Biological Wastewater Treatment, Nitrification & Sludge Wasting
Activated-Sludge SRT (MCRT), F/M Ratio & WAS Flow Formula
Calculate Aeration Bioreactor Biomass Inventory (kg MLVSS), Food-to-Microorganism F/M Ratio (d^-1), Required Daily Waste Activated Sludge Mass (kg/d), and WAS Pump Flow (m³/d).
Deduct effluent VSS lost over the clarifier weir before setting your daily WAS wasting pump!
Mean Cell Residence Time—also called Solids Retention Time (SRT = Total_Aeration_Biomass_kg / Total_Solids_Leaving_Plant_kg_d)—controls whether slow-growing nitrifying bacteria survive or wash out! Operators setting daily Waste Activated Sludge (WAS) pump flow for a Target_SRT must subtract biomass already escaping unintentionally in secondary effluent (Effluent_Loss_kg_d = Q_m3_d * X_eff_VSS_mg_L / 1,000) from Total Required Daily Purge (Aeration_Biomass_kg / Target_SRT), then divide by Underflow Volatile Concentration (X_WAS_VSS_mg_L / 1,000)! Note: if trainees practice these mass balances in the Academy, read-only ChatGPT connector tools (list_lessons, get_lesson, get_learning_progress in 0.1.0, currently In review / Not published) can inspect lesson steps and server-verified verifiedLessons, while interactive exercise grading and certification always happen inside Arte Sheets.
Verify on a 20,000 m³/d Municipal Bioreactor—Plant_Flow Q = 20,000 m³/d (B2), Primary_Effluent_BOD = 240 mg/L (4,800 kg BOD/d, B3), Aeration_Volume V = 6,000 m³ (B4) at MLVSS = 2,500 mg/L (B5 -> Biomass Inventory = 6,000 * 2.50 = 15,000.00 kg in E2; F/M Ratio = 4,800 / 15,000 = 0.32 d^-1 in E3), Target_SRT = 10.0 days (1,500 kg/d total purge, B6), and Underflow_WAS_VSS = 6,500 mg/L with 10 mg/L Effluent VSS (200 kg/d effluent loss, B7): Intentional Daily WAS Mass equals 1,500 - 200 = 1,300.00 kg/d (E4), requiring 1,300 / 6.50 = 200.00 m³/d of WAS Pumping (E5)!
| SRT & WAS Control KPI (20,000 m³/d, 240 BOD, 6,000 m³ @ 2,500 MLVSS, SRT = 10 d) | Formula | Verified Output |
|---|---|---|
| Aeration Biomass Inventory (kg) | Aeration_Vol_m3 * MLVSS_mg_L / 1000 | 15,000.00 kg |
| Food-to-Microorganism F/M (d^-1) | (Q_m3_d * BOD_mg_L) / (Vol_m3 * MLVSS_mg_L) | 0.32 d^-1 |
| Intentional WAS Mass Wasted (kg/d) | (Biomass_kg / SRT_d) - (Q_m3_d * 10 / 1000) | 1,300.00 kg/d (800.00 @ 15 d SRT) |
| Required WAS Pump Flow (m³/d) | WAS_Mass_kg_d / (WAS_VSS_mg_L / 1000) | 200.00 m³/d (123.08 @ 15 d SRT) |
SRT-Controlled Daily WAS Pump Flow Formula
Validate Flow > 0, BOD > 0, Volume > 0, MLVSS > 100, Target_SRT in [2, 40] days, and WAS_VSS > MLVSS!
=LET(q_in, B2, bd_i, B3, vl_a, B4, ml_v, B5, sr_t, B6, xr_v, B7, IF(OR(q_in <= 0, bd_i <= 0, vl_a <= 0, ml_v <= 100, sr_t < 2, sr_t > 40, xr_v <= ml_v), "Invalid SRT Control Input", LET(ms_b, vl_a * ml_v / 1000, ef_l, q_in * 10 / 1000, ws_m, MAX(0, ms_b / sr_t - ef_l), ROUND(ws_m / (xr_v / 1000), 2))))Winter Nitrification Longer-SRT Check (Set Target SRT = 15.0 Days)
Raise Target_SRT B6 from 10.0 days to 15.0 days to protect cold-weather nitrifiers: Intentional WAS Mass E4 drops from 1,300.00 kg/d to (15,000 / 15) - 200 = 800.00 kg/d, cutting Daily WAS Pump Flow E5 from 200.00 m³/d down to 123.08 m³/d!
=IF(ISTEXT(E5), E5, ROUND((B2 * B3) / (B4 * B5), 2))Try the example
Use the original values or change them to test your understanding.