Hong Life CalculatorsUnderstanding the activated sludge calculator — concept and principle
This calculator gives four numbers activated sludge operators check most: the food-to-microorganism ratio (F/M), hydraulic retention time (HRT), solids retention time or sludge age (SRT) and sludge volume index (SVI). Together they show whether the aeration tank is sensibly loaded, the biomass stays long enough, and the sludge will settle.
How it is calculated
- F/M = Q × BOD ÷ (V × MLSS), in kg BOD per kg MLSS per day. The mg/L and m³ units cancel, because 1 mg/L × 1 m³ = 1 g on both top and bottom.
- HRT = V ÷ Q × 24, in hours.
- SRT = V × MLSS ÷ (Qw × Xw), in days, where Qw is the waste sludge flow and Xw its suspended solids. Solids lost in the effluent are ignored.
- SVI = SV30 × 1000 ÷ MLSS, in mL/g, where SV30 is the settled sludge volume after 30 minutes in a 1 L cylinder.
The principle
Activated sludge is a mass balance of food and bugs. F/M compares the daily BOD load with the mass of microorganisms available to eat it: too high and the biomass is overfed and treatment is incomplete; too low and it starves. SRT is the average time a particle of sludge stays in the system, so it equals the solids inventory divided by the solids removed each day. Because slow-growing organisms such as nitrifiers wash out if SRT is shorter than their doubling time, SRT is the main design and control parameter. SVI is the space one gram of sludge occupies after settling.
Worked example
- Inputs: Q = 10,000 m³/d, BOD = 200 mg/L, V = 3,000 m³, MLSS = 3,000 mg/L, Qw = 100 m³/d, Xw = 8,000 mg/L, SV30 = 250 mL/L.
- BOD load = 10,000 × 200 ÷ 1,000 = 2,000 kg/d; biomass = 3,000 × 3,000 ÷ 1,000 = 9,000 kg.
- F/M = 2,000 ÷ 9,000 = 0.222 kg BOD/kg MLSS·d.
- HRT = 3,000 ÷ 10,000 × 24 = 7.2 h.
- Wasted solids = 100 × 8,000 ÷ 1,000 = 800 kg/d, so SRT = 9,000 ÷ 800 = 11.25 days.
- SVI = 250 × 1,000 ÷ 3,000 = 83.3 mL/g.
| Aeration volume (m³) | F/M (kg BOD/kg MLSS·d) |
|---|---|
| 750 | 0.8888888889 |
| 1,500 | 0.4444444444 |
| 2,250 | 0.2962962963 |
| 3,000 | 0.2222222222 |
| 3,750 | 0.1777777778 |
| 4,500 | 0.1481481481 |
| 6,000 | 0.1111111111 |
How to read the result
For conventional activated sludge, textbook ranges are roughly F/M 0.2–0.4, SRT about 3–15 days, HRT about 4–8 hours and MLSS 1,500–3,000 mg/L; extended aeration runs at much lower F/M and longer SRT. An SVI below about 100 mL/g usually means good settling, while values above about 150 mL/g suggest bulking sludge. The example is a typical, well-settling plant.
Common mistakes
- Using MLVSS in one formula and MLSS in another; be consistent with your plant's convention.
- Using influent BOD after primary settling for one value and raw BOD for another.
- Ignoring effluent solids when they are significant, which overstates SRT.
Frequently asked questions
What is the difference between SRT and HRT?
HRT is how long the water stays in the tank; SRT is how long the solids stay. Recycling sludge from the clarifier makes SRT much longer than HRT.
How do I increase SRT?
Waste less sludge per day. With the same inventory, halving the waste rate doubles the sludge age.
Sources: Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery, McGraw-Hill · APHA/AWWA/WEF, Standard Methods for the Examination of Water and Wastewater, Method 2710 (Tests on Sludges)