Water operator math tutorial
Mean Cell Residence Time (MCRT/SRT)
Divide the solids in the system by the solids removed each day.
MCRT, also called sludge retention time, is the average number of days a solids particle stays in the activated sludge system. Operators adjust wasting to hold it steady.
Count solids in both the aeration tank and clarifier, and count solids leaving by wasting and in the effluent.
The formula
MCRT (days) = [MLSS (mg/L) × (aeration + clarifier volume, MG) × 8.34] ÷ [(WAS flow × WAS TSS + effluent flow × effluent TSS) × 8.34]
| Variable | Unit |
|---|---|
| MLSS | mg/L |
| Aeration tank volume | MG |
| Clarifier volume | MG |
| WAS flow | MGD |
| WAS TSS | mg/L |
| Effluent flow | MGD |
| Effluent TSS | mg/L |
| Result: MCRT | days |
Conversion factors used: 8.34 lb per gallon of water (cancels in the ratio).
Applies to: Wastewater Treatment.
Common exam tip: Write two lines: solids in the system, solids leaving per day. Then divide. Do not skip the effluent.
Calculator
MCRT
9.08 days
- 1. Solids in system = 2,500 × (1 + 0.25) × 8.34 = 26,063 lb
- 2. Solids removed = (0.04 × 8,000 + 2 × 12) × 8.34 = 2,869 lb/day
- 3. MCRT = 26,063 ÷ 2,869 = 9.08 days
For instructional use. Results assume the standard conversion factors shown on this page. Actual field calculations may need chemical strength, density, temperature, and other adjustments, so check your plant’s procedures.
Worked examples
Example 1
MLSS 2,500 mg/L, aeration tank 1.0 MG, clarifier 0.25 MG, WAS 0.04 MGD at 8,000 mg/L, effluent 2.0 MGD at 12 mg/L.
- Solids in system = 2,500 × (1 + 0.25) × 8.34 = 26,063 lb
- Solids removed = (0.04 × 8,000 + 2 × 12) × 8.34 = 2,869 lb/day
- MCRT = 26,063 ÷ 2,869 = 9.08 days
Answer: 9.08 days
Example 2
MLSS 3,000 mg/L, aeration tank 2.0 MG, clarifier 0.5 MG, WAS 0.1 MGD at 7,500 mg/L, effluent 6.0 MGD at 10 mg/L.
- Solids in system = 3,000 × (2 + 0.5) × 8.34 = 62,550 lb
- Solids removed = (0.1 × 7,500 + 6 × 10) × 8.34 = 6,755.4 lb/day
- MCRT = 62,550 ÷ 6,755.4 = 9.26 days
Answer: 9.26 days
Common mistakes
Wrong result: 7.27 days
counting only the aeration tank and ignoring the clarifier
Wrong result: 7.81 days
leaving the effluent solids out of the solids removed
Practice questions
1. MLSS 2,200 mg/L, tank 0.8 MG, clarifier 0.2 MG, WAS 0.03 MGD at 9,000 mg/L, effluent 1.5 MGD at 15 mg/L. MCRT?
- A7.52 days
- B6.02 days
- C6.52 days
- D75.2 days
Show answer and explanation
Correct answer: A. Solids in system = 2,200 × (0.8 + 0.2) × 8.34 = 18,348 lb Solids removed = (0.03 × 9,000 + 1.5 × 15) × 8.34 = 2,439.5 lb/day MCRT = 18,348 ÷ 2,439.5 = 7.52 days Answer: 7.52 days. A common slip is counting only the aeration tank and ignoring the clarifier, which gives 6.02 days.
2. MLSS 2,800 mg/L, tank 1.5 MG, clarifier 0.4 MG, WAS 0.06 MGD at 7,000 mg/L, effluent 4.0 MGD at 8 mg/L. MCRT?
- A9.29 days
- B11.77 days
- C10 days
- D117.7 days
Show answer and explanation
Correct answer: B. Solids in system = 2,800 × (1.5 + 0.4) × 8.34 = 44,369 lb Solids removed = (0.06 × 7,000 + 4 × 8) × 8.34 = 3,769.7 lb/day MCRT = 44,369 ÷ 3,769.7 = 11.77 days Answer: 11.77 days. A common slip is counting only the aeration tank and ignoring the clarifier, which gives 9.29 days.
3. MLSS 3,500 mg/L, tank 3.0 MG, clarifier 0.8 MG, WAS 0.12 MGD at 6,500 mg/L, effluent 8.0 MGD at 9 mg/L. MCRT?
- A12.32 days
- B13.46 days
- C15.61 days
- D156.1 days
Show answer and explanation
Correct answer: C. Solids in system = 3,500 × (3 + 0.8) × 8.34 = 110,922 lb Solids removed = (0.12 × 6,500 + 8 × 9) × 8.34 = 7,105.7 lb/day MCRT = 110,922 ÷ 7,105.7 = 15.61 days Answer: 15.61 days. A common slip is counting only the aeration tank and ignoring the clarifier, which gives 12.32 days.
Where this formula applies
This calculation can appear in the disciplines below. Exact exam coverage depends on your state, certification level, and official exam outline.
Wastewater Treatment
Study guides
Keep going with the full guide
Water Operator Math Made Simple walks through operator math step by step and includes printable references plus a full practice exam.
Water Operator Math Made Simple
A Step-by-Step Guide to the Math Every Water Operator Needs to Know