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

v
�
�C�Cx) �
� C0
�
ln��
C�x���
M � � 1
�
�
( k C � C(
x)
k
x C
(25).
a 0
max 0
max
With the same type of center line
investigation data used for the estimation of
the first order degradation rate constant (i.e.
local concentrations, heads, hydraulic conductivities),
eq. (25) can be utilized to
estimate the MM parameters kmax and MC
by linear regression.
The Monte Carlo scenario definition and
site investigation procedure for this study
are similar to those explained in section 3.1.
Numerical simulations of plume development
in homogeneous and heterogeneous
aquifers were performed with the GeoSys /
Rockflow code. Here, however, the contaminant
plumes investigated were generated
using MM instead of first order degradation
kinetics. The parameters k max and M C
estimated with eq. (25) for the different
plume realizations were normalized to the
true values used in the numerical
simulations and are shown in a 3D-scatterplot
versus aquifer heterogeneity (Fig. 12).
Fig. 12: Normalized Michaelis-Menten parameters
(given as overestimation factors)
versus aquifer heterogeneity.
In general an overestimation of both k max
and M C is observed, which increases with
heterogeneity. An overestimation of k max increases
the velocity of contaminant degradation
as long as concentrations are much
higher than MC. The simultaneous overestimation
of MC counterbalances this effect
because the concentration threshold is
raised at which the kinetic begins to show a
dependence on concentration and transits
from zero to first order and hence decreases
the rate of degradation.
To obtain an indicator for the significance
of the estimated degradation potential, the
MM parameters determined were used in an
analytical transport model to estimate the
contaminant plume lengths. These then
were compared to the respective true plume
lengths from the numerical simulations
(Fig. 13 (a)). As a consequence of overestimating
the degradation parameters, calculated
plume lengths for high heterogeneities
are estimated to about 75 % of the true
length on average and thus are not conservative.
For low heterogeneities, however,
the suggested regression approach on average
yields good estimates of the plume
length and the degradation potential.
In addition to the effect of aquifer heterogeneity
on estimated MM parameters and the
resultant plume length estimates, also the
effect of a wrong process identification
(compare Fig. 5) is studied in Beyer et al.
(2006 [EP 3]). Although it is well known
that contaminant degradation in natural
aquifers is governed by complex processes
and kinetic laws, simple first order models
are routinely used at many field sites. This
study therefore highlights some of the
problems that result from an insufficient
wrong process identification. For this end
investigation of the plumes following MM
degradation kinetics is repeated, assuming
the appropriateness of a first order rate law
to approximate the contaminant degradation
behaviour. Hence the methods of Tab. 1
were used to derive first order rate constants
for the multiple plume realizations.
As for the estimated MM parameters the
estimated first order rate constants were
evaluated by analytical transport models to
yield estimates of the contaminant plume
length. Results for method 1 (Tab. 1) are
presented in Fig. 13 (b).
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