| Heterogeneous systems, characterized as consisting of a number of dissimilar or diverse ingredients or constituents, are frequently encountered within nature. While increased knowledge of the various internal structures within these systems would prove beneficial in a wide variety of applications, explicit details regarding system properties are often difficult to assess. Fortunately, nuclear magnetic resonance (NMR) provides an effective and noninvasive probe of these systems when appropriate fluids are introduced. The relaxation effects of these fluid are sensitive to the internal structure of the media, and suitable analysis of the relaxation data provides a wealth of information concerning the underlying composition.; Methodologies affording quantitative analysis of NMR data in engineering applications and procedures permitting the determination of storage and transport property distributions within permeable media from these data are set forth. First, a methodology used to analyze discrete NMR relaxation data in terms of a continuous relaxation distribution is developed. A critical step is the solution of a Fredholm integral equation which requires a good estimate of the regularization parameter. A systematic procedure, based on nonparametric regression theory, is developed for automatically selecting the optimal regularization parameter and the associated relaxation distribution. Second, a methodology for quantitatively analyzing magnetic resonance imaging (MRI) data is developed to determine the intrinsic magnetization intensity associated with each voxel within an image. These quantities are subsequently used to determine multi-dimensional distributions of porosity and saturation.; Finally, a methodology is developed for determining absolute permeability distributions in porous media samples using macroscopic velocity data obtained from a novel NMR imaging scheme. A nonlinear inverse problem is posed and solved to determine a suitable permeability distribution. An objective function describing the discrepancy between observed data and that predicted by a numerical simulation using a particular permeability distribution is systematically minimized. A Broyden-Fletcher-Goldfarb-Shanno (BFGS) variable metric method is used to iteratively update the permeability estimates, and the necessary gradient information is provided by a method based on optimal control theory. |
