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technical guidance documents - Institute for Health and Consumer ...

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Concentration (% of initial)<br />

160<br />

140<br />

120<br />

100<br />

80<br />

60<br />

40<br />

20<br />

0<br />

0 50 100 150 200 250 300 350<br />

tim e (d a ys )<br />

Figure 12 The concentration in soil after 10 years. The shaded area is the integrated concentration<br />

over a period of 180 days<br />

ENVIRONMENTAL EXPOSURE ASSESSMENT<br />

order to determine biomagnification effects <strong>and</strong> indirect human exposure, it is more appropriate<br />

to use an extended period of 180 days.<br />

This averaging procedure is illustrated in Figure 12 where the average concentration is given by<br />

the area of the shaded surface, divided by the number of days.<br />

The local concentration in soil is defined as the average concentration over a certain time period<br />

T. The average concentration over T days is given by:<br />

1<br />

T<br />

Clocal soil = C soil (t) dt<br />

T 0<br />

• ∫ (54)<br />

Solving this equation <strong>for</strong> the range 0 to T gives the final equation <strong>for</strong> the average concentration<br />

in this period:<br />

Explanation of symbols<br />

Clocal<br />

soil<br />

=<br />

D<br />

k<br />

air<br />

1<br />

+<br />

k T<br />

⎡<br />

⎢<br />

⎣<br />

C<br />

soil<br />

(0) -<br />

D<br />

k<br />

air<br />

⎤<br />

⎥<br />

⎦<br />

•<br />

−kT<br />

[ 1-<br />

e ]<br />

Dair aerial deposition flux per kg of soil [mg . kg -1. d -1 ] eq. (52)<br />

T averaging time [d] Table 11<br />

k first order rate constant <strong>for</strong> removal from top soil [d -1 ] eq. (56)<br />

Csoil (0) initial concentration (after sludge application) [mg . kg -1 ] eq. (63)<br />

Clocalsoil average concentration in soil over T days [mg . kg -1 ]<br />

(55)<br />

81

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