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ENVIRONMENTAL EXPOSURE ASSESSMENT<br />

Explanation of symbols<br />

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

t time [d]<br />

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

Csoil concentration in soil [mg . kg -1 ]<br />

In the <strong>for</strong>mula above, the aerial deposition flux is used in mg substance per kg of soil per day.<br />

Dair can be derived by converting the total deposition flux (DEPtotalann) as follows:<br />

Explanation of symbols<br />

80<br />

D air =<br />

DEPtotalann<br />

DEPTH RHO<br />

soil • soil<br />

DEPtotalann annual average total deposition flux [mg . m -2. d -1 ] eq. (44)<br />

DEPTHsoil mixing depth of soil [m] Table 11<br />

RHOsoil bulk density of soil [kg . m -3 ] eq. (18)<br />

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

The differential equation (51) has an analytical solution, given by:<br />

C<br />

soil<br />

(52)<br />

Dair<br />

⎡ Dair<br />

⎤ - k t<br />

( t)<br />

= - - Csoil<br />

• e<br />

k ⎢<br />

(0)<br />

⎣ k ⎥<br />

(53)<br />

⎦<br />

With this equation, the concentration can be<br />

calculated at each moment in time, when the<br />

initial concentration in that year is known.<br />

Accumulation of the substance may occur<br />

when sludge is applied over consecutive<br />

years. This is illustrated in Figure 11. As a<br />

realistic worst-case exposure scenario, it is<br />

assumed that sludge is applied <strong>for</strong> 10<br />

consecutive years. To indicate <strong>for</strong> potential<br />

persistency of the substance, the percentage<br />

of the steady-state situation is calculated. As<br />

shown in Figure 11, the concentration in soil<br />

is not constant in time.<br />

The concentration will be high just after<br />

sludge application (in the beginning of the<br />

growth season), <strong>and</strong> lower at the end of the<br />

year due to removal processes. There<strong>for</strong>e, <strong>for</strong><br />

exposure of the endpoints, the concentration<br />

needs to be averaged over a certain time period. Different averaging times should be considered<br />

<strong>for</strong> these endpoints: <strong>for</strong> the ecosystem a period of 30 days after application of sludge is used. In<br />

Concentration (% of initial)<br />

160<br />

140<br />

120<br />

100<br />

80<br />

60<br />

40<br />

20<br />

0<br />

0<br />

1 2<br />

time (year)<br />

3 4<br />

Figure 11 Accumulation in soil due to several<br />

years of sludge application

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