Nuclear magnetic resonance imaging and analysis for determination of porous media properties

Abstract

Advanced nuclear magnetic resonance (NMR) imaging methodologies have been developed to determine porous media properties associated with fluid flow processes. This dissertation presents the development of NMR experimental and analysis methodologies, called NMR probes, particularly for determination of porosity, permeability, and pore-size distributions of porous media while the developed methodologies can be used for other properties. The NMR relaxation distribution can provide various information about porous systems having NMR active nuclei. The determination of the distribution from NMR relaxation data is an ill-posed inverse problem that requires special care, but conventionally the problem has been solved by ad-hoc methods. We have developed a new method based on sound statistical theory that suitably implements smoothness and equality/inequality constraints. This method is used for determination of porosity distributions. A Carr-Purcell-Meiboom-Gill (CPMG) NMR experiment is designed to measure spatially resolved NMR relaxation data. The determined relaxation distribution provides the estimate of intrinsic magnetization which, in turn, is scaled to porosity. A pulsed-field-gradient stimulated-echo (PFGSTE) NMR velocity imaging experiment is designed to measure the superficial average velocity at each volume element. This experiment measures velocity number distributions as opposed to the average phase shift, which is conventionally measured, to suitably quantify the velocities within heterogeneous porous media. The permeability distributions are determined by solving the inverse problem formulated in terms of flow models and the velocity data. We present new experimental designs associated with flow conditions to enhance the accuracy of the estimates. Efforts have been put forth to further improve the accuracy by introducing and evaluating global optimization methods. The NMR relaxation distribution can be scaled to a pore-size distribution once the surface relaxivity is known. We have developed a new method, which avoids limitations on the range of time for which data may be used, to determine surface relaxivity by the PFGSTE NMR diffusion experiment.