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

7.10.1 Level III D Values
©2001 CRC Press LLC
7.10 LEVEL III CALCULATIONS
In this chapter, we have examined the nature of molecular and eddy diffusivity,
introduced the concept of mass transfer coefficients (k), and treated the problem of
resistances occurring in series and parallel as material diffuses from one phase to
another. Two new D values have been introduced, a kAZ product and a BAZ/DY
product. We can treat situations in which various D values apply in series and in
parallel.
In some situations, diffusion D values may be assisted or countered by advective
transfer D values. For example, PCB may be evaporating from a water surface into
the atmosphere only to return by association with aerosol particles that fall by wet
or dry deposition. We can add D values when the fugacities with which they are
multiplied are identical, i.e., the source is the same phase. This is convenient, because
it makes the equations algebraically simple and enables us to compare the rates at
which materials move by various mechanisms between phases.
We thus have at our disposal an impressive set of tools for calculating transport
rates between phases. We need Z values, mass transfer coefficients, diffusivities,
path lengths, and advective flow rates. Quite complicated models can be assembled
describing transfer of a chemical between several media by a number of routes. In
general, the total D value for movement from phase A to phase B will not be the
same as that from B to A. The reason is that there may be an advective process
moving in only one direction. Diffusive processes always have identical D values
applying in each direction. D values for loss by reaction can also be included in the
mass balance expression. We are now able to use these concepts to perform a Level
III calculation.
These calculations were suggested and illustrated in a series of papers on fugacity
models (Mackay, 1979; Mackay and Paterson 1981, 1982; and Mackay et al. 1985).
It is important to emphasize that these models will give the same results as other
concentration-based models, provided that the intermedia transport expressions are
ultimately equivalent. A major advantage of the fugacity approach is that an enormous
amount of detail can be contained in one D value, which can be readily
compared with other D values for different processes. It is quite difficult, on the
other hand, to compare a reaction rate constant, a mass transfer coefficient, and a
sedimentation rate and identify their relative importance.
Figure 7.10 depicts the simple four-compartment evaluative environment with
the intermedia transport processes indicated by arrows. In addition to the reaction
and advection D values, which were introduced in Level II, there are seven intermedia
D values. The emission rates of chemicals must now be specified on a medium-bymedium
basis whereas, in Level II, only the total emission rate was needed.
Table 7.1 lists the intermedia D values and gives the equations in terms of
transport rate parameters. Subscripts are used to designate air, 1; water, 2; soil, 3;
and sediment, 4.
Table 7.2 gives order-of-magnitude values for parameters used to calculate intermedia
transport D values. These values depend on the environmental conditions and