McKay, Donald. "Front matter" Multimedia Environmental Models ...

2.3.3 Summary
In summary, our simplest view of the environment is that of a small number of
phases, each of which is homogeneous or well mixed and unchanging with time.
When this is inadequate, the number of phases may be increased; heterogeneity may
be permitted in one, two, or three dimensions; and variation with time may be
included. The modeler’s philosophy should be to concede each increase in complexity
reluctantly, and only when necessary. Each concession results in more mathematical
complexity and the need for more data in the form of kinetic or equilibrium
parameters. The model becomes more difficult to understand and thus less likely to
be used, especially by others. This is not a new idea. William of Occam expressed
the same sentiment about 650 years ago, when he formulated his principle of
parsimony or “Occam’s Razor,” stating
©2001 CRC Press LLC
Essentia non sunt multiplicanda praeter necessitatem
which can be translated as, “What can be done with fewer (assumptions) is done in
vain with more,” or more colloquially, “Don’t make models more complicated than
is necessary.”
2.4 MASS BALANCES
When describing a volume of the environment, it is obviously essential to define
its limits in space. This may simply be the boundaries of water in a pond or the air
over a city to a height of 1000 m. The volume is presumably defined exactly, as are
the areas in contact with adjoining phases. Having established this control “envelope”
or “volume” or “parcel,” we can write equations describing the processes by which
a mass of chemical enters and leaves this envelope.
The fundamental and now axiomatic law of conservation of mass, which was
first stated clearly by Antoine Lavoisier, provides the basis for all mass balance
equations. Rarely do we encounter situations in which nuclear processes violate this
law. Mass balance equations are so important as foundations of all environmental
calculations that it is essential to define them unambiguously. Three types can be
formulated and are illustrated below. We do not treat energy balances, but they are
set up similarly.
2.4.1 Closed System, Steady-State Equations
This is the simplest class of equation. It describes how a given mass of chemical
will partition between various phases of fixed volume. The basic equation simply
expresses the obvious statement that the total amount of chemical present equals the
sum of the amounts in each phase, each of these amounts usually being a product of
a concentration and a volume. The system is closed or “sealed” in that no entry or
exit of chemical is permitted. In environmental calculations, the concentrations are
usually so low that the presence of the chemical does not affect the phase volumes.