Environmental Engineering Reference
In-Depth Information
Chapter 8
Transport and Equilibrium Reactions
8.1
Introductory Example
The situation that environmentally relevant species take part in chemical reactions,
while being transported through a compartment of the environment, was already
treated in Chap. 7. In this chapter the same situation is taken up again with the
difference concerning the time scale of the reactions. Here we deal with reactions
which are fast in comparison to transport processes.
The situation that chemical reactions are fast compared to other environmental
processes is met quite often but on very different time scales. The scale difference is
related to the fact that the transport time scale deviates significantly in different
compartments. There are systems which are almost in a no-flow state. In deep
underground reservoirs transport is measured in geological time scales, and most
chemical transformations can be assumed to be fast in comparison. In near-surface
aquifers velocities are often in the range of several meters per year or higher, and
some chemical processes may not reach their equilibrium. Sedimentation rates in
the deep ocean or in lakes are in the order of several mm per year; this sets the scale
for fast and slow reactions in those systems. Therefore, each environmental com-
partment has its own time-scale and is related to chemical processes in a different
manner.
Reactions with a characteristic time, which is in the same scale as transport or
even slower, can be included in the mathematical description as shown in the
previous chapter. The reaction rate has to be formulated in dependence of
concentrations and maybe some other state variables, like temperature, and added
as another term in the differential equation. As the reaction contributes to the mass
balance, which is expressed by the differential equation, the mathematical formu-
lation is straight forward. More difficult is the determination of rate expressions that
are relevant in practice from the chemical point of view. But this has to be left to
chemists and is outside of the scope of this topic.
For fast reactions, the rate law is not relevant. Instead, the equilibrium charac-
teristic is brought into play. A widely accepted formulation is given by the law of
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