Activated-Sludge Biological Treatment, ASCE 2-06 Fine-Bubble SOTR to Field AOTR
ASCE Fine-Bubble Diffuser SOTR to Field AOTR Formula
Calculate Dissolved-Oxygen Driving Deficit Ratio, Arrhenius Theta Temperature Factor, Overall Field-to-Clean-Water Transfer Ratio, and Actual Oxygen Transfer Rate AOTR (kg O2/h).
Buying blowers straight off a brochure 185 kg/h clean-water SOTR curve starves nitrifying bacteria—because surfactants (alpha = 0.58), fouling, and 2.0 mg/L DO cut real AOTR to 74 kg/h!
Diffuser vendors test **EPDM / Polyurethane Fine-Bubble Membrane Discs** under **ASCE `2-06` Clean-Water Standard Conditions (`SOTR`: `20°C` tap water, `0.0` mg/L dissolved oxygen, `1` atm, brand-new pores)**! Inside an active mixed-liquor aeration basin, surfactants coat rising `2`-mm bubbles (**`alpha` factor `0.40–0.65`**), carbonate/bio-slime stiffens membrane slits (**Fouling factor `F = 0.65–0.90`**), dissolved salts depress saturation (**`beta ~= 0.95`**), maintaining aerobic residual **`C_{DO} = 2.0` mg/L** shrinks the concentration driving gradient `(beta * C_{sat,T} - C_{DO}) / C_{sat,20}`, and basin temperature `T` (`°C`) scales diffusivity via **`theta^(T - 20)` (`theta = 1.024`)**! Combining all five terms yields **Field Actual Oxygen Transfer Rate `AOTR = SOTR * alpha * F * ((beta * C_{sat,T} - C_{DO}) / C_{sat,20}) * (1.024^(T - 20))`** (`kg O_2/h`, typically just **`35%–45%` of `SOTR`**)!
Verify on a `4.5`-m Deep Municipal Nitrification Basin—Brochure_Clean-Water_`SOTR` = 185 kg `O_2`/h (B2), Surfactant_`alpha` = 0.58 (B3), Membrane_Fouling_`F` = 0.88 (B4), Salinity_`beta` = 0.96 (B5), Field_Depth-Corrected_`C_{sat,T}` = 10.4 mg/L (B6), Target_Basin_`DO` = 2.00 mg/L (B7), Clean-Water_`20°C`_`C_{sat,20}` = 11.2 mg/L (B8), and Basin_Temp `T` = 24.0°C (B9): DO Driving-Deficit Ratio equals `0.713` (E2), Arrhenius Temperature Factor equals `1.0995` (E3), Overall Field Correction `AOTR / SOTR` equals **`0.400`** (`40.0%`! E4), delivering **`74.0` kg `O_2`/h** of real biological oxygen (E5)!
| ASCE 2-06 Fine-Bubble Transfer KPI (SOTR=185 kg O2/h, Csat20=11.2 mg/L) | Formula | Verified Output |
|---|---|---|
| DO Driving-Force Ratio | (beta * Field_CsatT - Target_DO) / Std_Csat20 | 0.713 (0.397 @ 4.2 mg/L over-aeration!) |
| Arrhenius Temp Factor | 1.024 ^ (Basin_Temp_C - 20) | 1.0995 @ 24°C (1.2981 @ 31°C summer) |
| Field-to-Standard Ratio (AOTR/SOTR) | alpha * Fouling_F * DO_Ratio * Temp_Factor | 0.400 (0.126 = 87.4% transfer loss!) |
| Actual Field AOTR (kg O2/h) | Clean_Water_SOTR_kg_hr * Field_Ratio | 74.0 kg O2/h (23.3 kg O2/h blower stall!) |
ASCE / WEF MOP 8 Alpha-Beta-Theta-Fouling Field Oxygen Transfer Formula
Validate `SOTR > 0` kg/h, `alpha` in `[0.20, 1.00]`, `Fouling F` in `[0.40, 1.00]`, `Salinity beta` in `[0.70, 1.00]`, `Field C_{sat,T}` in `[5.0, 18.0]` mg/L, `Operating DO` in `[0, beta * C_{sat,T} - 0.5]` mg/L, `Std C_{sat,20}` in `[8.0, 16.0]` mg/L, and `Temp T` in `[4, 40]`°C!
=LET(st_r, B2, al_f, B3, fl_f, B4, bt_s, B5, cs_t, B6, do_m, B7, cs_z, B8, tp_c, B9, df_r, (bt_s * cs_t - do_m) / cs_z, th_t, 1.024 ^ (tp_c - 20), rt_x, al_f * fl_f * df_r * th_t, IF(OR(st_r <= 0, al_f < 0.2, al_f > 1, fl_f < 0.4, fl_f > 1, bt_s < 0.7, bt_s > 1, cs_t < 5, cs_t > 18, do_m < 0, do_m > bt_s * cs_t - 0.5, cs_z < 8, cs_z > 16, tp_c < 4, tp_c > 40), "Invalid AOTR Input", ROUND(st_r * rt_x, 1)))Aged Fouled Discs + Detergent Slug + High DO Setpoint (`alpha=0.36`, `F=0.68`, `DO=4.2` mg/L) Check
Dump high-surfactant laundry wastewater (`B3 = 0.36`) onto `6`-year-old scaled EPDM discs (`B4 = 0.68`, `B5 = 0.94`) during a `B9 = 31°C` heatwave (`C_{sat,T}` drops to `B6 = 9.2` mg/L) while an uncalibrated probe holds `B7 = 4.2` mg/L DO: Field Ratio E4 collapses to **`0.126`**, slashing real oxygen transfer E5 to **`23.3` kg `O_2`/h** (`3.2x` blower kWh waste)!
=IF(ISTEXT(E5), E5, ROUND(B3 * B4 * ((B5 * B6 - B7) / B8) * (1.024 ^ (B9 - 20)), 3))Try the example
Use the original values or change them to test your understanding.