Materials Science · Resources, reuse, recycling and lifecycle evidence

Functional units and lifecycle boundaries

Translate a protected-delivery function into actual packaging and reuse flows, repair an incomplete process boundary, and test how shared-process allocation changes an assigned inventory.

Useful background: Energy, stability and environmental context; Measuring and checking material claims. Each worked case explains the quantities it uses.

Back to the chapter

After reading, you can

Define a functional unit and compare consistent lifecycle boundaries.
Calculate the products and intervening operations needed for a specified service.
Diagnose a ranking changed by omitted return and washing processes.
Partition a shared production inventory transparently and distinguish that accounting choice from a physical process change.
Keep material quantities, energy inputs, freshwater withdrawal and environmental impact conclusions distinct.

Compare a service, not unmatched kilograms

A functional unit specifies the service being compared, such as carrying a given load over a distance for a duration. Materials can require different masses or replacement counts to deliver it. A per-kilogram comparison answers another question.

Consider a small packaging comparison before calculating any impact. The required service is 1000 protected deliveries, each carrying the same specified 1 kg payload over the same fixed route and meeting the same protection criterion. Both systems are stipulated to meet that criterion. These are original invented teaching inputs, not observations of a real package or evidence that a proposed design protects a product.

System P needs two new single-use inserts per delivery, each of mass 0.100 kg. System Q needs one reusable carrier per delivery, of mass 0.200 kg, and every carrier completes exactly ten uses before retirement. There are no failed deliveries, losses, standby carriers or spare inserts in this model. Ten uses includes the first use; it is not ten additional reuses.

The functional unit states the quantified performance being compared. Reference flows are the quantities of products required to provide it. Here P needs 1000 × 2 = 2000 new inserts. Q needs 1000/10 = 100 new carriers. Their supplied new packaging product masses are 2000 × 0.100 = 200 kg and 100 × 0.200 = 20 kg. These are product masses, not total ore, fuel or upstream material inputs. Resource extraction and material supply pathways explains that distinction.

One Q carrier makes nine between-use return-and-wash trips, followed by its tenth delivery and terminal collection. Across 100 carriers that is 900 between-use events and 100 terminal collections. Count the final collection in terminal treatment, once. There is no final wash. A useful check is 100 first uses + 900 further uses = 1000 deliveries.

Resources, useful life and environmental consequences supplies the earlier replacement-and-service comparison. Here the extra step is to connect a functional unit to physical reference flows, process counts and shared-process assignments. Comparable results and independent reproduction gives preparation for checking what the quantities and conditions actually mean.

Original stipulated service and product flows for 1000 equally protected deliveries. Each Q carrier finishes all ten uses; no remaining service is carried beyond the comparison.
Quantity	P: single-use inserts	Q: reusable carriers
New product mass per item (kg)	0.100	0.200
Items used per delivery	2	1
Uses completed per new item	1	10
New items supplied	2000	100
New packaging product mass supplied (kg)	200	20
Between-use return-and-wash events	0	900
Items terminally collected/treated	2000	100

Boundaries determine what is counted

Include relevant extraction, production, use, maintenance and end-of-life stages. State allocations and scenarios where they affect results. Climate impact, water demand and other indicators remain different measures; one low indicator does not establish every benefit.

A system boundary specifies which processes belong to the account. A consistent comparison includes the relevant processes needed by each solution to deliver the same function. It need not force identical operations onto both: P has no washing operation here, while Q needs one between uses. Omitting an operation that Q requires is different from recording a process that P does not have.

Use the supplied energy-input inventory below. Every entry is on the same chosen energy-accounting basis, in megajoules (MJ). Production includes the assigned extraction, materials manufacture, fabrication and their energy supply; it excludes the separately listed forward delivery, return/washing and terminal treatment. Those later entries include their own associated energy supply. No entry overlaps another, and no additional contributions are present in this bounded model. These invented totals are not a complete environmental impact assessment.

Each new P insert carries 1.00 MJ of production input and 0.100 MJ of terminal treatment. Each new Q carrier is initially assigned 20.0 MJ of production input and 1.00 MJ of terminal treatment. Forward delivery totals 1000 MJ for either solution in this particular scenario. Equal forward input is a stipulation, not a rule that transport is independent of mass, route or vehicle loading.

Each Q between-use event adds 0.800 MJ for return transport and 0.200 MJ for washing, hence 1.00 MJ per event. The 900 events therefore add 900 MJ. Terminal collection is already included in the treatment entry; adding another 100 return events or a final wash would count operations outside this stated schedule.

The inventory total is the sum of each process count multiplied by its per-process input, plus any stated whole-service total. For P this gives 2000 × 1.00 + 1000 + 2000 × 0.100 = 3200 MJ. For Q it gives 100 × 20.0 + 1000 + 900 × 1.00 + 100 × 1.00 = 4000 MJ. Omitting Q’s returns and washes gives 3100 MJ, apparently below P’s 3200. Restoring the missing 900 reverses that ranking: the complete supplied Q inventory is 800 MJ higher.

Zero in the table means no such contribution in this invented model; it does not mean an unavailable real measurement may be replaced by zero. A production-only study can answer a production question, but it cannot establish the ranking of these full-service totals. Reuse, repair, remanufacture and recycling explains why the achieved loop, rather than a reusable label, determines the required operations.

Energy-input ledger for the same 1000 deliveries, with Q production initially assigned as explained in the next section. Entries are mutually exclusive and totals are conditional on the stipulated model.
Process group	P total (MJ)	Q total (MJ)
Assigned production	2000	2000
Forward delivery	1000	1000
Between-use return transport	0	720
Between-use washing	0	180
Terminal collection and treatment	200	100
Complete supplied inventory	3200	4000

Original invented schedule for 1000 protected deliveries. P supplies 2000 new single-use inserts, with two inserts per delivery and 2000 inserts terminally treated. Q supplies 100 new carriers, each completing ten uses. A distinct loop links Q delivery to 900 between-use returns and washes and back to delivery. The final 100 collections are included in terminal treatment, with no final wash. Resource input and manufacture feed both systems; terminal material recovery would need its own stated pathway. This schematic has no physical length or flow-width scale.

Allocation partitions an inventory; it does not change a process

Suppose one joint production batch makes all 100 Q carriers, of total mass 20 kg, together with 80 kg of a saleable co-product. A co-product is another useful output of the shared process. The joint production system supplying this batch uses 4000 MJ on the same accounting basis and withdraws 4.00 m³ of freshwater. These are additional invented inputs. The material source of both outputs is not specified, so their mass ratio does not establish virgin-resource requirements.

The initial scenario assigns half of each shared input to the carrier output and half to the co-product. Q receives 0.50 × 4000 = 2000 MJ and 0.50 × 4.00 = 2.00 m³. Dividing by 100 carriers explains the earlier 20.0 MJ per carrier. This equal-share assignment is a declared accounting scenario, not evidence that the carriers physically caused exactly half the joint input.

Now test an alternative mass-based allocation. Q’s output-mass fraction is 20/(20 + 80) = 0.20. Assigning that fraction of the same shared inputs gives Q 800 MJ and 0.800 m³; the co-product receives 3200 MJ and 3.20 m³. Check the partitions: 800 + 3200 = 4000 MJ and 0.800 + 3.20 = 4.00 m³. Neither input has vanished or been counted twice.

Q’s other energy inputs still total 1000 + 720 + 180 + 100 = 2000 MJ. Its complete assigned energy inventory becomes 800 + 2000 = 2800 MJ, below P’s 3200, rather than the original 4000 MJ above it. No carrier, trip, wash or energy input to the joint production system has physically changed. The assignment to the studied function changed. This is not evidence of a process improvement or of the consequences of buying more carriers.

Do not choose an allocation merely because it produces a preferred ranking. Investigate whether process-level data can separate the operations, or whether an expanded comparison delivering both outputs’ functions can avoid the partition. Where allocation remains necessary, explain why its basis fits the study question and test plausible alternatives. Neither equal shares nor mass shares is declared universally correct here. A recycling credit is also a modelling choice requiring its own basis, not an automatic extra subtraction after a burden has already been assigned.

Two explicit assignments of the same joint batch. Complementary co-product shares remain in the full account; they are not another benefit credited to Q.
Assignment	Q production energy (MJ)	Co-product energy (MJ)	Q production freshwater (m³)
Equal shares: Q receives 50%	2000	2000	2.00
Mass shares: Q receives 20%	800	3200	0.800

State which result the inventory can support

Track freshwater withdrawal separately from energy. In this invented case P production withdraws 2.00 L per insert, so 2000 inserts require 4000 L = 4.00 m³. Q production receives 2.00 m³ under equal shares, and each of its 900 washes withdraws 2.00 L: another 1800 L = 1.80 m³. All other freshwater withdrawals are stipulated zero within this model. Q therefore totals 3.80 m³ under equal shares, or 0.800 + 1.80 = 2.60 m³ under mass allocation.

The equal-share comparison gives Q less new packaging product mass and slightly less freshwater withdrawal, but more assigned energy input. Report those separate findings. Freshwater withdrawal is water taken from a source; it is not the same quantity as consumption after return flows, nor an assessment of local scarcity or ecological effect. Similarly, MJ does not directly specify greenhouse-gas emissions. A climate comparison needs the relevant emissions and a stated impact method.

The 0.20 m³ withdrawal difference between 4.00 and 3.80 is arithmetic on supplied inputs. No uncertainty or variability estimates have been provided, so it is not an established robust difference between real systems. Replacing the inputs by actual data requires relevant production routes, place, time, return behaviour and washing conditions. Keep data gaps explicit and test changes that could alter the conclusion.

Do not treat collection as successful material recovery or subtract all collected mass as avoided virgin input. Impurities, sorting and recovered material quality distinguishes collected material from usable output. Design choices that affect material recovery develops the connection to real processing pathways. Here terminal treatment is counted with no recovery credit, and the next-use fate of that material is not being predicted.

A defensible statement identifies the function, reference flows, process boundary, assignment and result. For example: “For the invented 1000-delivery service, the full supplied energy inventory is 3200 MJ for P and 4000 MJ for Q under equal-share production allocation; Q falls to 2800 MJ under the tested mass allocation.” That statement exposes the assumption controlling this ranking without claiming overall environmental superiority.

Two separate zero-based scales compare the same invented 1000-delivery service under the complete supplied boundary. P is filled, Q with a 50 percent joint-production share is hollow with solid outlines, and Q with a 20 percent mass-based share is hollow with dashed outlines. Assigned energy totals are respectively 3200, 4000 and 2800 megajoules. Freshwater withdrawal totals on a separate scale are 4.00, 3.80 and 2.60 cubic metres. Between Q assignments the same joint production system and service operations are unchanged. These are separate inventory quantities, not environmental impact scores or uncertainty intervals.

Worked examples

Work through the case

A package is half as heavy but requires twice as many units for the same protected delivery. Does per-package mass establish lower material use?

Use the matched delivery as functional unit.
Multiply mass per package by packages required.
Compare total input on that basis.

Not automatically; the simplified mass totals could be equal.

Repair a favourable-looking incomplete comparison

A report uses the initial equal-share production assignment. It gives Q a total of 3100 MJ and says it beats P’s 3200 MJ for the same 1000 deliveries. Reconstruct the counts and identify the error.

P needs 2000 new inserts. Q needs 100 new carriers used ten times each; 100 × (10 − 1) = 900 between-use events. A new carrier’s first use needs no preceding return or wash.
Q’s stated 3100 MJ equals 2000 production + 1000 forward delivery + 100 terminal treatment. It leaves out all between-use operations, although those operations are required for the stipulated reuse.
Restore return transport: 900 × 0.800 = 720 MJ. Restore washing: 900 × 0.200 = 180 MJ. Together they add 900 MJ, giving Q 4000 MJ.
Compare the same full model: 4000 − 3200 = 800 MJ more for Q. The incomplete calculation instead gave 3100 − 3200 = −100 MJ. The 900 MJ omission explains the entire reversal.
Keep the 20 kg versus 200 kg product-mass finding separate. It remains correct within the service assumptions, but is not an energy ranking or an overall environmental conclusion.

The report omitted 900 required return-and-wash events. Q’s complete supplied energy total is 4000 MJ, 800 MJ above P, under the initial allocation.

Change an assignment without claiming a physical saving

For the joint Q batch, compare the equal-share and mass-share assignments. Recalculate Q’s complete energy and freshwater inventories. What has changed physically?

The full joint production system still uses 4000 MJ and withdraws 4.00 m³ while supplying 20 kg of carriers and 80 kg of co-product. Equal shares assign Q 2000 MJ and 2.00 m³.
The mass share for Q is 20/100 = 0.20. It assigns Q 800 MJ and 0.800 m³; the complementary 80% gives the co-product 3200 MJ and 3.20 m³.
The other Q energy inputs are unchanged at 2000 MJ. Hence full Q totals are 4000 MJ under equal shares and 2800 MJ under mass shares. The assigned reduction is 1200 MJ, not a measured process saving.
Washing still withdraws 1.80 m³. Full Q withdrawals are 2.00 + 1.80 = 3.80 m³ and 0.800 + 1.80 = 2.60 m³. The physical withdrawals of the joint batch and washes are unchanged.
Q remains 100 carriers, 20 kg of new carrier product and 900 between-use events. Explain and test the assignment rather than reporting an allocation-driven reversal as proof that the design became cleaner.

Q changes from assigned totals 4000 MJ and 3.80 m³ to 2800 MJ and 2.60 m³. The physical process and delivered function are unchanged; only the shared-production partition changed.

Try the reasoning

Can production-only and whole-life results be ranked without adjustment?
Show the answer and reasoning
No.
Their boundaries differ. In the invented model, counting Q production, forward delivery and treatment but omitting returns and washes gives 3100 rather than 4000 MJ. Reconcile relevant processes before interpreting the ranking.
Why include replacements?
Show the answer and reasoning
They deliver the required service over time.
Ignoring them changes the functional comparison. Count actual new items and intervening operations. A ten-use carrier needs nine between-use events, not ten; its final collection belongs to the stated terminal entry.
Suppose every Q carrier now completes exactly five uses, with the same 0.200 kg mass, 20.0 MJ production and 1.00 MJ terminal input per new carrier. Between-use return plus wash remains 1.00 MJ per event, and forward delivery remains 1000 MJ. Both systems still meet the same 1000-delivery function. Find Q’s carrier count, product mass, between-use events and complete energy input.
Show the answer and reasoning
200 new carriers, 40.0 kg of carrier product, 800 between-use events and 6000 MJ.
The count is 1000/5 = 200. Each contributes four further uses, so events total 200 × 4 = 800, also 1000 − 200. Energy is 200 × 20 + 1000 + 800 × 1 + 200 × 1 = 6000 MJ. Fewer washes do not imply a lower total: twice as many new carriers are produced and terminally treated. This scenario explicitly retains the supplied per-carrier assignment; it does not assume a new joint batch has the old total input.
A learner counts 100 Q carriers × 10 returns = 1000 between-use events, then also retains all 100 terminal collection/treatment entries. With the original ten-use schedule, how much does that overstate Q’s energy total?
Show the answer and reasoning
It adds 100 nonexistent between-use return-and-wash events, overstating the total by 100 MJ: 4100 rather than 4000 MJ.
There are only nine between-use events per carrier. Final collection is already in terminal treatment, and no final wash is specified. Use the actual sequence, not one return per delivery plus a second final collection.
Another hypothetical joint batch uses 6000 MJ and makes 30 kg of the studied output plus 70 kg of co-product. Use mass allocation. Someone assigns 1800 MJ to the studied output and all 6000 MJ to the co-product. Find the correction and explain whether this proves the studied product caused only 1800 MJ of physical consumption.
Show the answer and reasoning
The studied share is 30%, or 1800 MJ; the co-product receives the complementary 70%, or 4200 MJ. The proposed 7800 MJ sum double counts 1800 MJ. Allocation alone does not establish causal consumption.
The shares are 30/(30 + 70) and 70/(30 + 70), summing to one. Their assigned inputs must sum to the same 6000 MJ for this partition. The joint process still consumes 6000 MJ; assigning it is different from measuring how the process would respond to a change in demand.
Under equal shares, Q has 20 kg of supplied carrier product, 4000 MJ of energy input and 3.80 m³ of freshwater withdrawal. A report adds the three numbers to make a single environmental score and calls Q climate-superior because its product mass is lower. Identify the errors.
Show the answer and reasoning
The different quantities and units cannot be added as one unexplained score, and lower product mass does not establish a climate result.
Report each quantity on the stated functional basis. A climate indicator needs relevant emission flows and a stated characterisation method. Withdrawal volume also does not by itself measure local water scarcity, consumption after returns or ecological damage.
A thinner package uses fewer inputs per attempted trip, but a test now shows it fails the specified protection criterion for some payloads. Can its original per-trip inventory be ranked directly against a system delivering all 1000 protected payloads?
Show the answer and reasoning
No. It no longer represents the same delivered function. Establish the design and processes that actually provide 1000 protected deliveries, including relevant replacement payloads or extra packaging, before comparing.
Equal numbers of attempted trips are not equal numbers of successfully protected deliveries. Avoid inventing a failure rate from the wording; use actual performance evidence, an explicit service model and relevant additional flows. A small packaging mass cannot repair a mismatch in function.

What to carry forward

Match function and boundary.
Keep distinct impact indicators separate.
Translate the specified service into new product counts and actual intervening operations before multiplying process inputs.
An omitted process can reverse a ranking; a consistent boundary includes each solution’s relevant processes.
Allocation partitions shared inputs transparently. Changing the partition is different from changing the physical process.
Energy inputs and freshwater withdrawals are separate inventory quantities, not a complete impact assessment or a universal material ranking.

References

Teaching resources and research supporting this lesson’s explanations and examples.