Understanding generalized inversions of nuclear magnetic resonance transverse relaxation time in porous media.

The nuclear magnetic resonance transverse relaxation time T2, measured using the Carr-Purcell-Meiboom-Gill (CPMG) experiment, is a powerful method for obtaining unique information on liquids confined in porous media. Furthermore, T2 provides structural information on the porous material itself and has many applications in petrophysics, biophysics, and chemical engineering. Robust interpretation of T2 distributions demands appropriate processing of the measured data since T2 is influenced by diffusion through magnetic field inhomogeneities occurring at the pore scale, caused by the liquid/solid susceptibility contrast. Previously, we introduced a generic model for the diffusion exponent of the form -ante(k) (where n is the number and te the temporal separation of spin echoes, and a is a composite diffusion parameter) in order to distinguish the influence of relaxation and diffusion in CPMG data. Here, we improve the analysis by introducing an automatic search for the optimum power k that best describes the diffusion behavior. This automated method is more efficient than the manual trial-and-error grid search adopted previously, and avoids variability through subjective judgments of experimentalists. Although our method does not avoid the inherent assumption that the diffusion exponent depends on a single k value, we show through simulation and experiment that it is robust in measurements of heterogeneous systems that violate this assumption. In this way, we obtain quantitative T2 distributions from complicated porous structures and demonstrate the analysis with examples of ceramics used for filtration and catalysis, and limestone of relevance to the construction and petroleum industries.

Low-field permanent magnets for industrial process and quality control.

In this review we focus on the technology associated with low-field NMR. We present the current state-of-the-art in low-field NMR hardware and experiments, considering general magnet designs, rf performance, data processing and interpretation. We provide guidance on obtaining the optimum results from these instruments, along with an introduction for those new to low-field NMR. The applications of lowfield NMR are now many and diverse. Furthermore, niche applications have spawned unique magnet designs to accommodate the extremes of operating environment or sample geometry. Trying to capture all the applications, methods, and hardware encompassed by low-field NMR would be a daunting task and likely of little interest to researchers or industrialists working in specific subject areas. Instead we discuss only a few applications to highlight uses of the hardware and experiments in an industrial environment. For details on more particular methods and applications, we provide citations to specialized review articles.

Modeling two-dimensional magnetic resonance measurements in coupled pore systems.

We present numerical simulations of a two-dimensional (2D) nuclear magnetic resonance process, T_{2}-storage-T_{2}, on a simple mixed porosity system, the micrograin consolidation (µGC) model. The results of these calculations are compared with predictions based on the analytic two-site exchange model, for which we have independently established numerical values for all the input parameters. Although there is qualitative and semiquantitative agreement between the two models, we identify specific instances where the two-site model fails to properly describe the combined effects of relaxation and diffusion. Generally, these instances occur when a gradient in magnetization within the large pores of the µGC model is established during the initial phase of the 2D process. The two-site model assumes that the magnetization is spatially uniform within each of its subpore systems and thus cannot describe such effects.

Measurement of the true transverse nuclear magnetic resonance relaxation in the presence of field gradients.

A measure of the nuclear spin transverse relaxation time T2, as determined using the nuclear magnetic resonance Carr-Purcell Meiboom-Gill (CPMG) experiment, provides unique information characterizing the microstructure of porous media which are themselves ubiquitous across fields of petrophysics, biophysics, and chemical engineering. However, the CPMG measurement is sensitive to diffusion in large magnetic field gradients. Under such conditions an effective relaxation time T2,eff is observed instead, described by a combination of relaxation and diffusion exponents. The relaxation exponent always varies as nte (where n is the number, and te is the temporal separation, of spin echoes). The diffusion exponent varies as nte (k), where 1 < k ≤ 3, although the exact analytic form is often unknown. Here we present a general approach to separating the influence of relaxation and diffusion by utilizing a composite diffusion exponent. Any T2,eff component with a power of k > 1 is removed to provide a measure of the true T2 relaxation time distribution from CPMG data acquired in the presence of a strong background gradient. We apply the technique to discriminate between the effects of relaxation and diffusion in porous media using catalysts and rocks as examples. The method is generally applicable to any CPMG measurements conducted in the presence of a static magnetic field gradient.

Emulsion droplet sizing using low-field NMR with chemical shift resolution and the block gradient pulse method.

Pulsed Field Gradient (PFG) measurements are commonly used to determine emulsion droplet size distributions based on restricted self-diffusion within the emulsion droplets. Such measurement capability is readily available on commercial NMR bench-top apparatus. A significant limitation is the requirement to selectively detect signal from the liquid phase within the emulsion droplets; this is currently achieved using either relaxation or self-diffusion contrast. Here we demonstrate the use of a 1.1 T bench-top NMR magnet, which when coupled with an rf micro-coil, is able to provide sufficient chemical shift resolution such that unambiguous signal selection is achieved from the dispersed droplet phase. We also improve the accuracy of the numerical inversion process required to produce the emulsion droplet size distribution, by employing the Block Gradient Pulse (bgp) method, which partially relaxes the assumptions of a Gaussian phase distribution or infinitely short gradient pulse application inherent in current application. The techniques are successfully applied to size 3 different emulsions.

Obtaining true transverse relaxation time distributions in high-field NMR measurements of saturated porous media: Removing the influence of internal gradients.

It is well known that nuclear magnetic resonance (NMR) transverse relaxation measurements of porous media at high magnetic field strengths provide only an effective relaxation time T(2,eff), as opposed to the true T(2), due to molecular diffusion through magnetic field gradients induced by the magnetic susceptibility contrast between the adsorbent and the adsorbate. Here, we deconvolve the diffusion and surface relaxation contributions to measurements of T(2,eff) and thus obtain the true T(2) relaxation time distribution. This technique is applicable within the short time diffusion regime where the diffusion exponent varies as t(E) (3), while the surface relaxation exponent varies as t(E), where t(E) is the echo time in a standard Carr-Purcell Meiboom-Gill measurement. We demonstrate this technique on measurements of water in contact with glass spheres across a range of magnetic field strengths from B(0)=50 mT to 7.4 T. A direct measurement of T(2,eff) suggests that the transverse relaxation rate increases with field strength, in contrast to theoretical predictions. We show that when the effects of the susceptibility induced gradients, which are known to increase with magnetic field strength, are deconvolved from the T(2,eff) measurement, the true T(2) relaxation rate does indeed decrease with increasing field strength. We also apply the T(2) correction in multidimensional NMR experiments using the example of a T(1)-T(2) relaxation correlation. Here, the correction is essential in order to obtain the true T(1)/T(2) ratio as a function of magnetic field strength, which provides a measure of mobility for surface-adsorbed species; without this correction, we see surface residence times overestimated by up to two orders of magnitude. This novel approach enables the accurate determination of T(2) distributions, and hence T(1)/T(2) ratios, on high-field spectrometers that would have previously been deemed inappropriate for the study of liquids in porous media because of the intrinsic susceptibility effects.

Nuclear magnetic resonance relaxation and diffusion in the presence of internal gradients: the effect of magnetic field strength.

It is known that internal magnetic field gradients in porous materials, caused by susceptibility differences at the solid-fluid interfaces, alter the observed effective Nuclear Magnetic Resonance transverse relaxation times T2,eff. The internal gradients scale with the strength of the static background magnetic field B0. Here, we acquire data at various magnitudes of B0 to observe the influence of internal gradients on T2-T2 exchange measurements; the theory discussed and observations made are applicable to any T2-T2 analysis of heterogeneous materials. At high magnetic field strengths, it is possible to observe diffusive exchange between regions of local internal gradient extrema within individual pores. Therefore, the observed exchange pathways are not associated with pore-to-pore exchange. Understanding the significance of internal gradients in transverse relaxation measurements is critical to interpreting these results. We present the example of water in porous sandstone rock and offer a guideline to determine whether an observed T2,eff relaxation time distribution reflects the pore size distribution for a given susceptibility contrast (magnetic field strength) and spin echo separation. More generally, we confirm that for porous materials T1 provides a better indication of the pore size distribution than T2,eff at high magnetic field strengths (B0>1 T), and demonstrate the data analysis necessary to validate pore size interpretations of T2,eff measurements.

Rapid encoding of T(1) with spectral resolution in n-dimensional relaxation correlations.

Nuclear magnetic resonance (NMR) T(1) relaxation times have been encoded in the second dimension of two-dimensional relaxation correlation and exchange experiments using a rapid "double-shot"T(1) pulse sequence. This technique also retains chemical shift information (delta) for short T(2)( *) materials. In this way, a spectral dimension can be incorporated into a T(2)-T(1)-delta correlation without an increase in experimental time compared to the conventional, chemically insensitive T(1)-T(2) correlation. Here, the T(2)-T(1)-delta pulse sequence is used to unambiguously identify oil and water fractions in a permeable rock. A novel T(1)-T(1)-(delta) relaxation exchange measurement is also introduced and used to observe diffusive exchange of water in cellulose fibres.