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ABSTRACT: Magnetic resonance imaging and relaxation analysis are combined in a spatially resolved technique (relaxation tomography), which is able to quantify the parameters connected to the local structure in the internal regions of a porous material saturated by water, giving information on the pore space structure beyond the nominal instrumental resolution. Voxel-by-voxel longitudinal (T1) and transverse (T2) relaxation curves are acquired in order to obtain T1, T2 and S(0) maps, where S(0) is the extrapolation to zero time of the total equilibrium magnetization corrected for T2 decay. The proposed method permits evaluation of the porosity (ratio of pore space to total volume), at different length scales, from the sample to the voxel, not all achievable by traditional methods. More striking is its ability to describe how porosity is shared among different classes of surface-to-volume ratios of diffusion cells (the regions that the individual water molecules, starting at their particular positions, can experience by diffusion before relaxing). This is a consequence of the fact that relaxation times of water confined in a porous material can, under favorable circumstances, distinguish regions with the same local porosity but with different pore sizes and connections. So, parameters can be introduced, such as the microporosity fraction, defined as the fraction of the “micropore” volume with respect to the total pore volume, and several voxel average porosities, defined as the average porosities of the voxels characterized by particular classes of diffusion cells. Moreover, the imaging methods enable us to get all this information in a user-defined region of interest. The method has been applied to quantify changes in the structure of carbonate cores with wide distributions of pore sizes induced by repeated cycles of freezing and heating of the sample. With freezing, the microporosity fraction decreases significantly; the voxel average porosity of voxels with T1 shorter than for free water tend to decrease; and the distributions of porosity as functions of T1 show a trend, with much more signal with the T1 of free water, in accordance with the picture suggesting large vugs breaking, with fractures contributing to homogenizing the structure of the pore space and favoring coupling between neighboring pores. © 2001 American Institute of Physics.
Journal of Applied Physics 07/2001; 90(3):1155-1163. · 2.17 Impact Factor
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ABSTRACT: The basic method of UPEN (uniform penalty inversion of multiexponential decay data) is given in an earlier publication (Borgia et al., J. Magn. Reson. 132, 65-77 (1998)), which also discusses the effects of noise, constraints, and smoothing on the resolution or apparent resolution of features of a computed distribution of relaxation times. UPEN applies negative feedback to a regularization penalty, allowing stronger smoothing for a broad feature than for a sharp line. This avoids unnecessarily broadening the sharp line and/or breaking the wide peak or tail into several peaks that the relaxation data do not demand to be separate. The experimental and artificial data presented earlier were T(1) data, and all had fixed data spacings, uniform in log-time. However, for T(2) data, usually spaced uniformly in linear time, or for data spaced in any manner, we have found that the data spacing does not enter explicitly into the computation. The present work shows the extension of UPEN to T(2) data, including the averaging of data in windows and the use of the corresponding weighting factors in the computation. Measures are implemented to control portions of computed distributions extending beyond the data range. The input smoothing parameters in UPEN are normally fixed, rather than data dependent. A major problem arises, especially at high signal-to-noise ratios, when UPEN is applied to data sets with systematic errors due to instrumental nonidealities or adjustment problems. For instance, a relaxation curve for a wide line can be narrowed by an artificial downward bending of the relaxation curve. Diagnostic parameters are generated to help identify data problems, and the diagnostics are applied in several examples, with particular attention to the meaningful resolution of two closely spaced peaks in a distribution of relaxation times. Where feasible, processing with UPEN in nearly real time should help identify data problems while further instrument adjustments can still be made. The need for the nonnegative constraint is greatly reduced in UPEN, and preliminary processing without this constraint helps identify data sets for which application of the nonnegative constraint is too expensive in terms of error of fit for the data set to represent sums of decaying positive exponentials plus random noise.
Journal of Magnetic Resonance 01/2001; 147(2):273-85. · 2.14 Impact Factor
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ABSTRACT: NMR relaxation data and those from many other physical measurements are sums of exponentially decaying components, combined with some unavoidable measurement noise. When decay data are inverted in order to give quasi-continuous distributions of relaxation times, some smoothing of the distributions is normally implemented to avoid excess variation. When the same distribution has a sharp peak and a much broader peak or a "tail," as for many porous media saturated with liquids, an inversion program using a fixed smoothing coefficient may broaden the sharp peak and/or break the wide peak or tail into several separate peaks, even if the coefficient is adaptively chosen in accord with the noise level of the data. We deal with this problem by using variable smoothing, determined by iterative feedback in such a way that the smoothing penalty is roughly constant. This uniform-penalty (UP) smoothing can give sharp lines, not broadened more than is consistent with the noise, and in the same distribution it can show a tail decades long without breaking it up into several peaks. The noise level must be known approximately, but it can be determined more than adequately by a preliminary inversion. The same iterative procedure is used to implement constraints such as non-negative (NN) or monotonic-from-peak (MT). The significance of an additional resolved peak may be tested by finding the cost of using MT to force a unimodal solution. A bimodal constraint can be applied. Decay data representing sharp lines in contact with broad features can require substantial computing time and some controls to stabilize the iterative sequence. However, UP can be made to function smoothly for a very wide variety of decay curves, which can be processed without adjustment of parameters, including the dimensionless smoothing parameters. Extensive testing has been done with artificial data. Examples are shown for artificial data, biological tissues, ceramic technology, and sandstones. Expressions are given relating noise level to line width and for significance of increase or decrease in error of fit.
Journal of Magnetic Resonance 06/1998; 132(1):65-77. · 2.14 Impact Factor
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ABSTRACT: Fluid-flow properties of porous media, such as permeability k and irreducible water saturation Swi, can be estimated from water 1H nuclear magnetic resonance (NMR) relaxation data, but there are basic questions regarding data processing and interpretation. We found that Swi and k are better estimated if different forms of “average” relaxation time are used. NMR longitudinal relaxation data for a suite of 106 water-saturated clean sandstones were used. Sandstones represent a specialized class of porous media, where even for small porosity, substantially all pore space is connected. The sandstones exhibit distributions of relaxation times ranging over factors from at least 10 to more than 103. We tried several forms of “average” relaxation time T. One family of Ts is 〈Tp〉1/p, where lim p→0 gives the geometric mean. The best estimator we found for Swi uses a form of average relaxation time only, rather than relaxation time cutoff. The time used can be any of several forms of T, giving more emphasis to short times than the geometric mean does. On the contrary, the best T for estimating permeability without other information is precisely the geometric mean. The best estimates of permeability came from fits of ln (k/ϕ) using Ts with emphasis at slightly longer times. While Swi is better estimated by using all the data points (starting from our minimum 0.4 ms), k is better estimated by starting at a few ms, that is by ignoring a non-negligible fraction of the signal for some samples. These results can be obtained also by using computations that do not need to invert multiexponential relaxation data, and good results are obtained even with only a few data points. The results are compatible with the reasonable picture, where high surface-to-volume pores, giving signal components with short relaxation times but not contributing to the permeability, are important in determining the fraction of the wetting phase which remains trapped in the solid matrix after displacement with a nonwetting phase. © 1997 American Institute of Physics.
Journal of Applied Physics 10/1997; 82(9):4197-4204. · 2.17 Impact Factor
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ABSTRACT: The simplest model for the contribution of pore surfaces to nuclear magnetic resonance (NMR) relaxation of a pore fluid gives R, the average relaxation rate minus the bulk rate, equal to a constant ρ, the velocity at which nuclear magnetization flows out of the pore fluid at the surfaces, times the pore‐space surface‐to‐volume ratio S/V. Although ρ can vary widely, a great variety of porous media exhibit ρ values of the order of a few μm/s for longitudinal relaxation when S/V is measured by gas adsorption by the Brunauer, Emmett, and Teller (BET) method or high pressure mercury injection. For samples with wide distributions of relaxation rates it is of interest to find what functions of the relaxation data correlate best with S/V measurements and how different relaxation parameters relate to each other. Longitudinal relaxation data were taken for 77 sandstone samples of different origin, which had been cleaned and saturated with brine. After the NMR measurements the samples were dried and surface areas measured by BET. The samples have S/V from 1.5 to 150 (μm)<sup>-1</sup>, porosity from 3% to 28%, and permeability from less than 0.1 mD to more than 1 D. Longitudinal relaxation data were taken from 400 μs to 6 s and analyzed in many different ways, including stretched‐exponential fits and multiexponential fits up to five components. S/V and ln(S/V) were correlated with various relaxation rates derived from these computed parameters. In principle, the relaxation parameter to use with a ρ value is the average rate, which is initial slope divided by initial amplitude, namely, R(0), where R(t)=(d/dt)ln S(t) at t=0 and S(t) is the relaxing signal. One can extrapolate an n component fit to t=0 to get R n (0), but very good signal quality is required even to get small short components reliably for t well within the times covered by the data. Over half of the points have <-
1;’s within a factor of 2 of the minimum value 0.9 μm/s when the average rate of a five‐component fit to the data is used. There are numerous points with ρ up to 7 μm/s, but none of the high‐ρ points are for samples with high S/V. All samples with high S/V have wide distributions of relaxation rates, but not vice versa. The best simple correlation with ln(S/V) was ln(S/V)≊1.81 ln(R 33 )-5.73, where R 33 is the highest rate of a three‐component fit without regard to the corresponding amplitude, and where S/V is in (μm)<sup>-1</sup> and rate in s<sup>-1</sup>. This result was unexpected. This fit does not represent proportionality to a velocity ρ and does not correspond to any obvious physical model, but it can be of practical interest to estimate in a very simple and noninvasive manner S/V at the BET scale in sandstones. © 1996 American Institute of Physics.
Journal of Applied Physics 05/1996; · 2.17 Impact Factor
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ABSTRACT: For a large suite of consolidated sandstone samples low in shale content we have measured the permeability k, irreducible water saturation Swi, porosity phi, electrical-resistivity formation factor F, porosity by NMR, geometric-mean relaxation times T1g, and stretched-exponential relaxation times T1s. We find that T1g (or T1s) is the decisive parameter for the estimation of k or Swi of porous sandstones by other than direct measurements of these quantities. The additional use of phi or F brings appreciable, but not decisive, improvement. We show isovalue maps of the error factor delta, which show substantial regions of near-minimum values of delta and show basic compatibility of our estimators for permeability with different published estimators. The exponents of T1g (or T1s) in our power-law estimators and those of various published estimators for k are not very far from 2.0 if either or both of phi and F are also used in the estimators.
Magnetic Resonance Imaging 02/1996; 14(7-8):751-60. · 1.99 Impact Factor
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ABSTRACT: A method is presented to compute values of geometric mean time Tg that uses only a few data points equispaced in the logarithm of time (or equispaced in time and weighted by 1/t) and a few elementary operations for the computation. The method has been tested on a large number of synthetic relaxation data and on actual NMR relaxation measurements in porous samples, using as few as four points (including the two points needed to normalize the relaxation for decay from 1.0 to 0) on each relaxation curve. This computation of the geometric-mean rate very adequately matches the synthetic data and the results of multiexponential inversion of many (or only a few) data points from NMR measurements. When many computations are needed in short times, as for voxel-by-voxel computations in magnetic resonance imaging (MRI) or for depth-by-depth computation in nuclear magnetism logging (NML) of oilwells, a very quickly computed estimate of Tg should be useful.
Magnetic Resonance Imaging 02/1996; 14(7-8):895-7. · 1.99 Impact Factor
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ABSTRACT: The local determination of porosity is an extremely valuable target because of different applications in petrophysics. In fact, obtaining a reliable profile of porosity or saturations could considerably improve the evaluation of transport properties of porous media, especially if applied to multiphase flow test (i.e., for relative permeability characterisation). However, the best procedure to adopt for these kind of studies is currently under debate, involving different experimental choices both for acquisition and hardware solutions. The choice of a reliable procedure could be particularly important especially if heterogeneous samples (i.e., vugular or fractured carbonates) are approached. We have investigated selected carbonate cores, characterised by fractures and large vugs, using different instrumental solutions in order to assess usefulness of application of NMR imaging methods as a porosity measurement tool for heterogeneous samples. Local porosity data have been obtained and discussed relative to conventional measurements and petrographical aspects of rock samples.
Magnetic Resonance Imaging 02/1996; 14(7-8):919-21. · 1.99 Impact Factor
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ABSTRACT: NMR Relaxation and Imaging have been applied to study preparation processes of ceramic porous samples. Relaxation analysis gives a clear characterization of the materials, with high sensitivity. Differences in the method of preparation and steps as low as 25 degrees C in the firing temperatures are well detectable. Furthermore, the images permit distinguishing the different samples. The effects of the contrast in relaxation times dominate those due to the different porosities of the samples. Scanning Electron Microscopy confirms the interpretation that the changes in relaxation times are due to different pore space structures associated with the different firing temperatures. The higher the firing temperature, the larger are the pores and the higher is the amount of compact, sintered matrix, leading to higher relaxation times.
Magnetic Resonance Imaging 02/1996; 14(7-8):899-901. · 1.99 Impact Factor
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ABSTRACT: A number of features of T2 measurements for fluids in porous media have shown behavior contrary to that suggested by intuition developed in other areas. For porous media with relatively uniform pore spaces the following have been observed, in each case for certain ranges only of Xv (susceptibility difference times frequency), D (diffusion coefficient), a (a pore dimension), porespace shape and distribution, echo-time t for single echoes and half-echo-spacing tau for CPMG): (1) In S(t) for FID (free induction decay, S for signal) with constant slope after an initial period of increasing slope; (2) In Ss(t) for single (subscript s) echoes linear (instead of cubic) in t after an initial period; (3) for CPMG R(tau) = 1/T2(tau) - 1/T2(tau-->0) linear in tau over a substantial range; (4) slope of R(tau) independent of D and alpha for this range; (5) slope R(s) of In Ss(t) independent of D and a, and (6) R(s)(t) and R(tau) at long times linear (instead of quadratic) in Xv. These features appear to be compatible with the assumption of a truncated Cauchy-Lorentz distribution of the local magnetic fields due to susceptibility differences. The statistics of repeated sampling of local fields in different parts of the porespace during diffusion lead to a suppression, after a short time, of the effects of diffusion on the FID decay rate and the single-echo decay rate over significant ranges of the parameters. Data are presented to extend the range of parameters studied previously.
Magnetic Resonance Imaging 01/1996; 14(7-8):731-6. · 1.99 Impact Factor
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ABSTRACT: Irreducible fluid saturation in porous media is the fraction of the wetting phase which remains trapped in the solid matrix after displacement with a nonwetting phase. Methods have been proposed to estimate irreducible saturation in fully water‐saturated porous samples by means of proton nuclear magnetic resonance relaxation times, but the results are quite varied. Some features are discussed of the trapped fluid and it is shown that the fraction of nonmobile water can be well estimated for a varied suite of clean sandstones, using only measurements on the fully saturated samples. This is done by combining relaxation measurements with those of electrical resistivity factor F. One of several simple correlations is S wi ∝√F/T 1s , where T 1s is the stretched‐exponential relaxation time.
Journal of Applied Physics 07/1994; · 2.17 Impact Factor
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ABSTRACT: The results are reported of a systemic T1 and T2 investigation of natural (sandstones) and artificial (microporous porcelain) porous media, after each step of a water desaturation process by centrifugation in air. The analysis of the relaxation curves permitted distinguishing well the different behaviour of the natural samples as compared to the artificial ones, which can be explained by the different pore structures. In both kinds of samples the evolution of the relaxation time distributions yielded a clear picture of the changes of the water distribution in the pore framework following the displacement process, until irreducible water saturation was attained. The results are compatible with the assumption of a fixed amount of surface area contributing to the relaxation of decreasing amounts of fluid as SW is reduced.
Magnetic Resonance Imaging 02/1994; 12(2):191-5. · 1.99 Impact Factor
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G C Borgia
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ABSTRACT: In the late 1980s, there were definite signs that the time was ripe for a direct exchange of experiences and ideas of groups who, independently and often by very different routes, were working on NMR for heterogeneous systems. At a time when NMR techniques were being applied on an increasingly wide scale in various fields from biomedical to oil, the idea of a meeting based on an interdisciplinary approach was suggested by historic circumstances. The explosive growth of magnetic resonance (MR) imaging and relaxation for fluids in porous media, and the interdisciplinary approach adopted, determined the success of the First International Meeting on NMR Applications to Porous Media held in Bologna, from 14th to 16th November 1990. Many facets characterized and still characterize the work on MR for fluids in porous media. The distance normally separating purely scientific research from its possible technological fall-out is reduced. The wide range of applications induce specialists with different backgrounds to compare their experiences in a constructive way and often to work together. This does not mean reducing the research work of biologists, physicists, chemists, physicians, and reservoir engineers to the same criteria and methods of analysis; rather it means looking for unifying ideas, together with the critical transfer of techniques. Also, NMR offers an example of the possibility of a fruitful cooperation between industry and university.(ABSTRACT TRUNCATED AT 250 WORDS)
Magnetic Resonance Imaging 02/1994; 12(2):163-5. · 1.99 Impact Factor
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ABSTRACT: So far, one of the major obstacles to the development of special purpose MRI imaging apparatus has been the lack of a magnetic technology that could cater to the need for a light, compact and efficient magnet, capable of providing the required field uniformity at a reasonable cost. Today, recent advances in magnet design permit attaining, with the use solely of ferrite, low-cost, small-scale scanners, which can open up new areas of application of MRI, in both medical and industrial fields. A novel apparatus (ARTOSCAN) is described and some examples of applications in different fields are shown. The apparatus has been designed specifically for the imaging of extremities, but possible applications on the industrial side are numerous and not yet all identified. Such a device could be used, for example, in the agricultural, food, and oil industries, where some of the needs for nondestructive quality-control devices could be fulfilled. Some tests have been performed that demonstrate the potential of the apparatus in the study of rock properties, of the drying process of pasta and wood, and to display flaws that could be present in ceramic materials before firing.
Magnetic Resonance Imaging 02/1994; 12(2):329-31. · 1.99 Impact Factor
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ABSTRACT: The inversion of data to be represented by sums or continuous distributions of exponentials is done by different algorithms and compared. The published CONTIN program presents a chosen solution with an appropriate amount of detail. An in-house program EXDISTR allows operative choice of various constraints in order to show the consequences in quality of fit of allowing various features such as extra maxima or minima. Another in-house program based on the system theory approach, IDENT, treats the data as the output samples of a linear, time-invariant, autonomous dynamic system.
Magnetic Resonance Imaging 02/1994; 12(2):209-12. · 1.99 Impact Factor
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ABSTRACT: NMR Spectroscopy and Imaging (MRI) have been used in determining the presence and the distribution of residual water inside a dolomite core saturated with oil. 1H relaxation analysis revealed the presence of different "classes" of water within the core as a function of drying temperature. The results appear to be consistent with the peculiar porosity distribution of the rock, as shown by MRI and X-ray CT analysis. The latter technique provided details of the rock matrix complementary to the information acquired by the NMR method. This kind of approach, based on the application of different techniques, was found to be very useful for an accurate evaluation of petrophysical properties of rocks, a task of relevant interest for an oil company.
Magnetic Resonance Imaging 02/1994; 12(2):221-4. · 1.99 Impact Factor
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ABSTRACT: Experimental data are reported that show the analogy of longitudinal and transverse proton relaxation in heterogeneous systems
as different as biological tissues and water-saturated rocks. Published data on the τ-dependence of the transverse-relaxation
rate for biological tissues with magnetite grains, used as a contrast agent in MRI, are discussed in the light of our recent
results on water-saturated porous media, and give for the liver another case of a behaviour parallel to that in rocks. There
are enough similarities between NMR relaxation in tissues and in other porous media that, for work in either area, attention
to the other is likely to be fruitful.
Il Nuovo Cimento D 01/1993; 15(7):1025-1029.
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ABSTRACT: NMR relaxation of water1H confined in restricted geometries, whatever is the nature of the system (porous media saturated by water as well as biological
tissues), exhibits common characteristics. Artificial microporous media saturated by water have been chosen as model systems
to study the longitudinal and transverse relaxation of1H magnetization of water molecules diffusing in restricted geometries. These systems are very stable, easy to prepare, with
well-characterized pore size distribution and connections, and with highly homogeneous surface properties. The response was
compared with that from more complex natural porous media. Scanning Electron Microscopy techniques demonstrated spatial characteristics
and surface properties of the samples. The information content of longitudinal relaxation curves associated with spatial structure
and due to restricted diffusion is shown in these samples. The effect on transverse relaxation of self-diffusion in the presence
of spatially varying magnetic fields due to susceptibility differences is shown. A simple linear relationship has been found
in all samples between the transverse relaxation rate and the interpulse delay in CPMG experiments, in spite of the variety
of pore shapes and sizes. In general, one can say that relaxation curves beardiffusion-weighted information on the pore space framework. The role of the investigated relaxation mechanisms is important also in the response
of biological tissues, including in the presence of MR Imaging contrast agents inducing microscopic magnetic-field gradients.
Il Nuovo Cimento D 01/1992; 14(7):745-759.
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ABSTRACT: The 1H spin-lattice relaxation curves of water in samples of natural porous media can be thought of as "fingerprints" of the porous samples. Also the whole of traditional petrophysical properties (permeability, irreducible water saturation, etc.) can be thought of as "fingerprints" of the porous samples. The characteristics of the pore space determine on one hand the relaxation curve shape, and on the other the petrophysical properties. The understanding of this correspondence can contribute to a better definition of the concept of the architecture of a porous medium. At this purpose we have obtained 1H spin-lattice relaxation curves from a collection of standard sandstone cores of known petrophysical properties and characterized by the same surface properties. The results corroborate the idea that the structure of relaxation curves contains information on the distance scale and on the architecture of the pore space, even if it is difficult to extract it without ambiguities. Different methods of curve fitting were performed and compared with the aim of getting the maximum information from the relaxation curves. Several aspects of this kind of investigation indicate the analogies between 1H response of water confined in porous media and in biological tissues.
Magnetic Resonance Imaging 02/1990; 8(4):435-47. · 1.99 Impact Factor
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ABSTRACT: One of the most critical structural parameters in elastomeric materials is the density of cross-linking between the polymeric chains. This chemical feature greatly affects chain motions and is determinant in controlling mechanical properties of the final product. NMR techniques are widely and efficiently applied to investigation of such materials. In this study we have measured both transverse and longitudinal 1H relaxation times of a series of polybutadiene rubber samples with increasing crosslink density induced by chemical treatment. This approach allowed the observation of T(1) and T(2) decrease with the increase of crosslink density in the samples examined. The data obtained have been analyzed and compared to theoretical models.
Magnetic Resonance Imaging 19(3-4):405-9. · 1.99 Impact Factor
