η ¼
δ 0
δ i
ð10Þ
where δ i is the input exergy current and δ 0 is the output exergy
current.
K is the net exergy financial coefficient, the ratio of delivered
exergy to invested exergy (money) [24]:
K ¼
de d
dt ∙τ
e c þ e l
ð11Þ
where e d is the delivered exergy, e c is the invested exergy needed for
system construction and e l is the invested labor, and τ is system
operation time.
And E is the ecological or ecosystem efficiency of the energy
conversion system based on the eco-exergy flow. We will use a ratio
of eco-exergy before and after energy system construction and use:
E ¼
de d
dt ∙τ
e i
ð12Þ
where e i is the consumed eco-exergy, which is described by the
reduced ability of ecosystem to perform work:
e i ¼ e eco 0 À e eco τ
ð13Þ
The environmental exergonomics main criterion function is
defined as:
Z env ¼
1
η
þ
1
K
þ
1
E
ð14Þ
Assuming that K and E are independent, for the arbitrary
functions K(η) and E(η):
dZ env
dη
¼ À
1
η 2 þ À
dK
dη
K
2
þ À
dE
dη
E
2
ð15Þ
For
dZ env
dη ¼ 0:
η
2
¼
K
2 E
2
ÀE
2dK
dη À K
2dE
dη
ð16Þ
and thus
Z min ¼
ÀE
2dK
dη À K
2dE
dη
1=2 þ K þ E
KE
ð17Þ
and
Design and Analysis of Offshore Macroalgae Biorefineries
17