A more accurate estimate of T2 distribution from direct analysis of NMR measurements.

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.

Estimation of petrophysical and fluid properties using integral transforms in nuclear magnetic resonance.

In the past decade, low-field NMR relaxation and diffusion measurements in grossly inhomogeneous fields have been used to characterize properties of porous media, e.g., porosity and permeability. Pulse sequences such as CPMG, inversion and saturation recovery as well as diffusion editing have been used to estimate distribution functions of relaxation times and diffusion. Linear functionals of these distribution functions have been used to predict petro-physical and fluid properties like permeability, viscosity, fluid typing, etc. This paper describes an analysis method using integral transforms to directly compute linear functionals of the distributions of relaxation times and diffusion without first computing the distributions from the measured magnetization data. Different linear functionals of the distribution function can be obtained by choosing appropriate kernels in the integral transforms. There are two significant advantages of this approach over the traditional algorithm involving inversion of the distribution function from the measured data. First, it is a direct linear transform of the data. Thus, in contrast to the traditional analysis which involves inversion of an ill-conditioned, non-linear problem, the estimates from this new method are more accurate. Second, the uncertainty in the linear functional can be obtained in a straight-forward manner as a function of the signal-to-noise ratio (SNR) in the measured data. We demonstrate the performance of this method on simulated data.

Continuous moment estimation of CPMG data using Mellin transform.

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 and σ(lnT(2)) often used to characterize rocks. We demonstrate the performance of the method on simulated data.

Mellin transform of CPMG data.

This paper describes a new method for computing moments of the transverse relaxation time T(2) from measured CPMG data. This new method is based on Mellin transform of the measured data and its time-derivatives. The Mellin transform can also be used to compute the cumulant generating function of lnT(2). The moments of relaxation time T(2) and lnT(2) are related to petro-physical and fluid properties of hydrocarbons in porous media. The performance of the new algorithm is demonstrated on simulated data and compared to results from the traditional inverse Laplace transform. Analytical expressions are also derived for uncertainties in these moments in terms of the signal-to-noise ratio of the data.

Uncertainty analysis of visible and near-infrared data of hydrocarbons.

Measurement of physical and chemical properties of hydrocarbons plays an important role in the exploration and production of oil wells. In situ measurement of chemical properties of hydrocarbons makes use of visible and near-infrared (vis-NIR) absorption spectra of hydrocarbons. Uncertainty analysis of these fluid properties is central to developing a fundamental understanding of the distribution of hydrocarbons in the reservoir. In this manuscript, we describe an algorithm called the fluid comparison algorithm (FCA), which provides a statistical framework to quantify and compare hydrocarbon fluid properties and associated uncertainties derived from vis-NIR measurements. The inputs to FCA are the magnitude and uncertainty of vis-NIR spectroscopy data of two hydrocarbons. The output of FCA is a probability that two fluids are statistically different. FCA lays the foundations for subsequent optimization and capture of representative reservoir hydrocarbons. Furthermore, in some circumstances, it can also enable real-time decisions to identify reservoir compartmentalization and hydrocarbon composition gradients in natural oil reservoirs.

Determining the resolution of Laplace inversion spectrum.

In experiments involving decaying signals, it is often desirable to analyze the data as a sum of exponential decays using the Laplace inversion method. However, Laplace inversion is an ill-conditioned problem, and it is difficult to ascertain the stability of the reconstruction method and resolution of the resulting spectrum. This paper provides an easily computed approximate bound of the resolution and offers guidelines on how to design experiments to improve the spectral resolution.