Nuclear magnetic resonance secular relaxation measurements as a method of extracting internal magnetic field gradients and pore sizes

Abstract

Nuclear magnetic resonance (NMR) has been used as a common and powerful tool for petrophysical investigation of fluid-bearing porous media. A major complication of NMR analysis occurs, however, when diffusion of fluid protons through magnetic field heterogeneities becomes nonnegligible. A quantity called the secular relaxation rate ([Formula: see text]) has been defined as the difference in transverse and longitudinal relaxation rates ([Formula: see text]-[Formula: see text]) and can be shown to isolate the effects of diffusion as a function of pore system parameters. We have developed results that extract internal magnetic field gradient strengths based on changes in [Formula: see text] as a function of the NMR interecho spacing. We also indicated that an optimization algorithm can be used to invert for volumetrically weighted mean pore sizes. The benefit of these types of analyses is to provide simple methodologies for inferring the average strengths of internal magnetic field gradients and pore sizes from NMR measurements without the need for independent measurements of pore size, such as from mercury injection porosimetry. In addition, secular relaxation analysis removes complicating effects provided by bulk fluid and other nondiffusion relaxation mechanisms.