Distinguish collection from usable material recovery

Collection is an intermediate step

A hypothetical program starts with 100 kg of dry polymer. It collects 80% of that stream. Of the collected input, 70% becomes usable recovered material after sorting, processing and quality acceptance. Predict the final usable mass before reading the answer. Which number is the denominator for each percentage?

Collection brings 80 kg into the process. Usable recovery is 80 × 0.70 = 56 kg. The other 24 kg of collected material becomes processing residue, while 20 kg was never collected by this route. The three final destinations sum to 56 + 24 + 20 = 100 kg. Residue and uncollected material still exist; their eventual destinations are outside this model.

The EPA explanation of the recycling system distinguishes collection, processing and remanufacturing. Our numbers are assigned teaching values, not statistics for a particular town, resin or year. The processing-yield control combines several stages into one usable-output fraction; an actual investigation would need a clearer breakdown.

Define the boundary and the denominator

Write M₀ for the original mass, c for the fraction collected and y for the usable fraction of collected input. Here M₀ = 100 kg, c = 0.80 and y = 0.70. The three final streams are:

• Usable recovered mass: M₀cy.
• Collected processing residue: M₀c(1 − y).
• Uncollected mass: M₀(1 − c).

Each term has units of mass because the fractions are dimensionless. Their sum is M₀. The collected mass M₀c is an intermediate total, already divided between usable output and residue. Adding it again to the three destinations would double-count the collected material.

The overall recovery fraction is usable divided by original input, or cy = 0.56. The processing yield is usable divided by collected input, or 0.70. The collection fraction is 0.80. All three statements can be true at the same time. A report that gives only “70% recycled” leaves the measurement boundary unclear.

The diagram uses a fixed 100 kg scale. Each segment is a different destination, and text gives the same quantities without relying on color. A zero-width segment means zero assigned mass; it does not hide a separate unreported stream.

Compare improvements fairly

Capture the 80% collection, 70% yield baseline. Increase collection to 90%, holding yield at 70%. Usable output becomes 63 kg, a gain of 7 kg. Residue becomes 27 kg and uncollected mass becomes 10 kg. Better collection has increased usable output, but it also sends more material into the process that becomes residue.

Reset to the baseline, then increase yield to 80% while holding collection at 80%. Usable output becomes 64 kg, a gain of 8 kg. Residue falls to 16 kg; uncollected mass stays at 20 kg. The same ten-percentage-point change at different stages does not necessarily produce the same mass gain.

This comparison does not establish which intervention costs less, saves more energy or is easier to implement. No such inputs were supplied. It identifies a material consequence under fixed assumptions. A decision brief should pair that result with evidence about feasibility and other effects rather than inventing a universal recommendation.

Treat empty inputs honestly

Set collection to 0% while leaving assigned yield at 70%. No material enters the process, so usable output and residue are both zero. The ratio usable/collected is 0/0, which is undefined. The assigned yield remains a scenario parameter, but it has not been inferred from this empty flow.

Now collect all 100 kg and set yield to 0%. Usable output is still zero, but the process has a nonempty input: its inferred yield is genuinely 0%. These cases have equal usable output and different evidence. A zero result is not the same as an undefined ratio.

At 100% collection and 100% yield, the ledger sends all original mass to usable output. That is an ideal endpoint of the model, not a claim that physical recovery is loss-free or energy-free. The mass boundary omits added water, chemicals, additives and other inputs; a real process study must include them where relevant.

Separate recovered material from actual replacement

The ledger also considers a separate next batch of 100 kg. It assumes every kilogram of usable recovered polymer can replace one kilogram of virgin polymer, with no additional manufacturing losses. Under the baseline, that next batch uses 56 kg recovered + 44 kg virgin input. The 44 kg is new material in a second scenario, not another destination of the original 100 kg.

Suitability and actual use matter. A recovered material may differ in molecular-mass distribution, contamination, additives, appearance or performance. Some applications may need a blend or may reject the material. A claim about one-for-one replacement therefore needs product-quality and use evidence. Merely collecting material does not prove that it was remanufactured or displaced virgin production.

The EPA recycling terminology distinguishes recyclable products from products containing recycled material. A label about possible end-of-use handling and a measurement of recycled content describe different things. Local acceptance, technical processing and actual material use must be checked separately.

Evaluate a resource choice with more than one number

A complete comparison could include the service provided, product life, reuse, collection distance, processing inputs, residual disposal and the quality of the next product. Compare the same useful service and consistent boundaries. A lighter product is not necessarily preferable if it must be replaced much more often; a high recovery percentage is not by itself an emissions calculation.

Mechanical reprocessing, chemical conversion and energy recovery also produce different outputs. Burning material to recover energy does not return the original polymer mass as usable polymer. Fragmenting a material into smaller pieces does not necessarily produce reusable monomers or harmless biological products. The current widget treats usable output as a specified material stream and does not simulate these mechanisms.

Transfer: A 200 kg stream is 60% collected, with 75% of the collected material accepted as usable. Calculate all three final streams, overall recovery and the virgin input needed for a separate 200 kg next batch under one-for-one replacement. Identify one assumption you would test before making an environmental claim.

Check the material-recovery transfer

Collected input is 120 kg. Usable output is 90 kg; collected residue is 30 kg; uncollected material is 80 kg. The three destinations total 200 kg. Overall recovery is 90/200 = 45%; the separate next batch needs 110 kg virgin input under the stated substitution assumption. Product suitability, actual replacement, energy inputs, transport, lifetime and residual handling are possible evidence needs; none is established by the mass ledger alone.