Engineering calculators · Wastewater
Activated sludge design calculator
Size a complete-mix, nitrifying activated sludge plant from its flow and loads. The calculator finds the sludge age needed to nitrify at the design temperature, then works through biomass production, reactor volume at the chosen MLSS, hydraulic retention time, F/M, oxygen demand for carbon and ammonia, the return sludge ratio and the waste sludge rate. It follows the steady-state method in Metcalf & Eddy, with checks against the ranges used in WEF MOP 8 and ATV-DVWK-A 131.
Inputs
Nitrifier kinetics are fixed at the Metcalf & Eddy values: μmax,A = 0.9/d and bA = 0.17/d at 20 °C, θ = 1.072 and 1.029, Kn = 0.5 mg N/L, Ko = 0.5 mg/L, YA = 0.15 g VSS/g N. Heterotroph decay uses θ = 1.04, cell debris fraction 0.15, and bCOD = 1.6 × BOD5. For flows and loads from a population, see the flows and loads calculator.
Results
- SRT of 10.7 d is 1.5 times the washout SRT for nitrification at 12 °C.
- F/M of 0.16 kg BOD/kg MLVSS/d is within the 0.04 to 0.4 range for conventional to extended aeration plants.
- HRT of 15.7 h is within the usual 4 to 36 h range.
- MLSS of 3,500 mg/L is within the usual 1,500 to 5,000 mg/L range.
- RAS ratio of 0.78 is within the usual 0.25 to 1.5 range.
Intermediate values
| Quantity | Value | How |
|---|---|---|
| Nitrifier μmax at T | 0.516 /d | 0.9 × 1.072(T − 20) |
| Nitrifier decay at T | 0.135 /d | 0.17 × 1.029(T − 20) |
| Net nitrifier growth rate | 0.140 /d | μmax × N/(Kn+N) × DO/(Ko+DO) − bA |
| Heterotroph decay at T | 0.0877 /d | b × 1.04(T − 20) |
| Heterotrophic biomass | 379 kg VSS/d | Q Y (S0 − S) / (1 + bT SRT) |
| Cell debris | 53.4 kg VSS/d | fd bT × biomass × SRT |
| Nitrogen oxidised | 28.4 mg N/L | TKN − NH4-Ne − 0.12 × biomass/Q |
| Non-biodegradable VSS and inert solids | 60.0 + 50.0 mg/L | fnb × VSS0; TSS0 − VSS0 |
| MLVSS | 2,427 mg/L | MLSS × (VSS production / TSS production) |
| Volumetric loading | 0.38 kg BOD/m³/d | Q S0 / V |
Sensitivity to design temperature
All other inputs as above. With SRT set from kinetics the sludge age follows the temperature; with a manual SRT only decay and the washout margin change.
| Temperature, °C | Washout SRT, d | Design SRT, d | Volume, m³ | HRT, h | Oxygen, kg/d | Sludge, kg TSS/d |
|---|---|---|---|---|---|---|
| 8 | 11.4 | 17.1 | 4,934 | 23.7 | 2,081 | 1,010 |
| 10 | 8.95 | 13.4 | 3,992 | 19.2 | 2,029 | 1,041 |
| 12 | 7.14 | 10.7 | 3,273 | 15.7 | 1,983 | 1,069 |
| 15 | 5.22 | 7.82 | 2,472 | 11.9 | 1,921 | 1,106 |
| 20 | 3.23 | 4.84 | 1,600 | 7.68 | 1,835 | 1,158 |
| 25 | 2.07 | 3.10 | 1,064 | 5.11 | 1,764 | 1,200 |
How the calculation works
- Washout SRT for nitrification. The net specific growth rate of the ammonia oxidisers at the design temperature, effluent ammonia N and dissolved oxygen is μn = μmax,A θ(T−20) × N/(Kn + N) × DO/(Ko + DO) − bA. The minimum (washout) SRT is 1/μn, and the design SRT is that times the safety factor [M&E].
- Biomass production. Heterotrophs: PX,H = Q Y (S0 − S)/(1 + bT SRT), with bT = b × 1.04(T−20). Cell debris: fd bT PX,H SRT. Nitrifiers: Q YA NOx/(1 + bA,T SRT). The nitrogen oxidised, NOx, is the TKN less the effluent ammonia less the 12% of biomass that is nitrogen, found by iteration.
- Solids production. Biomass is 85% volatile, so TSS production = biomass/0.85 + non-biodegradable VSS + inert inorganic solids (TSS − VSS) in the influent, all × Q.
- Reactor volume from the solids mass balance: V = PX,TSS × SRT / MLSS. HRT = V/Q and F/M = Q S0/(V × MLVSS), where MLVSS is the MLSS scaled by the VSS:TSS ratio of the sludge produced.
- Oxygen demand. Ro = Q (bCOD0 − bCOD) − 1.42 PX,bio + 4.57 Q NOx. The 1.42 g O2/g VSS credits the COD locked into biomass that leaves as sludge; 4.57 g O2/g N is the stoichiometric demand of nitrification to nitrate. Denitrification credit is not included.
- Return and waste sludge. A solids balance round the clarifier gives the RAS ratio R = X/(Xr − X). Wasting from the RAS line at Xr removes the daily production in Qw = PX,TSS/Xr.
Worked example with the default inputs
Q = 5,000 m³/d, BOD 250 mg/L, TKN 40 mg N/L, effluent ammonia 1 mg N/L, 12 °C, DO 2 mg/L. At 12 °C, μmax,A = 0.9 × 1.072−8 = 0.516/d and bA = 0.135/d, so μn = 0.516 × (1/1.5) × (2/2.5) − 0.135 = 0.140/d and the washout SRT is 7.14 d. With a safety factor of 1.5 the design SRT is 10.7 d. Heterotrophic biomass is 5,000 × 0.6 × 245 / (1 + 0.0877 × 10.7) = 379 kg VSS/d; with debris and nitrifiers the biomass is 441 kg/d and total TSS production 1,069 kg/d. The reactor volume is 1,069 × 10.7 / 3.5 kg/m³ = 3,273 m³, an HRT of 15.7 h. Oxygen demand is 5,000 × 1.6 × 245/1000 − 1.42 × 441 + 4.57 × 5,000 × 28.4/1000 = 1,983 kg O2/d. The RAS ratio is 3500/(8000 − 3500) = 0.78.
What this cannot tell you. This is a steady-state, complete-mix, single-sludge model at one temperature. It does not model anoxic zones or the oxygen and alkalinity credits from denitrification, biological phosphorus removal, peak-hour oxygen demand, oxygen-limited nitrification in plug-flow tanks, or the storage of load in the sludge over a day. The nitrifier coefficients are literature values; a plant receiving inhibitory industrial trade effluent can have a much lower growth rate. Alkalinity consumption (7.14 g CaCO3 per g N nitrified) must be checked separately. For a design that will be built, confirm with a dynamic simulator (ASM-type model) and the final clarifier solids flux.
Sources
- Metcalf & Eddy / AECOM (2014). Wastewater Engineering: Treatment and Resource Recovery, 5th ed., ch. 7 and 8 (suspended growth kinetics, Table 8-14 nitrification coefficients, Example 8-5)
- ATV-DVWK-A 131E (2000). Dimensioning of Single-Stage Activated Sludge Plants. DWA, Hennef
- WEF (2017). Design of Water Resource Recovery Facilities, Manual of Practice No. 8, 6th ed., ch. 14 suspended growth biological treatment
Frequently asked questions
Why does the design SRT change so much with temperature?
Nitrifier growth rate falls by about 7% per degree (θ = 1.072), so the washout SRT roughly doubles between 20 °C and 10 °C. UK plants are normally sized for the coldest sustained winter mixed liquor temperature, typically 8 to 12 °C, and the aeration tank is then larger than a warm-climate design.
Is the oxygen demand here the AOR for blower sizing?
Yes. The figure is the process oxygen demand at field conditions (actual oxygen requirement, AOR) averaged over the day. Apply a diurnal peaking factor of 1.3 to 1.5 for peak-hour sizing, then convert to standard conditions and air flow with the aeration blower sizing calculator.
How is sludge production related to the waste rate?
At steady state the solids produced each day must be wasted each day. The waste flow is the daily TSS production divided by the concentration it is wasted at. Wasting from the RAS line uses the settled sludge concentration; wasting from the aeration tank would use the MLSS and give a much larger volume.
What does the ATV-DVWK-A 131 method do differently?
ATV-A 131 chooses the aerobic sludge age from a table against temperature and plant size, with a process factor of 1.6 to 2.4, and sizes the reactor from a sludge production per kg BOD. The results are usually close to the kinetic method used here, but ATV is more conservative for small plants. Where a German-style design basis is required, use the ATV sludge age as the manual SRT input.
Related reading: activated sludge process design, activated sludge modelling with ASM1, clarifier sizing calculator.