Wastewater Process Control, Activated Sludge & Secondary Clarification
Sludge Volume Index (SVI) & Return-Sludge RAS Ratio Formula
Calculate Mohlman Sludge Volume Index SVI (mL/g), Theoretical Maximum Return-Sludge Concentration X_R (mg/L), Minimum RAS Recycle Ratio Q_r/Q, and Filamentous Bulking Status.
Multiply 30-minute settleometer mL/L by 1,000 before dividing by MLSS—and watch SVI > 150 bulking!
In activated-sludge wastewater operations, the 30-minute Mallory settleometer test measures Settled Sludge Volume SV30 (in mL/L) while lab filtration measures Mixed Liquor Suspended Solids MLSS (in mg/L). Because 1,000 mg = 1 g, Mohlman’s Sludge Volume Index (volume in mL occupied by 1 gram of dry biomass) is SVI = (SV30_mL_L * 1,000) / MLSS_mg_L! Healthy compact flocs exhibit SVI = 70–120 mL/g, whereas SVI > 150 mL/g diagnoses filamentous sludge bulking! Furthermore, assuming settled underflow compacts to X_R_max = 1,000,000 / SVI (mg/L), steady-state secondary clarifier mass balance requires a Minimum Return Activated Sludge (RAS) Recycle Ratio Q_r / Q = MLSS / (X_R_max - MLSS) = SV30 / (1,000 - SV30)!
Verify on a Well-Settling Municipal Aeration Basin—Settleometer_SV30 = 200 mL/L (B2) and Aeration_MLSS = 2,500 mg/L (B3): Sludge Volume Index equals (200 * 1,000) / 2,500 = 80.00 mL/g (E2), Theoretical Max Return-Sludge Concentration X_R hits 1,000,000 / 80 = 12,500.00 mg/L (E3), Minimum RAS Recycle Ratio Q_r / Q is 2,500 / (12,500 - 2,500) = 0.25 (25.0% of influent flow, E4), and Settling Status reads "GOOD SETTLING: <=150" (E5)!
| Activated-Sludge Settling KPI (SV30 = 200 mL/L, MLSS = 2,500 mg/L) | Formula | Verified Output |
|---|---|---|
| Sludge Volume Index SVI (mL/g) | (SV30_mL_L * 1000) / MLSS_mg_L | 80.00 mL/g (200.00 Bulking) |
| Max Underflow Solids X_R (mg/L) | 1000000 / SVI_mL_g | 12,500.00 mg/L (5,000.00 Bulking) |
| Minimum RAS Ratio (Q_r / Q) | MLSS / (X_R_Max - MLSS) | 0.25 (1.00 @ SV30 = 500) |
| Clarifier Bulking Diagnostic | IF(SVI > 150, "BULKING: >150", "GOOD SETTLING: <=150") | GOOD SETTLING: <=150 |
Mohlman SVI & Minimum RAS Recycle Ratio Formula
Validate SV30 in (10, 950] mL/L (below 1,000 mL cylinder height!) and MLSS in [200, 15,000] mg/L!
=LET(sv_m, B2, ml_s, B3, IF(OR(sv_m <= 10, sv_m > 950, ml_s < 200, ml_s > 15000), "Invalid Settleometer Input", ROUND((sv_m * 1000) / ml_s, 2)))Filamentous Bulking RAS Pump Overload Check (Set SV30 = 500 mL/L)
Simulate a filamentous Microthrix outbreak where SV30 B2 swells from 200 mL/L to 500 mL/L at 2,500 mg/L MLSS: SVI E2 jumps to 200.00 mL/g ("BULKING: >150" in E5), Max Underflow Solids E3 drops to 5,000.00 mg/L, and Minimum RAS Recycle Ratio E4 quadruples from 0.25 to 1.00 (requiring 100% of plant influent flow in RAS pumping to prevent blanket washout)!
=IF(ISTEXT(E2), E2, IF(E2 > 150, "BULKING: >150", "GOOD SETTLING: <=150"))Try the example
Use the original values or change them to test your understanding.