Date of Award
Doctor of Philosophy
Geological and Environmental Sciences
Donald M. Reeves, Ph.D.
Daniel Patrick Cassidy, Ph.D.
Duane Hampton, Ph.D.
Melinda Koelling, Ph.D.
Contaminants, crystal symmetry, dispersion, lattice networks, solute transport
Multi-dimensional expansion of the advection-dispersion equation necessitated the representation of dispersivity as a 4th rank tensor. This tensorial form of dispersivity has 81 terms in three-dimensions with a maximum of 36 independent terms that may be used to describe Fickian spreading of a dissolved contaminant plume according to intrinsic properties of a porous medium. The complexity of the 4th rank tensor has led to the common practice of simplifying the tensor to only 2 or 3 independent terms by assuming isotropic conditions, although isotropic porous media are uncommon in nature as many natural geologic systems exhibit pronounced anisotropy. A broad set of crystallographic symmetries are investigated for application to the dispersivity tensor. Listed in order of high to low symmetry, these symmetries include isotropic, hexagonal, tetragonal, orthorhombic, monoclinic, and triclinic. A framework is developed for each of these symmetries to identify and quantify connections between individual dispersivity terms with principal values of the 2nd rank dispersion tensor. A sensitivity analysis is performed to determine the influence of individual terms of dispersivity on principal components of dispersion. A numerical method allowing for visualization of resultant multi-Gaussian densities for any of these axial symmetries is also presented. Conservative particle transport in lattice networks is used to parameterize the full dispersivity tensor for hexagonal, tetragonal, and orthorhombic symmetries.
Fan, Xiang, "A Framework for Assessing The 4th Rank Dispersivity Tensor Under Anisotropic Axial Symmetries" (2022). Dissertations. 3910.