Activated sludge process control

F/M ratiosludge ageSRTMCRTSVIRAS rateMLSS

F/M ratio, sludge age, SVI, RAS rate and organic loading — the five numbers an operator uses to steer an activated sludge plant.

Food-to-Microorganism (F/M) Ratio

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

Food-to-microorganism ratio: BOD applied per day divided by the mass of mixed liquor solids holding it, in kg BOD per kg MLVSS per day.

Mean Cell Residence Time (Sludge Age)

\text{SRT} = \frac{V \, X}{Q_w \, X_w}

Solids retention time of an activated sludge plant: the mass of solids under aeration divided by the mass wasted each day.

Sludge Volume Index (SVI)

\text{SVI} = \frac{SV_{30}}{X}

Sludge volume index in mL/g: the volume a gram of mixed liquor solids occupies after settling thirty minutes in a litre cylinder.

Return Activated Sludge Rate

Q_r = \frac{Q \, X}{X_r - X}

Return sludge flow needed to hold a target mixed liquor concentration, from a solids balance around the aeration basin.

BOD Mass Loading

W = Q \, C

Mass of BOD, COD or solids arriving per unit time from a flow and its concentration, on the sanitary basis of 1 mg/L = 1 g/m³.

Volumetric Organic Loading Rate

L_v = \frac{Q \, S_0}{V}

Organic load applied per unit of reactor volume, returned in kg BOD per cubic metre per day — the sizing number for basins and digesters.

BOD Removal Efficiency

E = \frac{C_i - C_e}{C_i} \times 100

Percent removal across a treatment unit or a whole plant, from the influent and effluent concentrations of BOD, TSS or any pollutant.

How they fit together

An activated sludge plant is a farm, and these are the herd numbers. F/M is how much food each pound of bugs gets per day; sludge age is how long the average organism stays in the system before it is wasted; SVI is how well the resulting sludge settles, in mL per gram. They are not independent — the wasting rate you choose sets the sludge age, which sets the inventory, which sets the F/M, which shows up a week later in the SVI.

Control on sludge age, watch F/M, and diagnose with SVI. Sludge age is the better lever because it responds to what you actually control (the waste rate) and because nitrification simply will not hold below roughly 8 to 10 days at 20 °C, longer when it is cold. SVI below about 100 settles well, above 150 says filaments are taking over and the clarifier is heading for a solids washout. The mistake that catches operators is chasing today's number: an activated sludge plant responds over one to three sludge ages, so a big waste rate change made on Monday's MLSS reading is still arriving three weeks later, usually on top of the correction you made in the meantime. Change one thing, change it by a small fraction, and wait.