, however, no well defined phase transition temperatures exist and in general a coexistence of two different phases over a broad temperature range is observed, i.e. a more glassy behavior. From the pore diameter of 7.6 nm of the silica SBA-15 and the relative amount of the surface phase (60%) of the benzene the average range of the solid-liquid interaction is estimated as 1.4 nm, which corresponds to approximately 3 molecular layers of benzene. PII: S0730-725X(01)00313-7
Trabecular bone microstructure by means of multiples spin echo Capuani Sa, Alessandri F.M.a, Maraviglia Ba, Bifone Ab. a INFM UdR Roma 1 and Dpt. di Fisica Universita` “La Sapienza”, 00185 Roma, Italy. bCRC Clinical Magnetic Resonance Research Group, The Institute of Cancer Research, Sutton, Surrey SM2 5PT, UK. The most common NMR methods of assaying trabecular bone quality is based on the measurement of bone marrow T2 and T*2 relaxation times. During normal aging and disease processes such as osteoporosis, trabeculation is reduced with a concomitant loss in bone strength. However the sensitivity of these MR imaging techniques is not sufficient to detect small changes in trabecular density that are typical of the first stage of osteoporosis disease. Recently, a new contrast mechanism by means Multiple Spin Echo (MSE) sequence has been successfully applied [1–3] in human brain. The MSE sequence exploits the residual dipolar coupling between distant spins to give rise to the refocusing of a train of echoes. The second echo amplitude depends on T2 and on apparent diffusion coefficient more strongly than the first echo. Furthermore the MSE signals come primarily from spins separated by a distance d ⫽ /( ␥ G )-half a cycle of the magnetisation helix generated by gradient G4 and this distance can be much smaller than a conventional voxel size. We have used the MSE sequence to analyse calf bone samples characterised by small differences in trabecular density. The ratio between the second and the first echo amplitudes (A2/A1) shows, at delay time varying and at fixed field gradient G, some minima. We have observed that these minima appear when the size of the trabecular porous system is equal to the characteristic distance d. By using the imaging version of MSE method realised with the ⫽ * corresponding to the (A2/A1) minima, we can resolve different porous sizes in relation to the *, independently of image resolutions. These preliminary ex vivo results show that MSE is more sensitive than conventional NMR techniques to bone microstructure, and might provide a powerful means for improved diagnosis of osteoporosis at an early stage.
571
References [1] [2] [3] [4]
Bifone A, Payne GS, Leach MO. J Magn Reson 1998;135:30. Zhong J, Chen Z, Kwok E. Magn Reson Med 2000;43:335. Rizi RR, Ahn S, et al. Magn Reson Med 2000;43:627. Richter W, Lee S, Warren WS, He Q. Science 1995;267:654. PII: S0730-725X(01)00314-9
Multiple spin echoes technique as a tool for the evaluation of stone pore size Cauani S, Alesiani M, Alessandri FM, Maraviglia B. INFM UdR Roma 1 and Dpt. di Fisica Universita` “La Sapienza”, 00185 Roma, Italy. The most common NMR methods for the evaluation of stone pore size are based on the measurements of relaxation times and diffusion coefficient of water inside the porous system. Recently, it has been recognised that intermolecular residual dipolar couplings provide a novel contrast mechanism to study heterogeneity in tissues [1,2]. When the sample magnetisation is spatially modulated, typically by applying field gradients G that generate a magnetisation helix, dipolar couplings between distant nuclear spins affect the NMR signal. Most importantly, the intensity of the NMR signal depends on the sample heterogeneity over a distance d ⫽ /( ␥ G )-half a cycle of the magnetisation helix [1]. Multiple Spin Echoes (MSE) technique exploits this residual dipolar coupling between distant spins to give rise to the refocusing of a train of echoes. The second echo amplitude (A2) depends on T2 and on diffusion coefficient more strongly than the first echo (A1). We have observed, in trabecular bone samples, that it is possible to know the pore size of trabecular microstructure from the ratio between the second and the first echo amplitudes (A2/A1) obtained at a delay time varying. Where the ratio A2/A1 reaches a minimum, for *, we have verified that the characteristic distance d, calculated in *, becomes equal to the trabecular porous size. In this communication we present the first application of MSE technique for the pore size evaluation of stones. We have analysed travertine and Carrara marble samples characterised by a sufficiently long T2 to have a large domain for the ratio A2/A1 analysis. By using MSE method we have evaluated the pore size of our samples, which match with the results obtained with a mercury porosimeter. These preliminary results show that MSE can provide a new means for porosity investigation of stone and rocks.
References [1] Bifone A, Payne GS, Leach MO. J Magn Reson 1998;135:30. [2] Richter W, Lee S, Warren WS, He Q. Science 1995;267:654. PII: S0730-725X(01)00315-0
A study of formation damage of drilling mud invasion by NMR Quan Chena,b, Chaohui Yea, Yong Yue.a aLab. of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box 71010, Wuhan 430071, China. bInstitute of porous Flow, CNPC & Chinese Academy of Sciences, P.O. Box 44, Langfang, Hebei 065007, China. The invasion of drilling mud into a near well bore formation can reduce hydrocarbon production potential of a reservoir substantially. The research of formation damage of drilling mud invasion is very important for petroleum exploitation. Using nuclear magnetic resonance 2D and 3D imaging, and relaxation time spectrum measurement techniques, this paper researched the drilling (D2O based) mud invasion into the sandstone of formation during drilling of wells for petroleum exploitation. Invasion depth and velocity of drilling
572
Abstracts / Magnetic Resonance Imaging 19 (2001) 569 –589
mud, voxel porosity and pore size distribution of formation before and after drilling mud invasion were obtained by nuclear magnetic resonance. These parameters can not be obtained by traditional methods. The results indicated that the porosity, permeability, voxel porosity and pore size distribution decreased after invasion of drilling mud and recovered partly after backflooding with oil. The recovery ratio of porosity and permeability decreased with the decrease of the original formation permeability. As flow resistance increased and mud cake was gradually produced, the invasion velocity decreased with increasing invasion time. So the earlier a mud cake is produced the less drilling mud invades the formation. Compared with the horizontal permeability (in direction of the formation bedding), the vertical permeability was decreased to a much higher degree. This obviously reduced the degree of formation damage. Therefore the damage of formation occurred mainly in horizontal direction, parallel to the formation. PII: S0730-725X(01)00316-2
Investigation of perforation damage characteristics of Berea sandstone by MRI Quan Chena,b, Chaohui Yea, Yong Yuea. aLab. of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box 71010, Wuhan 430071, China. bInstitute of porous Flow, CNPC & Chinese Academy of Sciences, P.O. Box 44, Langfang, Hebei 065007, China. Shaped charge jet perforation is the most widely used method of establishing flow pathways from an oil or gas formation to the inside of a wellbore in oil and gas producing well. Perforation causes a reduction in permeability in a region around the perforation tunnel known as the “perforation damaged zone”. The amount of permeability reduction and its extent has an important impact on the productivity of the well. A combination of novel petro-physical methods has been used for an integrated investigation of perforation damage characteristics of Berea sandstone with diameter of 17.8 cm. After perforating, the distribution of porosity and permeability was measured by magnetic resonance imaging (MRI), the pore size distribution was detected by nuclear magnetic resonance (NMR) relaxation time distribution and mercury porosimetry, the pore microstructure and mine composition were examined by environment scanning electron microscopy (ESEM), thin sections, and energy spectrum. To the knowledge of authors, this paper was the first time to investigate perforation damage by MRI and NMR. Analysis of perforated Berea sandstone samples indicated that an average porosity reduction of 18% and an average permeability reduction of 76% occurred within a damage zone of an average thickness of 1.25 cm. The mechanisms of perforation damage are that large pores are compacted or destroyed as a result microfracturing on quartz grains or are filled by broken pieces of grains. This resulted in reduction of porosity, permeability and diameter of large pores within damage zone. PII: S0730-725X(01)00317-4
Studies of the dissolution of structured surfactant using spatially localised double quantum filter and J-cyclic-cross polarisation edited NMR Ciampi Ea, Goerke Ua, McDonald PJa, Chambers J.b, Newling Bb. a School of Physics and Chemistry, Department of Physics, University of Surrey, Guildford, GU2 7XH, UK. bUnilever Research Port Sunlight Laboratory, Quarry Road East, Bebington, Wirral, CH63 3JW, UK. Magnetic resonance microscopy techniques are well developed for the study of a wide range of problems in materials science. Advantages of the method include its non invasive nature and the availability of contrast based on spin relaxation time differences. However, often relaxation time based contrast alone is insufficient, or the number of components to be differentiated is too great to be practical. An example of such a system is the dissolution of structured surfactant, where liquid crystalline phases,
having a transverse spin relaxation time intermediate between those of bulk water and crystalline surfactant, form at the water/surfactant interface. It is the objective of this paper to explore the efficacy of spatially localised double quantum filter edited NMR [1] and J-cyclic-cross polarisation edited PFG diffusometry [2] to determine the spatial and temporal distribution of the different components in a developing model surfactant solution. In the former case, the anisotropic motion of deuterated water in the liquid crystalline phases offers a very selective visualisation of the surfactant/water interface. The quadrupolar splittings offer a quantitative measure of surfactant concentration independent of relaxation time. By comparison with completely dissolved samples at different water concentrations, the composition of the liquid crystalline phases is followed with time at different sample locations. In the latter case, the chemical selectivity of the J-cyclic-cross polarisation technique is used to specifically detect the hydrogen resonance of CH2 units in mobile surfactant molecules. This approach is used to explore the micellar region and is compared to standard 1 H PFG diffusometry.
References [1] Tsoref L, Shinar H, Seo Y, Eliav U, Navon G. Magn Res Med 1998;40:720. [2] McDonald PJ, Ciampi E, Keddie JL, Heidenreich M, Kimmich R. Phys Rev E 1999;59:874. PII: S0730-725X(01)00318-6
Structural characterisation of porous media using experimental and simulated Q-space imaging Colgan G, Johns ML, Sederman AJ, Gladden LF. Department of Chemical Engineering, University of Cambridge, Cambridge CB2 3RA, UK. The echo attenuation function E(q) has been used to probe pore scale geometry in a packed bed of spheres. It has previously been shown that diffraction peaks in E(q) yield important structural information characterising a porous medium in a manner analogous to X-Ray diffraction [1]. In this paper, we report the development of a numerical technique which predicts the experimentally-determined E(q) data for a given pore structure. A lattice-Boltzmann simulation of water flow through a sphere pack was performed to generate a 3-D velocity field; the 3-D simulation lattice was derived from an MRI visualisation of a water-saturated sphere pack. The displacement propagator, P(x,y,z,⌬), was then calculated from this predicted flow field. E(q) was then derived from the calculated P(z,⌬) by summing the incremental phase shifts corresponding to the displacements in P(z,⌬) to obtain an overall phase vector with real and imaginary points. The magnitude of this vector is the amplitude of E(q). E(q) is then compared with the experimentally-determined function recorded under the same flow conditions. Results will be presented for Pulsed Field Gradient NMR measurements of E(q) for water flowing in a 50 m sphere pack over a range of observation times (⌬). As expected, E(q) clearly shows a diffraction peak in reciprocal space at approximately the inverse of the sphere diameter [2]. This diffraction peak was strongest when the average displacement was between one and two times greater than the sphere diameter. The diffraction peaks observed in the derived E(q) appear at the same point in q-space as those acquired experimentally. These results illustrate that a simple phase vector method can be used to yield an E(q) which is in good agreement with that obtained from an MR experiment. This method is now being used to explore the extent to which the structural characteristics of a porous solid can be determined from an experimentally-determined E(q).