A method for approximating fractional power average relaxation times without inversion of multiexponential relaxation data

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.

T₂ distribution mapping profiles with phase-encode MRI

Two 1-D phase-encode sequences for T₂ mapping, namely CPMG-prepared SPRITE and spin-echo SPI, are presented and compared in terms of image quality, accuracy of T₂ measurements and the measurement time. The sequences implement two different approaches to acquiring T₂-weighted images: in the CPMG-prepared SPRITE, the T₂-weighting of magnetization precedes the spatial encoding, while in the spin-echo SPI, the T₂-weighting follows the spatial encoding. The sequences are intended primarily for T₂ mapping of fluids in porous solids, where using frequency encode techniques may be problematic either due to local gradient distortions or too short T₂. Their possible applications include monitoring fluid-flow processes in rocks, cement paste hydration, curing of rubber, filtering paramagnetic impurities and other processes accomplished by changing site-specific T₂.

Magnetic resonance for fluids in porous media at the University of Bologna

The magnetic resonance in porous media (MRPM) community is now a vast community of scientists from all over the world who recognize magnetic resonance as an instrument of choice for the characterization of pore space and of the distribution, diffusion and flow of fluids inside a vast range of different materials. The MRPM conferences are the occasions in which this community gets together, compares notes and grows. The scene was different in 1990, when this series of conferences was promoted at Bologna. I will go briefly over the history of these events, showing the role played by the University of Bologna and in particular by the intuition, ingenuity and passion of Giulio Cesare Borgia. The MRPM work at Bologna began in the mid-1980s. New correlations were found among parameters from NMR relaxation measurements and oil field parameters such as porosity, permeability to fluid flow, irreducible water saturation, residual oil saturation and pore-system surface-to-volume ratio, and fast algorithms were developed to give the different NMR parameters. Interest in valid interpretation of data led to extensive work also on the inversion of multiexponential relaxation data and the effects of inhomogeneous fields from susceptibility differences on distributions of relaxation times. In the last few years, extensive developments were made of combined magnetic resonance imaging and relaxation measurements in different fields.

Estimates of permeability and irreducible water saturation by means of a new robust computation of fractional power average relaxation times

In a suite of water-saturated sandstones, we have recently demonstrated that irreducible water saturation can be well estimated using relaxation time only, in the form of any of several "averages" giving more emphasis to short times than does the geometric mean time. The best estimate of permeability came from fits giving more emphasis to slightly longer times. In this paper we present estimates of irreducible water saturation and permeability using approximations (here called Robusta approximation) to the fractional power average relaxation time (Tp)1/p. The advantage of this approximation is that it does not involve previous computation of exponential components; therefore, it does not depend on the choice of the inversion method, and it permits a very fast computation. The Robusta approximation gives some of the best correlations using p = -0.55 for irreducible water saturation and p = +0.18 for permeability.