Environmental Engineering Reference
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code. Whereas a full three-dimensional model would generally represent all possible
geometric boundaries for the involved processes in the most realistic way, it is useful
to reduce the dimensionality of the model as far as possible to reduce computational
demand. An approach to reduce such models from 2 into 1 dimension by elimina-
tion of the flow distance by travel time was outlined in Maier and Grathwohl ( 2006 ).
Further it is recommendable to use two or more different codes with different numer-
ical approaches and underlying computational methods to improve confidence in the
results and to prove their consistency.
Numerical tools have the advantage of their applicability to a wide range of sce-
narios and can easily be adapted to field conditions. Values of dispersivity that are
significantly smaller than grid spacing, however, are a challenge for the accuracy
of numerical models. Coarse grids bear the risk of artificial mixing which can lead
to overprediction of mixing and Natural Attenuation rates. Several strategies were
applied to overcome this potential source of inaccuracy. Different models using
different numerical approaches were compared and yielded consistent results. In
a sensitivity analysis, the effect of reducing
α T was investigated and grid spacing
was carefully refined until no more influence of the choice of grid spacing could be
observed.
The width of the contaminant plume of 300 m is considerably larger than
its thickness, so lateral transport of oxygen into the plume can be assumed of
minor influence. Therefore two-dimensional models in a vertical (xz)-plane were
discretized using BIONAPL, an operator-splitting finite element code (Molson
et al. 2002 ) and MIN3P, a global implicit finite volume code (Mayer et al.
2002 ). The site is assumed to consist of an aerobic aquifer that is contaminated
over its whole thickness. An average aquifer thickness of 4.5 m, groundwater
flow velocity of 2.7 m/day, porosity of 35%, an average influx concentration of
NH 4 + of 15 mg L 1 , and an oxygen concentration at the water table of 8 mg L 1
were simulated. Grid spacing was 1 m/0.1 m in x- and z-direction, respectively,
resulting in a model domain of 1,000 by 450 elements.
The parameter for the quantification of the amount of mixing within the model
domain of the aquifer is transverse dispersivity
α T , which is not known initially.
A very important aspect is to extract an aquifer scale value of dispersivity under
field conditions. The aim was to reproduce the depth-averaged concentration of
NH 4 + of 1.5 mg L 1
encountered at the control plane 450 m down-gradient of
the landfill by fitting
α T by repeated model runs until satisfactory agreement was
achieved. In the two-dimensional model, the best fit was achieved with transverse
vertical dispersivity
α T of 3.2 cm. A length of the plume of 570 m was obtained
which agrees with the field observations. Figure 19.16 shows the concentrations of
ammonium and oxygen at the aquifer bottom for 250, 350, 500 and 600 days of
simulation.
Concentrations at different times show that steady state was already established
after about 500 days for a groundwater velocity (v) of 2.7 m day 1 . It should be
noted that the fitted
3.2 cm is a bulk parameter that accounts for the whole
aquifer in the area of investigation, i.e. including possible effects of heterogeneity
that cannot be resolved in detail in a large scale investigation.
α T =
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