Industrial Wastewater, Dissolved Air Flotation & Sludge Thickening
Dissolved Air Flotation (DAF) Air-to-Solids Ratio Formula
Calculate DAF Saturator Net Released Air Factor (f*P - 1), Released Microbubble Air Concentration (mg/L), Mass Air-to-Solids Ratio A/S (kg air / kg TSS), and Recycle Pump Flow (m³/hr).
Subtract 1.0 atm atmospheric saturation—only EXCESS dissolved air precipitates microbubbles!
Dissolved Air Flotation (DAF) floats algae, oil/grease, and waste-activated sludge by saturating a clarified Recycle Stream R = Q_recycle / Q_feed with compressed air at absolute pressure P_abs (atm) and flashing it across a needle valve into an atmospheric tank (1.0 atm). Because effluent leaving at 1.0 atm STILL retains 1.0 atm of dissolved air, Net Precipitated Microbubble Air per liter of recycle is 1.3 * s_a * (f * P_abs - 1), where 1.3 mg/mL is air density, s_a (mL/L, ~18.0 mL/L near 22°C) is 1-atm air solubility, and f (~0.80–0.90) is packed-saturator efficiency! Dividing by Influent TSS X_f (mg/L) gives the design Mass Air-to-Solids Ratio A / S = (1.3 * s_a * (f * P_abs - 1) * R) / X_f (targeting 0.010–0.030 kg air / kg TSS)!
Verify on a 200 m³/hr Dairy/Sludge DAF Unit—Influent_Flow = 200.0 m³/hr (B2), Influent_TSS = 1,500 mg/L (B3), Air_Solubility_1atm = 18.0 mL/L (B4), Saturator_Efficiency f = 0.85 (B5), Saturator_Abs_Pressure = 5.0 atm (4.0 bar gauge, B6 -> Net Release Factor = 0.85 * 5.0 - 1 = 3.25 in E2), and Recycle_Ratio R = 0.30 (30.0%, B7): Released Air in Recycle is 1.3 * 18.0 * 3.25 = 76.05 mg/L (E3), Mass Air-to-Solids Ratio A/S hits (76.05 * 0.30) / 1,500 = 0.0152 kg/kg (E4), and Recycle Pump Flow is 60.00 m³/hr (E5)!
| DAF Microbubble Sizing KPI (200 m³/hr, 1,500 mg/L TSS, P = 5.0 atm, R = 30%) | Formula | Verified Output |
|---|---|---|
| Net Saturation Factor (f*P - 1) | Saturator_Eff * Abs_Pressure_atm - 1 | 3.25 |
| Released Air in Recycle (mg/L) | 1.3 * Solubility_mL_L * (f * P_abs - 1) | 76.05 mg/L |
| Air-to-Solids Ratio A/S (kg/kg) | (Released_Air_mg_L * Recycle_R) / TSS_mg_L | 0.0152 (0.0051 @ R = 10%!) |
| Pressurized Recycle Flow (m³/hr) | Influent_Flow_m3_hr * Recycle_Ratio_R | 60.00 m³/hr (20.00 @ R = 10%) |
Pressurized-Recycle DAF Air-to-Solids (A/S) Formula
Validate Flow > 0, TSS > 0, Solubility > 0, Saturator_f in (0.40, 1.0], f * P_abs > 1.2 (net positive bubble release!), and Recycle_Ratio in (0.02, 2.0]!
=LET(q_in, B2, xf_t, B3, sa_m, B4, ef_s, B5, p_at, B6, rc_r, B7, IF(OR(q_in <= 0, xf_t <= 0, sa_m <= 0, ef_s <= 0.4, ef_s > 1, ef_s * p_at <= 1.2, rc_r <= 0.02, rc_r > 2), "Invalid DAF Saturator Input", LET(rl_a, 1.3 * sa_m * (ef_s * p_at - 1), ROUND((rl_a * rc_r) / xf_t, 4))))Under-Recycled Floc Sinking Failure Check (Set Recycle Ratio R = 0.10)
Throttle Recycle_Ratio B7 from 0.30 down to 0.10 (20.00 m³/hr recycle E5): Air-to-Solids Ratio E4 drops 3x to 0.0051 kg/kg—starving heavy sludge flocs of buoyancy so solids sink to the DAF floor!
=IF(ISTEXT(E4), E4, ROUND(B2 * B7, 2))Try the example
Use the original values or change them to test your understanding.