Exercise set

Wastewater Biological Treatment Load, SRT, and Aeration Exercises

Solved wastewater biological-treatment exercises for BOD load, HRT, F/M, SRT, wasting, oxygen demand, aeration margin, sludge yield and release gates.

Branch: Environmental Engineering
Content: Exercise set
Updated: Jul 03, 2026
Revision: v1.0.0 · reviewed

These exercises focus on the biological-treatment barrier in wastewater plants. They cover pollutant load, hydraulic residence time, food-to-microorganism ratio, solids retention time, mixed-liquor inventory, waste activated sludge, oxygen demand, aeration transfer, dissolved-oxygen evidence, temperature guard, blower power, sludge yield and process release gates.

Assume simplified screening calculations unless an exercise states otherwise. Field release requires flow data, composite sampling, lab QA, MLSS and MLVSS records, aeration status, dissolved-oxygen probes, sludge wasting logs, recycle flows, temperature history and effluent monitoring.

Release Evidence Notes

Biological-treatment evidence should keep load, biomass and oxygen on the same time basis. A plant can have enough tank volume but too little active biomass, enough air capacity but poor transfer, or acceptable average BOD removal while failing during cold or wet-weather conditions.

SRT evidence should include solids inventory and actual wasting. A target SRT is not real unless MLSS, tank volume, WAS flow, WAS concentration and effluent solids losses reconcile.

Aeration evidence should connect required oxygen, delivered oxygen, blower status, diffuser condition, DO sensor calibration and basin profile. A running blower does not prove oxygen transfer.

Engineering Boundary Notes

These calculations do not replace activated-sludge modeling, nitrification design, process-control testing, lab QA, permit reporting or operator certification. They are screening exercises for biological treatment release.

Common Release Mistakes

calculating BOD load from average flow when peak wet-weather load controls the basin;
using MLSS as if all solids were active biomass;
changing wasting before confirming current SRT and sludge age;
judging aeration from blower status rather than oxygen transfer and DO profile;
combining biology, clarification and disinfection into one generic treatment margin.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Load and volume	1, 2, 3, 4	BOD/COD load, HRT and F/M ratio	Decide whether the basin loading basis is credible.
Biomass and wasting	5, 6, 7, 12, 14	SRT, WAS, inventory, temperature guard and sludge yield	Decide whether solids control supports treatment.
Oxygen and monitoring	8, 9, 10, 11, 13, 16, 17	oxygen demand, transfer margin, DO evidence, alkalinity, blower power and monitoring	Decide whether biological operation is releasable.
Release gate	18	all-of biological release	Decide whether biological treatment can close.

Exercise 1: Daily BOD Load

Influent flow is $8200\ \text{m}^3/\text{d}$ and influent BOD is $185\ \text{mg/L}$ . Calculate daily BOD load.

Solution

Use $1\ \text{mg/L}=1\ \text{g/m}^3$ :

L=QC=8200(185)=1517000\ \text{g/d}

L=1517\ \text{kg/d}

Engineering Comment

This load is the starting point for aeration, sludge production and process capacity checks.

Plausibility Check

Thousands of cubic meters per day at hundreds of milligrams per liter should produce tonnes per day of BOD load.

Exercise 2: COD-to-BOD Load Screen

Influent COD is $420\ \text{mg/L}$ at the same flow of $8200\ \text{m}^3/\text{d}$ . Compute COD load and COD:BOD load ratio using the BOD load from Exercise 1.

Solution

L_{COD}=8200(420)=3444000\ \text{g/d}=3444\ \text{kg/d}

R=\dfrac{3444}{1517}=2.27

Engineering Comment

The ratio is a biodegradability screen. A high or drifting ratio can signal industrial load, toxicity or weak biological availability.

Plausibility Check

COD is a little more than twice BOD, so the load ratio should also be a little above two.

Exercise 3: Aeration Basin Hydraulic Residence Time

Aeration basin volume is $3100\ \text{m}^3$ and flow is $8200\ \text{m}^3/\text{d}$ . Compute hydraulic residence time.

Solution

HRT=\dfrac{3100}{8200}=0.378\ \text{d}

HRT=0.378(24)=9.07\ \text{h}

Engineering Comment

HRT is hydraulic exposure time, not biological age. SRT must be checked separately.

Plausibility Check

A basin volume a little over one third of daily flow gives a little over one third of a day.

Exercise 4: Food-to-Microorganism Ratio

Aeration volume is $3100\ \text{m}^3$ , MLVSS is $2400\ \text{mg/L}$ and BOD load is $1517\ \text{kg/d}$ . Compute F/M ratio.

Solution

Biomass mass:

M=3100(2400)\ \text{g}=7440000\ \text{g}=7440\ \text{kg}

F/M:

\dfrac{F}{M}=\dfrac{1517}{7440}=0.204\ \text{d}^{-1}

Engineering Comment

F/M helps interpret loading state, but it should be used with SRT, oxygen and settling evidence.

Plausibility Check

A tonne-scale daily load over several tonnes of biomass should give a fraction per day.

Exercise 5: Solids Retention Time

Total solids inventory in aeration and clarifiers is $9200\ \text{kg}$ . WAS solids removed are $720\ \text{kg/d}$ and effluent solids loss is $80\ \text{kg/d}$ . Compute SRT.

Solution

SRT=\dfrac{9200}{720+80}=11.5\ \text{d}

Engineering Comment

Effluent solids loss is part of the SRT denominator. Ignoring it overstates sludge age during washout.

Plausibility Check

Losing about $800\ \text{kg/d}$ from a $9200\ \text{kg}$ inventory gives a little over eleven days.

Exercise 6: WAS Rate for Target SRT

Target SRT is $10\ \text{d}$ . Solids inventory is $9200\ \text{kg}$ and effluent solids loss is $80\ \text{kg/d}$ . Compute required WAS solids removal.

Solution

Total required solids removal:

M_{out}=\dfrac{9200}{10}=920\ \text{kg/d}

WAS solids:

M_{WAS}=920-80=840\ \text{kg/d}

Engineering Comment

The wasting target should be converted to a WAS flow using measured WAS concentration.

Plausibility Check

Shortening SRT from $11.5$ to $10$ days requires removing more solids each day.

Exercise 7: WAS Flow From Solids Concentration

Required WAS solids removal is $840\ \text{kg/d}$ . WAS concentration is $7800\ \text{mg/L}$ . Compute WAS flow.

Solution

Convert concentration:

7800\ \text{mg/L}=7.8\ \text{kg/m}^3

Flow:

Q_{WAS}=\dfrac{840}{7.8}=107.7\ \text{m}^3/\text{d}

Engineering Comment

WAS concentration drift changes the real wasting mass even if the pump flow setpoint is unchanged.

Plausibility Check

At about $8\ \text{kg/m}^3$ , moving roughly $100\ \text{m}^3/\text{d}$ removes roughly $800\ \text{kg/d}$ .

Exercise 8: Carbonaceous Oxygen Demand

Assume $1.1\ \text{kg O}_2$ is required per kg of BOD removed. BOD load is $1517\ \text{kg/d}$ and removal is $92\%$ . Compute oxygen demand.

Solution

Removed BOD:

L_r=1517(0.92)=1396\ \text{kg/d}

Oxygen demand:

O_2=1.1(1396)=1536\ \text{kg O}_2/\text{d}

Engineering Comment

This covers carbonaceous demand only. Nitrification, endogenous respiration and process factors can add demand.

Plausibility Check

Oxygen demand near the removed BOD load is expected for carbon oxidation.

Exercise 9: Aeration Transfer Margin

Required oxygen is $1536\ \text{kg/d}$ . Field oxygen transfer capacity is $1880\ \text{kg/d}$ . Compute aeration margin.

Solution

\text{margin}=\dfrac{1880-1536}{1536}=0.224=22.4\%

Engineering Comment

A $22.4\%$ margin can disappear with diffuser fouling, warm water, altitude correction or higher ammonia load.

Plausibility Check

The spare capacity is about $340\ \text{kg/d}$ over a $1500\ \text{kg/d}$ requirement, so about one fifth is plausible.

Exercise 10: Dissolved-Oxygen Evidence Gate

Four basin zones have calibrated DO readings of $1.8$ , $2.1$ , $2.4$ and $0.9\ \text{mg/L}$ . The operating floor is $1.5\ \text{mg/L}$ . Decide whether the DO profile passes.

Solution

The minimum reading is:

DO_{min}=0.9\ \text{mg/L}

Since:

0.9<1.5

the profile fails.

Engineering Comment

Average DO would hide the oxygen-deficient zone. Release should use the limiting profile.

Plausibility Check

One zone is visibly below the operating floor, so the gate cannot pass.

Exercise 11: Alkalinity Demand Screen

Nitrification removes $210\ \text{kg/d}$ as nitrogen. Use $7.14\ \text{kg alkalinity as CaCO3}$ per kg N. Compute alkalinity consumed.

Solution

A=210(7.14)=1499\ \text{kg/d as CaCO3}

Engineering Comment

Alkalinity demand links biological treatment to pH stability. Low alkalinity can reduce nitrification even when oxygen is adequate.

Plausibility Check

The factor is about seven, so $210\ \text{kg/d}$ N creates about $1500\ \text{kg/d}$ alkalinity demand.

Exercise 12: Cold-Weather SRT Guard

Cold-weather operating guidance requires SRT above $14\ \text{d}$ . Current SRT is $11.5\ \text{d}$ . Compute shortfall.

Solution

\Delta SRT=14-11.5=2.5\ \text{d}

Engineering Comment

The response may be reduced wasting, more solids inventory or load reduction, but clarifier capacity must be checked before increasing MLSS.

Plausibility Check

The plant is a few days below the cold-weather target.

Exercise 13: Blower Power Screen

Total blower power is $185\ \text{kW}$ while delivering $1880\ \text{kg O}_2/\text{d}$ . Compute specific energy in $\text{kWh/kg O}_2$ .

Solution

Daily energy:

E=185(24)=4440\ \text{kWh/d}

Specific energy:

e=\dfrac{4440}{1880}=2.36\ \text{kWh/kg O}_2

Engineering Comment

Specific energy is not a release gate alone, but rising values can reveal diffuser fouling or control instability.

Plausibility Check

Thousands of kWh per day over thousands of kilograms oxygen per day gives a few kWh per kilogram.

Exercise 14: Sludge Yield Estimate

BOD removed is $1396\ \text{kg/d}$ and observed sludge yield is $0.55\ \text{kg TSS/kg BOD removed}$ . Estimate waste sludge production.

Solution

M_s=0.55(1396)=768\ \text{kg TSS/d}

Engineering Comment

The yield estimate should be compared with actual WAS and effluent solids. A mismatch indicates inventory change or measurement error.

Plausibility Check

Yield near one half of removed BOD gives several hundred kilograms per day.

Exercise 15: Effluent BOD Mass Limit

Permit limit is $25\ \text{mg/L}$ BOD as a daily concentration at $8200\ \text{m}^3/\text{d}$ . Compute equivalent daily mass limit.

Solution

L_{lim}=8200(25)=205000\ \text{g/d}=205\ \text{kg/d}

Engineering Comment

Mass and concentration limits should both be checked when flows vary.

Plausibility Check

The limit concentration is much lower than influent concentration, so the allowed load is much lower than influent load.

Exercise 16: Monitoring Completion Score

The biological release package requires BOD composite, COD check, MLSS, MLVSS, WAS concentration, DO profile, blower status, temperature, pH and effluent BOD. Eight of ten records are complete. Compute completion.

Solution

C=\dfrac{8}{10}=80\%

Engineering Comment

Completion is not enough if missing records are DO profile or effluent BOD, because those are direct release barriers.

Plausibility Check

Eight out of ten records is exactly $80\%$ .

Exercise 17: Process Stability Score

Assign one point each for SRT above target, aeration margin above $15\%$ , DO profile passing, pH in range and evidence completion above $90\%$ . Current status: SRT fails, aeration margin passes, DO fails, pH passes and evidence completion fails. Compute score.

Solution

Passing items are aeration margin and pH:

S=2\ \text{of}\ 5=40\%

Engineering Comment

The score shows why a single good aeration margin cannot release the biological process.

Plausibility Check

Two passing checks out of five is less than half.

Exercise 18: Biological Treatment Release Gate

A release gate requires SRT at least $14\ \text{d}$ , aeration margin above $15\%$ , DO profile passing, effluent BOD load below $205\ \text{kg/d}$ and monitoring completion above $90\%$ . Current values are SRT $11.5\ \text{d}$ , aeration margin $22.4\%$ , DO profile fail, effluent BOD load $180\ \text{kg/d}$ and completion $80\%$ . Decide release status.

Solution

Aeration margin passes and effluent load passes. SRT, DO profile and evidence completion fail:

11.5<14

80\%<90\%

Release status:

\text{hold}

Engineering Comment

The plant should hold biological release until sludge age, oxygen profile and evidence records are corrected.

Plausibility Check

An all-of biological gate fails when three required controls fail.

Validation Package Checklist

Flow, BOD, COD, biomass, wasting and effluent loads use the same operating window.
SRT includes solids inventory, WAS solids and effluent solids losses.
Aeration evidence includes required oxygen, delivered oxygen, DO profile, blower state and sensor calibration.
Release decisions separate biological treatment from clarifier and disinfection barriers.

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