Water tools

Activated sludge reactor volume from sludge age

Size a complete-mix activated sludge reactor the way the design equations intend: from the sludge age and the biomass concentration you will hold. Hydraulic retention time comes out as a check, not an input.

Design flowm³/d

Influent BOD₅ to the reactormg/LAfter primary settling, if any.

Target effluent soluble BOD₅mg/L

Sludge agedConventional 4 to 10 d, extended aeration 18 to 30 d.

MLVSSmg/LConventional 1,500 to 3,500, extended aeration 2,500 to 4,000.

Yield Yg VSS/g BOD₅0.5 to 0.7

Decay coefficient Kd1/d0.06 to 0.10

Biodegradable fraction of new biomass

Reactor volume

472m³

Hydraulic retention time

7.5h

Biodegradable fraction fb

0.73

F/M ratio

0.38kg BOD₅/kg VSS·d

Volumetric loading

0.95kg BOD₅/m³·d

BOD₅ load

450kg/d

How it works

The reactor is sized from a biomass balance at the chosen sludge age. The biodegradable fraction of the mixed liquor falls as the sludge ages:

f_{b} = \frac{f_{b}'}{1 + (1 - f_{b}') K_{d} θ_{c}}

(1)

and the volume follows from the yield, the sludge age and the BOD load:

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

(2)

t = \frac{V}{Q} \frac{F}{M} = \frac{Q S_{o}}{X_{v} V}

(3)

where

$V$: reactor volume, m³
$Y$: yield, g VSS per g BOD₅ removed
$θ_{c}$: sludge age, d
$Q$: design flow, m³/d
$S_{o}$: influent BOD₅, mg/L
$S$: effluent soluble BOD₅, mg/L
$X_{v}$: mixed liquor volatile suspended solids, mg/L
$K_{d}$: endogenous decay coefficient, 1/d
$f_{b}'$: biodegradable fraction of freshly grown biomass, typically 0.8
$f_{b}$: biodegradable fraction of the mixed liquor at the sludge age
$t$: hydraulic retention time, d
$F / M$: food to microorganism ratio, kg BOD₅ per kg VSS per day

where Y is the yield in g VSS per g BOD₅, θ_c the sludge age in days, Q the flow, S_o and S the influent and effluent soluble BOD₅ in mg/L, X_v the MLVSS and K_d the decay coefficient.

Retention time is an output. Two wastewaters with the same BOD load need the same volume whatever their flow, so the tank is sized on load and sludge age and the retention time is checked afterwards for hydraulic stability. Assumes a complete-mix reactor at steady state with influent solids neglected.

Activated sludge reactor volume from sludge age

How it works

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