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X<br />

X =<br />

P<br />

Inert<br />

⋅<br />

where Xinert is the amount <strong>of</strong> particulate inert COD in the influent [mgCOD/ℓ]<br />

and f XI , eff<br />

( 1− f ) ( COD − COD − X ⋅ ( 1−<br />

f ) )<br />

HRT<br />

XI , eff<br />

+<br />

in<br />

out<br />

HRT<br />

Inert<br />

209<br />

XI , eff<br />

Eq. A5- 16<br />

is the fraction <strong>of</strong> the influent particulate inert COD that appears in the effluent<br />

during pseudo-steady-state operation.<br />

• This model makes no allowance for solids that are initially retained and later released through<br />

e.g. physical displacement or sludge decay. These effects are implicitly contained in the single<br />

XP value. This is not an unreasonable approach since it would be impossible to determine rate<br />

constants for these processes if modelled explicitly without long-term solids residence time<br />

distribution tests. However, the exclusion from the model may result in overestimation <strong>of</strong><br />

sludge age if the ultimate sludge production from a package i <strong>of</strong> influent COD is<br />

overestimated from short-term experimental data.<br />

• Finally, the sludge ages calculated from this model are fundamentally different to those<br />

calculated for a steady-state system since the probability distribution for solids leaving the<br />

<strong>reactor</strong> are fundamentally different, particularly when considering different micro-organism<br />

sub-populations with differing retention characteristics. Thus comparison <strong>of</strong> sludge ages<br />

calculated with the two different methods should be undertaken with care since the behaviour<br />

<strong>of</strong> sludge (e.g. in terms <strong>of</strong> methanogenic activity) from an accumulating system may well be<br />

substantially different to one <strong>of</strong> the same calculated sludge age from a steady-state system.<br />

Specifically, conclusions from other studies that methanogenesis establishes for sludge ages<br />

longer than a specific value will not necessarily be valid for the accumulating system with<br />

SRT calculated as above.

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