Chemistry · Lesson

Material lifecycles, recycling and design trade-offs

Compare equal functional service, sequential recovery yields and circulation models while making inventory boundaries and environmental trade-offs explicit.

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By the end, you can

Count complete replacement units for the specified service.
Multiply sequential usable-recovery yields on the correct inventories.
Conserve initial input, replacement input, stock and losses across repeated loops.
Identify a model ranking that changes with an uncertain input.

A lifecycle comparison starts with the service delivered

Compare materials through a defined function and required service, rather than by equal masses automatically. Lifetime, maintenance, replacement and losses can change how much material is needed to deliver that function. State the time and performance requirement.

A system boundary determines which extraction, manufacture, transport, use and end-of-life contributions are included. Leaving out a stage changes the claim a total can support. Several environmental indicators may reveal different trade-offs.

Equal service and usable recovery need their own denominators

Assign one functional unit: 120 hours of the same specified service at fixed performance. Count complete newly purchased units, including unused residual life without a credit. System A uses 1.20 kg units lasting 40.0 hours, each with assigned production climate indicator 8.00 kg CO₂e and use power 10.0 W. System B uses 1.80 kg units lasting 60.0 hours, with assigned production indicator 11.0 kg CO₂e per unit and use power 14.0 W. These are invented inputs.

A needs three units and B two, so each purchased-material inventory is 3.60 kg. Electricity over 120 hours is 1.20 kWh for A and 1.68 kWh for B. With assigned electricity intensity 0.400 kg CO₂e kWh⁻¹, production-plus-use model totals are 24.48 and 22.672 kg CO₂e. Transport, maintenance and end-of-life are excluded from this particular boundary.

Changing only B life to 40.0 hours requires three B units and 5.40 kg purchased material. Its use electricity remains 1.68 kWh, but its model climate total becomes 33.672 kg CO₂e; A remains 24.48. The original lower B result therefore depends on the lifetime assumption, rather than proving an unconditional material preference.

For a separate unchanged-material recovery ledger, start with 100 kg and collection fraction 0.800. A sorting yield 0.900 applies to the 80.0 kg collected; usable-recovery yield 0.750 applies to the 72.0 kg sorted. The stipulated specification-satisfying recovered amount is 54.0 kg, with losses 20.0 kg not collected, 8.00 kg sorting rejects and 18.0 kg recovery losses. Total loss 46.0 kg plus recovered 54.0 kg equals the input.

Improving only collection to 0.950 gives 95.0 kg collected, 85.5 kg sorted and 64.125 kg usable material. Overall usable yield is 0.64125, with 35.875 kg total loss. Sequential fractions multiply because each uses a different remaining inventory; adding them would not conserve this material.

Collection, separation and usable recovery are distinct stages

A collected fraction can be multiplied by later yields to estimate usable recovered material when the fractions refer to sequential inventories. Material lost at one stage is unavailable to the next. A label such as recyclable does not establish collection or actual recovery.

Recovered material also needs to meet its intended specification. Chemical changes, contamination, additives and mixed compositions can limit an application even when mass is recovered. Count virgin inputs, recovered inputs and losses on a consistent basis.

A circulation boundary and an uncertain factor can change the conclusion

Use two separately defined circulation models starting with 100 kg and retaining fraction f=0.700 per complete cycle. With no replacement, three cycles leave 100f³=34.3 kg and cumulative loss 65.7 kg. This decreasing-stock model does not maintain the same inventory for every cycle.

In the second model, maintain 100 kg after every cycle, including the final one. Each cycle loses 30.0 kg and receives 30.0 kg external replacement. After three cycles, replacement totals 90.0 kg; external input including the initial stock is 190 kg. Final stock 100 kg plus loss 90.0 kg balances that input. Repeated throughput is not newly created mass, and the final replacement is counted as stock rather than another delivered service.

For another independent invented comparison per the same defined service, let route A’s production-plus-use climate indicator be C_A=18+24I and B’s be C_B=26+12I, in kg CO₂e. Here I is the assigned electricity intensity in kg CO₂e kWh⁻¹; the coefficients 24 and 12 are use electricity in kWh. Assign separate water-use indicators 90.0 L for A and 140 L for B.

At I=0.200, climate indicators A/B are 22.8 / 28.4 kg CO₂e; at I=0.800 they are 37.2 / 35.6. Their difference C_B−C_A=8−12I crosses zero at I=2/3 kg CO₂e kWh⁻¹. The graph shows this ranking change without combining the separate water indicator. B’s lower climate result at the higher factor does not also minimize the given water use.

These totals describe the explicitly invented boundary and factors. No weighting, allocation, substitution credit or broader environmental superiority is inferred. A comparison needs its service definition and sensitivity rather than a single favourable label.

An uncertain electricity factor changes the sign of the climate-indicator difference

(C_B − C_A) / kg CO₂e

Electricity intensity I / kg CO₂e kWh⁻¹

Assigned difference comparisons
— Difference 8−12I

Underlying data

Electricity intensity I / kg CO₂e kWh⁻¹	(C_B − C_A) / kg CO₂e
0.2	5.6 · Assigned difference comparisons
0.6666666666666666	0 · Assigned difference comparisons
0.8	-1.6000000000000014 · Assigned difference comparisons
1	-4 · Assigned difference comparisons

Original independent same-service sensitivity model C_A=18+24I and C_B=26+12I in kg CO₂e, with I in kg CO₂e kWh⁻¹. Circles show I=0.200 / 0.800, the equality point 2/3, and changed-input 1.00; the dashed line is C_B−C_A=8−12I. Negative difference means B has the lower assigned climate indicator in this boundary. The separate water indicators 90 / 140 L are not combined or shown as offsets. All inputs are invented.

A repeated loop still needs a mass balance

A circulation model can track a retained fraction through repeated cycles. Unless retention is complete, losses accumulate and may require replacement to maintain the same service. Counting the same circulating material repeatedly is different from creating that amount of new material.

Mechanical reprocessing, chemical conversion and other recovery routes have different reactions, energy needs and outputs. A simplified loop cannot establish that one route is environmentally preferable without a comparable full account.

A design choice needs comparable evidence and uncertainty

A lower result for one indicator can coexist with a higher result for another. Lifetime assumptions, energy supply, location and allocation choices can affect the comparison. Report a range or sensitivity analysis where those inputs remain uncertain.

The original lifecycle ledgers below show how boundaries and sequential yields alter a comparison. They are invented material inventories, rather than environmental certifications or recommendations to buy a particular product.

Worked examples

Count complete units for equal service

Use 120 hours, A 40 hour / 1.20 kg units and B 60 hour / 1.80 kg units under the assigned production/use inputs.

A needs three units; B needs two. Both purchased-material totals are 3.60 kg.
Use electricity is 1.20 / 1.68 kWh.
At intensity 0.400 kg CO₂e kWh⁻¹, model totals are 24.48 / 22.672 kg CO₂e.

Equal service, unit lifetime and the stated boundary determine the comparison.

Apply each yield to the remaining stream

Use 100 kg, collection 0.800, sorting 0.900 and usable recovery 0.750.

Collected 80.0 kg becomes sorted 72.0 kg.
Usable material is 54.0 kg, an overall 0.540 yield.
Losses 20.0+8.00+18.0=46.0 kg balance the input.

Three stage percentages cannot be added as if they had one denominator.

Include final stock in the maintained-loop balance

Use 100 kg, f=0.700 and three cycles under two different boundaries.

Without replacement, stock 34.3 kg plus loss 65.7 kg equals 100 kg.
With 100 kg restored after each cycle, total replacement 90.0 kg gives external input 190 kg.
Final stock 100 kg plus total loss 90.0 kg equals 190 kg.

The final replacement is an inventory input, not extra delivered service.

Find the crossover before claiming a fixed ranking

Use the separate assigned pair C_A=18+24I, C_B=26+12I.

C_B−C_A=8−12I.
The equality occurs at I=2/3 kg CO₂e kWh⁻¹.
At I=0.200, A is lower; at I=0.800, B is lower. Water indicators remain 90 / 140 L.

A model ranking for one indicator can change without improving every other indicator.

Try it yourself

Reduce only B lifetime to 40.0 hours for the original 120 hour service, keeping all other inputs fixed. Find purchased material and model climate totals.
Show the answer and reasoning
A: 3 units / 3.60 kg / 24.48 kg CO₂e; B: 3 units / 5.40 kg / 33.672 kg CO₂e. B is no longer lower.
Replacement count changes B production input, while its total 120 hour electricity stays 1.68 kWh.
Improve only collection to 0.950 at unchanged sorting/recovery fractions. Find usable material, total loss and yield.
Show the answer and reasoning
Usable 64.125 kg; total loss 35.875 kg; yield 0.64125.
95.0×0.900×0.750=64.125. Losses 5.00 + 9.50 + 21.375 balance the rest.
Use retention 0.850 for three cycles in each separately defined loop. Find no-replacement stock and maintained-loop external input/loss/final stock.
Show the answer and reasoning
No-replacement stock 61.4125 kg and loss 38.5875 kg. Maintained-loop input 145 kg, loss 45.0 kg and final stock 100 kg.
The maintained model replaces 15.0 kg after each of three cycles, including the last.
For the sensitivity pair set I=1.00 kg CO₂e kWh⁻¹. Find climate totals/difference and whether the lower-climate route also minimizes given water use.
Show the answer and reasoning
C_A=42.0 kg CO₂e, C_B=38.0 kg CO₂e; difference −4.00 kg CO₂e. B does not minimize water: 140 L versus A 90.0 L.
Evaluate both assigned functions while preserving the separate water indicator and common service boundary.

What to carry forward

Compare materials over the same function, service life and system boundary.
Sequential recovery fractions apply to the material that remains.
A maintained stock requires replacement inputs that belong in its balance.
A ranking can change with assumptions and with the environmental quantity compared.

References

Teaching resources and reference material supporting this lesson’s explanations and examples.