Environmental Engineering Reference
In-Depth Information
t
i
t
i
u
≤
α
⋅
x
i=1,…,N t=0,...,T-1
(2.9)
i
u
i
≥
t
0
i=1,…,N t=0,...,T-1
(2.10)
PCI
N
CAP
=
MV
u
t
i
=
t=0,...,T-1
(2.11)
i
3600
⋅
8000
η
i
1
e
Besides, respect to the static model, another constraints has to be introduced: that
representing the dynamics of biomass growth. To describe such a phenomenon the
mathematical model adopted by Berryman (1981), Begon and Mortimer (1981), and Bernetti
(1998) has been used. This model expresses the describes the dynamics of the growth as
&
2
x
=
b
x
−
b
1
x
(2.12)
o
where values of b
0
and b
1
value are different for each type of biomass. However, the quantity
of biomass in a parcel depends on the growth dynamics, as well as on the quantity of biomass
collected, that is
&
2
x
=
b
x
−
b
x
−
u
(2.13)
0
1
The above continuous-time model can be discretized as follows
2
x
(t
+
Δt)
=
[1
+
Δtb
]
x
(t)
−
b
Δt
x
(t)
−
Δt
u
(t)
(2.14)
0
1
Thus, selecting a unitary discretization interval, namely Δ
t=1
, and taking into account all
the parcels, the following dynamic constraints arise
i
t
i
t
i
t
2
i
t
x
=
(1
+
b
)
x
−
b
(
x
)
−
u
(2.15)
+1
0,i
1,i
t=0,...(T-1) i=1,…,N
2.3. The Case Study
The DSS has been applied to a territory within the Savona District, where it was
necessary to evaluate the environmental impact and the sustainability of a plant producing
only electric energy to be built in a specific area. Actually, from a purely economic point of
view, a plant that produces energy from biomasses is not particularly advantageous, above all
if the production is limited to electric energy. Regarding the environmental benefits, it is not
easy to quantify them in monetary terms. However, it is possible to affirm that, for the
considered study area, the installation of this type of activity on the territory would produce a
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