Biochemical stabilization timeline: Approximately how long does it take for complete stabilization (ultimate BOD exertion) of organic matter in polluted water at standard conditions used in design problems?

Introduction / Context:
Biochemical Oxygen Demand (BOD) reflects the oxygen required by microorganisms to oxidize biodegradable organic matter. While the standard BOD test is 5 days at 20°C (BOD5), full biochemical stabilization (ultimate BOD) takes longer.

Given Data / Assumptions:

• Standard wastewater engineering convention at 20°C.
• Ultimate BOD approaches asymptote over several weeks.

Concept / Approach:
BOD exertion follows first-order kinetics: BOD(t) = L0 * (1 − e^(−k*t)), where L0 is ultimate BOD and k is the deoxygenation rate constant. At 5 days, only a fraction of L0 is exerted; practical “complete stabilization” for design approximations is taken near 20 days for typical domestic wastewater at 20°C.

Step-by-Step Solution:
Recognize BOD5 is a standard test period, not full stabilization.Use the conventional design approximation: ultimate exertion within roughly 20 days at 20°C.Select the corresponding option.

Verification / Alternative check:
Plotting BOD kinetics with a representative k (say 0.23 day^-1 at 20°C) shows BOD exerted by 20 days is very close to L0, supporting the rule-of-thumb period.

Why Other Options Are Wrong:

• 5 or 10 days: too short for ultimate BOD; used for standard sampling and reporting.
• 30 or 40 days: beyond the customary engineering reference; offers little additional design insight.

Common Pitfalls:

• Equating BOD5 with complete stabilization—this underestimates oxygen demand for long retention processes.

Final Answer:
20 days