Microbiology, BOD Kinetics & Monod Growth
Key Takeaways
- BOD measures oxygen demand of biodegradable organics.
- First-order BOD kinetics: dL/dt = -kL.
- Monod growth: μ = μmax S/(Ks+S).
- Activated sludge design uses SRT, HRT, F/M ratio.
- Nitrifiers grow slower than heterotrophs — need longer SRT.
Quick Answer: BOD is oxygen demand. First-order decay for carbonaceous BOD. Monod describes growth vs substrate. SRT controls biomass and nitrification.
BOD Kinetics
[ L_t = L_0 e^{-k_d t} ]
Ultimate BOD L₀; deoxygenation rate k_d (day⁻¹). NBOD from ammonia oxidized separately.
Monod Equation
[ \mu = \mu_{max} \frac{S}{K_s + S} ]
At low S, growth is first-order in substrate; at high S, μ → μmax.
Activated Sludge Parameters
| Parameter | Role |
|---|---|
| SRT (θc) | Solids retention — nitrification needs ~8–15 d at 20°C |
| HRT | Hydraulic detention in aeration basin |
| F/M | Food to microorganism ratio — loading rate |
Oxygen Requirements
1 mg/L NH₃-N oxidized ≈ 4.6 mg/L O₂ stoichiometrically.
Exam Traps
- BOD₅ is not ultimate BOD — only fraction in 5 days.
- Lower temperature → slower kinetics → longer SRT needed.
Multi-Step Workflow
List givens with units, select the governing relationship, convert to a consistent unit set, solve, and compare to a rough estimate.
BOD Kinetics and Monod Growth
| Model | Equation idea | Use |
|---|---|---|
| First-order BOD | $L_t=L_0 e^{-kt}$ | Stream/BOD remaining |
| Ultimate BOD | $L_0$ | Long-term oxygen demand |
| Monod | $\mu=\mu_{max}S/(K_s+S)$ | Activated sludge growth |
| F/M | food/microorganisms | Aeration tank loading |
Worked BOD
If $k=0.23,d^{-1}$ (base e) and $L_0=200$ mg/L, BOD remaining at t=5 d: $L_5=200 e^{-0.23\times5}\approx 63$ mg/L. BOD exerted = $200-63=137$ mg/L.
On the Exam: Confirm whether $k$ is base-10 or base-e; NCEES problems state the convention. Mixing them flips the answer.
BOD Kinetics and Monod Growth
| Model | Equation idea | Use |
|---|---|---|
| First-order BOD | $L_t=L_0 e^{-kt}$ | Stream/BOD remaining |
| Ultimate BOD | $L_0$ | Long-term oxygen demand |
| Monod | $\mu=\mu_{max}S/(K_s+S)$ | Activated sludge growth |
| F/M | food/microorganisms | Aeration tank loading |
Worked BOD
If $k=0.23,d^{-1}$ (base e) and $L_0=200$ mg/L, BOD remaining at t=5 d: $L_5=200 e^{-0.23\times5}\approx 63$ mg/L. BOD exerted = $200-63=137$ mg/L.
On the Exam: Confirm whether $k$ is base-10 or base-e; NCEES problems state the convention. Mixing them flips the answer.
BOD Kinetics and Monod Growth
| Model | Equation idea | Use |
|---|---|---|
| First-order BOD | $L_t=L_0 e^{-kt}$ | Stream/BOD remaining |
| Ultimate BOD | $L_0$ | Long-term oxygen demand |
| Monod | $\mu=\mu_{max}S/(K_s+S)$ | Activated sludge growth |
| F/M | food/microorganisms | Aeration tank loading |
Worked BOD
If $k=0.23,d^{-1}$ (base e) and $L_0=200$ mg/L, BOD remaining at t=5 d: $L_5=200 e^{-0.23\times5}\approx 63$ mg/L. BOD exerted = $200-63=137$ mg/L.
On the Exam: Confirm whether $k$ is base-10 or base-e; NCEES problems state the convention. Mixing them flips the answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Additional review point: verify assumptions, boundary conditions, and whether the problem is steady-state or transient before selecting an answer.
Longer SRT in activated sludge generally: