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

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92 C. Beyer et al. / Journal of Contaminant Hydrology 87 (2006) 73–95 constitutes a more accurate estimate of the true plume length than any of the first order methods used. Only when aquifer heterogeneity is very high, L4 is able to yield plume length estimates of almost comparable accuracy. This is mainly, because increased transverse dispersion produces concentration profiles that allow a log-linear fit of a first order rate constant. 7. Summary and conclusions In this study the Virtual Aquifer concept is used to assess the uncertainty involved in estimating down stream contaminant concentrations and plume lengths in heterogeneous aquifers. For such an analysis a key element is the quantification of the degradation rate at the site under study. Therefore, the main focus of this work is on the influence of this parameter on the estimated plume lengths. Three different scenarios are analysed. In case A, four different standard field methods based on the center line investigation strategy are tested and compared with regard to their capability of estimating first order degradation rate constants and the contaminant plume length in heterogeneous aquifers. The four methods are applied to plumes following first order degradation kinetics. It is found that both, the estimated degradation rate constants and the calculated plume lengths, are subject to high uncertainty. On average, estimated rate constants exceed the true degradation rate constant, causing calculated plume lengths that are too short. Both bias and uncertainty of estimated degradation rate constants increase with the degree of heterogeneity to about a factor in the order of a magnitude, respectively. However, the uncertainty observed in the rate constants does not fully propagate to the plume length estimates. On average plume lengths are underestimated by about 50% of the true plume length, and up to a factor of ten in the worst cases. Of the four different methods, the approach of Wiedemeier et al. (1996) using concentrations normalized to a conservative tracer yields the best results for the rate constants and for the plume lengths. Consequently, this method should preferably be used. However, the presence of a suitable recalcitrant compound may not always be given. In this case, the most simple of the four approaches, which is based on the advection equation and neglects dispersive processes should be used to determine the degradation potential, as this method yields closer estimates of the first order rate constant than the approaches using the one- (Buscheck and Alcantar, 1995) and two-dimensional advection dispersion equations (Zhang and Heathcote, 2003). The non-conservative plume length estimates might cause threats to down stream receptors, as the risk of contamination could be underrated. The high uncertainty when estimating plume dimensions could result in incorrect decisions regarding the necessity and dimensioning of engineered remediation measures or when considering the applicability of natural attenuation. All four methods are only applicable to steady state plumes. In reality, however, contaminant plumes often show temporal variations in extent and orientation as the plume expands, the source slowly depletes, or the flow regime changes over time. For expanding plumes, application of methods 1–4 wouldresultinan overestimation of the rate constant, and thus in underestimation of the plume length at steady state. This is because the down stream transient contaminant concentrations are lower than those at steady state, causing a higher concentration decrease along the center line, which would be falsely attributed to the degradation process. For the same reason rate constants would also be overestimated for shrinking plumes. An examination of the current state of the plume is necessary, when one of the four methods is to be applied at a site. An overview of techniques for this purpose is given by Newell et al. (2002). Case B analyses the additional error that results from application of the four methods, although the true degradation kinetics deviate from first order. Here plumes following Michaelis–Menten degradation kinetics are investigated. Results show that for the three approaches without correction of concentrations to a conservative tracer, an additional underestimation occurs which
is largest for low heterogeneities. For the approach using the tracer correction, the estimated plume lengths still match the true lengths on average. However, the uncertainty of the plume lengths is significantly increased as compared to case A. In case C, a regression approach is introduced to estimate the parameters of the MM kinetics and to calculate the plume lengths for the same plumes as investigated in case B. Since longitudinal and transverse dispersion are neglected in this method, the MM parameters are overestimated on average. Overestimation increases from less than a factor of two for low degrees of heterogeneity to a factor of roughly four for high heterogeneity. Consequently an underestimation of the corresponding plume lengths is observed for most realizations. For low heterogeneity, the plume length is estimated precisely with low uncertainty, for high heterogeneity the average estimated plume length is about 80% of the true plume length, with estimates as low as 40–35% in the worst cases. However, in comparison with the first order approximation investigated in case B the error resulting from this approach is significantly reduced, with the uncertainty of the plume length estimates being reduced by a factor of three. Therefore, if field data collected along the center line of a plume gives evidence of MM kinetics (linear behaviour of concentrations vs. distance in a linear plot, concave down behaviour in a semi-logarithmic plot (Bekins et al., 1998)), this approach is recommended. Generally, the Virtual Aquifer concept has proven useful in assessing the performance of methods for investigating first order rate constants and plume lengths from plume center line measurements. The main advantage is, that individual factors, as here the hydraulic heterogeneity and the assumption of a wrong plume kinetics, can be studied either individually in detail or in combination and under otherwise ideal conditions. However, the restrictions from the simplified setup of the model scenario have to be kept in mind when drawing conclusions for field applications. In reality, contaminant degradation follows more complicated rate laws, depending e.g. on electron acceptor and donor availability, may include transient effects, or dilution and phase changes to the unsaturated zone. Further studies will thus incorporate more realistic degradation kinetics as well as influences from e.g. measurement errors. Acknowledgements This work is funded by the German Ministry of Education and Research (BMBF) under grant 033 05 12/033 05 13 as part of the KORA priority program, sub-project 7.2. We wish to thank Robert Walsh for his helpful comments on the manuscript. We also wish to thank our project partners at the Christian-Albrechts-University Kiel Andreas Dahmke and Dirk Schäfer for their support in our research. We acknowledge Uwe Wittmann, Iris Bernhardt and Ludwig Luckner for coordination of the project work. Furthermore we would like to acknowledge the thoughtful reviews of the anonymous reviewers and the Editor. Their comments have greatly improved the manuscript. References C. Beyer et al. / Journal of Contaminant Hydrology 87 (2006) 73–95 Aziz, C.E., Newell, C.J., Gonzales, A.R., Haas, P., Clement, T.P., Sun, Y., 2000. BIOCHLOR Natural Attenuation Decision Support System User's Manual. U.S. EPA, Office of Research and Development, EPA/600/R-00/008, Washington D.C. Bauer, S., Kolditz, O., 2005. Assessing contaminant mass flow rates by the integral groundwater investigation method by using the virtual aquifer approach. In: ModelCARE 2005, Fifth International Conference on Calibration and Reliability in Groundwater Modelling. From Uncertainty to Decision Making. Pre-published Proceedings, The Hague (Scheveningen), The Netherlands, June 2005, pp.301–307. 93
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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
Page 40 and 41: Schäfer, D., Dahmke, A., Kolditz,
Page 43: Enclosed Publication 1 Bauer, S., B
Page 46 and 47: Assessing measurements of first-ord
Page 55 and 56: WATER RESOURCES RESEARCH, VOL. 42,
Page 57 and 58: W01420 BAUER ET AL.: ASSESSING FIRS
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Page 98 and 99: Einführung In dieser Arbeit wird e
Page 100 and 101: Entlang der so bestimmten Grundwass
Page 102 and 103: Für die letztgenannten Methoden m
Page 104 and 105: Um diesen Effekt zu verdeutlichen s
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Page 130 and 131: Einleitung und Zielsetzung In Deuts
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keinen Einfluss auf die abgebaute M
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Carsell, R. F., Parish, R. S.: Deve
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van Genuchten, M.T.: A closed form
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