Sludge production – model calculations

Indicative estimate of excess sludge production based on biomass parameters and WWTP loading. Results are rough estimates — for design use detailed models or mass balances.

Common inputs for all calculations

Biomass parameters

Yb – biomass yield coefficient [g TSS / g BOD₅]

b – biomass decay coefficient [1/day]

sludge age θc [d]

MLSS in aeration X [g/L]

β – non-degradable fraction of new biomass [-]

fm,0 – mineral fraction in new cells [-]

kd(20 °C) – decay constant [1/day]

temperature T [°C]

Cake solids [%]

Influent parameters

Q – annual flow to WWTP [m³/yr]

cᵢ – influent BOD₅ [mg/L]

f – influent inert TSS fraction [%]

Xi – influent TSS [mg/L]

Effluent parameters

cₑ – effluent BOD₅ [mg/L]

Xe – effluent TSS [mg/L]

1. Simple calculation using Yb, b and sludge age

Good for a quick estimate, mainly for systems with sludge age up to ~5 days.

Yobs

0.368

BOD₅ removed [t/yr]

1.84 t/yr

Biomass growth

0.68 t DS/yr

Inert contribution

0.29 t/yr

Sludge in effluent

0.01 t/yr

Total dry solids

0.96 t DS/yr

Wet sludge

4.78 t/yr

2. More detailed calculation for higher sludge ages

Uses an extended expression for the observed yield. Needs more parameters; wrong estimates may reduce accuracy compared to the simple approach.

Yobs

0.390

Biomass growth

0.72 t DS/yr

Inert contribution

0.29 t/yr

Sludge in effluent

0.01 t/yr

Total dry solids

1.00 t DS/yr

Wet sludge

4.98 t/yr

3. Chemical sludge from P-precipitation (very rough)

Rough estimate of sludge from ferric dosing. Assumes ferric phosphate and ferric hydroxide; other effects are neglected.

Coagulant dose [t/year]

Fe content in coagulant [%]

Fe utilisation efficiency [%]

Fe dose [t/year]

1.13 t/yr

Chemical sludge

3.05 t DS/yr

Note: the calculation assumes formation of ferric phosphate and ferric hydroxide; other effects are neglected.

Note: all calculations are indicative and for checks or preliminary estimates only, not as the sole basis for design.