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François et al. Carbon Footprints 2026, 5, 22 Page 7 of 22
Figure 2. Comparison of static and dynamic approaches. GHG: Greenhouse gases; LCD: life cycle duration.
Figure 2B shows the same case study with a dynamic approach: all emissions of the inventory system model
are now spread between t 0 and t . The total integration time corresponding to Equation 9 can be rewritten
max
by introducing t as follows:
max
) 3H=0<82 = (C <0G − C 0 ) + (C G − C <0G ) = ! + (C G − C <0G ) (11)
To build a unified framework between static and dynamic approaches, the static equation should be derived
from the dynamic one. By setting t = t 0, corresponding to all emissions occurring at time t 0, expressions of
max
T are equals:
(12)
8 5 C <0G = C 0 ⇔ ) 3H=0<82 = 0 + (C G − C <0G ) = ) BC0C82
Giving therefore the following relationship for the static expression:
) BC0C82 = (C G − C <0G ) = ) (13)
