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

The total of all D values is 0.7587.
Therefore,
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E = 40
f = 40/SD = 52.7
The total amount is 1264 mols, giving a mean residence time of 31.6 hours. The
most important loss process is advection in air, which accounts for 21.08 mol/h.
Next is soil reaction at 7.31 mol/h, the water advection at 5.27 mol/h, etc. Each
individual rate is D f mol/h.
6.4.1 Advection as a Pseudo Reaction
Examination of these equations shows that the group G/V plays the same role
as a rate constant having identical units of h –1 . It may, indeed, be convenient to
regard advective loss as a pseudo reaction with this rate constant and applicable to
the phase volume of V. Note that the group V/G is the residence time of the phase
in the system. Frequently, this is the most accessible and readily remembered quantity.
For example, it may be known that the retention time of water in a lake is 10
days, or 240 hours. The advective rate constant, k, is thus 1/240 h –1 , and the D value
is V Z k, which is, of course, also G Z.
It is noteworthy that this residence time is not equivalent to a reaction half-time,
which is related to the rate constant through the constant 0.693 or ln 2. Residence
time is equivalent to 1/k.
6.4.2 Residence Times and Persistence
Confusion may arise when calculating the residence time or persistence of a
chemical in a system in which advection and reaction occur simultaneously. The
overall residence time in Example 6.4 is 31.6 hours and is a combination of the
advective residence time and the reaction time. The presence of advection does not
influence the rate constant of the reaction; therefore, it cannot affect the persistence
of the chemical. But, by removing the chemical, it does affect the amount of chemical
that is available for reaction, and thus it affects the rate of reaction. It would be
useful if we could establish a method of breaking down the overall persistence or
residence time into the time attributable to reaction and the time attributable to
advection. This is best done by modifying the fugacity equations as shown below
for total input I.
I = SD Aif + SD Rif
But I = M/t O, where M is the amount of chemical and t O is the overall residence
time. Furthermore, M = SVZf or fSVZ. Thus, dividing both sides by M and cancelling
f gives