| Summary: | In this thesis, I investigated two methods of recovering the surface area to volume
ratio (S/V), or pore size distribution, of water filled porous geological materials using
Nuclear Magnetic Resonance (NMR) data. The NMR relaxation times T₁ and T₂ depend
on the quantity of magnetic sites on the solid pore surface, which is characterized by a
parameter called the surface relaxivity, denoted as p₁ and p₂ respectively. This parameter
must be estimated in order to determine the S/V.
Magnetic susceptibility was explored as a method of estimating pi, as it also
depends on the amount of magnetic material in a sample. Magnetite and hematite were
combined with quartz for measurement. Mixtures of 0.5, 1 and 2 percent magnetite by
weight and 2.1, 3, 6, 9, 12, 30 and 60 percent hematite by weight were created.
The magnetic susceptibility and pi of both the magnetite and hematite mixtures
showed good correlation and the results indicate magnetic susceptibility could be used to
predict p₁ for unconsolidated sediments.
A second method for determining the S/V using T₂ data was studied. T₂ is
affected by diffusion of the protons through internal magnetic field inhomogeneities, a
process that does not influence T₁. These inhomogeneities can be modeled as an
effective gradient, G, which must be estimated.
A parameter estimation inversion code was developed to solve for P₂, S/V and G.
Evaluation of the algorithm was completed on a synthetic data, which was created with
7% incorporated noise. G and the product of pi and S/V were reliably recovered but
distinguishing between pi and S/V was not possible for this data set.
The inversion was then carried out on T₂ data from the same hematite samples
discussed above. This data set allowed better distinction between p₂ and S/V. p₂ and G
values were within the expected range, but the S/V was larger than expected, which was
partly due to the sample geometry. This parameter estimation algorithm shows potential
for determining the S/V of a pore space from T₂ measurements, but further
experimentation is required. === Science, Faculty of === Earth, Ocean and Atmospheric Sciences, Department of === Graduate
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