Applied numerical modeling of saturated / unsaturated flow and ...

structure. Four different cases with increasing heterogeneity, i.e. ln(K) variances σY 2 of 0.38, 1.71, 2.7
and 4.5, respectively, are considered in this study, representing mildly to highly heterogeneous
conductivity fields. The parameters lY and σY 2 =0.38 are taken from the Borden field site (Sudicky,
1986); the value of 1.71 was found at the Testfeld Süd in southern Germany (Herfort, 2000); the
values of 2.7 and 4.5 were reported for the Columbus Air Force Base site (Rehfeldt et al., 1992). A
constant porosity n of 0.33 is used, resulting in a mean flow velocity va of 1.16·10 −5 ms −1 . For each
of the four degrees of heterogeneity, ensembles of 100 realizations of the random field are generated
by unconditional Gaussian simulation. The Monte-Carlo strategy is chosen in order to obtain
statistical measures of the errors and uncertainties introduced by the heterogeneity of K. Plumes of
the three compounds are generated in each virtual aquifer using a process based numerical flow and
reactive transport model. The GeoSys/RockFlow simulation code (Kolditz et al., 2004)isusedhere,
which solves the flow and transport equations by finite element methods. The governing equations
are given as (e.g. Bear, 1972; Kolditz, 2002):
jðKjhÞ ¼0 ð11Þ
∂C
∂t ¼ −vajC þ jðDjCÞ−C ð12Þ
with h as the piezometric height, K the tensor of hydraulic conductivity, C concentration, D the
dispersion tensor, t time and Γ a sink term representing first order or MM degradation kinetics. For
local dispersivities αL and αT values of 0.25 m and 0.05 m were used. Details of numerical and
software issues can be found in Kolditz (2002) and Kolditz and Bauer (2004). All model parameters
are summarized in Table 4.
5. Investigation of the synthetic plumes
The steady state contaminant plumes in each virtual aquifer are investigated by the center line
method (see Fig. 2). Initially three observation wells are present in the aquifer (Fig. 2 (a)), one being
located directly in the source in the center of the aquifer (full circle) at [13.0 m; 32.0 m], showing
high concentrations. This setup is the starting point for the investigation of all realizations. The initial
knowledge on the site comprises only the hydraulic heads at the three wells. The full concentration,
Table 4
Model parameters used in the numerical simulations
Parameter Value
Kef Effective conductivity 7.19·10 − 5 − 1
ms
σY 2
ln(K)-variance 0, 0.38, 1.71, 2.7, 4.5
lY Integral scale 2.67 m
n Porosity 0.33
I Hydraulic gradient 0.053
αL Longitudinal dispersivity 0.25 m
α T Transverse dispersivity 0.05 m
λ First order degradation rate constant 5.87·10 − 7 − 1
s
kmax
Maximum degradation velocity a
1.45·10 − 7 − 1
s
MC
C. Beyer et al. / Journal of Contaminant Hydrology 87 (2006) 73–95
Half saturation concentration a
a In normalized units, see explanation in the text.
0.0497
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