Date of Award


Document Type


Degree Name

Master of Science (MS)


Environmental Engineering and Earth Sciences

Committee Member

Ronald W. Falta, Committee Chair

Committee Member

Lawrence C. Murdoch

Committee Member

Timothy A. Devol


The invasion of dissolved chlorinated volatile organic compounds (CVOCs) into low permeability zones can cause contaminant persistence above maximum contaminant levels (MCLs) in adjacent aquifers due to the phenomenon of matrix diffusion. Numerical studies have been conducted to simulate matrix diffusion effects between aquifers and aquitards. However, existing numerical approaches for simulating matrix diffusion of CVOCs require fine discretization of the aquifer and aquitard into tens of layers of grid blocks, resulting in large computational effort. Considering the inefficiency of numerical approaches, a semi-analytical method was developed to only discretize the aquifer and mathematically approximate the diffusive response in the underlying aquitard.

The semi-analytical method was originally developed in petroleum reservoir engineering for approximating the conductive heat flux from a permeable reservoir into an underlying impermeable cap rock [Vinsome and Westerveld, 1980]. With some modification, a similar semi-analytical method can be applied directly to the problem of CVOC matrix diffusion. The objective of this study is to implement and test the new semi-analytical method for simulating matrix diffusion effects between an aquifer and an aquitard.

This study has three sub-objectives. First of all, grid refinement studies were performed by constructing two simple numerical models for simulating DNAPL pool dissolution in an aquifer with advection and vertical dispersion and matrix diffusion in an aquitard, respectively. The numerical simulations were validated with two simple analytical solutions. The results showed that a grid spacing of ∆x= 1.0 m and ∆z= 0.2 m was fine enough to simulate both cases.

Second, a test was performed with the numerical method by comparing a two-layer numerical model with the more complex Dandy-Sale analytical solution (Sale et al., 2008) for 2-D transport in an aquifer with matrix diffusion in an underlying aquitard. In the numerical simulation, the two-layer model was constructed with fine grid spacing of ∆x= 1.0 m and ∆z= 0.15 m. The results showed that numerical solutions were in good quantitative agreement with analytical solutions in Dandy-Sale model.

Third, the new semi-analytical method was employed for the problem of CVOC matrix diffusion in the two-layer model and was tested against the more complex Dandy-Sale analytical solutions. The comparison of semi-analytical and analytical results indicated that the semi-analytical method is an accurate approximation of CVOC matrix diffusion effects between an aquifer and an aquitard.



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