Water tools

Activated sludge production and excess sludge wasting

Excess sludge is the biomass the plant grows minus what endogenous respiration destroys. At steady state production equals wasting, so the result also sets the WAS pump duty.

Influent flowm³/d

Influent BOD₅mg/L

Effluent soluble BOD₅mg/L

Sludge aged

MLVSSmg/L

Reactor volumem³

Yield Yg VSS/g BOD₅

Decay coefficient Kd1/d

Biodegradable fraction of new biomass

VSS/TSS of mixed liquor

Return sludge SSmg/L

Effluent SSmg/LDiscounted from the load to waste.

Production

Net VSS production

220kg VSS/d

Total solids production

275kg SS/d

Observed yield

0.50g VSS/g BOD₅

Solids per kg BOD₅ removed

0.63kg SS/kg

VSS destroyed by respiration

28%

Wasting

Load to waste (less effluent SS)

230kg SS/d

WAS from the reactor (at MLSS)

73m³/d

WAS from the return line (at Xr)

23m³/d

Hydraulic control V/θc

89m³/d

Wasting this volume of mixed liquor each day holds the sludge age without measuring solids. It ignores influent solids.

How it works

Net biological solids are the biomass grown minus the biomass destroyed by endogenous respiration:

P_{x v} = Y Q (S_{o} - S) - K_{d} f_{b} X_{v} V

(1)

Y_{o b s} = \frac{Y}{1 + f_{b} K_{d} θ_{c}} P_{x v} = Y_{o b s} Q (S_{o} - S)

(2)

P_{x} = \frac{P_{x v}}{V S S / T S S} VSS destroyed = \frac{f_{b} K_{d} θ_{c}}{1 + f_{b} K_{d} θ_{c}}

(3)

Wasting from the reactor needs a flow of P_x/X; from the return line, P_x/X_r, a flow smaller by the ratio X_r/X but carrying the same solids. Effluent suspended solids leave by themselves and are discounted from the load to waste:

Q_{e x} = \frac{P_{x} - Q X_{e}}{X} or Q_{e x} = \frac{P_{x} - Q X_{e}}{X_{r}}

(4)

where

$P_{x v}$: net volatile solids produced, kg VSS/d
$P_{x}$: total solids produced, kg SS/d
$Y$: yield, g VSS per g BOD₅
$Y_{o b s}$: observed yield after decay, g VSS per g BOD₅
$Q$: influent flow, m³/d
$S_{o}, S$: influent and effluent soluble BOD₅, mg/L
$K_{d}$: decay coefficient, 1/d
$f_{b}$: biodegradable fraction of the mixed liquor
$θ_{c}$: sludge age, d
$X_{v}, X$: mixed liquor volatile and total suspended solids, mg/L
$V$: reactor volume, m³
$X_{r}$: return sludge suspended solids, mg/L
$X_{e}$: effluent suspended solids, mg/L
$Q_{e x}$: waste sludge flow, m³/d

These balances neglect inert influent solids. For domestic sewage with primary settling the specific production is typically 0.6 to 1.0 kg SS per kg BOD₅ removed once influent solids are counted; without primary settling it is higher.

Activated sludge production and excess sludge wasting

How it works

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