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

8.11.2 Model of a Chemical Evaporating Indoors
We treat a situation in which a pool of chemical is evaporating into the basement
air space of a two-room (basement plus ground level) building with air circulation.
If the building were entirely sealed and the chemical were nonreactive, evaporation
would continue until the fugacity throughout the entire building equalled that of the
pool (f P). Of course, it is possible that the pool would have been completely evaporated
by that time.
The evaporation rate can be characterized by a D value D 1 corresponding to
kAZ, the product of the mass transfer coefficient, pool area, and air phase Z value.
If the chemical were in solution, it would be necessary to invoke liquid and gas
phase D values in series, i.e., the two-film theory as discussed in Chapter 7.
The evaporated chemical may then be advected from one room to another with
a D value D 2 defined as GZ, the product of the air flow or exchange rate and the air
phase Z value. From this second room, it may be advected to the outdoors with
another D value D 3. These advection rates are normally characterized as “air changes
per hour” or ACH, which is the advection rate G divided by the room or building
volume and is the reciprocal of the air residence time. Typical ACHs for houses
range from 0.25 to 1.5 per hour. The outdoor air has a defined background fugacity f A.
It is apparent that the chemical experiences three D values in series in its journey
from spill to outdoors, thus the total D value will be given by
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1/D T = 1/D 1 + 1/D 2 + 1/D 3
and the flux N is D T(f P – f A) mol/h.
Of interest are the intermediate fugacities in the rooms, which can be estimated
from the equations.
N = D 1(f P – f 1) = D 2(f 1 – f 2) = D 3(f 2 – f A)
This is essentially a “three-film” or “three-resistance” model. Degrading reactions
could be included, leading to more complex, but still manageable, equations. Sorption
to walls and floors could also be treated, but it is probably necessary to include
these processes as differential equations.
Worked Example 8.3
An example of a “spill” of a small quantity (1 g) of PCB over 0.01 m 2 (e.g.,
from a fluorescent ballast) was considered by Mackay and Paterson (1983). The
PCB fugacity was 0.12 Pa and the outdoor concentration was taken as 4 ng/m 3 or
3.7 ¥ 10 –8 Pa. The three D values (expressed as reciprocals) are
1/D 1 = 49000, 1/D 2 = 30, 1/D 3 = 15
Thus, D T is essentially D 1, most resistance lying in the slow evaporation process
from the small spill area. The molar mass is 260 g/mol, and the evaporation rate N
is then