Water tools

Nitrification: growth rate, minimum sludge age, oxygen and alkalinity

Nitrifiers grow slowly and are the first organisms washed out when the sludge age drops or the water cools. This tool checks whether your reactor can nitrify, and what it costs in oxygen and alkalinity.

Influent flowm³/d

Aerobic reactor volumem³

Sludge aged

MLVSSmg/L

Influent TKN to the reactormg N/L

Target effluent ammoniamg N/L

Temperature°C

pHCorrection applies between 6.0 and 7.2; constant from 7.2 to 8.0.

Dissolved oxygenmg/L

Influent alkalinitymg/L as CaCO₃Raw sewage usually 100 to 250.

μmax at 20 °C1/dTypical 0.3 to 0.7.

KN (ammonia)mg N/LTypical 0.5 to 1.0.

KO (oxygen)mg O₂/LTypical 0.4 to 1.0.

Temperature coefficient θ1.08 to 1.13.

Nitrifier yield YNg cells/g N0.05 to 0.10.

Safety factor on sludge age1.5 to 2.5.

Kinetics

Nitrifier growth rate μ

0.2141/d

Ammonia factor

0.74

Temperature factor

1.00

pH factor

0.75

DO factor

0.77

Sludge age

Minimum sludge age

4.7d

Design sludge age (with safety factor)

7.0d

Safety factor at your sludge age

1.28

Capacity

TKN oxidised

250kg N/d

TKN taken up in sludge

123kg N/d

Nitrification capacity

321kg N/d

Nitrifier fraction of VSS

2.0%

Oxygen and alkalinity

Oxygen for nitrification

1,143kg O₂/d

Alkalinity consumed

1,786kg CaCO₃/d

Alkalinity available

1,473kg CaCO₃/d

Lime make-up Ca(OH)₂

231kg/d

Sludge age is above the minimum but below the design safety factor.
Alkalinity deficit: pH will fall and nitrification self-limit unless alkalinity is dosed or denitrification recovers part of it.

How it works

Nitrifier growth rate, each factor applied to the 20 °C maximum:

μ = μ_{m a x} \frac{N H_{4}}{K_{N} + N H_{4}} θ^{T - 20} [1 - 0.83 (7.2 - p H)] \frac{D O}{K_{O} + D O}

(1)

The pH term applies between 6.0 and 7.2 and is 1 above. The minimum sludge age and the design value follow:

θ_{c, m i n} = \frac{1}{μ} θ_{c, d e s i g n} = S F θ_{c, m i n} (S F = 1.5 to 2.5)

(2)

TKN removed splits into nitrogen taken up by sludge (12% of VSS produced) and nitrogen oxidised. The nitrifier fraction, the volumetric rate and the capacity of the reactor are

f_{N} = \frac{Y_{N} T K N_{o x}}{P_{x v}} r_{N} = \frac{f_{N} X_{v} μ}{Y_{N}} L_{T K N} = V r_{N}

(3)

If the capacity is below the load, the shortfall leaves as ammonia. Stoichiometry per gram of ammonia nitrogen oxidised:

O_{2} = 4.57 T K N_{o x} Alk = 7.14 T K N_{o x} ({as CaCO}_{3})

(4)

where

$μ$: specific growth rate of the nitrifiers, 1/d
$μ_{m a x}$: maximum growth rate at 20 °C, 1/d
$N H_{4}$: effluent ammonia nitrogen, mg N/L
$K_{N}$: half-saturation constant for ammonia, mg N/L
$θ$: temperature coefficient
$T$: temperature, °C
$D O$: dissolved oxygen, mg/L
$K_{O}$: half-saturation constant for oxygen, mg/L
$θ_{c}$: sludge age, d
$S F$: safety factor
$f_{N}$: nitrifier fraction of the volatile solids
$Y_{N}$: nitrifier yield, g cells per g N oxidised
$T K N_{o x}$: Kjeldahl nitrogen oxidised, kg N/d
$P_{x v}$: volatile solids produced, kg VSS/d
$r_{N}$: volumetric nitrification rate, g N/m³·d
$X_{v}$: mixed liquor volatile solids, mg/L
$L_{T K N}$: nitrification capacity of the reactor, kg N/d
$V$: aerobic volume, m³
$Alk$: alkalinity consumed, kg CaCO₃/d

100 mg/L of alkalinity as CaCO₃ is 74 mg/L of hydrated lime. Single-stage nitrification with a unified biomass and nitrifier decay ignored; influent TKN is taken as available ammonia, which is conservative.

Nitrification: growth rate, minimum sludge age, oxygen and alkalinity

How it works

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