Abstract:
This thesis introduces new NMR techniques which use the inhomogeneous internal
magnetic fields present in the pore space of a porous medium exposed
to an external magnetic field to obtain information about the pore size and
heterogeneities of the the sample. Typically internal field inhomogeneities are
regarded as unwanted due to their effect on various material properties such
as relaxation and diffusion. However, in the experiments presented here, we
choose samples specifically for their inhomogeneous internal fields and use
multi-dimensional NMR methods and simulations to obtain our pore space and
heterogeneity information.
We first describe software developed to specifically simulate the internal
magnetic field and diffusion through the pore space of a simple sphere pack
system. This software generates a sphere pack and calculates the internal magnetic
field generated by z-aligned magnetic dipoles placed at the center of each
sphere. 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 a
sphere is introduced. We work through the development of this software and
the mathematics behind the algorithms used. This simulation is used in all subsequent
experimental chapters.
We then use a two-dimensional exchange experiment to separate the susceptibility
induced line broadening with the broadening caused by diffusion
through the inhomogeneous field. We observe off-diagonal line broadening as
the mixing time increases. We attempt to quantify this off-diagonal growth by
selecting points on either side of the off-diagonal maximum and plotting their
average as a function of mixing time. A biexponential fit to the average intensities
with respect to mixing time results in a characteristic time and from that
a characteristic length as a fraction of bead diameter. This experiment is simulated
and a biexponential growth is also observed in the simulated off-diagonal
with characteristic lengths comparable to experiment.
To obtain a correlation length directly from experiment and not deduce one
from a characteristic time, we add a spatial dimension to our exchange experiment
in the form of a propagator dimension. This dimension allows us to select
2D spectra based on their Z-displacement. We observe off-diagonal growth due
to both an increase in Z-displacement and an increase in mixing time. We move
away from the biexponential fit and move to a relationship based on mixing
time, effective diffusion, and Z-displacement to directly calculate a characteristic
length. We see these same traits in the simulated data which agrees well with
experiment.
Lastly, we move away from exchange experiments and move to correlating
the transverse relaxation time with the internal field offset. We find that there
is correlation at large magnetic field offsets and small T2 times which appear to
be indicative of sample heterogeneities. To confirm this we use a highly heterogeneous
rock core sample which increases the correlations seen at the previous
offsets and times. This experiment is more qualitative than the previous two as
we do not have a concrete value for the heterogeneity of our samples. The simulation
used throughout the thesis, while showing a definite correlation between
field offset and T2 relaxation, is unable to accurately simulate the experiment
and requires more development.
