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

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to 5, Methods 1, 2 and 3 show a success probability of about 1, while Method 4 yields
a probability of 0.7. Figure 3 also illustrates that all methods exhibit a decreasing
probability of success when the degree of heterogeneity is increased. An error factor
of 5 yields a success probability of about 1 for the lowest degree of heterogeneity
(0.38) for Method 1; this probability decreases to 0.7, 0.5 and 0.35 for a σ²ln(KF) of
1.71, 2.7 and 4.5, respectively. For Method 2 the corresponding success probabilities
are 1.0, 0.9, 0.8 and 0.6; Method 3 yields values of 1.0, 0.55, 0.35 and 0.25; and
Method 4 0.7, 0.7, 0.6 and 0.4.
To achieve the degradation rate within a factor of 10 of the correct degradation
rate (for high hydraulic heterogeneity, Fig. 3(c)), the success probabilities were found
to be 0.8, 0.95, 0.8 and 0.6 for Methods 1 through 4, respectively. For all degrees of
heterogeneity, Method 2 yielded the highest probability for achieving the correct
degradation rate. For medium to very high heterogeneity, Method 4 was second best,
and was the worst for aquifers that were only slightly heterogeneous (Fig. 3(a)). Method
1, although the simplest method, yielded similar probabilities as Method 4, except
Method 1 works well for aquifers of low heterogeneity. Method 3 yielded the lowest
success probabilities, with the exception of an aquifer of low heterogeneity.
CONCLUSIONS
From the study presented, it can be concluded that the four methods for examining
decay coefficients behave differently when heterogeneity is increased. All methods
show a decrease in success probability with increasing heterogeneity. Figure 2
illustrated that the decrease in success probability is attributed to an overestimation of
the degradation rate constant. The overestimation was largest for Method 3, yielding
the lowest success probability. Method 2 was the least affected by an increase in
heterogeneity and was also the method that depicted the lowest overestimation of
degradation rates. Methods 3 and 4, the most realistic since they are based on the 1-D
and 2-D transport equations, illustrated low success probabilities and high overestimation
of degradation rates, Method 3 being the worst. Methods 3 and 4 were
prone to errors due to the introduction of longitudinal and transverse dispersivities,
which were required to calculate the degradation rate constant. Method 1, the simplest
method, yielded results comparable to Method 4.
It can be concluded from this study, that Method 2 (using a non-reactive cocontaminant)
is the preferred method for field investigations, where first-order
degradation rates are to be estimated. If this co-contaminant is not available, then
Method 1 is preferred as then no uncertainty regarding the dispersivities is introduced.
Although widely used and published in the literature, the method of Buscheck &
Alcantar (1995), Method 3, yielded the worst results in this study.
Acknowledgements This work is funded by the German Ministry of Education and
Research as part of the KORA priority programme, sub-project 7.2.