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

An interesting observation is that the differences between the three methods of strategy A are not as distinct as observed
in Bauer et al. (2006a). One explanation for this finding is that due to the larger number of observation wells used for the
site investigation in this study, the plume center line positions are better identified on average and concentration samples
are taken closer to the true plume axis. Methods A1, A2 and A3 show a different sensitivity on deviations of
measurement locations from the plume center line. This is because in method A1, the rate constant estimate is linearly
related to ln( C( x)
/ C0
) / ∆x
, while in method A2 this term appears in linear as well as squared form after rearrangement
of equation (4). As a consequence, increasing deviations of observation well locations from the plume center line and
thus lower measured contaminant concentrations will result in increasingly stronger overestimation of λ by A2 relative to
A1. For method A3, the correction factor β has to be taken into account additionally (cf. equation (5)). For significant
deviations from the center line, however, the same effect as for A2 can be shown.
In Figure 5 the degradation rate constants ΛA1 estimated with method A1 were plotted against the number of observation
wells with relative concentrations C/C0 > 0.001 in the respective monitoring networks. A clear relationship between the
number of wells and the accuracy of ΛA1 is neither observed for WS = 4 m nor for WS = 16 m. It seems, however, that the
spread of estimated rate constants decreases slightly with increasing numbers of wells, but a larger number of samples,
especially for numbers of monitoring wells > 30 would be required to derive more meaningful results. For the other
methods A2 and A3, the similar observations are made (not shown here).
norm. deg. rate constant Λ A1 [-]
50
10
1
0.1
Y = -0.074 * X + 6.531; R
0 20 40 60 80
no. of wells with C/C0 > 0.001
2 = 0.063
Y = -0.043 * X + 3.174; R2 linear fits
= 0.072
Figure 5: Degradation rate constants ΛA1 for source widths of 4 m (grey diamonds) and 16 m (black crosses) versus the
number of wells showing relative concentrations C/C0 > 0.001.
9
W S = 4 m
W S = 16 m
Strategy B - Two-dimensional evaluation
Applying method B it is not always possible to obtain a rate constant λB > 0 when minimizing the sum of squared
residuals of concentration. The concentration distribution calculated with the analytical model indicates absence of
contaminant degradation for the closest fit to the measured data for six out of 47 plumes when WS = 4 m. For the
remaining 41 plumes, usage of method B on average yields ΛB = 4.51 (Table 4, Figure 6), which is considerably closer to
the true rate constant than for methods A1 - A3 with using only local measurements of hydraulic conductivity along the
center line (cf. Table 2). The standard deviation for method B, however, is slightly larger than for A1 and A2. With WS =
16 m for five out of 38 plumes no ΛB > 0 is found. Here, the improvement over methods A1 – A3 is even more distinct
with the mean ΛB = 1.92. Also the spread of single realizations is reduced for the larger source width. However, no
definite improvement of ΛB over those obtained by strategy A using the field scale estimate of Kef (cf. Table 3) is
observed. For WS = 4 m the mean ΛB is slightly lower than the mean ΛA1, but slightly larger than ΛA3. Also the variability
of estimated ΛB is larger than for methods A1 – A3. For WS = 16 m the mean ΛB is slightly lower than for all methods of
strategy A, while the observed spread is only lower in comparison to A3.
In the estimation of λ with method B the source concentration is included as a fitting parameter. On average the true
source concentration is overestimated by a factor of three for WS = 4m, while for WS = 16m deviations are lower than 5
%. As for strategy A a distinct relationship between the number of observation wells in the monitoring network and the
quality of the degradation rate estimates is not observed.