Upscaling and Inverse Modeling of Groundwater Flow and Mass ...

26 CHAPTER 2. A COMPARATIVE STUDY OF THREE- . . .
Normalized Mass
1
0.1
0.01
0.001
0 50 100 150 200 250
Downstream Distance [m]
Mass distribution t=27 days
Realization #26
Geometric mean
Harmonic mean
Arithmetic mean
Power mean with ω =0.5
Figure 2.8: Longitudinal mass distribution profiles of the tritium plume from
the fine scale reference realization, and predictions by some simple averaging
upscaling approaches at the coarse scale for t = 328 days.
in the flow patterns within the block of the boundary conditions used in the
local flow models in favor of the influence of the nearby conductivities from
the reference aquifer.
Since most of the commonly available groundwater flow simulators only
accept diagonal tensors as input parameter values, a test was made by solving
the flow and transport in the coarse scale ignoring the off-diagonal components
of the tensors used in Figure 2.9D. The results are shown in Figure
2.9E and they are qualitatively similar to those in Figure 2.9D. In this specific
case, in which the reference axes of the numerical model are aligned with the
main directions of the statistical anisotropy of hydraulic conductivity it could
be expected that the off-diagonal components of the upscaled block conductivity
tensors were small, and therefore, flow predictions neglecting them go
almost unaffected. In a general setting with complex geology, cross-beddings,
or non-uniform anisotropies, the use of a full tensor block conductivity would
be necessary for a good reproduction of the aquifer response (Bierkens and
Weerts, 1994).
Finally, Figure 2.9F shows that the best results are achieved when the
upscaling is performed on a non-uniform coarse grid, which has been refined
in the areas of highest velocities (see grid in Figure 2.15), using an interfacecentered
Laplacian-with-skin upscaling. While this result is expected, since the
number of model blocks is larger in the non-uniform grid, the improvement is