Environmental Engineering Reference
In-Depth Information
Chapter 7
Transport and Kinetics
7.1
Introduction
Very often biogeochemical reactions in which several species of the environment
participate play an important role for the fate and the distribution of species of
environmental relevance. Due to reactions a potentially hazardous component can
be gradually degraded and may reach concentration levels above limits set by
environmental regulations. Another scenario is also important: potentially harmful
chemical species may emerge as products of a reaction along a flow path within
a compartment.
In this and the following chapter the focus is on modeling the simultaneous
action of transport and reactions. It will be shown that for mathematical modeling it
is relevant whether reactions are slow or fast in comparison to the considered
transport processes. In this chapter we stay with slow reactions, while fast reactions
are the topic of the next chapter.
The characteristic time for a slow reaction is at least in the same scale as
advection and dispersion/diffusion. In applications at different length and velocity
scales in different environmental compartments, the classification of slow and fast
reactions may differ significantly. A reaction, which has to be classified as slow in
a flowing river, can be fast in aquatic sediments or in aquifers.
The rate of reactions is quite different. According to Cox (
1994
), the lower limit
for the characteristic time lies between 10
12
and 10
13
s. H-bond formation in
metal complexes can be as fast as 10
10
s, macromolecular complex formation
exceeds 10
7
s, and hydrolysis 10
3
s. All these processes are surely fast in all
environmental systems, unless they are inhibited by specific biogeochemical
conditions leading to much higher reaction times.
CO
2
hydration is in the order of 10
3
s, Fe(II) oxidation by O
2
in the order of 10
4
s
(Morel and Hering
1993
). SO
2
transformation and deposition as H
2
SO
4
or SO
4
2
in
the atmosphere has a time characteristic of 10 h and 33 h respectively (Deaton and
