Methodology¶

All foreground quantities are derived from a small parameter store (parameters.yaml) by pure physics functions in aluminum_bottle_lca.model. Each equation is reproduced below so reviewers can annotate the derivation directly.

Foreground accounting¶

Primary aluminum¶

The bottle is 97 % primary aluminum by mass. An internal trim-loss fraction \( f_\mathrm{scrap} \) is recycled in-house but still needs to enter the foreground at the casting stage:

\[ m_\mathrm{Al} \;=\; \frac{f_\mathrm{Al}}{1 - f_\mathrm{scrap}}\,m_\mathrm{bottle} \]

Epoxy lacquer¶

The inner liner is treated as a fixed mass fraction \( f_\mathrm{coat} \) of the bottle mass:

\[ m_\mathrm{coat} \;=\; f_\mathrm{coat}\, m_\mathrm{bottle} \]

Electricity and process heat¶

Forming (impact extrusion + trimming) and annealing each get a specific-energy intensity:

\[ E_\mathrm{elec} \;=\; e_\mathrm{form}\, m_\mathrm{bottle} \qquad E_\mathrm{th} \;=\; e_\mathrm{ann}\, m_\mathrm{bottle} \]

Transport¶

Truck transport from the plant to a filling line at distance \( d \):

\[ T \;=\; d \cdot \frac{m_\mathrm{bottle}}{1000} \quad [\mathrm{t\,km}] \]

Impact assessment¶

For each impact method \( j \) and foreground input \( i \), the score is the dot product of foreground quantities \( q_i \) and characterisation factors \( c_{ij} \):

\[ S_j \;=\; \sum_i c_{ij}\, q_i \]

The share of foreground \( i \) in method \( j \) reported in the contribution table is:

\[ r_{ij} \;=\; \frac{c_{ij}\,q_i}{S_j} \]

Worked numbers¶

The defaults from parameters.yaml are:

Parameter	Value	Unit
\( m_\mathrm{bottle} \)	0.015	kg
\( f_\mathrm{Al} \)	0.97	—
\( f_\mathrm{coat} \)	0.02	—
\( f_\mathrm{scrap} \)	0.01	—
\( e_\mathrm{form} \)	0.32	kWh / kg
\( e_\mathrm{ann} \)	0.18	kWh / kg
\( d \)	250	km

Substituting these gives the per-bottle foreground vector tabulated on Impact assessment.