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

W01420 BAUER ET AL.: ASSESSING FIRST-ORDER RATES
Figure 7. Ensemble medians of estimated first-order rate constants L 4 for (a) s Y 2 = 0.38, (b) 1.71,
(c) 2.7, and (d) 4.5 for different values of a L versus a T. Values for method 3 are obtained using
L 3(a L)=L 4(a L, a T = 0). Medians for L 1 and L 2 are depicted in each diagram by dashed and dash-dotted
horizontal lines for reference.
region, aL will show lower values. aT grows with travel
distance until aT reaches peak values at about 2.5 lY of 0.1,
0.44, 0.69 and 1.15 m, respectively. The asymptotic limit
of aT is 0. For nonzero but small local dispersivities (aL,T
l 1
Y 1), aL is unaffected or slightly reduced, while aT
increases and a non zero long time limit will establish
[Zhang and Neuman, 1996]. As the observation wells used
for the investigation of the plumes are located within 3.8 to
11.2 lY from the contaminant source, it is expected, that the
asymptotic limits of aL and aT are not yet reached. Thus
for methods 3 and 4, aL values below those listed above
should be used. Similarly, aT values in the range between
the peak values and the asymptotic limit should be used
for method 4. As this rough estimation already shows,
applying the stochastically derived values in a real field
case may introduce uncertainty, as the local conditions are
generally not known exactly.
[33] To study the influence of dispersivity parameterization
on rate constants estimated with methods 3 and 4, the
sensitivity of L3 and L4 on different values of aL and aT is
investigated. Because in a real field application these values
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will be always uncertain, this investigation is performed as a
sensitivity analysis, which allows to cover a wider range of
values for aL and aT. For aL values of 12, 9, 6, 3, 0.8 and
0.25 m are used, while for aT values of 2, 1.15, 1, 0.75, 0.5,
0.3, 0.07 and 0 m are used. Thus the range of reasonable
values of aL and aT up to the maximum values for each sY 2
is well represented. Figure 7 presents for each sY 2 the
medians of estimated rate constants L3, using L3(aL) =
L4(aL, aT = 0), and L4(aL, aT) in dependence on aT for the
different values of aL. For reference, also medians for L1
and L2 (compare Figure 4) are included. Because method 2
corrects for dispersion as well as for measuring off the
plume center line, but not for errors in the estimated
transport velocity, and the same value of the transport
velocity is used for all four methods, L2 can be seen as
the optimal lower limit for methods 3 and 4. Method 1
involves no correction for longitudinal and transverse dispersion
or measuring off the center line. Thus a good
parameterization of aL and aT for method 4 should result
in rate constant estimates L4 < L1. However, L4 < L2 would
indicate over correction for transverse dispersion.