Water tools

Effluent BOD from an activated sludge plant

At steady state the soluble BOD leaving a complete-mix reactor depends only on sludge age and the kinetic constants. Most of what the permit measures is particulate BOD riding on the solids the clarifier lets through. This tool gives both halves.

Sludge aged

Maximum specific growth rate μmax1/d

Half-saturation constant Ksmg BOD₅/L

Decay coefficient Kd1/d

Biodegradable fraction of new biomass

Design effluent suspended solidsmg/L

VSS/TSS of effluent solidsConventional 0.70 to 0.85, extended aeration 0.60 to 0.75.

Influent BOD₅ (for efficiency)mg/L

Total effluent BOD₅

25.2mg/L

Soluble BOD₅ (Monod)

7.9mg/L

Particulate BOD₅

17.3mg/L

BOD₅ per mg effluent SS

0.58mg/mg

Minimum reachable soluble BOD₅

2.0mg/L

Overall BOD₅ removal

91.6%

How it works

At steady state in a complete-mix reactor the soluble BOD depends only on the sludge age and the kinetic constants:

S = \frac{K_{s} (1 / θ_{c} + K_{d} f_{b})}{μ_{m a x} - (1 / θ_{c} + K_{d} f_{b})}

(1)

The floor for a single complete-mix reactor, reached as the sludge age tends to infinity, is

S_{m i n} = \frac{K_{s} K_{d} f_{b}}{μ_{m a x} - K_{d} f_{b}}

(2)

Biodegradable cells need 1.42 g O₂ per g to stabilise and about 68% of that demand is exerted in five days, so each mg of biodegradable VSS is about 1 mg BOD₅. Scaled to total solids:

{BOD}_{5} per mg SS = \frac{V S S}{T S S} f_{b} {BOD}_{5, t o t a l} = S + X_{e} \frac{V S S}{T S S} f_{b}

(3)

where

$S$: effluent soluble BOD₅, mg/L
$K_{s}$: half-saturation constant, mg BOD₅/L
$θ_{c}$: sludge age, d
$K_{d}$: decay coefficient, 1/d
$f_{b}$: biodegradable fraction of the mixed liquor
$μ_{m a x}$: maximum specific growth rate of the heterotrophs, 1/d
$S_{m i n}$: lowest soluble BOD₅ a single complete-mix reactor can reach, mg/L
$X_{e}$: effluent suspended solids, mg/L
$V S S / T S S$: volatile fraction of the effluent solids

where X_e is the effluent suspended solids. The particulate term is typically 0.45 to 0.65 mg BOD₅ per mg SS for conventional plants and 0.25 to 0.50 for extended aeration. Effluent suspended solids are a design assumption, not a prediction, and the BOD test has no sensitivity to decimals.

Effluent BOD from an activated sludge plant

How it works

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