Exercise set

Waste-to-Energy Combustion, Efficiency, and Residuals Exercises

Solved waste-to-energy exercises for LHV, boiler input, net efficiency, auxiliary load, CHP, emissions, ash, residue volume and release gates.

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

These exercises focus on waste-to-energy combustion and residual controls. They cover heating value, boiler input, net electrical efficiency, auxiliary load, combined heat and power, availability, excess air, flue gas, reagent demand, particulate load, NOx, continuous monitoring, bottom ash, stabilization and residue disposal.

Assume simplified screening calculations unless an exercise states otherwise. Field release requires waste characterization, bunker controls, combustion records, boiler performance, turbine output, auxiliary load, air-pollution-control data, continuous emissions monitoring, ash testing and residue destination records.

Release Evidence Notes

Waste-to-energy evidence should distinguish gross energy input, gross electricity, net export and useful heat. A plant can produce power while still failing release if auxiliary load, downtime, emissions, ash quality or residue disposal is outside the allowed envelope.

Combustion evidence should state heating value basis, moisture, throughput, excess air, furnace temperature, residence time, burnout and upset periods. Averaged performance should not hide startup, shutdown or bypass events.

Residual evidence should include bottom ash, fly ash, reagent residues, metals stabilization, leachability testing and final disposal or beneficial-use destination.

Engineering Boundary Notes

These calculations do not replace permitted stack testing, combustion-control validation, ash hazardous-waste classification, grid interconnection studies or public-health risk assessment. They are screening calculations for release readiness and operating evidence.

Common Release Mistakes

reporting gross generator output instead of net export after auxiliary load;
using design heating value when current waste moisture has changed;
treating air-emissions compliance as separate from the waste-to-energy release gate;
ignoring ash mass and leachability when claiming diversion from landfill;
averaging away startup, bypass, CEMS invalid hours or reagent-feed interruptions.

Scenario Map

Scenario	Exercises	Primary check	Engineering decision
Energy conversion	1, 2, 3, 4, 5, 6	LHV, boiler input, net efficiency, auxiliary load, CHP and availability	Decide whether energy performance is credible.
Combustion and emissions	7, 8, 9, 10, 11, 12	excess air, flue gas, reagent, particulate, NOx and CEMS validity	Decide whether combustion controls support operation.
Residuals	13, 14, 15, 16, 17	ash mass, stabilization, landfill volume, bunker residence and evidence	Decide whether residual handling is controlled.
Release gate	18	all-of WTE release	Decide whether the package can close.

Exercise 1: Waste Heating Value Blend

A waste feed is $70\%$ municipal solid waste at $9.5\ \text{MJ/kg}$ and $30\%$ commercial waste at $13.0\ \text{MJ/kg}$ . Estimate blended lower heating value.

Solution

LHV_b=0.70(9.5)+0.30(13.0)=10.55\ \text{MJ/kg}

Engineering Comment

The heating value basis should be tied to current waste characterization, not only historical design data.

Plausibility Check

The result lies between $9.5$ and $13.0\ \text{MJ/kg}$ , closer to municipal waste because it is the larger fraction.

Exercise 2: Boiler Thermal Input

A WTE unit burns $18\ \text{t/h}$ of waste with $LHV=10.55\ \text{MJ/kg}$ . Compute thermal input in MW.

Solution

Mass flow:

\dot{m}=18{,}000\ \text{kg/h}=5.0\ \text{kg/s}

Thermal input:

\dot{Q}=5.0(10.55)=52.75\ \text{MW}_{th}

Engineering Comment

This is fuel energy input. Boiler efficiency and auxiliary losses must be applied before claiming useful output.

Plausibility Check

Five kilograms per second at about $10\ \text{MJ/kg}$ gives about $50\ \text{MW}$ .

Exercise 3: Net Electrical Efficiency

Thermal input is $52.75\ \text{MW}_{th}$ . Gross generator output is $14.2\ \text{MW}$ and auxiliary load is $2.1\ \text{MW}$ . Compute net electrical efficiency.

Solution

Net export:

P_n=14.2-2.1=12.1\ \text{MW}

Net efficiency:

\eta_n=\dfrac{12.1}{52.75}=0.229=22.9\%

Engineering Comment

Net efficiency is the release-relevant electricity metric because fans, pumps, conveyors, reagent systems and controls consume real output.

Plausibility Check

WTE net electrical efficiency commonly sits well below a modern gas turbine, so a value near one quarter is plausible.

Exercise 4: Auxiliary Load Sensitivity

If auxiliary load rises from $2.1$ to $3.0\ \text{MW}$ while gross output stays $14.2\ \text{MW}$ , compute the reduction in net export.

Solution

Old net export:

P_{n1}=14.2-2.1=12.1\ \text{MW}

New net export:

P_{n2}=14.2-3.0=11.2\ \text{MW}

Reduction:

\Delta P=12.1-11.2=0.9\ \text{MW}

Engineering Comment

Higher air-pollution-control pressure drop or cooling load can materially reduce net export even if combustion rate is unchanged.

Plausibility Check

The auxiliary load increased by $0.9\ \text{MW}$ , so net export falls by the same amount.

Exercise 5: Combined Heat and Power Efficiency

Net electrical export is $12.1\ \text{MW}$ and useful district heat is $18.0\ \text{MW}_{th}$ . Thermal input is $52.75\ \text{MW}_{th}$ . Compute useful CHP efficiency.

Solution

\eta_{CHP}=\dfrac{12.1+18.0}{52.75}=0.571=57.1\%

Engineering Comment

Useful heat must be actually delivered to a load. Dumped condenser heat should not be counted as CHP benefit.

Plausibility Check

Adding a large heat load roughly doubles useful output compared with electricity alone, so the efficiency rises materially.

Exercise 6: Availability-Adjusted Energy Export

Net export is $12.1\ \text{MW}$ when operating. Annual availability is $82\%$ . Estimate annual net export.

Solution

E=12.1(8760)(0.82)=86940\ \text{MWh/yr}

Engineering Comment

Availability must include forced outage, planned maintenance, grid curtailment and permit-driven shutdowns if they limit export.

Plausibility Check

A $12\ \text{MW}$ plant running all year would export about $105000\ \text{MWh}$ ; $82\%$ availability brings it below $90000\ \text{MWh}$ .

Exercise 7: Excess Air Ratio

Stoichiometric combustion air is $6.2\ \text{kg air/kg waste}$ . Actual air feed is $9.0\ \text{kg air/kg waste}$ . Compute excess air.

Solution

EA=\dfrac{9.0-6.2}{6.2}=0.452=45.2\%

Engineering Comment

Excess air supports burnout but increases flue-gas flow and can reduce boiler efficiency if too high.

Plausibility Check

Actual air is about one and a half times stoichiometric air, so excess air near $45\%$ is credible.

Exercise 8: Flue Gas Flow Screen

Waste feed is $18\ \text{t/h}$ and actual air feed is $9.0\ \text{kg air/kg waste}$ . Estimate air mass flow to the furnace.

Solution

\dot{m}_{air}=18{,}000(9.0)=162000\ \text{kg/h}

\dot{m}_{air}=45.0\ \text{kg/s}

Engineering Comment

Flue-gas flow drives induced-draft fan load, residence time and air-pollution-control sizing.

Plausibility Check

Combustion air is several times larger than waste mass flow, so tens of kilograms per second is reasonable.

Exercise 9: Acid Gas Reagent Demand

An acid-gas control system injects $1.8\ \text{kg}$ reagent per tonne of waste. Waste throughput is $420\ \text{t/d}$ . Compute reagent use.

Solution

m_r=1.8(420)=756\ \text{kg/d}

Engineering Comment

Reagent feed evidence should be paired with inlet acid-gas load, outlet concentration and residue generation.

Plausibility Check

About two kilograms per tonne over a few hundred tonnes per day gives several hundred kilograms per day.

Exercise 10: Particulate Load to Baghouse

Flue gas flow is $160000\ \text{m}^3/\text{h}$ and particulate concentration entering the baghouse is $1.25\ \text{g/m}^3$ . Compute particulate mass loading.

Solution

\dot{m}=160000(1.25)=200000\ \text{g/h}

\dot{m}=200\ \text{kg/h}

Engineering Comment

The baghouse and ash-handling system must handle this load without blinding, hopper plugging or bypass.

Plausibility Check

One gram per cubic meter over a very large flow creates hundreds of kilograms per hour.

Exercise 11: NOx Compliance Margin

Measured NOx is $145\ \text{mg/Nm}^3$ . Permit limit is $180\ \text{mg/Nm}^3$ . Compute compliance margin.

Solution

\text{margin}=\dfrac{180-145}{180}=0.194=19.4\%

Engineering Comment

The margin should be reviewed across load, waste composition, ammonia or urea feed and averaging period.

Plausibility Check

The plant is $35\ \text{mg/Nm}^3$ below a $180\ \text{mg/Nm}^3$ limit, roughly one fifth of the limit.

Exercise 12: CEMS Valid-Hours Check

A reporting month has $720$ hours. The continuous emissions monitoring system has $681$ valid hours. The valid-data target is $95\%$ . Determine whether the target is met.

Solution

f=\dfrac{681}{720}=0.946=94.6\%

The target is not met because:

94.6\%<95\%

Engineering Comment

Energy performance cannot close the release package if emissions data completeness fails.

Plausibility Check

The plant is short by a few hours: $0.95(720)=684$ required hours.

Exercise 13: Bottom Ash Mass

Waste throughput is $420\ \text{t/d}$ . Bottom ash is $22\%$ of waste mass. Compute bottom ash production.

Solution

m_{ash}=0.22(420)=92.4\ \text{t/d}

Engineering Comment

Bottom ash remains a major residual stream even when waste volume is reduced.

Plausibility Check

About one fifth of $420\ \text{t/d}$ is a little over $80\ \text{t/d}$ , so $92.4\ \text{t/d}$ is plausible.

Exercise 14: Ash Stabilization Margin

A treated fly ash sample has leachate lead of $3.2\ \text{mg/L}$ . The release criterion is $5.0\ \text{mg/L}$ . Compute margin.

Solution

\text{margin}=\dfrac{5.0-3.2}{5.0}=0.36=36\%

Engineering Comment

The margin is useful only if sampling is representative of current reagent dose, waste composition and operating condition.

Plausibility Check

The result is comfortably below the criterion, leaving a little more than one third of the limit as margin.

Exercise 15: Residue Landfill Volume

Combined ash and residues are $110\ \text{t/d}$ . Compacted residue density is $1.15\ \text{t/m}^3$ . Compute daily landfill volume required.

Solution

V=\dfrac{110}{1.15}=95.7\ \text{m}^3/\text{d}

Engineering Comment

WTE reduces raw waste volume, but it does not eliminate disposal planning for ash and air-pollution-control residues.

Plausibility Check

At density a little above one tonne per cubic meter, tonnes per day and cubic meters per day are similar.

Exercise 16: Waste Bunker Residence Time

The waste bunker contains $2100\ \text{t}$ of usable inventory. Furnace throughput is $420\ \text{t/d}$ . Compute residence time.

Solution

t=\dfrac{2100}{420}=5.0\ \text{d}

Engineering Comment

Bunker residence time affects odor, fire risk, crane mixing and ability to ride through collection interruptions.

Plausibility Check

At $420\ \text{t/d}$ , five days consumes $2100\ \text{t}$ .

Exercise 17: WTE Evidence Completion

A WTE release checklist has $12$ required records: waste LHV, throughput, furnace temperature, excess air, gross output, auxiliary load, reagent feed, CEMS validity, NOx margin, particulate control, ash test and residue destination. Ten are complete. Compute completion.

Solution

C=\dfrac{10}{12}=0.833=83.3\%

Engineering Comment

The package is incomplete if missing records are emissions, ash or residue controls, even when energy output is documented.

Plausibility Check

Ten of twelve is five sixths, or about $83\%$ .

Exercise 18: WTE Release Gate

A release gate requires net electrical efficiency above $20\%$ , NOx margin above $10\%$ , CEMS valid hours at least $95\%$ , ash stabilization margin above $20\%$ and evidence completion above $90\%$ . Current values are $22.9\%$ , $19.4\%$ , $94.6\%$ , $36\%$ and $83.3\%$ . Decide release status.

Solution

Net efficiency passes, NOx margin passes and ash margin passes. CEMS validity and evidence completion fail:

94.6\%<95\%

83.3\%<90\%

Release status:

\text{hold}

Engineering Comment

The plant may be operating well energetically, but the release package cannot close without emissions-data completeness and full residual evidence.

Plausibility Check

An all-of release gate fails when any mandatory monitoring or evidence threshold fails.

Validation Package Checklist

Heating value, throughput, boiler input, gross output, auxiliary load and net export use the same operating window.
Combustion evidence includes excess air, furnace conditions, CEMS validity, reagent feed and air-pollution-control status.
Ash and residue records include mass, stabilization, leachability, storage and final destination.
Release decisions preserve startup, shutdown, bypass, invalid data and residue exceptions instead of averaging them away.

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