G.C. Borgia

Nuclear magnetic resonance relaxivity and surface‐to‐volume ratio in porous media with a wide distribution of pore sizes

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)−1, 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 Rn(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 ρ’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(R33)−5.73, where R33 is the highest rate of a three‐component fit without regard to the corresponding amplitude, and where S/V is in (μm)−1 and rate in s−1. 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.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 me...

Study of water penetration in rock materials by Nuclear Magnetic Resonance Tomography: hydrophobic treatment effects

Abstract The penetration of water in rock materials is the main cause of deterioration of stone surfaces exposed to rainfall. Their protection is generally achieved using water-repellents, in order to reduce the absorption of water. Nuclear Magnetic Resonance Imaging (MRI) provides a new tool to visualize the presence of water inside the stone and, hence, the performance of hydrophobic treatments. This technique can also give indirect information on the distribution of the hydrophobic product inside the rock.

Performance evolution of hydrophobic treatments for stone conservation investigated by MRI.

1H-MRI has been applied to the evaluation of the performances of a hydrophobic polymer (Paraloid B72), widely used for the conservation of monumental buildings and other stone artifacts. By this technique it has been possible to visualize the water diffusion in a treated rock material (Pietra di Lecce, a highly porous Italian biocalcarenite) and then indirectly the spatial distribution of the polymer in the rock. The effects of wetting-drying cycles on the hydrophobic efficacy of the acrylic polymer in the inner layers of the rock were also studied. A notable decrease in the water-repellence inside the stone was detected and attributed to a loss of adhesion of the polymer to the substrate, promoted by the action of water.

Different “average” nuclear magnetic resonance relaxation times for correlation with fluid-flow permeability and irreducible water saturation in water-saturated sandstones

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 ...

Wettability effects on oil‐water‐configurations in porous media: A nuclear magnetic resonance relaxation study

1H spin‐lattice relaxation and other physical properties are compared to study the oil‐water‐surface interplay in suitably chosen and prepared natural porous media of different wettability. Whereas the water‐oil arrangement is well established for both strongly water wet and strongly oil wet porous media, the problem is still open for intermediate wettability surfaces. Relaxation behavior reflects the pore space geometry and shows wettability effects on sweeping efficiency and on immiscible liquid arrangement in well‐defined equilibrium situations. A simple picture at the pore‐length scale is verified for strongly water wet samples, whereas a more complex picture arises for intermediate wettability samples.

Effects of hydrophobic treatments of stone on pore water studied by continuous distribution analysis of NMR relaxation times

The effects of protective hydrophobic products applied to porous media such as stone or mortar vary greatly with the product, the porous medium, and the mode of application. Nuclear Magnetic Resonance (NMR) measurements on fluids in the pore spaces of both treated and untreated samples can give information on the contact of the fluid with the internal surfaces, which is affected by all the above factors. Continuous distributions of relaxation times T(1) and T(2) of water in the pores of both synthetic and natural porous media were obtained before and after hydrophobic treatment. The synthetic porous media are ceramic filter materials characterized by narrow distributions of pore dimensions and show that the treatment does not produce large changes in the relaxation times of the water. For three travertine samples most of a long relaxation time component, presumably from the largest pores, remains after treatment, while the amplitude of an intermediate component is greatly reduced. For three pudding-stone samples, treatment leads to a substantial loss from the long component and an even greater loss from the intermediate component.

Developments in core analysis by NMR measurements

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.

Water-air saturation changes in restricted geometries studied by proton relaxation

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.

Problems in identifying multimodal distributions of relaxation times for NMR in porous media

Abstract NMR data for some water-saturated sandstones show distributions of relaxation times covering ranges of a thousand or more. Pore size distributions have been associated with distributions of relaxation times and can also cover wide ranges. Several dozen good sets of NMR relaxation data for water in porous sandstones have been analyzed in terms of continuous distributions of exponential components. About a dozen of these are for sandstones having significant relaxation time components over ranges of factors of a thousand. In all cases adequately good fits to the data could be obtained with distributions of relaxation times that were monomodal when plotted as functions of log-time (or log-rate). Thus, it appears that bimodality (or multimodality) for the logarithmic plots is not demanded by these particular sets of data, although these distributions plotted linearly are not monomodal. On the other hand, many multimodal distributions can always be found giving adequate fits to the data, since excessively sharp detail is not resolvable. Many programs using regularization methods to prevent excessive detail in computed distributions tend to give undershoot at sides of peaks, and noise tends to give not-quite-periodic oscillations. Lack of adequate range and density of either data points or computed points can lead to multimodal computed solutions. Some resolution expressions are used to indicate what level of detail in a computed distribution is meaningful for a given data set.

The effect of diffusion and susceptibility differences on T2 measurements for fluids in porous media and biological tissues

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.