|
 rediction
of dissolved contaminant spread in ground water aquifers is necessary in designing
ground water protection and remediation measures. These predictions are usually accomplished
by solving the convection-dispersion equation (CDE). The dispersion coefficient in
the CDE is assumed to be constant in standard practice, but this coefficient is now
recognized to depend on space and time.
The research team of Professor John L. Nieber, Graduate Students AbdelKarim Abulaban,
Paul Oduro, and Hung Nguyen, and Research Associate Cam Nguyen of the Biosystems
and Agricultural Engineering Department at the University of Minnesota have undertaken
an effort to quantify effects of multiscale spatial heterogeneity on solute plume
spread. In addition, they are working on ways to estimate the dispersion coefficient
in natural porous media. In this work, solute plumes are simulated using a particle
tracking random walk solution of the CDE. This work is being accomplished in cooperation
with Dr. John Peters and Dr. Stacy Howington from the United States Army Waterways
Experiment Station Laboratory in Vicksburg, Mississippi. This cooperation is supported
by the Army High-Performance Computing Research Center at the University of Minnesota.
Sample results of the current work are shown in Figures 1 and 2. Sample ground water
velocity fields are shown in four different conditions for an aquifer with dimensions
of 200 meters by 2000 meters. In Figures 1a-1c, velocity fields for various levels
of hydraulic conductivity
(K2) heterogeneity are shown. For each field, the hydraulic
conductivity is statistically homogeneous (constant mean and variance of K2). Note
that the color scale for each graph is relative to the maximum value of the variable
depicted in that graph. The variable s represents the standard deviation of ln(
K2)
and L represents the spatial correlation of ln(K2). In contrast, the velocity field
shown in Figure 1d is for the condition where multiple scales of K2heterogeneity
(mean and variance of K2are not constant) are represented. Solute plumes for a conservative
solute (non-sorbing, non-degrading) were generated using each of these velocity fields,
and the plume at 500 days associated with each velocity field is displayed immediately
beneath the associated velocity field plot. It is observed in Figures 1a-1c that
the solute plume spread increases as the values of s and L increase. The plume in
Figure 1d is even more spread, showing the effects of the multiple scales of heterogeneity.
The simulation of the solute plume for each velocity field was performed using 200,000
particles with the solute initially concentrated within a 10 m2 area. Each of these
simulations required a high- resolution representation of the aquifer hydraulic conductivity.
Further research is attempting to mimic high-resolution simulations with a simpler
particle tracking model. The simpler model incorporates multiscale spatial heterogeneity
into a random velocity generator superimposed onto a mean flow field. Because of
this, high-resolution representations are not needed. A solute plume generated with
this approach is shown in Figure 2.
In future research, this group will derive parameters from the high-resolution fields
to be input into the simpler dispersion model. This work will make it capable to
closely predict behavior of the high-resolution simulations. Further work will investigate
the effects of solute sorption, multicomponent chemical reactions, and biodegradation
on solute plume behavior when multiscale spatial heterogeneity is present.
 |
| Figure 1a: Longitudinal velocity and
concentration profile of ground water for s = 0.5 and L = 5 m. |
 |
| Figure 1b: Longitudinal velocity and
concentration profile of ground water for s = 1.0 and L = 10 m. |
 |
| Figure 1c: Longitudinal velocity and
concentration profile of ground water for s = 2.0 and L = 20 m. |
 |
| Figure 1d: Longitudinal velocity and
concentration profile of ground water for the sum of the hydraulic conductivity fields
for figures 1a-1c. |
 |
| Figure 2: A solute plume generated
with a random velocity generator, representing multiscale spatial heterogeneity,
superimposed onto a mean flow field. |
|
|
