Environment · Simulator 090
Recycling is a chain: people must put material in the right bin, a sorting plant must separate it, and a reprocessor must turn it into new material. Change each step and follow 100 tonnes through the system. See where material is lost, why contamination can make whole loads worthless, and how many times material is used before it is gone.
Each link in the chain passes on only part of what it receives, so the overall recycling yield is a product:
recycled = collected × sorted correctly × reprocessing yield = c × s × y
Non-recyclable items in the recycling bin (contamination, often "wishcycling") do not add any material, but the sorting plant must remove them. With sorting accuracy s, recyclables go to bales with probability s and contaminants are removed with probability s, so bale purity is
purity = s R / (s R + (1 − s) X)
for R tonnes of recyclables and X tonnes of contaminants collected. Reprocessors set a minimum purity; bales below it are rejected and the whole load is lost.
If the same yield r = c s y applies every time a product is used and recycled, the share of the original material still in use after n cycles is rⁿ, and on average each tonne is used 1 / (1 − r) times in total. Raising r from 0.5 to 0.8 raises the average from 2 uses to 5.
Illustrative steady flows: one material at a time, fixed yields, no quality loss (downcycling) between cycles, no stockpiles or export, and a sharp purity threshold. Real yields vary by plant and market.
A city collects 70% of its aluminium cans, sorts them with 95% accuracy, and the smelter recovers 95% of the metal. What is the recycling yield per cycle, and how many times on average is each tonne of aluminium used?
r = 0.70 × 0.95 × 0.95 ≈ 0.632, so about 63% comes back each cycle. Average number of uses = 1 / (1 − 0.632) ≈ 2.7. Raising collection to 90% gives r ≈ 0.81 and about 5.3 uses: collection is usually the cheapest lever.