Exercise set

Material Recovery, MRF Diversion, and Contamination Exercises

Worked material-recovery exercises for waste characterization, verified diversion, bale contamination, MRF bottlenecks, rejects, batteries and release gates.

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

These exercises practise material recovery as an auditable production system. They cover waste characterization, verified diversion, contamination, buyer rejection, collection capacity, MRF bottlenecks, surge storage, equipment availability, marketable recovery, optical-sorter capture, quality-control staffing, hot loads, lithium-battery capture and release gates.

The goal is not to count material that passed across a belt. The goal is to prove where material went, what quality it had, what was rejected and whether downstream acceptance supports the recovery claim.

How to Use These Exercises

For each calculation, define:

the incoming waste boundary and time basis;
the product, reject, contamination and inventory streams;
the quality specification or buyer rule;
the equipment, staffing or safety constraint;
the records required to close the diversion claim.

The common mistake is treating sorted material as recovered material. Recovered material is defensible only when contamination, residuals, rejection, storage and buyer acceptance are included.

Release Evidence Notes

Material-recovery calculations should close a mass balance. Scale tickets, bale weights, reject loads, contamination samples, inventory changes and buyer acceptances should all reconcile.

Sampling evidence should match the product claim. A clean visual sample does not release a full bale or day of production unless sampling method, contaminant definition and buyer specification are controlled.

Facility-capacity evidence should include bottlenecks and surge. A line can fail at the optical sorter, manual QC station, baler, residue conveyor, storage bay or fire-watch process even if feed capacity appears adequate.

Fire-risk evidence should be treated as process evidence. Lithium batteries, aerosols, hot ashes and reactive loads can turn recovery into an unsafe operation if capture, isolation and response procedures are weak.

Scenario Map

Scenario	Exercises	Primary calculation	Engineering decision
Recovery accounting	1-4, 10-11	characterization, diversion, contamination, residual and rejection	Decide whether recovery claims are defensible.
Facility capacity	5-9, 12-14	collection capacity, bottleneck rate, surge storage, availability, sorter capture and staffing	Decide whether the MRF can operate at the claimed throughput.
Safety and release	15-18	RPN, battery capture, evidence closure and release gate	Decide whether material recovery can continue normally.

Exercise 1: Waste Characterization by Mass

A facility receives:

42\ \text{t/day}

of mixed waste. A study estimates organics $38\%$ , paper/cardboard $22\%$ , plastics $14\%$ , metals/glass $11\%$ and residuals $15\%$ . Calculate each daily mass.

Solution

Organics:

m_o=0.38(42)=15.96\ \text{t/day}

Paper/cardboard:

m_p=0.22(42)=9.24\ \text{t/day}

Plastics:

m_{pl}=0.14(42)=5.88\ \text{t/day}

Metals/glass:

m_m=0.11(42)=4.62\ \text{t/day}

Residuals:

m_r=0.15(42)=6.30\ \text{t/day}

Engineering Comment

Composition estimates should state sampling season, source mix, moisture basis and sorting method. A single audit can be a weak basis for facility design.

Plausibility Check

The percentages sum to $100\%$ , and the masses sum to $42\ \text{t/day}$ .

Exercise 2: Verified Diversion with Rejects

A MRF receives:

120\ \text{t/day}

It ships:

72\ \text{t/day}

to buyers. Buyers reject:

9\ \text{t/day}

Calculate verified diversion.

Solution

Accepted recovered mass:

m_a=72-9=63\ \text{t/day}

Verified diversion:

\displaystyle D_v=\frac{63}{120}=0.525

Therefore:

D_v=52.5\%

Engineering Comment

Shipped recovery would be $60\%$ , but verified diversion is lower because buyer rejection is real residual material.

Plausibility Check

Rejected material reduces accepted recovery by $9$ tonnes, so verified diversion must be below shipped diversion.

Exercise 3: Bale Contamination Rate

A recovered plastic bale has mass:

m_b=820\ \text{kg}

Contaminant mass is:

m_c=54\ \text{kg}

Buyer limit is:

5.0\%

Check the bale.

Solution

Contamination rate:

\displaystyle C=\frac{54}{820}(100)=6.59\%

Since:

6.59\%>5.0\%

the bale fails.

Engineering Comment

The corrective action may be rework, downgrade, buyer notification or process adjustment. A contamination fail should feed back into sorting settings and upstream education.

Plausibility Check

Fifty-four kilograms is more than one twentieth of $820\ \text{kg}$ , so contamination above $5\%$ is plausible.

Exercise 4: Residual Rate

A facility receives:

120\ \text{t/day}

Accepted recovery is:

63\ \text{t/day}

Residue tickets show:

51\ \text{t/day}

Calculate residual rate and unreconciled mass.

Solution

Residual rate:

\displaystyle R=\frac{51}{120}=42.5\%

Accounted mass:

63+51=114\ \text{t/day}

Unreconciled mass:

120-114=6\ \text{t/day}

Engineering Comment

Unreconciled mass can be inventory change, moisture loss, scale mismatch, sort loss or reporting error. It should be explained before claiming final performance.

Plausibility Check

Accepted recovery and residue account for most but not all incoming mass. A $6\ \text{t/day}$ gap is visible and needs investigation.

Exercise 5: Collection Vehicle Payload Capacity

A collection truck has legal payload:

9.5\ \text{t}

Average compacted waste density is:

0.32\ \text{t/m}^3

Body volume is:

28\ \text{m}^3

Which limit controls?

Solution

Volume-limited mass:

m_v=(0.32)(28)=8.96\ \text{t}

Since:

8.96<9.5

volume controls before payload.

Engineering Comment

Low-density loads can cube out before they weigh out. Route planning should use both payload and volume, especially for recyclables and bulky material.

Plausibility Check

The computed mass is close to but below legal payload, so volume is the controlling constraint.

Exercise 6: Route Trip Count

A route collects:

34\ \text{t/day}

Each truck trip can carry:

8.96\ \text{t}

Calculate required full-equivalent trips.

Solution

Trips:

\displaystyle N=\frac{34}{8.96}=3.79

Round up:

N=4\ \text{trips}

Engineering Comment

Rounding matters operationally. A fractional trip may require overtime, route split, transfer change or larger vehicle.

Plausibility Check

Four trips at about $9\ \text{t}$ each can move about $36\ \text{t}$ , enough for the route.

Exercise 7: Sorting-Line Bottleneck

A line feed rate is:

18\ \text{t/h}

The optical sorter can process:

15\ \text{t/h}

Manual QC can process:

16\ \text{t/h}

Find bottleneck and excess feed.

Solution

The bottleneck is the minimum capacity:

Q_b=15\ \text{t/h}

Excess feed:

Q_e=18-15=3\ \text{t/h}

Engineering Comment

The line is only as strong as the bottleneck. Excess feed becomes surge storage, bypass, contamination, downtime or residue.

Plausibility Check

The optical sorter has the lowest capacity, so it controls the line.

Exercise 8: Surge Storage Time

Surge storage has usable capacity:

24\ \text{t}

Excess feed during a bottleneck is:

3\ \text{t/h}

Estimate time to fill.

Solution

Time:

\displaystyle t=\frac{24}{3}=8\ \text{h}

Engineering Comment

Eight hours may cover a shift but not a multi-day market disruption or maintenance outage. Fire lanes and stockpile rules also limit usable storage.

Plausibility Check

At $3\ \text{t/h}$ , eight hours accumulates $24\ \text{t}$ exactly.

Exercise 9: Sorting Equipment Availability

A line needs conveyor, screen and baler in series. Availability values are:

0.97,\quad 0.95,\quad 0.96

Calculate series availability.

Solution

Series availability:

A=(0.97)(0.95)(0.96)=0.884

Therefore:

A=88.4\%

Engineering Comment

Series equipment availability can be much lower than individual component availability. MRF planning should include downtime, bypass and catch-up capacity.

Plausibility Check

Multiplying three values below one should produce a lower value. The result is plausible.

Exercise 10: Marketable Recovery and Unreconciled Mass

A MRF receives:

96\ \text{t/day}

Bales shipped:

48\ \text{t/day}

Average bale contamination:

4\%

Residue tickets:

42\ \text{t/day}

Calculate marketable recovery and unreconciled mass.

Solution

Marketable recovery:

m_m=48(1-0.04)=46.08\ \text{t/day}

Marketable recovery rate:

\displaystyle R_m=\frac{46.08}{96}=48.0\%

Accounted mass:

46.08+42=88.08\ \text{t/day}

Unreconciled mass:

96-88.08=7.92\ \text{t/day}

Engineering Comment

Marketable recovery is stricter than shipped recovery because contamination is not accepted product. The unreconciled mass must be explained.

Plausibility Check

Four percent contamination only slightly reduces shipped mass, but the residue plus marketable mass still leaves a clear accounting gap.

Exercise 11: Buyer Rejection Impact

If buyer rejection rises from:

9\ \text{t/day}

to:

15\ \text{t/day}

while shipped mass remains $72\ \text{t/day}$ and inbound remains $120\ \text{t/day}$ , calculate verified diversion.

Solution

Accepted recovery:

m_a=72-15=57\ \text{t/day}

Verified diversion:

\displaystyle D_v=\frac{57}{120}=47.5\%

Engineering Comment

Buyer rejection can turn an apparently stable sorting line into a failed diversion program. Feedback from buyers is part of process control.

Plausibility Check

Higher rejection lowers accepted recovery, so verified diversion falls from $52.5\%$ to $47.5\%$ .

Exercise 12: Optical Sorter Capture Efficiency

Target plastic entering an optical sorter is:

6.4\ \text{t/h}

Recovered target plastic is:

5.5\ \text{t/h}

Calculate capture efficiency.

Solution

Capture efficiency:

\displaystyle \eta_c=\frac{5.5}{6.4}=0.859

Therefore:

\eta_c=85.9\%

Engineering Comment

Capture efficiency should be paired with purity. A sorter can capture a large fraction of target material while also pulling contaminants.

Plausibility Check

Recovered target mass is slightly below inlet target mass, so efficiency below $100\%$ and above $80\%$ is plausible.

Exercise 13: Product Purity from Sorter Output

Sorter product contains:

5.5\ \text{t/h}

target plastic and:

0.6\ \text{t/h}

contaminants. Calculate purity.

Solution

Total product:

m_p=5.5+0.6=6.1\ \text{t/h}

Purity:

\displaystyle P=\frac{5.5}{6.1}=90.2\%

Engineering Comment

Product release should consider both capture and purity. A buyer may reject the product even when capture efficiency looks good.

Plausibility Check

Contaminants are about one tenth of product mass, so purity near $90\%$ is expected.

Exercise 14: Manual QC Staffing Rate

A manual QC station can inspect:

1.8\ \text{t/h}

per worker. The station receives:

7.0\ \text{t/h}

How many workers are required?

Solution

Workers:

\displaystyle N=\frac{7.0}{1.8}=3.89

Round up:

N=4

Engineering Comment

QC staffing should account for fatigue, visibility, belt speed, contaminant type and safety access. Arithmetic capacity is a minimum.

Plausibility Check

Four workers provide $7.2\ \text{t/h}$ of nominal capacity, just above the load.

Exercise 15: Hot-Load Failure Mode RPN

A hot-load fire scenario has severity:

S=9

occurrence:

O=4

and detection:

D=5

Calculate RPN.

Solution

RPN:

RPN=SOD=(9)(4)(5)=180

Engineering Comment

High severity keeps fire risk important even when occurrence is moderate. Controls should focus on detection, isolation, hot-load protocol and lithium-battery removal.

Plausibility Check

The product of three one-digit factors gives a three-digit RPN. The value is credible.

Exercise 16: Lithium Battery Capture Residual Risk

Incoming battery count is estimated as:

N=240\ \text{batteries/day}

Screening captures:

92\%

of batteries. Estimate residual batteries per day.

Solution

Missed fraction:

1-0.92=0.08

Residual count:

N_r=240(0.08)=19.2

Approximately:

19\ \text{batteries/day}

Engineering Comment

Even high capture leaves a meaningful residual count when incoming batteries are common. Fire watch, isolation bins, thermal cameras and upstream education still matter.

Plausibility Check

Eight percent of $240$ is about twenty, so the estimate is reasonable.

Exercise 17: Recovery Evidence Closure

A verified diversion claim requires six records. Five are complete. Calculate completion fraction and decide release if all six are required.

Solution

Completion fraction:

\displaystyle F=\frac{5}{6}=83.3\%

Because all six are required, the claim is not closed.

Engineering Comment

Missing evidence may be buyer acceptance, contamination sampling, inventory change or residue tickets. Any one can change the diversion result.

Plausibility Check

Five of six is above $80\%$ , but the all-required gate still fails.

Exercise 18: MRF Release Gate

A daily MRF review reports:

Evidence item	Result
verified diversion margin	$+4\%$
bale contamination	fail
bottleneck surge storage	$8\ \text{h}$
equipment availability	$88.4\%$
battery residual count	$19/day$
buyer acceptance record	complete

Decide release status.

Solution

The bale contamination fails, and battery residual risk remains material. Therefore:

\text{status}=\text{restricted release or rework}

Normal recovery claims should be held until contamination and battery-control evidence improve.

Engineering Comment

Diversion margin does not override product-quality and safety failures. Recovery must be marketable, traceable and safe.

Plausibility Check

The review has a clear quality failure and a fire-risk concern, so unrestricted release is not defensible.

Engineering Boundary Notes

MRF diversion, product purity, buyer acceptance and residual disposal are separate metrics. A high belt recovery rate can still produce a poor verified diversion result.

Facility capacity must include bottlenecks and downtime. Feed rate alone does not prove throughput if sorting, baling, residue handling or QC staffing cannot keep up.

Fire-risk controls are part of recovery release. Battery capture, hot-load isolation and emergency access affect whether operations can continue safely.

Common Release Mistakes

counting shipped material as accepted recovery;
ignoring buyer rejection;
using one clean sample to release a full day;
hiding residuals in inventory;
reporting capture without purity;
feeding a sorting line above its bottleneck;
ignoring surge storage limits;
treating battery misses as rare after a high capture percentage;
accepting an average availability without common-cause downtime;
closing recovery claims with missing scale or buyer records.

Validation Package Checklist

inbound scale tickets reconciled;
product weights and buyer acceptances recorded;
contamination samples representative;
residue tickets included;
inventory changes explained;
line bottleneck and surge capacity checked;
fire-risk controls verified;
battery capture and residual risk recorded;
QC staffing and sorter settings documented;
final decision states normal release, restricted release, rework, hold or investigation.

REF