Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Environmental Engineering and Earth Science

Committee Chair/Advisor

Ronald W. Falta

Committee Member

Larry Murdoch

Committee Member

Kevin Finneran

Committee Member

Joe Rossabi


A semi-analytic trial function model is applied to simulate matrix diffusion in systems of parallel fractures, 2-D/3-D discrete fracture networks, and in 3-D heterogeneous media. The trial function model gives low normalized root mean square error (NRMSE) when compared to the parallel fracture analytical solution over a range of fracture spacing, with considerations for retardation and decay. The semi-analytic trial function model is efficient in time and maintains less than 6% NRMSE when it simulates matrix diffusive transport in 2-D/3-D discrete fracture networks (DFN). The model can predict DFN plume within a few meters of accuracy compared to fine-grid DFN models. In two material distributions of a heterogeneous media, the semi-analytic model is similarly efficient and accurate. The matrix diffusion modeling parameters of the trial function model can be directly computed in fractured and porous media using either the fracture properties or subsurface core/boreholes. An effort to improve the semi-analytic model by including a variable diffusion area is considered. The use of the variable diffusion area yields about a 5% gain in accuracy. In contrast to the semi-analytic trial function model, the dual-porosity model is shown to be a less robust equivalent porous media approach. The dual-porosity model relies on a first-order mass transfer coefficient, which is time-dependent. The mass transfer coefficient can be initially estimated as the inverse of the characteristic diffusion time. The dual-porosity model gives low NRMSEs in small fracture spacing cases. However even with calibration, in cases of large fracture spacing, the dual-porosity model is unable to match analytical solutions and fine-grid results.

Author ORCID Identifier 0000-0001-6940-4861



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