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

1. Fallout of chemical from air to water or soil in dustfall, rain, or snow
2. Deposition of chemical from water to sediments in association with suspended
matter which deposits on the bed of sediment
3. The reverse process of resuspension
4. Ingestion and egestion of food containing chemical by biota
The mathematical expressions for these rates are quite different. For diffusion,
the net rate of transfer or flux is written as the product of the departure from
equilibrium and a kinetic quantity, and the net flux becomes zero when the phases
are in equilibrium. We examine these diffusive processes in Chapter 7. For nondiffusive
processes, the flux is the product of the volume of the phase transferred (e.g.,
quantity of sediment or rain) and the concentration. We treat nondiffusive processes
in Chapter 6.
We use the word flux as short form for transport rate. It has units such as mol/h
or g/h. Purists insist that flux should have units of mol/h·m 2 , i.e., it should be area
specific. We will apply it to both. It is erroneous to use the term flux rate since flux,
like velocity, already contains the “per time” term.
©2001 CRC Press LLC
2.8 RESIDENCE TIMES AND PERSISTENCE
In some environments, such as lakes, it is convenient to define a residence time
or detention time. If a pond has a volume of 1000 m 3 and experiences inflow and
outflow of 2 m 3 /h, it is apparent that, on average, the water spends 500 h (20.8 days)
(i.e., 1000 m 3 /2 m 3 /h) in the lake. This residence or detention time may not bear
much relationship to the actual time that a particular parcel of water spends in the
pond, since some water may bypass most of the pond and reside for only a short
time, and some may be trapped for years. The quantity is very useful, however,
because it gives immediate insight into the time required to flush out the contents.
Obviously, a large lake with a long residence time will be very slow to recover from
contamination. Comparison of the residence time with a chemical reaction time (e.g.,
a half-life) indicates whether a chemical is removed from a lake predominantly by
flow or by reaction.
If a well mixed lake has a volume V m 3 and equal inflow and outflow rates G
m 3 /h, then the flow residence time t F is V/G (h). If it is contaminated by a nonreacting
(conservative) chemical at a concentration C O mol/m 3 at zero time and there is no
new emission, a mass balance gives, as was shown earlier,
C = C 0 exp(–Gt/V) = C 0 exp (–t/t F) = C O exp(–k F t)
The residence time is thus the reciprocal of a rate constant k F with units of h –1 . The
half-time for recovery occurs when t/t F or k Ft is ln 2 or 0.693, i.e., when t is 0.693t
or 0.693/k.
If the chemical also undergoes a reaction with a rate constant k R h –1 , it can be
shown that
C = C 0 exp[–(k F + k R)t] = C 0 exp(–k Tt)