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

Table 1
Overview of scenarios studied
Case Contaminant plume
following
parameters to the plume lengths is analysed. Results are set in relation to cases A and B to discuss
advantages and disadvantages, potentials and limitations of the MM parameter estimation approach.
An overview of the three different cases is given in Table 1.
4. Methods
C. Beyer et al. / Journal of Contaminant Hydrology 87 (2006) 73–95
Degradation rate
determined with
4.1. Estimation of degradation rate constants
Plume length
determined with
A First order kinetics First order kinetics (Eqs. (1)–(4)) First order kinetics (Eqs. (7)–(9)) 6.1
B Michaelis–Menten
kinetics
First order kinetics (Eqs. (1)–(4)) First order kinetics (Eqs. (7)–(9)) 6.2
C Michaelis–Menten
kinetics
Michaelis–Menten kinetics (Eq. (5)) Michaelis–Menten kinetics (Eq. (10)) 6.3
Results in
section
Four different standard methods for the determination of the first order degradation rate
constant λ (Table 2, Eqs. (1)–(4)) are compared in this study. Each of the four methods requires
concentration-distance relations obtained by measuring contaminant concentrations in several
observation wells along the center line of a steady state plume. The degradation rate constant λ is
estimated by fitting a linear function to the logarithms of concentration vs. distance from the source
by linear regression. Methods 1–4 are introduced only briefly here, more details are given in Bauer
et al. (2006). Furthermore, a regression approach that allows the estimation of MM kinetics
parameters from center line data is developed and tested as method 5 (Table 2, equation (5)).
Method 1 (Table 2, equation (1)) is based on the one dimensional transport equation, considering
advection and first order degradation only. Rate constants determined with method 1 can
be considered rather an overall or bulk attenuation rate than a degradation rate constant (Newell et
al., 2002) as all concentration changes that result from processes other than degradation, such as
diffusion, dispersion, volatilization and dilution, are attributed to the degradation process. Method
2(Table 2, equation (2); Buscheck and Alcantar, 1995) is based on the steady state solution to the
one dimensional transport equation considering advection, longitudinal dispersion and first order
degradation. Method 2 thus requires an estimate of longitudinal dispersivity αL [m]. Method 3
(Table 2, equation (3)) was proposed by Zhang and Heathcote (2003) and represents a twodimensional
modification of method 2. A correction term derived from the analytical solution of
the two-dimensional transport equation including first order decay (Domenico, 1987) is used to
account for lateral spreading and the width of the source zone. A similar approach, which also
allows the inclusion of measurements off the plume center line was presented by Stenback et al.
(2004). Method 4 (Table 2, equation (4); Wilson et al., 1994; Wiedemeier et al., 1996) is based on
the same transport equation as method 1. However, measured concentrations of the reactive
contaminant are scaled by up and down gradient concentration C0 ⁎ and C(x)⁎ [M L − 3 ] of a nondegrading
conservative solute spreading from the same source. Since dispersion and measuring off
the center line also affect the measured concentrations of non-reactive solutes, this procedure
allows a correction for both effects. Method 5 (Table 2, equation (5)) is valid for contaminant
plumes following Michaelis–Menten (MM) degradation kinetics (Beyer et al., 2005). When the
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