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

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