Engineering calculators · Wastewater

Aeration and blower sizing calculator

Convert a process oxygen demand into the standard oxygen transfer rate a diffuser system must be rated for, then into air flow, blower discharge pressure, power and annual energy. The corrections for alpha, beta, fouling, temperature, residual DO, diffuser depth and site altitude follow the US EPA fine pore aeration manual and ASCE 2-06, and the blower power uses the adiabatic compression equation in Metcalf & Eddy. Take the oxygen demand from the activated sludge design calculator.

Inputs

Alpha, beta and F are the EPA fine pore manual corrections: alpha for the wastewater, beta (about 0.95) for dissolved salts lowering saturation, F for diffuser fouling between cleans. Blower efficiency is the overall adiabatic efficiency of the machine, typically 0.6 to 0.8 for lobe, screw and turbo blowers. Pressure losses are in kPa (10 kPa = 100 mbar = about 1 m of water).

Results

Standard oxygen requirement229 kg/hSOR/AOR = 2.7, total SOTE 32.5%

Air flow2,356 Nm³/h39.3 Nm³/min, 2,569 m³/h at inlet

Discharge pressure59.1 kPa g591 mbar g, pressure ratio 1.60

Electrical power54.0 kWshaft 51.3 kW, 0.64 kWh/kg O₂

Energy a year£118,220472,879 kWh

Alpha of 0.5 is within the range reported for diffused aeration (EPA fine pore manual).
DO driving force (β C* − C) of 7.49 mg/L against a standard 9.09 mg/L.
Total SOTE of 32.5% is realistic for the diffuser depth (fine bubble 5 to 7% per metre, falling at high air flux per diffuser).

Intermediate values

Quantity	Value	How
Atmospheric pressure at site	100.7 kPa	Standard atmosphere at the elevation
DO saturation at T, 1 atm	9.09 mg/L	USGS table, interpolated [USGS]
O₂ in off-gas	15.2 %	21(1 − SOTE)/[79 + 21(1 − SOTE)]
Mean saturation at depth, C*_∞	9.99 mg/L	C_s,T × (P_atm/101.325) × ½(P_d/P_atm + O_t/21) [M&E]
Field correction, AOR/SOR	0.371	α F (β C*_∞ − C)/9.09 × θ^{(T − 20)}
Air mass flow	0.846 kg/s	Nm³/h × 1.293 kg/Nm³ ÷ 3600
Inlet and discharge pressure (abs)	99.73 / 159.8 kPa	P_atm − inlet loss; P_atm + 9.81 × depth + diffuser + pipe losses
Standard aeration efficiency (wire)	4.25 kg O₂/kWh	SOR ÷ electrical power

Sensitivity to alpha

Alpha is the least certain input. All other inputs as above.

Alpha	SOR, kg/h	SOR/AOR	Air, Nm³/h	Electrical, kW	kWh/kg O₂	Cost a year
0.35	327	3.9	3,366	77.1	0.91	£168,885
0.45	255	3.0	2,618	60.0	0.71	£131,355
0.55	208	2.5	2,142	49.1	0.58	£107,472
0.65	176	2.1	1,812	41.5	0.49	£90,938
0.75	153	1.8	1,571	36.0	0.42	£78,813
0.85	135	1.6	1,386	31.8	0.37	£69,541

How the calculation works

Saturation at depth. Clean-water DO saturation at the mixed liquor temperature and 1 atm comes from the USGS table [USGS], scaled to the site barometric pressure. For a diffused system the mean saturation over the tank depth is C*_∞ = C_s,T × ½ (P_d/P_atm + O_t/21), where P_d is the absolute pressure at the diffuser and O_t the oxygen content of the gas leaving the surface after SOTE has been removed [M&E eq. 5-70].
AOR to SOR. SOR = AOR ÷ [α F (β C*_∞ − C)/C_s,20 × θ^(T−20)] with C_s,20 = 9.09 mg/L and θ = 1.024 [EPA] [ASCE 2-06].
Air flow. Each Nm³ of air (0 °C, 101.325 kPa) carries 0.299 kg of oxygen, of which the diffusers transfer the SOTE fraction: air = SOR / (SOTE × 0.299). The SOTE per metre of submergence is a rule of thumb for fine bubble diffusers at moderate flux (about 6 to 7%/m at 5 m); use the manufacturer's clean-water curve when you have it, entered as a total SOTE. The actual inlet volume scales by T₁/273.15 and 101.325/P₁.
Discharge pressure = atmospheric + hydrostatic (9.81 kPa per metre of submergence) + diffuser loss + pipework and valve losses. Inlet pressure = atmospheric − filter and silencer loss.
Blower power. Adiabatic compression, P_w = w R T₁ / (28.97 × 0.283 × e) × [(p₂/p₁)^0.283 − 1] in kW, with w in kg/s, R = 8.314 kJ/kmol·K, T₁ the inlet temperature in K and e the blower efficiency [M&E eq. 5-77]. The US-unit form is P = w R T₁ / (29.7 n e) [(p₂/p₁)^0.283 − 1] in hp. Electrical power divides by the motor and drive efficiency; energy and cost multiply by running hours and price.

Worked example with the default inputs

AOR 85 kg O₂/h, α 0.5, β 0.95, F 0.9, 20 °C, DO 2 mg/L, 5 m submergence, 50 m elevation, 6.5%/m. Atmospheric pressure is 100.7 kPa and C_s,20 = 9.09 mg/L. SOTE = 6.5 × 5 = 32.5%, so the off-gas holds 15.2% oxygen and C*_∞ = 9.99 mg/L. The field correction is 0.5 × 0.9 × (0.95 × 9.99 − 2)/9.09 = 0.371, giving SOR = 85/0.371 = 229 kg/h. Air = 229 / (0.325 × 0.299) = 2,356 Nm³/h, or 0.846 kg/s. Discharge pressure = 100.7 + 49.1 + 10 = 159.8 kPa abs (59.1 kPa g), pressure ratio 1.60. Shaft power = 0.846 × 8.314 × 293.15 / (28.97 × 0.283 × 0.7) × (1.60^0.283 − 1) = 51.3 kW; electrical 54.0 kW, or 0.64 kWh per kg of oxygen delivered.

What this cannot tell you. It sizes one duty point. It does not check blower turndown against the minimum mixing air (typically 1.2 to 2 Nm³/h per m² of floor for fine bubble grids), the air needed at peak-hour load, diffuser flux limits (SOTE falls as the flow per diffuser rises), summer inlet density, or the surge line of a turbo blower. Alpha varies along a plug-flow tank and with SRT, so a single value is an average. The energy figures assume constant load for the hours entered; real plants modulate with DO control and use less.

Sources

Frequently asked questions

What is the difference between AOR and SOR?

AOR (actual oxygen requirement) is the oxygen the process needs at site conditions: warm, dirty water with a residual DO. SOR (standard oxygen requirement) is the equivalent transfer in clean water at 20 °C, 1 atm and zero DO, which is how diffuser manufacturers test and quote their equipment (ASCE 2-06). The SOR is always larger; a ratio of 2 to 3 is normal for fine bubble aeration.

Why is alpha so important and what value should I use?

Alpha is the ratio of oxygen transfer in mixed liquor to that in clean water. For fine bubble diffusers it is often 0.4 to 0.65 and falls with surfactants, low SRT and high loading; it can be below 0.3 at the inlet of a plug-flow tank. The EPA fine pore manual is the standard reference. Because SOR is inversely proportional to alpha, a 20% error in alpha is a 20% error in air flow, so the sensitivity table shows the whole plausible range.

Which temperature governs blower sizing?

Two different ones. The mixed liquor temperature sets the saturation value and the transfer coefficient; the warmest summer condition usually governs because saturation falls faster than the rate rises. The inlet air temperature sets the mass flow a blower delivers for a given volumetric flow and its power; a hot summer day is the design case for air flow, a cold day for motor power at full inlet density.

Does this include a peaking factor?

No. Enter the AOR you want to size for. Average daily demand from the activated sludge calculator is suitable for energy estimates; for blower selection apply a diurnal peak factor of 1.3 to 1.5 to the carbonaceous and nitrogenous demand, or use the peak-hour load directly. Check minimum turndown against the mixing air requirement as well.

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