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

where V i is volume, Z i is bulk Z value, I i is the input rate (which may be a function
of time), each term D jif j represents intermedia input transfers, and D Tif i is the total
output. If an initial fugacity is defined for each medium, these four equations can
be integrated numerically to give the fugacities as a function of time, thus quantifying
the time response characteristics of the system.
It is noteworthy that the characteristic response time of a compartment is V iZ i/D Ti,
which can be deduced from the Level III steady-state version. These characteristic
times provide advance insight into how a Level IV system should respond to changing
emissions. This calculation is most useful for estimating recovery times of a
contaminated system that is now experiencing zero or reduced emissions.
Hand Calculation
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7.12 CONCLUDING EXAMPLES
Using only air, water, and sediment from the four-compartment environments
and the chemicals treated in the Level II example at the conclusion of Chapter 6,
draw a Level III diagram similar to Figure 7.11, showing the compartments, the VZ
values for each, and the advection and reaction D values. Write in somewhat arbitrary
values for the six intermedia transport D values, but assigning values that lie in the
range of 0.1 to 1% of VZ of the source phase. This gives rate constants for transport
of 10 –3 to 10 –2 h –1 . Feel free to round off all VZ and D values to facilitate calculation.
Assume total inputs into air of 100 mol/h, and into water of 20 mol/h.
Write down the three mass balance equations and solve by hand for the three
fugacities. Calculate all the fluxes and check the mass balance for each compartment
and the system as a whole. Calculate the three chemical residence times. Confirm
the validity of the linear additivity assertion by calculating the fugacity in water for
emissions only to air, and only to water, and show that their sum is the fugacity
calculated when both emissions apply simultaneously. Do the residence times depend
on the chemicals’ mode of entry to the environment?
Computer Calculation
Using the Level III program described in Chapter 8, compile a Level III mass
balance diagram for a chemical using data from Table 3.5 and postulated emission
rates in the range of 0.1 to 10 g per hour per square kilometre into air, water, and
soil. Discuss the results, including the primary media of accumulation, the important
processes, the relative media fugacities, and the residence times.
EQC Calculation
Using the EQC model described in Chapter 8, compile Level I, II, and III mass
balances for a chemical and discuss the results.