Environmental Engineering Reference
In-Depth Information
Winebrake
1999
), i.e. in the order of 10
5
-10
6
s. Photolysis of a pesticide (carbaryl)
and Mn(II) oxydation have a similar speed. Hydrolysis of an insecticide (disulfo-
ton) and heterogeneous Mn(II) oxidation can be observed in a time scale of 10
7
s.
More than a year can be estimated for the hydrolysis of methyl iodide in freshwater
and for homogeneous Mn(II) oxidation (Morel and Hering
1993
). Tributylin, an
ingredient of anti-fouling paints, is degraded in three steps, of which each has
a characteristic time between 1.5 and 3 years (Sarradin et al.
1995
).
Morel and Hering (
1993
) give amino acid racemization as an example for an
extremely slow process with a rate coefficient of 10
14
s. This can surely be classified
as a geological time-scale (it can be compared to petroleum formation).
For the modeler, the time scale of the process always has to be related to the
typical
time scale of interest
of the problem for which the model is designed.
Processes which are much faster than the time scale of interest need not to be
resolved in the model - neither processes which are much slower than the time scale
of interest. Only processes, for which the characteristic time is similar to the
problem time scale need to be treated as kinetic processes. Therefore any kinetics
classification has no general validity. It is rather problem and site specific.
Kinetics
is a branch of chemistry that deals with reactions, for which the reaction
rate has to be given as a function of environmental state variables. The determi-
nation of such kinetic rates is the main task of kinetics. It is often a formidable
task, because the number of state variables and the range of the validity of experi-
mentally determined reaction rates is not clear a priori.
The implementation of kinetics turns out to be unproblematic within the mathe-
matical framework used in this topic. Kinetics deals with reaction rates. The
transport differential equations are stated in terms of rates. Thus, in the differential
equation a rate
r
just has to be added, and the resulting transport equation for the
concentration
c
of a single species becomes:
y
@c
@t
¼r
y
j
ðcÞþq
with
j
ðcÞ¼
D
rcþ
vc
(7.1)
Within this formalism one can conceive decay and degradation as special cases
of kinetics with
q ¼
yl
c
n
for linear decay and
q ¼
yl
c
n
for general decay of
order
n
. If the factor
appears in all terms, it can be omitted; this will be assumed
for the remainder of this chapter.
In general, several reactants are involved in reactions, and it is often not suffi-
cient to consider a single species in a model. Let's assume that a simple reaction has
two reactants
a
and
b
and one reaction product
c
:
y
aþb ! c
(7.2)
The corresponding system of differential equations is obtained by adding the
reaction rate in all three differential equations, of which each represents the
