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Notes: 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. © 1996 American Institute of Physics.

Notes: 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.