GATE 2025 CE (CE2) – Question 62
A community generates 1 million litres/day (MLD) of wastewater. This wastewater is treated using activated sludge process (ASP). The working volume of the aeration tank of the ASP is 250 m$^3$, and the biomass concentration in the tank is 3000 mg/L. Analyses results showed that a biomass concentration of 10 mg/L is present in the treated effluent from the secondary sedimentation tank of the ASP. Sludge wastage from the system is at a rate of 5000 L/day with a biomass concentration of 10000 mg/L. The system is in steady state condition.
The biological sludge residence time (BSRT) of the system (in days) is ______ (round off to one decimal place).
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Correct answer: 12.44 to 12.56
Explanation
The BSRT is the mass of biomass in the tank divided by the mass leaving per day: $\theta_c = \frac{VX}{Q_wX_w + Q_eX_e}$. The biomass in the tank is $250 \times 3000 = 750000$ g. The wasted sludge removes $5 \times 10000 = 50000$ g/d. The effluent flow is $1000 - 5 = 995$ m³/d, which carries $995 \times 10 = 9950$ g/d. So $\theta_c = \frac{750000}{50000 + 9950} = 12.5$ days.