Activated Sludge Process Control & Mathematics
Biological wastewater treatment relies on balancing food (organic BOD load) and microorganisms (MLSS biomass). Grade 2, 3, and 4 wastewater certification exams test process control mathematics including F/M ratio, MCRT, SVI, and solids digestion.
1. Food-to-Microorganism (F/M) Ratio
The F/M ratio measures the daily incoming organic food supply relative to the active microbial population in the aeration basin:
F/M Ratio = [Influent BOD (lbs/day)] ÷ [Aeration Basin MLSS or MLVSS (lbs)]Food (lbs BOD/day) = Influent Flow (MGD) × Influent BOD (mg/L) × 8.34Microorganisms (lbs MLSS) = Tank Volume (MG) × MLSS (mg/L) × 8.34
Typical conventional activated sludge designs operate between 0.20 to 0.50 lb BOD / lb MLSS.
2. Mean Cell Residence Time (MCRT / Sludge Age)
MCRT represents the average length of time (in days) microorganisms remain in the biological system before wasting:
MCRT (days) = Total System MLSS Inventory (lbs) ÷ [WAS Solids Wasted (lbs/day) + Effluent Solids Lost (lbs/day)]
3. Sludge Volume Index (SVI)
SVI describes the settling characteristics and volume occupied by 1 gram of activated sludge:
SVI (mL/g) = [30-Minute Settled Sludge Volume (mL/L) × 1,000] ÷ MLSS (mg/L)
• SVI < 80 mL/g: Rapid settling, pin-point floc.
• SVI 80–150 mL/g: Ideal settling characteristics.
• SVI > 150 mL/g: Slow settling, filamentous bulking.
4. Anaerobic Digester Volatile Solids Reduction (Van Kleeck)
VS Reduction (%) = [(In - Out) ÷ (In - (In × Out))] × 100
5. Biological Nitrification Chemistry & Alkalinity Demand
Complete two-step autotrophic nitrification converts toxic un-ionized ammonia into nitrate:
Step 1 (Nitrosomonas): 2 NH₄⁺ + 3 O₂ → 2 NO₂⁻ + 4 H⁺ + 2 H₂O + Energy
Step 2 (Nitrobacter): 2 NO₂⁻ + O₂ → 2 NO₃⁻ + Energy
Key Nitrification Constants
- Alkalinity Consumed: Exactly 7.14 lbs of Alkalinity as CaCO₃ per 1 lb of Ammonia-N ($NH4-N$) oxidized.
- Oxygen Required: Exactly 4.57 lbs of O₂ per 1 lb of Ammonia-N oxidized.
- Optimal pH Range: 7.5 to 8.5 (Nitrification drops severely below pH 6.8).
- Required MCRT: 10 to 25 days depending on temperature.
Warning Signs of Nitrification Failure
- Aeration Basin pH Drop: Rapid drop below 6.8 indicates severe alkalinity depletion.
- Dissolved Oxygen Depletion: High ammonia loads overwhelm blower capacity.
- Effluent Turbidity Spikes: Low MCRT causes nitrifiers to wash out faster than their slow growth rate.
6. Gould Sludge Age vs MCRT
State exams frequently distinguish between Gould Sludge Age (influent solids loading based) and MCRT (mass balance wasting based):
Gould Sludge Age (days) = Aeration Tank MLSS (lbs) ÷ Primary Effluent / Influent TSS (lbs/day)
Related Exam Practice Flashcards
BOD & TSS Removal Efficiency (%)
Influent = 240 mg/L, Effluent = 18 mg/L.
PRACTICE FLASHCARD Q15Activated Sludge F/M Ratio
0.80 MG basin @ 2,400 mg/L MLSS, 1.5 MGD @ 180 mg/L BOD.
PRACTICE FLASHCARD Q16Mean Cell Residence Time (MCRT)
24,000 lbs MLSS, WAS = 2,800 lbs/day, Effluent = 200 lbs/day.
PRACTICE FLASHCARD Q17Sludge Volume Index (SVI mL/g)
30-min settled = 270 mL/L, MLSS = 2,500 mg/L.
PRACTICE FLASHCARD Q20Van Kleeck VS Reduction (%)
Raw sludge = 72% VS, Digested sludge = 52% VS.
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