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

WATER RESOURCES RESEARCH, VOL. 42, W01420, doi:10.1029/2004WR003878, 2006
Assessing measurement uncertainty of first-order
degradation rates in heterogeneous aquifers
Sebastian Bauer, Christof Beyer, and Olaf Kolditz
Center for Applied Geoscience, University of Tübingen, Tübingen, Germany
Received 7 December 2004; revised 7 October 2005; accepted 18 October 2005; published 31 January 2006.
[1] The principal idea of this paper is to simulate and evaluate the determination of
first-order degradation rate constants at heterogeneous contaminated sites under realistic
conditions. First, a set of heterogeneous and contaminated synthetic aquifers is generated;
second, the spreading of a solute plume subject to first-order degradation is simulated.
Third, this plume is investigated using ‘‘monitoring wells’’ placed along the presumed
plume center line. Using only piezometric heads, concentrations and hydraulic
conductivities obtained at these monitoring wells, first-order degradation rate constants are
calculated by methods typically used in field applications. The estimated rate constants
are compared to the ‘‘real’’ value known from the simulations. This comparison is
conducted for different degrees of heterogeneity, represented by lognormally distributed
random conductivity fields. The results indicate that, with increasing degree of
heterogeneity, ‘‘measured’’ degradation rate constants become uncertain with a high
variability around the true constant. Measured rate constants tend to overestimate the true
constant by up to one order of magnitude. A sensitivity analysis of the influences of source
width, transport velocity, and dispersivity shows that (1) with increasing source width,
measured rate constants decrease their relative error and increase their accuracy; (2) the
choice of dispersivity can produce both over- and under-estimation of the true rate
constant; and (3) that large-scale measurements of hydraulic conductivity yield better
estimates of flow velocities as compared to local scale measurements. These results
explain in part the high variability of field measured degradation rate constants reported in
the literature.
Citation: Bauer, S., C. Beyer, and O. Kolditz (2006), Assessing measurement uncertainty of first-order degradation rates in
heterogeneous aquifers, Water Resour. Res., 42, W01420, doi:10.1029/2004WR003878.
1. Introduction
[2] This work studies the uncertainty involved in estimating
first order degradation rate constants by the plume
center line method for the assessment of natural attenuation
at contaminated groundwater sites. Natural attenuation, also
known as intrinsic bioremediation, refers to the observed
reduction in contaminant concentration via natural processes
as contaminants migrate from the source into environmental
media [U.S. Environmental Protection Agency (EPA), 1999;
Wiedemeier et al., 1999]. The processes contributing to
natural attenuation include dilution, dispersion, sorption,
volatilization and biodegradation, where biodegradation is
the only process that decreases the total contaminant mass.
The relative efficiencies of the attenuation processes active
at a contaminated site must be carefully assessed before
natural attenuation can be adopted as a cleanup remedy or
risk reduction strategy. Thus degradation rates of the contaminants
under consideration may play an important role in
decision making and site management, when natural attenuation
is considered as a remedial alternative or a remedial
step in contaminated site management. Degradation rate
constants can be used to estimate (1) the total overall natural
Copyright 2006 by the American Geophysical Union.
0043-1397/06/2004WR003878$09.00
W01420
attenuation potential of an aquifer, (2) contaminant plume
lengths and (3) downstream concentrations. They can also be
used for identifying potential receptors and exposure levels
in case of a risk analysis.
[3] Several approaches for estimating biodegradation
rates in ground water in the field are commonly used,
including mass balances, in situ microcosm studies and
the use of concentration-distance relations obtained along
the plume center line [Chapelle et al., 1996; Wiedemeier et
al., 1999]. The latter include a batch-reaction solution
[Wiedemeier et al., 1996], normalization to a recalcitrant
co-contaminant [Wiedemeier et al., 1996, 1999] and the
method of Buscheck and Alcantar [1995]. The method of
Buscheck and Alcantar [1995] utilizes contaminant concentrations
measured along the plume center line, which are
evaluated by an analytical solution to the one-dimensional
transport equation with first-order degradation. The firstorder
degradation rate is calculated from the concentrations
and an assumed longitudinal dispersivity. An
additional requirement is, that the plume has reached
steady state. This approach has been used by a number
of authors, e.g., Chapelle et al. [1996], Wiedemeier et al.
[1996], Zamfirescu and Grathwohl [2001], Suarez and Rifai
[2002] or Bockelmann et al. [2003]. Recently, two- and
three-dimensional approaches were suggested [Zhang and
Heathcote, 2003; Stenback et al., 2004] as extensions to the
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