Bioprocess Engineering of Phototrophic Marine Organisms 9.4 Limiting Factors in Photobioreactor Design and Operation 289
Part B | 9.4
Table 9.7 Example values of intrinsic growth characteristics of a phototrophic suspension culture
Input parameter
Value and units
max
0:2 h 1
I k
50 mol photons m 2 s 1
K N
0:1 mmol N L 1
Y X=N
224 g cell mol 1 N
Y X=CO2
33:8 g cell mol 1 CO 2
k c
0:2 L.g cell cm/ 1
then the required k L a to avoid CO 2 -limited growth is
reduced to 57:3 h
1 , which is readily achievable. There
are many ways the aeration rate and bubble size can be
set to achieve this k L a value.
Finally, the sodium bicarbonate loading in the liquid medium necessary to maintain a pH of 8:0 at a CO 2
partial pressure of 3500 ppm must be calculated. From
(9.7) and Table 9.3, at 25
ı C the bicarbonate concentration needed in the liquid medium is
ŒHCO
3 D 10
.pKa;1pH/ P A
H
D 10
.6:08:0/
0:0035 atm
0:0339 l atm mmol 1
D 10:3 mmol l
1
:
Step 5. Determine the cultivation time and photobioreactor vessel dimensions necessary to achieve the
production schedule of 20 kg of biomass per day with
0
0.5
1.0
1.5
2.0
2.5
3.0
Cultivation time t (h)
Cell density C X (g cells L
–1 )
a)
0
2
4
6
8
10
12
Nutrient concentration C N
(mmol L
–1
)
C x
C N
0
5
10
15
20
25
30
0
50
100
150
200
250
300
Cultivation time t (h)
Mean light intensity I m
(µmol photons m
–2 s
–1
)
b)
0
1
2
3
4
5
6
CO 2 demand
(mmol CO 2 L
–1 h
–1 )
CO 2 demand
I m
0
5
10
15
20
25
30
Fig. 9.26a,b Planar photobioreactor design illustration: model simulation results. (a) Cell density (C x ) and limiting
nutrient concentration (C N ) versus cultivation time; (b) mean light intensity (I m ) and volumetric CO 2 demand versus
cultivation time
a final cell density of 2:0 g cell L
1 and initial cell density of 0:1 g cell L
1 . The cultivation time to achieve
C x;f is determined from the computed growth curve of
C x versus cultivation time. The prediction of C x versus
t in the photobioreactor is determined by integrating
equations (9.37a) and (9.37b) with respect to t using
the input parameters given in Table 9.7 and L D 15 cm,
˛ D 2, and C N;i D 8:5 mmol N L
1 .
dC x
dt
D C x D
C N
K N C C N
I m .C x /
I k C I m .C x /
max C x ;
with the initial condition t D 0, C x D C x;i D
0:1 g cell L
1 . At at a given value for C x , I m and
C N are estimated by
I m .C x / D
˛I o
k c C x L
1 e
kcCxL
;
C N D
.C x C x;i /
Y X=N
:
The differential equation can be numerically integrated
without much trouble using differential equation solver
utilities found in software packages such as MathCad
or MatLab. Plots of C x , C N , I m , and CO 2 demand versus cultivation time are presented in Figs. 9.26a,b. From
Fig. 9.26a, the final cultivation time (t f ) is 22:0 h at the
point where the limiting nutrient is consumed and the
cell density becomes constant. Based on this cultivation
time, the total culture volume to achieve the biomass
Part B | 9.4
Table 9.7 Example values of intrinsic growth characteristics of a phototrophic suspension culture
Input parameter
Value and units
max
0:2 h 1
I k
50 mol photons m 2 s 1
K N
0:1 mmol N L 1
Y X=N
224 g cell mol 1 N
Y X=CO2
33:8 g cell mol 1 CO 2
k c
0:2 L.g cell cm/ 1
then the required k L a to avoid CO 2 -limited growth is
reduced to 57:3 h
1 , which is readily achievable. There
are many ways the aeration rate and bubble size can be
set to achieve this k L a value.
Finally, the sodium bicarbonate loading in the liquid medium necessary to maintain a pH of 8:0 at a CO 2
partial pressure of 3500 ppm must be calculated. From
(9.7) and Table 9.3, at 25
ı C the bicarbonate concentration needed in the liquid medium is
ŒHCO
3 D 10
.pKa;1pH/ P A
H
D 10
.6:08:0/
0:0035 atm
0:0339 l atm mmol 1
D 10:3 mmol l
1
:
Step 5. Determine the cultivation time and photobioreactor vessel dimensions necessary to achieve the
production schedule of 20 kg of biomass per day with
0
0.5
1.0
1.5
2.0
2.5
3.0
Cultivation time t (h)
Cell density C X (g cells L
–1 )
a)
0
2
4
6
8
10
12
Nutrient concentration C N
(mmol L
–1
)
C x
C N
0
5
10
15
20
25
30
0
50
100
150
200
250
300
Cultivation time t (h)
Mean light intensity I m
(µmol photons m
–2 s
–1
)
b)
0
1
2
3
4
5
6
CO 2 demand
(mmol CO 2 L
–1 h
–1 )
CO 2 demand
I m
0
5
10
15
20
25
30
Fig. 9.26a,b Planar photobioreactor design illustration: model simulation results. (a) Cell density (C x ) and limiting
nutrient concentration (C N ) versus cultivation time; (b) mean light intensity (I m ) and volumetric CO 2 demand versus
cultivation time
a final cell density of 2:0 g cell L
1 and initial cell density of 0:1 g cell L
1 . The cultivation time to achieve
C x;f is determined from the computed growth curve of
C x versus cultivation time. The prediction of C x versus
t in the photobioreactor is determined by integrating
equations (9.37a) and (9.37b) with respect to t using
the input parameters given in Table 9.7 and L D 15 cm,
˛ D 2, and C N;i D 8:5 mmol N L
1 .
dC x
dt
D C x D
C N
K N C C N
I m .C x /
I k C I m .C x /
max C x ;
with the initial condition t D 0, C x D C x;i D
0:1 g cell L
1 . At at a given value for C x , I m and
C N are estimated by
I m .C x / D
˛I o
k c C x L
1 e
kcCxL
;
C N D
.C x C x;i /
Y X=N
:
The differential equation can be numerically integrated
without much trouble using differential equation solver
utilities found in software packages such as MathCad
or MatLab. Plots of C x , C N , I m , and CO 2 demand versus cultivation time are presented in Figs. 9.26a,b. From
Fig. 9.26a, the final cultivation time (t f ) is 22:0 h at the
point where the limiting nutrient is consumed and the
cell density becomes constant. Based on this cultivation
time, the total culture volume to achieve the biomass