macroalgae through the water bulk. Alternative mixing systems,
such as airlift, which push the whole volume of water with the
macroalgae are possible and the calculations of E mix for them will
be different, though following the same principle.
For the case of mechanical mixing when the macroalgae biomass is pushed through the bulk of water and assuming that k> > 1
and t dark > > t light , the net exergy gain with mixing is described by
Eq. 31:
ÀΔe 0 mix ¼
vt dark
l
E s À c D ρv
3 t dark l
2
∙
vt dark
l
ð31Þ
where ρ is the density of macroalgae, v is the speed of macroalgae
movement in the water, and c D is a drag coefficient of macroalgae
against the water. The drag force on macroalgae is defined through
the drag coefficient, F D ¼ c D ρv
2 , and the required power for mixing
is F D v. Equation 32 shows the objective function of the exergy
losses during cultivation which should be minimized:
ÀΔe 0 mix ¼
vt dark
l
E s À c D ρv
4 t dark
2 l
ð32Þ
The parameter under control in this type of mixing system is a
macroalgae movement velocity. Thus, for minimization of the
energy we differentiate the exergy losses during cultivation by the
macroalgae rotation velocity and derive the optimum mixing velocity: v opt ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
E s
4c D ρt dark l
2
3
q
And thus the maximum possible exergy gain (in Joules) in this
type of mixing system is:
ÀΔe 0 mix max ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
E s
4c D ρt dark l
2
3
q
∙t dark ∙E s
l
À c D ρt dark
2 l
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E s
4c D ρt dark l
2
3
s
4
ð33Þ
ÀΔe 0 mix max ¼ 0:47
E s
4
3 t dark
2
3
c D ρ
ð
Þ
1
3 l
5
3
Therefore, the impact of mixing on the total exergy efficiency
improvement of the biorefinery with a cultivation territory of a
characteristic size D (this area includes (D/l)
2 units of floating on
the surface of macroalgae thalli):
η max mix ¼ 1 À
e en þ e w þ e eco c À e 0 mix max
D
ð Þ
2
l
2
e s e þ e m e þ e m þ e k þ e l þ e eco
ð34Þ
Thus, using mixing approaches adapted for algae biology
would be possible to increase the systems yields.
Design and Analysis of Offshore Macroalgae Biorefineries
25
such as airlift, which push the whole volume of water with the
macroalgae are possible and the calculations of E mix for them will
be different, though following the same principle.
For the case of mechanical mixing when the macroalgae biomass is pushed through the bulk of water and assuming that k> > 1
and t dark > > t light , the net exergy gain with mixing is described by
Eq. 31:
ÀΔe 0 mix ¼
vt dark
l
E s À c D ρv
3 t dark l
2
∙
vt dark
l
ð31Þ
where ρ is the density of macroalgae, v is the speed of macroalgae
movement in the water, and c D is a drag coefficient of macroalgae
against the water. The drag force on macroalgae is defined through
the drag coefficient, F D ¼ c D ρv
2 , and the required power for mixing
is F D v. Equation 32 shows the objective function of the exergy
losses during cultivation which should be minimized:
ÀΔe 0 mix ¼
vt dark
l
E s À c D ρv
4 t dark
2 l
ð32Þ
The parameter under control in this type of mixing system is a
macroalgae movement velocity. Thus, for minimization of the
energy we differentiate the exergy losses during cultivation by the
macroalgae rotation velocity and derive the optimum mixing velocity: v opt ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
E s
4c D ρt dark l
2
3
q
And thus the maximum possible exergy gain (in Joules) in this
type of mixing system is:
ÀΔe 0 mix max ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
E s
4c D ρt dark l
2
3
q
∙t dark ∙E s
l
À c D ρt dark
2 l
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E s
4c D ρt dark l
2
3
s
4
ð33Þ
ÀΔe 0 mix max ¼ 0:47
E s
4
3 t dark
2
3
c D ρ
ð
Þ
1
3 l
5
3
Therefore, the impact of mixing on the total exergy efficiency
improvement of the biorefinery with a cultivation territory of a
characteristic size D (this area includes (D/l)
2 units of floating on
the surface of macroalgae thalli):
η max mix ¼ 1 À
e en þ e w þ e eco c À e 0 mix max
D
ð Þ
2
l
2
e s e þ e m e þ e m þ e k þ e l þ e eco
ð34Þ
Thus, using mixing approaches adapted for algae biology
would be possible to increase the systems yields.
Design and Analysis of Offshore Macroalgae Biorefineries
25