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

The rate constants in each case are 0.693/half-life. The sum of the V Z k terms
or D values is 0.2587, thus,
©2001 CRC Press LLC
f = E/SD = 96.6 Pa
Thus, each C is Z f and each amount m is VC, totaling 2318 mol. Each rate is V C
k or D f, totaling 25 mol/h.
It is clear that the D value V Z k controls the overall importance of each process.
Despite its low volume and relatively slow reaction rate, the soil provides a fairly
fast-reacting medium because of its large Z value. It is not until the calculation is
completed that it becomes obvious where most reaction occurs. The overall residence
time is 2318/25 or 93 hours.
Note that the persistence or M/E is a weighted mean of the persistence or
reciprocal rate constants in each phase. It is also SVZ/SD.
6.4 COMBINED ADVECTION AND REACTION
Advective and reaction processes can be included in the same calculation as
shown in the example below, which is similar to those presented earlier for reaction.
We now have inflow and outflow of air and water at rates given below and with
background concentrations as shown in Figure 6.1c. The mass balance equation now
becomes
I = E + G AC BA + G WC BW = G AC A + G WC W + SV iC ik i
This can be solved either by substituting K iWC W for all concentrations and solving
for C W, or calculating the advective D values as GZ and adding them to the reaction
D values. The equivalence of these routes can be demonstrated by performing both
calculations.
Worked Example 6.4
The environment in Example 6.3 has advective flows of 1000 m 3 /h in air and
1 m 3 /h in water as in Example 6.1 and reaction D values as in Example 6.3, with a
total input by advection and emission of 40 mol/h. Calculate the fugacity concentrations,
amounts, and chemical residence time.
Phase
Volume
(m 3 ) Z
D A
(advection)
D R
(reaction)
C
(mol/m 3 )
m
(mol)
Rate
(mol/h)
f(D A + D R)
Air 10000 4 ¥ 10 –4 0.4 0.0277 0.021 210 22.55
Water 100 0.1 0.1 0.0924 5.27 527 10.14
Soil 10 1.0 0.0 0.1386 52.7 527 7.31
Total 0.5 0.2587 1264 40