This thesis introduces new NMR techniques which use the inhomogeneous internalmagnetic fields present in the pore space of a porous medium exposedto an external magnetic field to obtain information about the pore size andheterogeneities of the the sample. Typically internal field inhomogeneities areregarded as unwanted due to their effect on various material properties suchas relaxation and diffusion. However, in the experiments presented here, wechoose samples specifically for their inhomogeneous internal fields and usemulti-dimensional NMR methods and simulations to obtain our pore space andheterogeneity information.We first describe software developed to specifically simulate the internalmagnetic field and diffusion through the pore space of a simple sphere packsystem. This software generates a sphere pack and calculates the internal magneticfield generated by z-aligned magnetic dipoles placed at the center of eachsphere. The internal magnetic field gradient is also calculated in the pore space.From there, a random walk method is developed and a realistic reflection off asphere is introduced. We work through the development of this software andthe mathematics behind the algorithms used. This simulation is used in all subsequentexperimental chapters.We then use a two-dimensional exchange experiment to separate the susceptibilityinduced line broadening with the broadening caused by diffusionthrough the inhomogeneous field. We observe off-diagonal line broadening asthe mixing time increases. We attempt to quantify this off-diagonal growth byselecting points on either side of the off-diagonal maximum and plotting theiraverage as a function of mixing time. A biexponential fit to the average intensitieswith respect to mixing time results in a characteristic time and from thata characteristic length as a fraction of bead diameter. This experiment is simulatedand a biexponential growth is also observed in the simulated off-diagonalwith characteristic lengths comparable to experiment.To obtain a correlation length directly from experiment and not deduce onefrom a characteristic time, we add a spatial dimension to our exchange experimentin the form of a propagator dimension. This dimension allows us to select2D spectra based on their Z-displacement. We observe off-diagonal growth dueto both an increase in Z-displacement and an increase in mixing time. We moveaway from the biexponential fit and move to a relationship based on mixingtime, effective diffusion, and Z-displacement to directly calculate a characteristiclength. We see these same traits in the simulated data which agrees well withexperiment.Lastly, we move away from exchange experiments and move to correlatingthe transverse relaxation time with the internal field offset. We find that thereis correlation at large magnetic field offsets and small T2 times which appear tobe indicative of sample heterogeneities. To confirm this we use a highly heterogeneousrock core sample which increases the correlations seen at the previousoffsets and times. This experiment is more qualitative than the previous two aswe do not have a concrete value for the heterogeneity of our samples. The simulationused throughout the thesis, while showing a definite correlation betweenfield offset and T2 relaxation, is unable to accurately simulate the experimentand requires more development.
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