Chemistry Reference
In-Depth Information
reactor with a single inlet and a single outlet, is
dC
res
dt
1
t
f
(
)
+
R
=
C
in
−
C
res
(1)
where
C
in
is the concentration of the species in the inflow,
R
is the rate, per unit volume,
at which the species
i
s produced in the reactor (note: when the species is being consumed
R
is negative), and
t
f
is the mean residence time (or transit time) of the carrier fluid in
the reactor:
V
Q
t
f
=
(2)
where
V
is the volume of the reactor and
Q
the volumetric flow in and out of the reactor.
The residence time thus emerges naturally as a fundamental property in the governing
mass balance equation. For reactors, the inflow and outflow are purely advective
transport fluxes. As can be seen from Equation (1), governing equations for reactor
models, and by extension those of biogeochemical box models, are ordinary differential
equations with time as the only independent variable.
Although mathematically similar, box models of biogeochemical cycles differ from
simple reactor models in at least two major ways. First, the reservoirs do not have to
occupy a continuous physical space, nor do they necessarily correspond to a reacting
system. Instead they refer to a collection of matter of a certain chemical type, within
given physical and/or biological boundaries. For example, a key reservoir in the carbon
cycle is living biomass of marine biota. Included in this reservoir are all organic carbon
atoms of living marine organisms. The oceans, as a well-defined physical space, contain
many more biogeochemical reservoirs, including other types of organic carbon, e.g.,
dissolved organic molecules and dead particulate organic matter. Similarly, marine biota
encompass other biogeochemically relevant reservoirs, for example, calcium carbonate
and nutrient elements such as N, P and Si.
Second, fluxes between reservoirs are not restricted to purely advective flows of
matter. Most often, a flux in a biogeochemical box model combines physical transport
and biogeochemical transformation processes. For example, the supply of silicic acid to
the oceans by weathering of rocks on land may be represented by a flux linking the
terrestrial rock reservoir to the marine dissolved silica reservoir. Clearly, this flux
encompasses a variety of processes acting in concert, including, uplift and erosion of
rocks on land, mineral dissolution and soil formation, continental drainage, and retention
of silica by terrestrial and estuarine ecosystems. A large number of geological and
environmental variables therefore affects the net flux of dissolved silicic acid to the
oceans. Different variables may dominate at different time-scales. Hence, on relatively
short time scales, say 10
3
years, storage of reactive silica in vegetation and estuaries
may be an important regulator of the supply of silicic acid to the oceans. On longer time
scales, however, variations in the rate of uplift, rock lithology and climate become the
major sources of variability in the supply flux.
The two main tasks facing the developer of a biogeochemical box model is the
definition of the reservoirs and the parameterization of the fluxes. There are no magic
guidelines, other than to clearly define the goals of the modeling effort and to start as
simple as possible. Obviously, a model only provides direct information on reservoirs,
fluxes and parameters that are explicitly represented. The reader is referred to the
excellent textbook on biogeochemical box modeling by Chameides and Perdue (1997),
for a step-by-step introduction to model building and scenario testing. A shorter overview
can be found in Rodhe (1992).
