Combined time-lapse magnetic resonance imaging and modeling to investigate colloid deposition and transport in porous media.

Colloidal particles can act as vectors of adsorbed pollutants in the subsurface, or be themselves pollutants. They can reach the aquifer and impair groundwater quality. The mechanisms of colloid transport and deposition are often studied in columns filled with saturated porous media. Time-lapse profiles of colloid concentration inside the columns have occasionally been derived from magnetic resonance imaging (MRI) data recorded in transport experiments. These profiles are valuable, in addition to particle breakthrough curves (BTCs), for testing and improving colloid transport models. We show that concentrations could not be simply computed from MRI data when both deposited and suspended colloids contributed to the signal. We propose a generic method whereby these data can still be used to quantitatively appraise colloid transport models. It uses the modeled suspended and deposited particle concentrations to compute modeled MRI data that are compared to the experimental data. We tested this method by performing transport experiments with sorbing colloids in sand, and assessed for the first time the capacity of the model calibrated from BTCs to reproduce the MRI data. Interestingly, the dispersion coefficient and deposition rate calibrated from the BTC were respectively overestimated and underestimated compared with those calibrated from the MRI data, suggesting that these quantities, when determined from BTCs, need to be interpreted with care. In a broader perspective, we consider that combining MRI and modeling offers great potential for the quantitative analysis of complex MRI data recorded during transport experiments in complex environmentally relevant porous media, and can help improve our understanding of the fate of colloids and solutes, first in these media, and later in soils.

Novel Experimental-Modeling Approach for Characterizing Perfluorinated Surfactants in Soils.

Soil contamination is still poorly understood and modeled in part because of the difficulties of looking inside the "black box" constituted by soils. Here, we investigated the application of a recently developed 1H NMR technique to 19F NMR relaxometry experiments and utilized the results as inputs for an existing model. This novel approach yields 19F T2 NMR relaxation values of any fluorinated contaminant, which are among the most dangerous contaminants, allowing us to noninvasively and directly monitor their fate in soils. Using this protocol, we quantified the amount of a fluorinated xenobiotic (heptafluorobutyric acid, HFBA) in three different environments in soil aggregate packings and monitored contaminant exchange dynamics between these compartments. A model computing HFBA partition dynamics between different soil compartments showed that these three environments corresponded to HFBA in solution (i) between and (ii) inside the soil aggregates and (iii) to HFBA adsorbed to (or strongly interacting with) the soil constituents. In addition to providing a straightforward way of determining the sorption kinetics of any fluorinated contaminant, this work also highlights the strengths of a combined experimental-modeling approach to unambiguously understand experimental data and more generally to study contaminant fate in soils.

Measurement of deformations by NMR.

Two NMR data acquisition protocols together with corresponding data processing algorithms for locating macroscopic objects, measuring distances between them or monitoring their displacements or deformations with microscopic precision are presented and discussed. The performance of the methods is demonstrated by applying them to the measurement of deformations of a freely supported beam under loading. We believe that our methods will find their applications in mechanics, civil engineering and medicine.

Extrapolation and phase correction of non-uniformly broadened signals.

The initial part of FID-signals cannot always be acquired experimentally. This is particularly true for signals characterised by strong inhomogeneous broadening, such as those in porous materials, e.g. cements, soils and rocks, those measured by portable NMR-apparatus, or EPR-signals. Here we report on a numerical method we designed to extrapolate those initial missing parts, i.e. to retrieve their amplitude and phase. Should the entire signal be available from an experiment, the algorithm can still be used as an automatic phase-corrector and a low-pass filter. The method is based on the use of cardinal series, applies to any oversampled signals and requires no prior knowledge of the system under study. We show that the method can also be used to restore entire one-dimensional MRI-data sets from those in which less than half of the k-space was sampled, thus not only potentially allowing to speed up data acquisition - when extended to two or three dimensions, but also to circumvent phase-distortions usually encountered when exploring the k-space near its origin.

Cardinal series to restore NMR-signals dominated by strong inhomogeneous broadening.

We have devised two numerical methods of restoring incomplete band-limited NMR-signals to integrity by either interpolating or extrapolating them. Both methods are based on use of the finite cardinal series, whose filtering properties were discussed previously, to model signals. They require no prior knowledge about the system under study, but only that the available parts of the signal were oversampled enough. The methods were tested on two types of computer-simulated signal. It proved superior to the linear prediction methods and Lagrange interpolation when applied to signals measured in highly inhomogeneous magnetic fields. The extrapolation method was then applied to restore experimentally-measured refocused FID-signals of a porous medium. The missing parts of the signal of up to several times the size of its Nyquist period could be recovered by either method.

Structure of the two-dimensional relaxation spectra seen within the eigenmode perturbation theory and the two-site exchange model.

The form of the two-dimensional (2D) NMR-relaxation spectra--which allow to study interstitial fluid dynamics in diffusive systems by correlating spin-lattice (T(1)) and spin-spin (T(2)) relaxation times--has given rise to numerous conjectures. Herein we find analytically a number of fundamental structural properties of the spectra: within the eigen-modes formalism, we establish relationships between the signs and intensities of the diagonal and cross-peaks in spectra obtained by various 1 and 2D NMR-relaxation techniques, reveal symmetries of the spectra and uncover interdependence between them. We investigate more specifically a practically important case of porous system that has sets of T(1)- and T(2)-eigenmodes and eigentimes similar to each other by applying the perturbation theory. Furthermore we provide a comparative analysis of the application of the, mathematically more rigorous, eigen-modes formalism and the, rather more phenomenological, first-order two-site exchange model to diffusive systems. Finally we put the results that we could formulate analytically to the test by comparing them with computer-simulations for 2D porous model systems. The structural properties, in general, are to provide useful clues for assignment and analysis of relaxation spectra. The most striking of them--the presence of negative peaks--underlines an urgent need for improvement of the current 2D Inverse Laplace Transform (ILT) algorithm used for calculation of relaxation spectra from NMR raw data.

Structural properties of 2D NMR relaxation spectra of diffusive systems.

Much has been learnt and speculated about the form of 2D NMR relaxation spectra of diffusive systems. Herein we show that the eigen-modes formalism can help to establish a number of fundamental structural properties, i.e. symmetries, overall intensities, signs and relative intensities of the diagonal and cross components, of such spectra, on which one can safely rely in analysing experimental data. More specifically, we prove that the correlation T(1)-T(2) spectra will always have negative peaks, thus making questionable the nowadays wide spread strategy in developing inverse Laplace transformation algorithms.

Cardinal series to filter oversampled truncated magnetic resonance signals.

Digital low pass filters are routinely used to improve the signal-to-noise ratio of NMR signals, e.g. FID or echoes, when pass band widths of the available analogue filters do not correspond to the spectral width of the signals. Applying digital filters will always necessitate an oversampling of the signal to filter. The digital filters with which the commercial spectrometers are nowadays equipped and most of those known to date from literature were designed to be applied to signals in the time domain. Nevertheless, most of them are aimed at optimising the filtering of signals in the frequency domain and tend to distort them in the time domain, especially when applied to truncated signals. Herein we propose a low pass filter that preserves all the features of the signal in both domains. The method consists in fitting raw NMR data with a finite sum of truncated cardinal sine functions and requires nothing but the signal being a band-limited function. We devised sensible and, in practice, hardly restrictive rules for setting parameters of the filter and applied it to various computer-simulated and experimentally measured truncated data sets to demonstrate its success in filtering both FID and echo signals.

MRI investigation of granular interface rheology using a new cylinder shear apparatus.

The rheology of granular materials near an interface is investigated through proton magnetic resonance imaging. A new cylinder shear apparatus has been inserted in the magnetic resonance imaging device, which allows the control of the radial confining pressure exerted by the outer wall on the grains and the measurement of the torque on the inner shearing cylinder. A multi-layer velocimetry sequence has been developed for the simultaneous measurement of velocity profiles in different sample zones, while the measurement of the solid fraction profile is based on static imaging of the sample. This study describes the influence of the roughness of the shearing interface and of the transverse confining walls on the granular interface rheology.

Cardinal series to sort out defective samples in magnetic resonance data sets.

NMR signals are unavoidably impaired with noise stemming from the electronic circuits of the spectrometer. This noise is most often white and Gaussian and can be greatly reduced by applying low pass analogue and digital filters. Nevertheless, extra noise with other statistics than Gaussian may interfere with the signal, e.g. when auxiliary electrical devices are placed near the magnet of the NMR spectrometer. This paper reports on how one can make use of this difference in statistics to remove the noise caused by electrical devices before any further data processing. The algorithm is based on the use of a new linear low pass filter, which consists in fitting NMR data in the time domain with a cardinal series and whose spectral width can be controlled. Over other filtering methods such filter has the advantage of not distorting the signal neither at the beginning nor the end of the acquisition period. The performance of the method is demonstrated by applying it to a data set collected in a flow PGSE experiment and impaired with noise emanated from a brushed DC electric motor.

Proton NMR relaxation as a probe for setting cement pastes.

We report a 20-MHz proton nuclear magnetic resonance T1 relaxation study of cement paste hydration in the early stages of setting, using different centimeter-sized samples of cements of various origins and different water-to-cement ratios. In every sample, during the first few minutes of hydration, it is found that inverse Laplace processing of inversion-recovery measurements systematically exhibits at least two T1 values: a long one, around 100 ms, whose value correlates well with water content and which may be attributed to bulk water surrounding cement grains; and a short one, around 2 ms, which is quite insensitive to water-to-cement ratio and which may be attributed to water embedded in floculated cement grains before setting occurs. The time evolution of the longest T1 value for several hours is also shown to exhibit a characteristic five-stage behavior that is well correlated with known stages of the hydration process: initial reaction, induction period, acceleration period, deceleration period and slow hydration reaction. These results are compared with calorimetric measurements and electrical conductivity literature.

An MRI-SPI and NMR relaxation study of drying-hydration coupling effect on microstructure of cement-based materials at early age.

Hydration and drying coupling effect monitoring with single point imaging profiles allowed us to evaluate "free" pore and "bounded" chemical water quantity. White cement pastes inverse Laplace analysis of T1 measurements shown original results with two components during setting. After hardening, we found three components. Single point imaging measures were also used to study the evolution of transition zone in repaired concrete. MRI results demonstrated its interest compared with destructive method for longitudinal study and phenomena kinetic monitoring.