BOD Equation
Biochemical Oxygen Demand measures how much dissolved oxygen microorganisms consume while breaking down organic matter in water. The standard 5-day BOD test (BOD₅) is the most common water-quality benchmark.
BODt = L(1 − 10⁻ᵏᵗ)
Unseeded BOD
The unseeded BOD test measures dissolved oxygen depletion in a sample that contains enough native bacteria for decomposition.
BOD = (D₁ − D₂) / P
Seeded BOD
For samples with few native bacteria, a seeded BOD test adds a known microbial culture. The seed’s own oxygen consumption is subtracted to isolate the sample’s demand.
BOD = ((D₁ − D₂) − f(B₁ − B₂)) / P
How It Works
Biochemical Oxygen Demand (BOD) measures how much dissolved oxygen microorganisms consume while breaking down organic matter in water. The BOD equation relates oxygen demand at any time to the ultimate BOD and a deoxygenation rate constant. The standard 5-day BOD test (BOD₅) is the most common water-quality benchmark. For samples with few native bacteria (e.g., industrial effluent), a seeded BOD test adds a known microbial culture. The seed’s own oxygen consumption is subtracted to isolate the sample’s demand.
Example Problem
A wastewater sample has an ultimate BOD (L) of 300 mg/L and a deoxygenation rate constant (k) of 0.23 per day. What is BOD₅?
- BOD₅ = 300 × (1 − 10⁻⁰·²³×⁵)
- 10⁻¹·¹⁵ ≈ 0.0708
- BOD₅ = 300 × 0.929 = 278.8 mg/L
About 93% of the ultimate oxygen demand is exerted within 5 days at this rate.
When to Use Each Variable
- Solve for BOD at time t — when you know the ultimate BOD, deoxygenation rate, and elapsed time, e.g., predicting oxygen demand after 5 days for a wastewater sample.
- Solve for Ultimate BOD (L) — when you have a BOD measurement at a known time and rate constant, e.g., estimating total oxygen demand from a BOD5 test result.
- Solve for Deoxygenation Rate (k) — when you have BOD and ultimate BOD measurements and need the rate constant, e.g., characterizing decomposition kinetics of an industrial effluent.
- Solve for Time (t) — when you know the BOD, ultimate BOD, and rate constant and need to find elapsed time, e.g., determining how long until a stream reaches a target oxygen demand.
- Solve for Unseeded BOD — when the sample has sufficient native bacteria and you measured initial and final dissolved oxygen with a known dilution ratio.
- Solve for Seeded BOD — when the sample lacks native bacteria and you added a seed culture, e.g., testing chlorinated or high-temperature industrial waste.
Key Concepts
BOD quantifies the biodegradable organic load in water by measuring how much dissolved oxygen microorganisms consume during decomposition. The first-order deoxygenation model uses rate constant k to describe how quickly oxygen is consumed relative to the ultimate demand L. The unseeded test works for samples with enough native bacteria, while the seeded test adds a known microbial culture and subtracts the seed's own oxygen consumption to isolate the sample's demand.
Applications
- Wastewater treatment plant design: sizing aeration basins based on influent BOD loading to ensure adequate oxygen supply
- Discharge permit compliance: demonstrating that treated effluent meets NPDES BOD5 limits (typically under 30 mg/L)
- Stream water quality modeling: predicting dissolved oxygen sag downstream of a discharge using BOD and reaeration rates
- Industrial pretreatment: assessing organic load from food processing, brewery, or paper mill waste before discharge to municipal sewers
Common Mistakes
- Using a seeded test when the sample has adequate native bacteria — the seed correction introduces unnecessary uncertainty; use unseeded BOD when the sample can decompose on its own
- Confusing BOD5 with ultimate BOD — BOD5 typically represents only 60-70% of the total oxygen demand; using BOD5 as the ultimate value underestimates the full organic load
- Storing samples too long before testing — biological activity continues during storage, which alters the initial dissolved oxygen reading and skews results; test within 24 hours or refrigerate at 4 degrees C
Frequently Asked Questions
What is a normal BOD level for wastewater?
Untreated domestic wastewater typically has a BOD₅ of 200–300 mg/L. After secondary treatment, effluent BOD₅ usually drops below 20 mg/L to meet discharge permits.
What is the difference between BOD and COD?
BOD measures oxygen consumed by biological decomposition over days, while Chemical Oxygen Demand (COD) uses a strong oxidant to measure total oxidizable matter in a few hours. COD is always equal to or higher than BOD because it includes non-biodegradable organics.
Why is the BOD test done over 5 days?
Five days was chosen historically because it approximates the travel time of major English rivers from source to sea. It captures roughly 60–70% of the ultimate oxygen demand and provides a practical, reproducible measurement window.
When should you use a seeded BOD test?
Use a seeded test when the sample lacks sufficient microorganisms for decomposition, such as chlorinated effluent, industrial waste, or high-temperature discharges. The seed provides the bacteria needed for accurate results.
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