CO2 Sequestration through Deep Saline Injection and ...

Scale-Up
Knowing how growth rates and energetic parameters are affected by scale up and developing a
basis of comparison between reactor types is important when developing an industrial process.
For a PBR, there are two important parameters in comparison between reactors and in scaleup:
the light energy supplied per unit volume (Io/V), and the light distribution coefficient (Kiv) [30].
It is obvious that the greater the light supplied per unit volume, the higher the rate will be. It
should also be obvious that for constant illumination area, cellular concentration, and volume,
that the growth rate will be linear below the saturation light intensity and will fall away from
linear in proportion to Es in Eq. (1) above the saturation intensity. However, it is also important
how the light is distributed within the reactor. This is something that varies with reactor type.
The light distribution coefficient is a measure of how the light is distributed and is defined as the
cell concentration at which 50% of the PBR volume received enough light to have positive
cellular yield [29]. The light intensity at which no net growth occurs can be found from Eq. (6)
by setting Y equal to zero. The volume that is above that light intensity can be found using Eqs
(2) and (3). The percentage can then be calculated from that volume. The concentration will
have to be varied until the fraction is 0.5, this concentration is taken as Kiv. Figure 4 shows this
concept for two different types of reactors.
Figure 4
Light Distribution Coefficient, Conceptual Example [30]
Because Kiv is higher for the lower reactor type in Figure 4 even though the total light
illumination is the same, the rate is higher because the sustained cellular concentration is higher.
It was shown that the growth rate is linear with respect to both Io/V and Kiv [30]. Thus a single
coefficient, the light supply coefficient (Io/V*Kiv), is a measure that can be used for comparison
between reactor types and for scale up [30]. That is to say, if data is collected in one reactor
type in the lab, it can be used to size and design a full scale reactor of any other type or size as
long as the light supply coefficient is the same between them. This is shown in Figure 5. The
linear portion of the growth rate vs light supply coefficient is linear because it falls below the
saturation light intensity. Equation (1) will have to be incorporated into the growth rate above
the saturation intensity. It is important to note that at high light intensities, Et becomes constant
with respect to light intensity at approximately 0.03 rather than 0.2 at low light intensities. It is
because of this that two linear or nearly linear regions exist in Figure 5. A low light supply
coefficient corresponds to low light intensity and vice versa. It would be expected that the rate
would be linear with respect to light supply coefficient until the point of light saturation and that
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