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Diffusion problems for Nuclear Magnetic Relaxation in permeable porous media

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NMR is now a well-established petrophysical measurement in petroleum well-logging and in surface core analysis. Brownian diffusion of fluid molecules within the pore space, subject to partially absorbing boundary conditions at the pore surface, is fundamental to interpretation of experimentally observable relaxation measurements. The archetype for interpretations in practical petrophysics remains that of an isolated pore, in the so-called fast diffusion regime, a correct limiting case but insufficient for several more complicated contexts commonly encountered in practice. Interesting analytical problems arise in the development of models which go beyond the archetype. We shall discuss two developments: (1) an analytical approach to a coupled diffusion problem for microporous rock textures where large and much smaller pores are closely adjacent (2) the extensions required where local contrasts in magnetic susceptibility cannot be neglected. The former topic addresses measured responses found in at least two practical contexts where the “isolated pore” model cannot be sustained: (a) carbonate grainstone textures typical of many oil-bearing formations in the Middle East (b) compacts made of kerogen isolates in current research on the NMR of hydrocarbon-bearing shales. The latter topic addresses measured responses in systems (typically sandstones) where induced internal magnetic field gradients require extensions to the governing diffusion equation, with analytical difficulties only partially solved. Implications for MRI will be discussed.

This talk is part of the Institute for Energy and Environmental Flows (IEEF) series.

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