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ENVIRONMENTAL EXPOSURE ASSESSMENT<br />

At the end of each year, a fraction Facc of the initial concentration remains in the top-soil layer.<br />

The initial concentration after 10 applications of sludge is given by:<br />

84<br />

9<br />

n<br />

[ ]<br />

Csludge (0) = Csludge (0) • 1 + ∑ Facc<br />

(62)<br />

soil 10 soil 1 n = 1<br />

The sum of both the concentration due to deposition <strong>and</strong> sludge is the initial concentration in<br />

year 10:<br />

C (0) = Cdep (0) + Csludge (0) (63)<br />

soil 10 soil 10 soil 10<br />

This initial concentration can be used in equation (54) to calculate the average concentration in<br />

soil over a certain time period.<br />

Indicating persistency of the substance in soil<br />

Ten consecutive years of accumulation may not be sufficient <strong>for</strong> some substances to reach a<br />

steady-state situation. These substances may accumulate <strong>for</strong> hundreds of years. To indicate<br />

potential problems of persistency in soil, the fraction of the steady-state concentration can be<br />

derived:<br />

Explanation of symbols<br />

Fst - st = C<br />

C<br />

soil<br />

soil ∞<br />

10 (0)<br />

(0)<br />

Csoil 10 (0) initial concentration after 10 years [mg . kg -1 ] eq. (63)<br />

Csoil ∞ (0) initial concentration in steady-state situation [mg . kg -1 ] eq. (65)<br />

Fst-st fraction of steady-state in soil achieved [-]<br />

The initial concentration in the steady-state year is given by:<br />

Explanation of symbols<br />

air<br />

C soil = D<br />

∞<br />

(0) + Csludge soil 1 (0)<br />

k<br />

•<br />

1<br />

1 - Facc<br />

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

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

Facc fraction accumulation in one year [-] eq. (61)<br />

Csludgesoil 1 (0) concentration in soil due to sludge in first year at t=0 [mg . kg -1 ] eq. (60)<br />

Csoil∞(0) initial concentration in steady-state situation [mg . kg -1 ]<br />

(64)<br />

(65)

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