Bioprocess Engineering of Phototrophic Marine Organisms 9.4 Limiting Factors in Photobioreactor Design and Operation 281
Part B | 9.4
The output cell density and limiting nutrient concentration for the well-mixed continuous-flow bioreactor described by (9.25) and (9.26) now become
C x D Y X=N C N;o
DK N
Im.Cx/
IkCIm.Cx/
max D
!
(9.38)
and
C N D
DK N
Im.Cx/
IkCIm.Cx/
max D
:
(9.39)
If the path length L is increased, then I m and also decrease. To illustrate, the effect of light path length L on
I m and for a planar vessel with one-sided illumination
(˛ D 1) is presented in Fig. 9.20.
Biomass production for light-limited growth of phototrophic liquid suspension cultures in tubular photobioreactors follows from the equations described above.
In the tubular photobioreactor, the tubular section improves the access of the culture to light. However, in
order to avoid CO 2 -limited growth, the residence time
of the culture within the tube is short and so the biomass
cell density is essentially constant for a single pass
through the tubes. Cumulative biomass production occurs over many passes between the aeration tank and
tubular section. Consequently, for batch operation of the
tubular photobioreactor, the material balance development parallels that of (9.37a), but with one important
modification. In the tubular photobioreactor, the aeration tank is not illuminated, and so only the tubular
section culture volume V t can promote photosynthetic
growth. In this case, the biomass production rate for
batch growth of the photosynthetic tubular photobioreactor under light-limited conditions is given by
dC x
dt
D
V t
V
C x D
V t
V
C N
K N C C N
I m .C x /
I k C I m .C x /
max C x :
(9.40)
Model predictions reveal how light transfer affects
biomass productivity in photobioreactors. The effect
of light attenuation on cell growth kinetics is shown
in Fig. 9.21. The batch cultivation is carried out in
a well-mixed planar photobioreactor illuminated from
one side. The growth curve (C x versus t) and substrate consumption curve (C N versus t) are generated by
numerically integrating (9.37a) and (9.37b) over time
using the model input parameters given in the caption
of Fig. 9.21 and (9.20) as the limiting nutrient bal0
0.5
1.0
1.5
2.0
2.5
3.0
0
1 0
2 0
3 0
4 0
5 0
6 0
Cultivation time t (h)
Cell density C x (g cells L
–1
)
L = 20 cm
L = 10 cm
L = 5 cm
Batch photobioreactor growth kinetics
effect of light path length
Fig. 9.21 Calculated effect of total light path length
(L) on the cell density versus time curve within a wellmixed planar photobioreactor under batch, light-limited
growth. Model input parameters: max D 0:2 h
1 , I k D
50 mol photons m
2 s
1 , K N D 0:1 mmol L
1 , Y X=N D
224 g cell mol
1 N,
k c D 0:5 L.g cell cm/
1 ,
C x;i D
0:1 g cells L
1 , C N;i D 10 mmol N L
1 , I o D 150 mol
photons m
2 s
1 , ˛ D 1 (one-sided illumination)
ance for estimation of C N . As the cell density (C x )
increases with time, the mean light intensity I m decreases, and the biomass production rate slows down.
When the limiting nutrient is completely consumed the
cell density becomes constant. As the path length for
light transfer in the planar photobioreactor is increased
from 5 to 20 cm, the biomass production rate decreases
markedly. The effect of light attenuation on cell growth
kinetics in a well-mixed continuous photobioreactor is
shown in Fig. 9.22. Increasing dilution rate D (9.23) by
increasing the volumetric flow rate of feed medium increases biomass productivity until washout is observed.
Increasing the light path length L from 5 to 10 cm
markedly decreases the optimum biomass production
rate. Therefore, increasing light attenuation by increasing the path length for light transfer significantly lowers
the performance of both batch and continuous photobioreactors in light-limited growth.
9.4.3 Carbon Dioxide-Limited Growth
Phototrophic liquid suspension cultures utilize dissolved CO 2 as the sole inorganic carbon source for
photosynthetic biomass production. Carbon dioxide is
supplied to the culture by contacting the liquid medium
with an aeration gas containing CO 2 , for example by
Part B | 9.4
The output cell density and limiting nutrient concentration for the well-mixed continuous-flow bioreactor described by (9.25) and (9.26) now become
C x D Y X=N C N;o
DK N
Im.Cx/
IkCIm.Cx/
max D
!
(9.38)
and
C N D
DK N
Im.Cx/
IkCIm.Cx/
max D
:
(9.39)
If the path length L is increased, then I m and also decrease. To illustrate, the effect of light path length L on
I m and for a planar vessel with one-sided illumination
(˛ D 1) is presented in Fig. 9.20.
Biomass production for light-limited growth of phototrophic liquid suspension cultures in tubular photobioreactors follows from the equations described above.
In the tubular photobioreactor, the tubular section improves the access of the culture to light. However, in
order to avoid CO 2 -limited growth, the residence time
of the culture within the tube is short and so the biomass
cell density is essentially constant for a single pass
through the tubes. Cumulative biomass production occurs over many passes between the aeration tank and
tubular section. Consequently, for batch operation of the
tubular photobioreactor, the material balance development parallels that of (9.37a), but with one important
modification. In the tubular photobioreactor, the aeration tank is not illuminated, and so only the tubular
section culture volume V t can promote photosynthetic
growth. In this case, the biomass production rate for
batch growth of the photosynthetic tubular photobioreactor under light-limited conditions is given by
dC x
dt
D
V t
V
C x D
V t
V
C N
K N C C N
I m .C x /
I k C I m .C x /
max C x :
(9.40)
Model predictions reveal how light transfer affects
biomass productivity in photobioreactors. The effect
of light attenuation on cell growth kinetics is shown
in Fig. 9.21. The batch cultivation is carried out in
a well-mixed planar photobioreactor illuminated from
one side. The growth curve (C x versus t) and substrate consumption curve (C N versus t) are generated by
numerically integrating (9.37a) and (9.37b) over time
using the model input parameters given in the caption
of Fig. 9.21 and (9.20) as the limiting nutrient bal0
0.5
1.0
1.5
2.0
2.5
3.0
0
1 0
2 0
3 0
4 0
5 0
6 0
Cultivation time t (h)
Cell density C x (g cells L
–1
)
L = 20 cm
L = 10 cm
L = 5 cm
Batch photobioreactor growth kinetics
effect of light path length
Fig. 9.21 Calculated effect of total light path length
(L) on the cell density versus time curve within a wellmixed planar photobioreactor under batch, light-limited
growth. Model input parameters: max D 0:2 h
1 , I k D
50 mol photons m
2 s
1 , K N D 0:1 mmol L
1 , Y X=N D
224 g cell mol
1 N,
k c D 0:5 L.g cell cm/
1 ,
C x;i D
0:1 g cells L
1 , C N;i D 10 mmol N L
1 , I o D 150 mol
photons m
2 s
1 , ˛ D 1 (one-sided illumination)
ance for estimation of C N . As the cell density (C x )
increases with time, the mean light intensity I m decreases, and the biomass production rate slows down.
When the limiting nutrient is completely consumed the
cell density becomes constant. As the path length for
light transfer in the planar photobioreactor is increased
from 5 to 20 cm, the biomass production rate decreases
markedly. The effect of light attenuation on cell growth
kinetics in a well-mixed continuous photobioreactor is
shown in Fig. 9.22. Increasing dilution rate D (9.23) by
increasing the volumetric flow rate of feed medium increases biomass productivity until washout is observed.
Increasing the light path length L from 5 to 10 cm
markedly decreases the optimum biomass production
rate. Therefore, increasing light attenuation by increasing the path length for light transfer significantly lowers
the performance of both batch and continuous photobioreactors in light-limited growth.
9.4.3 Carbon Dioxide-Limited Growth
Phototrophic liquid suspension cultures utilize dissolved CO 2 as the sole inorganic carbon source for
photosynthetic biomass production. Carbon dioxide is
supplied to the culture by contacting the liquid medium
with an aeration gas containing CO 2 , for example by