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205<br />

APPENDIX A5<br />

CALCULATION OF SOLIDS RETENTION TIME (SRT) IN STEADY-STATE AND<br />

ACCUMULATING SYSTEMS<br />

The solids retention time <strong>of</strong> a system is <strong>of</strong>ten regarded as an indicator that can be used to assess the<br />

condition <strong>of</strong> digestion, and diagnose <strong>reactor</strong> ills. In this section, the concept <strong>of</strong> sludge age or solids<br />

retention time in an accumulating system is considered.<br />

1 ZEEMAN AND LETTINGA MODEL OF SLUDGE AGE<br />

Assuming the sludge concentration in the <strong>reactor</strong> (X), the fraction <strong>of</strong> the influent suspended solids that<br />

is removed in the <strong>reactor</strong> (R) and the fraction <strong>of</strong> R that is removed through hydrolysis (H) are known:<br />

SRT is defined as the ratio <strong>of</strong> the sludge concentration in the <strong>reactor</strong> X [g COD/ℓ] to the (<strong>reactor</strong>) net<br />

sludge production XP [gCOD/ℓ.d]<br />

SRT = X<br />

X P<br />

Eq. A5- 1<br />

The net sludge production is calculated from the OLR [kg COD/m 3 .d] and the fraction <strong>of</strong> the total<br />

COD that is associated with suspended solids fSS = CODss/CODtotal: 1<br />

= OLR ⋅ f ⋅ R ⋅ 1<br />

X P<br />

SS<br />

( − H )<br />

Eq. A5- 2<br />

The OLR by definition is the ratio <strong>of</strong> COD influent concentration CODin [g COD/m 3 ] to the hydraulic<br />

retention time HRT [d]:<br />

COD<br />

OLR =<br />

in<br />

HRT<br />

Eq. A5- 3<br />

Eq. A5- 1, Eq. A5- 2 and Eq. A5- 3 may be solved simultaneously to show that for a desired SRT, the<br />

HRT may be calculated by Eq. A5- 4<br />

f SS<br />

HRT =<br />

⎛<br />

COD<br />

⎞<br />

⎜ ⋅ ⋅ R ⋅<br />

in X ⎟ 1<br />

⎝<br />

⎠<br />

( − H ) ⋅ SRT<br />

Eq. A5- 4<br />

1 The calculation <strong>of</strong> excess sludge production does not differentiate between influent suspended solids that<br />

accumulate in the <strong>reactor</strong> and solids that are biomass grown on the hydrolysed COD since these components are<br />

measured together in the sludge COD concentration measurement. (Zeeman and Lettinga, 1999)

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