Environmental Engineering Reference
In-Depth Information
weight). E i is the chemical transfer efficiency. A general expression for the rate of
respiration is (Connolly and Thomann, 1992)
= β i W i e ρ i T e v i u i ,
R e l (g/g/d)
(6.274)
where T is temperature (EC) and u i is the speed of movement of the organism in
water (m/s).
ρ i , and v i are constants typical to the given species.
The rate of ingestion is given by the product of the chemical assimilation capacity
of the organism i on another organism j , denoted as
β i ,
γ i ,
α ij , the rate of consumption of
organism i on organism j , denoted as C ij , and the concentration of the pollutant in
organism i , [A] org, i . C ij =
p ij C i , where p ij is the fraction of the consumption of i that
is on j and C i is the weight-specific consumption of i (kg of prey per kg of predator per
day). The value of C ij is dependent on the rate of respiration and the rate of growth:
C
=
(R
+ μ
) /
α
. The value of
α
varies from 0.3 to 0.8 and is specific to individual
species. The rate of uptake via ingestion of lower species is j α ij W org, i C ij [
A
] org, j .
The overall rate of ingestion of a chemical by the species is given by j α ij C ij [
A
] org, j .
The summation denotes the uptake of different species j
1, 2, ... , n by species i .
The rate of excretion via desorption of the chemical is given by k d i W org, i [
=
A
] org, i ,
where k d i has units of d 1 .
Now, since
d W org, j
d t
d (W org, i [
A
] org, j )
d
[
A
] org, j
d t
=
W org, j
+[
A
] org, j
(6.275)
d t
μ i = 1 /W org, i d W org, i / d t , we have (6.277)
The overall rate equation for bioaccumulation is, therefore, given by
and denoting the growth rate,
n
d
[
A
] org, i
d t
= k s i [
A
] w +
1 α ij C ij [
A
] org, i k d i [
A
] org, i − μ i [
A
] org, i .
(6.276)
j
=
This equation is applied to each age class of the organism. Within each age group
the various parameters are assumed constant. Since equilibrium is rapidly attained
for lower levels of the food chain, it may be appropriate to assume no significant
change in concentration with time for such species. This suggests a PSSA for [A] org, i .
Therefore, the concentration in the organism i at steady state is given by
] w + j = 1 α ij C ij [
k d i [
A
A
] org, i
] org, i =
[
A
.
(6.277)
(k d i + μ i )
Connolly and Thomann (1992) employed this equation to obtain the concentration
of PCBs in contaminated fish in Lake Michigan. Figure 6.72 shows the data where
it is assumed that for each age class, constant values of assimilation, ingestion, and
respiration rates are applicable.
If exposure of organism to pollutant A occurs only through the water route, we
have at steady state
k s i
(k d i + μ i ) [
] org, i =
[
A
A
] w .
(6.278)
 
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