Part B | 9.4
280 Part B Tools and Methods in Marine Biotechnology
r = R
r + dr
r
Cylindrical vessel
cross-section
I 0
Symmetric
illumination source
Fig. 9.19 Symmetrical, external light delivery to a cylindrical photobioreactor vessel
tubing diameter as path length for light transfer, then
(9.33) can still be used to provide the most conservative
approximation for the mean light intensity I m .
Often the vessel wall material itself is not perfectly transparent and attenuates light, as illustrated
in Fig. 9.16. Therefore, the transfer of light from the
outer surface of the vessel to the culture encounters two
0
20
40
60
80
100
120
0
5
10
15
0.02
0.04
0.06
0.08
0.10
0.12
0.14
20
Total light path length L (cm)
Specific growth rate
μ (h
–1
)
Mean light intensity I m (µmol photons m
–2 s
–1 )
I m
μ
Fig. 9.20 Calculated effect of total light path length (L) on
mean light intensity (I m ) and specific growth rate () for
one-dimensional light transfer. Model input parameters: I o D
100 mol photons m
2 s
1 , k c D 0:1 L .g cell cm/
1 , C x D
2 g cell L
1 , ˛ D 1
resistances in series: the vessel wall and the liquid suspension culture itself. From the Beer–Lambert law, the
light intensity incident to the outer vessel surface is related to the light intensity incident to the culture on the
inner vessel surface by
I
0
o D I o e
kwlw
;
(9.35)
where k w is the specific light attenuation constant for
the vessel wall material (cm
1
/, I
0
o is the light intensity incident to the outer vessel wall surface, and l w is
the thickness of the vessel wall. Typical values of k w
for a transparent Plexiglass sheet and translucent silicon rubber tubing are 0:05 and 0:5 cm
1 , respectively.
Values for k w are best determined experimentally. The
mean light intensity in terms of I
0
o can be estimated by
simply inserting (9.35) into (9.33).
Effects of Mean Light Intensity on Growth Rate
and Biomass Production
Light attenuation reduces the mean light intensity (I m )
experienced by the phototrophic liquid suspension culture within a photobioreactor vessel. If the culture is
uniformly mixed, the mean light intensity sets the specific growth rate. Therefore, in (9.11) the light intensity
(I) is replaced with I m , so that
D
C N
K N C C N
I m .C x /
I k C I m .C x /
max :
(9.36)
Recall from (9.33) that I m is a function of the incident light intensity I o , the path length for light transfer
into the photobioreactor, and the cell density C x . During phototrophic cultivation, the incident light intensity
and path length for light transfer are fixed. However,
as cell density C x increases, I m decreases and hence
the specific growth rate decreases. The process of
light attenuation therefore reduces biomass production.
In particular, if the culture is not CO 2 -limited, then
biomass production for the well-mixed batch bioreactor described by (9.17) now becomes
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 ;
(9.37a)
with
dC N
dt
D D
Y X=N
C x :
(9.37b)
Equations (9.37a) and (9.37b) are subject to the initial conditions C x D C x;i , C N D C N;i at t D 0.
280 Part B Tools and Methods in Marine Biotechnology
r = R
r + dr
r
Cylindrical vessel
cross-section
I 0
Symmetric
illumination source
Fig. 9.19 Symmetrical, external light delivery to a cylindrical photobioreactor vessel
tubing diameter as path length for light transfer, then
(9.33) can still be used to provide the most conservative
approximation for the mean light intensity I m .
Often the vessel wall material itself is not perfectly transparent and attenuates light, as illustrated
in Fig. 9.16. Therefore, the transfer of light from the
outer surface of the vessel to the culture encounters two
0
20
40
60
80
100
120
0
5
10
15
0.02
0.04
0.06
0.08
0.10
0.12
0.14
20
Total light path length L (cm)
Specific growth rate
μ (h
–1
)
Mean light intensity I m (µmol photons m
–2 s
–1 )
I m
μ
Fig. 9.20 Calculated effect of total light path length (L) on
mean light intensity (I m ) and specific growth rate () for
one-dimensional light transfer. Model input parameters: I o D
100 mol photons m
2 s
1 , k c D 0:1 L .g cell cm/
1 , C x D
2 g cell L
1 , ˛ D 1
resistances in series: the vessel wall and the liquid suspension culture itself. From the Beer–Lambert law, the
light intensity incident to the outer vessel surface is related to the light intensity incident to the culture on the
inner vessel surface by
I
0
o D I o e
kwlw
;
(9.35)
where k w is the specific light attenuation constant for
the vessel wall material (cm
1
/, I
0
o is the light intensity incident to the outer vessel wall surface, and l w is
the thickness of the vessel wall. Typical values of k w
for a transparent Plexiglass sheet and translucent silicon rubber tubing are 0:05 and 0:5 cm
1 , respectively.
Values for k w are best determined experimentally. The
mean light intensity in terms of I
0
o can be estimated by
simply inserting (9.35) into (9.33).
Effects of Mean Light Intensity on Growth Rate
and Biomass Production
Light attenuation reduces the mean light intensity (I m )
experienced by the phototrophic liquid suspension culture within a photobioreactor vessel. If the culture is
uniformly mixed, the mean light intensity sets the specific growth rate. Therefore, in (9.11) the light intensity
(I) is replaced with I m , so that
D
C N
K N C C N
I m .C x /
I k C I m .C x /
max :
(9.36)
Recall from (9.33) that I m is a function of the incident light intensity I o , the path length for light transfer
into the photobioreactor, and the cell density C x . During phototrophic cultivation, the incident light intensity
and path length for light transfer are fixed. However,
as cell density C x increases, I m decreases and hence
the specific growth rate decreases. The process of
light attenuation therefore reduces biomass production.
In particular, if the culture is not CO 2 -limited, then
biomass production for the well-mixed batch bioreactor described by (9.17) now becomes
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 ;
(9.37a)
with
dC N
dt
D D
Y X=N
C x :
(9.37b)
Equations (9.37a) and (9.37b) are subject to the initial conditions C x D C x;i , C N D C N;i at t D 0.