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GATE 2018 CE (CE2) – Question 62

Water and Waste Water Quality and Treatment · Primary, secondary and tertiary treatment, effluent standards · 2 marks · Numerical answer

The diagram shows a completely mixed biological reactor with solids recycle. Influent Q = 15000 m³/day, S₀ = 100 mg/L and X₀ ≈ 0. Tank S = 15 mg/L, X = 3000 mg/L and hydraulic detention time 2 h. Return flow is 5000 m³/day; return and waste sludge have Xu = 10000 mg/L. Waste flow is 50 m³/day. Effluent is 14950 m³/day with S = 15 mg/L and Xe ≈ 0. S denotes readily biodegradable soluble BOD and X microorganism concentration (MLVSS). Mean cell residence time, to one decimal, is ______ days.

Diagram for GATE 2018 CE (CE2) question 62

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Correct answer: 7.5 to 7.5

Explanation

Tank volume from nominal influent detention is $15000(2/24)=1250$ m³. Biomass inventory is $1250(3)=3750$ kg. With negligible effluent solids, daily solids removal is $50(10)=500$ kg/day. Thus mean cell residence time is $3750/500=7.5$ days. Recycle is internal, not an external loss.