Food-to-Microorganism (F/M) Ratio

Also known as F/M ratio

FM=QS0VX\frac{F}{M} = \frac{Q \, S_0}{V \, X}

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Learning zone

Activated sludge is a herd of microorganisms being fed a daily ration, and F/M is the ration per head: kilograms of BOD applied each day divided by kilograms of mixed liquor solids in the basin. It is the number Ardern and Lockett could not have written when they published their aeration experiments at Manchester's Davyhulme works in 1914 — they simply noticed that if you kept the "activated" sludge instead of throwing it away, the next batch cleaned up in hours instead of weeks — but it is the number every operator now runs the plant by. A basin of 4000 m³ at 2400 mg/L MLSS holds 9600 kg of bugs; feed it 4320 m³/d at 200 mg/L BOD, or 864 kg/d, and the ratio is 0.09 per day.

Where you sit on the F/M scale defines the process. Extended aeration lives at 0.05–0.15, conventional activated sludge at 0.2–0.4, and high-rate or contact-stabilisation plants at 0.4–1.0. Run too high and the bugs stay in log growth, never flocculate, and the clarifier turns cloudy; run too low and they starve, the floc breaks into pin-point particles, and the effluent goes turbid for the opposite reason. The pervasive trap is mixing the bases — F is BOD₅ but M should strictly be volatile suspended solids, not total, and MLVSS is typically 70–80% of MLSS, so quoting an F/M on total solids makes a plant look about a quarter better fed than it is. Pick one basis, write it on the log sheet, and never mix them mid-trend.

Food-to-Microorganism (F/M) Ratio
FM=QS0VX\frac{F}{M} = \frac{Q \, S_0}{V \, X}
Where
  • F/MF/M= Food-to-microorganism ratio
  • QQ= Influent flow rate
  • S0S_0= Influent BOD concentration
  • VV= Aeration basin volume
  • XX= Mixed liquor solids (MLSS)
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