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

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As Bauer et al. (2006a) demonstrated, the local flow velocity estimate is a crucial parameter for the estimation of the degradation rate constant. In a sensitivity study the authors found that inclusion of field scale information on hydraulic conductivity, which is more representative for the entire site, can improve the accuracy of estimated rate constants over usage of local information only. Therefore the center line data obtained in strategy A are re-evaluated using a field scale estimate of the effective conductivity at the investigated sites: Kef is calculated as the geometric mean of local conductivity values measured at all observation wells of the site and not only using those measured on the center line. Results for this approximation are presented in Table 3 and Figure 4. It is found that consideration of all conductivity measurements available improves the rate constants estimated for all three methods and both source widths. On average all estimates are closer to the true rate than those estimated using only local conductivity information. The average improvement is between a factor of 1.5 for WS = 4 m and a factor of two for WS = 16 m. Also the standard deviations from the mean values and the cv are lower. This finding is true for the settings investigated here, i.e. a correlation length smaller than the average distance between observation wells and a stationary K distribution. If the correlation length is on the order or longer than the average observation well distance or K is not stationary, this finding is probably not transferable. norm. degradation rate constant [-] 100 10 1 0.1 Table 3: Normalized degradation rate constants estimated with strategy A, re-evaluated using a field scale estimate of Kef. WS = 4 m method A1 method A2 method A3 mean 4.75 5.73 4.14 median 4.04 4.67 2.66 stdv. 3.75 4.33 4.06 cv 0.79 0.76 0.98 N 47 47 47 WS = 16 m method A1 method A2 method A3 mean 2.16 2.53 2.42 median 1.14 1.50 0.90 stdv. 2.08 2.45 3.98 cv 0.96 0.97 1.64 N 38 38 36 W S= 4 m W S = 16 m single realization result ensemble mean A1 1 A2 2 A3 3 A1 1 A2 2 A3 3 method method Figure 4: Normalized degradation rate constants estimated with strategy A and methods A1, A2 and A3 for source widths of 4 m (left diagram) and 16 m (right diagram), respectively. Kef used for rate estimation is calculated as a field scale estimate from all monitoring wells available for each investigated plume. 8
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.
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Applied numerical modeling of satur
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Abstract Applied numerical modeling
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Vorwort Die zurückliegenden drei J
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List of abbreviations and mathemati
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for the application studies outline
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path lengths of water molecules tha
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where vmax [s -1 ] is a maximum gro
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domain is discretized along advecti
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conceptional model error: wrong pro
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The conceptual model used is a rigo
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equires therefore a higher degradat
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studied for heterogeneous sites wit
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Fig. 13: Plume length overestimatio
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concentration maximum is for the ca
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possibilities can not be provided n
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technischen Bauwerken. (Model based
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Schäfer, D., Dahmke, A., Kolditz,
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Enclosed Publication 1 Bauer, S., B
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Assessing measurements of first-ord
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WATER RESOURCES RESEARCH, VOL. 42,
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W01420 BAUER ET AL.: ASSESSING FIRS
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Page 69: Enclosed Publication 3 Beyer, C., B
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Page 98 and 99: Einführung In dieser Arbeit wird e
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Page 130 and 131: Einleitung und Zielsetzung In Deuts
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