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Many naturally occurring fluids, such as crude oils, consist of a very large number of components. It is often of interest to determine the composition of the fluids in situ. Diffusion coefficients and nuclear magnetic resonance (NMR) relaxation times can be measured in situ and depend on the size of the molecules. It has been shown [D. E. Freed et al., Phys. Rev. Lett. 94, 067602 (2005)] that the diffusion coefficient of each component in a mixture of alkanes follows a scaling law in the chain length of that molecule and in the mean chain length of the mixture, and these relations were used to determine the chain length distribution of crude oils from NMR diffusion measurements. In this paper, the behavior of NMR relaxation times in mixtures of chain molecules is addressed. The author explains why one would expect scaling laws for the transverse and longitudinal relaxation times of mixtures of short chain molecules and mixtures of alkanes, in particular. It is shown how the power law dependence on the chain length can be calculated from the scaling laws for the translational diffusion coefficients. The author fits the literature data for NMR relaxation in binary mixtures of alkanes and finds that its dependence on chain length agrees with the theory. Lastly, it is shown how the scaling laws in the chain length and the mean chain length can be used to determine the chain length distribution in crude oils that are high in saturates. A good fit is obtained between the NMR-derived chain length distributions and the ones from gas chromatography. [ABSTRACT FROM AUTHOR]

Abstract: This paper provides a theoretical basis to directly estimate moments of transverse relaxation time T 2 from measured CPMG data in grossly inhomogeneous fields. These moments are obtained from Mellin transformation of the measured CPMG data. These moments are useful in computing petro-physical and fluid properties of hydrocarbons in porous media. Compared to the conventional method of estimating moments, the moments obtained from this method are more accurate and have a smaller variance. This method can also be used in other applications of NMR in inhomogeneous fields in characterizing fluids and porous media such as in the determination of hydrocarbon composition, estimation of model parameters describing relationship between fluid composition and measured NMR data, computation of error-bars on estimated parameters, as well as estimation of parameters 〈ln T 2〉 and often used to characterize rocks. We demonstrate the performance of the method on simulated data. [Copyright &y& Elsevier]

Abstract: In the past decade, low-field NMR relaxation and diffusion measurements in grossly inhomogeneous fields have been used to characterize pore size distribution of porous media. Estimation of these distributions from the measured magnetization data plays a central role in the inference of insitu petro-physical and fluid properties such as porosity, permeability, and hydrocarbon viscosity. In general, inversion of the relaxation and/or diffusion distribution from NMR data is a non-unique and ill-conditioned problem. It is often solved in the literature by finding the smoothest relaxation distribution that fits the measured data by use of regularization. In this paper, estimation of these distributions is further constrained by linear functionals of the measurement that can be directly estimated from the measured data. These linear functionals include Mellin, Fourier–Mellin, and exponential Haar transforms that provide moments, porosity, and tapered areas of the distribution, respectively. The addition of these linear constraints provides more accurate estimates of the distribution in terms of a reduction in bias and variance in the estimates. The resulting distribution is also more stable in that it is less sensitive to regularization. Benchmarking of this algorithm on simulated data sets shows a reduction of artefacts often seen in the distributions and, in some cases, there is an increase of resolution in the features of the T 2 distribution. This algorithm can be applied to data obtained from a variety of pulse sequences including CPMG, inversion and saturation recovery and diffusion editing, as well as pulse sequences often deployed down-hole. [Copyright &y& Elsevier]