Engineering calculators · Water treatment

Dissolved air flotation (DAF) sizing calculator

Size a dissolved air flotation unit from flow and suspended solids. The calculator works out the air released from a pressurised recycle using Henry's law solubility at the operating temperature and saturator pressure, then solves either the recycle flow for a target air to solids ratio or the A/S from a chosen recycle. From the hydraulic loading it gives the flotation area and tank dimensions, the solids loading, the float volume and polymer use. The method is that of Edzwald and Metcalf & Eddy, with checks against the loading ranges for conventional and high-rate DAF.

Inputs

Saturator efficiency is the fraction of the equilibrium air at the saturator pressure that actually dissolves: 50 to 70% for an unpacked tank, 80 to 95% for a packed saturator. Hydraulic loading 5 to 15 m/h is conventional DAF; 15 to 40 m/h is high-rate. For the recycle system and saturator hardware see the articles on saturator design and recycle system design.

Results

Air released85.1 g/m³per m³ of recycle; 10.0 g/m³ of influent, 1,000 g/h in total

Recycle flow11.8 m³/h11.8% of influent at A/S 0.020

Saturator air demand17.0 L/min1.02 Nm³/h, 1.32 kg/h dissolved, before margin

Flotation area14.0 m²5.91 × 2.36 m; 7.16 m/h on influent only

Solids loading3.58 kg/m²/h50.0 kg/h of solids applied

Float27.2 m³/d1,087 kg DS/d at 4% DS, 1.1% of influent

Polymer7.20 kg/dactive; 3,600 L/d of 0.2% solution

A/S of 0.020 g air/g solids is within the 0.005 to 0.06 range (Metcalf & Eddy).
Saturator pressure of 5 bar g is within the usual 3 to 7 bar g (Edzwald recommends 400 to 600 kPa).
Recycle of 11.8% of the influent is within the 5 to 50% range typical for DAF.
Hydraulic loading of 8.00 m/h (on influent plus recycle) is within the 5 to 15 m/h range for conventional DAF.
Solids loading of 3.58 kg/m²/h is at or below 15 kg/m²/h.

Sensitivity to saturator pressure

All other inputs as above. Air released rises almost linearly with absolute pressure, so recycle falls as pressure rises; the pumping energy depends on both.

Pressure, bar g	Air released, g/m³ recycle	Recycle, m³/h	Recycle, %	A/S	Area, m²	Saturator air, L/min
3	47.8	20.9	20.9	0.020	15.1	20.2
4	66.4	15.0	15.0	0.020	14.4	18.1
5	85.1	11.8	11.8	0.020	14.0	17.0
6	104	9.64	9.64	0.020	13.7	16.2
7	122	8.17	8.17	0.020	13.5	15.7

How the calculation works

Air solubility. Henry's law makes the dissolved air proportional to absolute pressure. The solubility at 1 atm, s_a, is interpolated from the table (29.2 mL/L at 0 °C, 22.8 at 10 °C, 18.7 at 20 °C, 15.7 at 30 °C, 13.6 at 40 °C) [M&E Table 5-20]; see also the air solubility article.
Air released per m³ of recycle = 1.3 s_a (f P − 1) in g/m³, where 1.3 mg/mL is the density of air, f the saturator efficiency and P the absolute pressure in atm. The "− 1" is the air the water already held at atmospheric pressure, which is not released.
Air to solids ratio. A/S = 1.3 s_a (f P − 1) R / (S_a Q), with R the recycle flow, S_a the influent solids and Q the influent flow [M&E eq. 5-56] [Edzwald 2010]. The calculator inverts this for R when the A/S is the target.
Saturator air demand = 1.3 s_a f P × R, the total air dissolved including the atmospheric share; expressed in L/min of free air at 1.293 g/L and in Nm³/h. Add a 20 to 50% margin for the compressor.
Area and dimensions. A = (Q + R) ÷ hydraulic loading; width = √(A ÷ L:W), length = width × L:W. Solids loading = Q × TSS ÷ A.
Float and polymer. Float solids = Q × TSS × removal + polymer, per day. Float volume = float solids ÷ (float % × 10 kg/m³). Polymer = dose × Q per day, and the made-down volume at the solution strength.

Worked example with the default inputs

Q = 100 m³/h, TSS 500 mg/L, A/S 0.02, 5 bar g, efficiency 70%, 15 °C, loading 8 m/h. At 15 °C, s_a = 20.8 mL/L. Absolute pressure = (5 × 100 + 101.3)/101.3 = 5.93 atm, so air released = 1.3 × 20.8 × (0.7 × 5.93 − 1) = 85.1 g/m³ of recycle. Air needed = 0.02 × 500 × 100 = 1,000 g/h, so the recycle is 1,000/85.1 = 11.8 m³/h (11.8%). The saturator must dissolve 1.3 × 20.8 × 0.7 × 5.93 × 11.8 = 1,317 g/h, about 17.0 L/min of free air. Area = (100 + 11.8)/8 = 14.0 m², say 5.91 × 2.36 m, with a solids loading of 100 × 0.5/14.0 = 3.58 kg/m²/h. Float at 90% removal plus polymer is 1,087 kg DS/d, or 27.2 m³/d at 4% DS.

What this cannot tell you. It does not predict removal efficiency or effluent quality; those depend on coagulation, flocculation and bubble-floc attachment, which a bench or pilot flotation test must establish. The contact zone, nozzle design, recycle pump and saturator vessel are sized separately. The solubility table is for fresh water; brines and effluents with high dissolved solids hold less air. Flow equalisation, oil and grease, and the effect of temperature on floc strength are outside the model. For potable water DAF, use the contact zone bubble concentration method in Edzwald rather than A/S.

Sources

Frequently asked questions

What A/S ratio should I use?

For thickening activated sludge, 0.02 to 0.04 g air per g solids; for clarifying industrial effluents and oily wastes with chemical flocs, 0.01 to 0.03; for potable water clarification the air is set by the contact zone concentration (6 to 10 g/m³ of influent) rather than A/S because the solids are so low. Confirm with a bench flotation test; see the article on the air to solids ratio.

Should hydraulic loading be based on the influent or on influent plus recycle?

Both appear in the literature. This calculator uses influent plus recycle, which is the total flow the separation zone must pass and is the more conservative choice. Manufacturers quoting high-rate units often use influent only, so check the basis before comparing figures. Both values are shown.

Why does the saturator air demand exceed the air released?

The recycle water already holds air at atmospheric saturation, and the saturator must raise it to the efficiency times the pressurised saturation before the nozzle releases the difference. The compressor is sized for the total dissolved, with a margin of 20 to 50% for venting and control. Packed saturators reach 80 to 95% of equilibrium; unpacked tanks 50 to 70%.

How does temperature affect DAF?

Air solubility falls with temperature (29 mL/L at 0 °C, 19 mL/L at 20 °C), so a warm effluent releases less air per m³ of recycle and needs a higher recycle or pressure for the same A/S. Warm water also has a lower viscosity, which helps the bubble-floc aggregates rise. Size for the warmest operating temperature when the A/S governs.

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