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L1644_C02.fm Page 52 Tuesday, October 21, 2003 3:07 PM

that constitute elements of the eco-vectors can be found in Expression 2.1 (for
instance, Boustead, 1993a, b, c and Frischknecht et al., 1996).
The product of any process mass ﬂow M [kg/s] and its corresponding eco-vector
(v m,M ) gives the rate of pollutants (P) — expressed in kg/s or EL/s — generated by

this mass ﬂow until the life-cycle phase of the system, and shown in Expression 2.2:

P = M v ⋅ (2.2)
m,M
In parallel, an eco-vector (v ) is deﬁned for the energy ﬂows. The elements of
e
(v ), in turn, are expressed in speciﬁc energy bases, e.g., kilograms of pollutant per
e
kiloJoule. The rows of (v ) have analogous elements compared to those of the mass
e
eco-vector, as presented by Expression 2.3:
 (kg / kg) or (EL / kg) 
 
 Renewable Raw Material 
Not Renewable Raw Material 
 
 Air Emissions 
 Liquid Emissions 
v =   (2.3)
e
 Solid Waste 
 Energy Losses 
 
 Radiation 
 
 Noise 
 Other Environmental Impacts  

The product of an energy ﬂow E [kW] and its corresponding vector (v ) gives
e,M
the pollutant ﬂow (P ) regarding an energetic ﬂow of the system in study. The
e
equation to calculate (P ) is shown in the following expression:
e
P = E v ⋅ (2.4)
e
The use of Expressions 2.2 and 2.4 makes it possible for the environmental loads
of the mass and energy ﬂow, both measured in the same units, to be handled together,
once the pollutant ﬂows obtained by these treatments are expressed respectively in
terms of natural resource consumption rate and waste release rate.
In this framework, each of the system’s inputs has an associated eco-vector and
its content must be distributed to the output of the system. The balance of each of
the elements of the eco-vector must be closed. This means that total amount of
output from a process is equal to the pollutant quantity that entered with the inlets
plus the amount of pollutant generated during its operation.
To enable this balance, the output is divided into products and wastes. In order
to differentiate both classes, a convention establishes that the waste ﬂows have eco-

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