Page 252 - Soil and water contamination, 2nd edition

13

Chemical transformation

13.1 INTRODUCTION

As well as being transported via advection and dispersion , chemical substances may undergo
a wide variety of chemical, physical, and biological transformation processes (see Chapter 2),
which must be accounted for in the transport equation s. To deal with this, the advection–
dispersion equation is extended with a reaction term r:
C C 2 C
u x D x p r (13.1)
t x x 2
where r = the rate of change in dissolved or particulate concentration due to physical,
-3
-1
chemical or biological reactions [M L T ]. This one-dimensional Equation (13.1) can, for
example, be used to calculate the evolution of the chemical concentration of a degradable
pollutant in a river downstream of an industrial wastewater discharge.
If the transformation processes proceed at a faster rate than the transport process, we
may assume that the reactions subsystem is in equilibrium . In this case the concentration
of the substance at a given location is largely governed by the reaction equilibrium. If the
reaction rate is slow, we also must consider the process kinetics that describe the change in
concentration resulting from the reaction as a function of time, i.e. the reaction rate. The
rates of physical transformation processes such as volatilisation and radioactive decay vary
considerably and depend on the physical properties of the chemical. Unlike volatilisation,
radioactive decay rates are independent of physico-chemical environmental factors such as
temperature, pH, or redox conditions. By comparison with transport processes, chemical
acid –base and complexation reactions are usually fast, but redox reactions (including most
biochemical transformations) are slow. The rates of chemical dissolution and precipitation
processes are very variable and some may be quite slow. Even if the reaction rate is slow and
the system is not in equilibrium, it is always useful to compute the equilibrium state of the
system, to know where the system is heading.
Extending the advection–dispersion equation (see Section 11.3.2) with a first-order
reaction , in which the chemical is removed from solution, gives:
C C 2 C
u x D x kC (13.2)
t x x 2
Figure 13.1 shows the evolution concentration profile after a pulse release into a river
according to Equation (13.2). Just as in Figure 11.6, the centre of the mass travels at a
velocity u and as a result of longitudinal dispersion the Gaussian curve becomes broader
x
while travelling downstream. In addition, the area of the Gaussian curve, which is
proportional to the total mass transported, decreases because of the chemical removal. Figure
13.2 shows the shape of the plume resulting from the continuous input into groundwater of
a contaminant subject to decay (compare Figure 11.10).

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