Water tools

Oxygen requirement of an activated sludge reactor

Oxygen demand is the ultimate BOD removed minus the oxygen locked in the cells you waste, plus 4.57 g per g of nitrogen nitrified. The chain from average field demand to installed aerator power is shown step by step.

Influent flowm³/d

Influent BOD₅mg/L

Effluent soluble BOD₅mg/L

Sludge aged

Yield Yg VSS/g BOD₅

Decay coefficient Kd1/d

Biodegradable fraction of new biomass

BODu / BOD₅ ratio1.2 to 1.6 for domestic sewage.

TKN oxidisedmg N/LEnter 0 for no nitrification. Use the nitrification calculator for the oxidised fraction.

Peak factorAbout Qmax/Qavg: 1.5 for medium and large plants, 2.0 for small ones.

Field to standard conditions divisor0.55 to 0.65 lumped factor.

Aerator standard oxygenation efficiencykg O₂/kWh

Average field demand

Carbonaceous demand (average)

371kg O₂/d

For synthesis a′·Sr

266kg O₂/d

For respiration b′·Xv·V

105kg O₂/d

Per kg BOD₅ removed

0.85kg O₂/kg

Nitrification demand

0kg O₂/d

Total average

371kg O₂/d

Design

Field maximum (peak)

556kg O₂/d

Standard conditions

927kg O₂/d

Aerator power

21kW

How it works

Oxygen demand is the ultimate BOD removed minus the oxygen locked in the cells wasted, written as a synthesis term and an endogenous respiration term:

O_{2} = a' Q (S_{o} - S) + b' X_{v} V

(1)

a' = \frac{B O D_{u}}{B O D_{5}} - 1.42 Y b' = 1.42 f_{b} K_{d}

(2)

X_{v} V = \frac{Y θ_{c} Q (S_{o} - S)}{1 + f_{b} K_{d} θ_{c}}

(3)

Older sludge means a larger biomass inventory, more respiration and more oxygen per kilogram of BOD. Nitrification adds 4.57 g O₂ per g of nitrogen oxidised:

O_{2, N} = 4.57 Q T K N_{o x}

(4)

Peak demand lags and is damped relative to the peak load, but a safety factor tied to maximum flow is still required. Standard conditions (20 °C, clean water, sea level) divide the field value by a lumped factor of 0.55 to 0.65, and aerator power follows from the standard oxygenation efficiency:

P = \frac{O_{2, s t d}}{24 η_{O_{2}}}

(5)

where

$O_{2}$: oxygen demand, kg/d
$a'$: oxygen for synthesis, kg O₂ per kg BOD₅ removed
$b'$: oxygen for endogenous respiration, kg O₂ per kg VSS per day
$B O D_{u} / B O D_{5}$: ultimate to five-day BOD ratio, about 1.46
$Y$: yield, g VSS per g BOD₅
$f_{b}$: biodegradable fraction of the mixed liquor
$K_{d}$: decay coefficient, 1/d
$X_{v} V$: biomass in the reactor, kg VSS
$θ_{c}$: sludge age, d
$Q$: flow, m³/d
$S_{o}, S$: influent and effluent soluble BOD₅, mg/L
$T K N_{o x}$: Kjeldahl nitrogen oxidised, mg N/L
$O_{2, s t d}$: demand at standard conditions, kg/d
$η_{O_{2}}$: aerator oxygenation efficiency, kg O₂/kWh
$P$: aerator power, kW

In warm climates nitrification occurs almost systematically even at low sludge ages; add its oxygen if only for safety. Denitrification credit applies only when designed for.

Oxygen requirement of an activated sludge reactor

How it works

Related reading