Geoscience Reference
In-Depth Information
shows that the dispersion coefficient increases significantly with increasing non-
dimensional time, approaching an asymptotic value for non-dimensional time
6.
The velocity reduces slightly, and also approaches an asymptotic value. When the
individual non-dimensional profile properties for each experiment were used in
(
6
)-(
8
), the results for non-dimensional time
>
6 were very noisy and the asymptotic
behaviour was more difficult to discern than when the average profile properties
were used.
>
5 Discussion
It is interesting that the cumulative development of the properties of the non-
dimensional concentration profiles shown in Figs.
3
and
4
exposes differences
between the profiles that are not apparent from the profiles themselves (shown in
Fig.
2
). Furthermore, Figs.
3
and
4
suggest that a non-dimensional time of 2 has
some significance for the study reach. When
t <
2 the properties of all the profiles
are very similar, but when
2 the properties diverge. Interestingly, however, they
all fall within an envelope. A possible reason for this behaviour is the effect of
transient storage.
Transient storage refers to the temporary trapping of material in dead zones and
bed interstices. It usually manifests itself by the presence of extended and elevated
trailing edges on concentration-time profiles. Certainly, the trailing edges on the
profiles are very long, but they are not significantly elevated. The divergence of the
profile properties in Figs.
3
and
4
could be caused by variations in the capacity of
the transient storage at different flow rates.
The cumulative development of the properties of the non-dimensional concen-
tration profiles also give useful insight into some of the disadvantages of the method
of moments for evaluating dispersion coefficients. In particular, the extremely
heavy dependence on the information in the trailing edges of the profiles, which
is a well-known phenomenon, is quantified. Figure
5
suggests that the disper-
sion coefficient can double between non-dimensional times of 2 and 8. Indeed,
an interesting question arises, namely, at what non-dimensional time should the
dispersion coefficient be evaluated? The answer depends on how the dispersion
coefficient is interpreted. For example, in the presence of transient storage, evalu-
ating the dispersion coefficient from the profile properties at large non-dimensional
times provides an overall dispersion coefficient, which includes the transient
storage effect. But this is not the same as the Taylor/Fischer shear flow dispersion
coefficient, which only describes the dispersion created by cross-sectional gradients
of (longitudinal) velocity and cross-sectional mixing (Taylor
1954
; Fischer
1967
).
If a non-dimensional time of 2 is significant for identifying the onset of the effects
of transient storage, perhaps the Taylor/Fischer shear flow dispersion coefficient
should be evaluated at this time.
The evaluation of the velocity is much more robust because it only depends on
the centroid times, which are more closely grouped than the variances, and shows
t >
