Bioprocess Engineering of Phototrophic Marine Organisms 9.4 Limiting Factors in Photobioreactor Design and Operation 283
Part B | 9.4
CO 2
O 2
Gas film
Liquid film
Gas/liquid interface
Bulk liquid phase
1, 2, 3
Liquid film
4, 5
Gas Bubble
Cell
Fig. 9.24 Interphase mass transfer of CO 2 from the aeration gas bubble to the photosynthetic cell, and the concurrent
transfer of O 2 evolved by the cell to the aeration gas bubble. The interphase mass transfer and consumption of CO 2
occurs in five steps: 1) mass transfer of gas-phase CO 2 through gas film inside gas bubble; 2) dissolution of CO 2 at the
gas bubble/liquid interface; 3) mass transfer of dissolved CO 2 through the liquid film surrounding the gas bubble; 4)
mass transfer of dissolved CO 2 through the liquid film surrounding the cell; 5) consumption of CO 2 by the cell
CO 2 Transfer Processes
The transfer of CO 2 from the aeration gas stream to the
photosynthetically active cell occurs in five steps, as illustrated in Fig. 9.24:
1. Flux of CO 2 through the stagnant gas film inside the
gas bubble to the gas/liquid interface (gas film mass
transfer).
2. Equilibrium partitioning of CO 2 between the gas
and liquid at the interface (absorption).
3. Flux of dissolved CO 2 through the stagnant liquid
film surrounding the bubble (liquid film mass transfer).
4. Flux of dissolved CO 2 through the stagnant liquid
film surrounding the cell.
5. Uptake and consumption of CO 2 by the cell for photosynthesis.
Thus the aeration gas serves as the source for CO 2
mass transfer and the photosynthetically active cells
serve as the sink for CO 2 mass transfer.
Four assumptions and conditions on the CO 2 transfer processes described above are invoked to make the
system more tractable for bioprocess engineering calculations. First, the equilibrium absorption of CO 2 from
the gas to the liquid is described by Henry’s law
P A D H C A
;
(9.41)
where P A is the partial pressure of CO 2 in the gas,
C A
is the concentration of CO 2 dissolved in the liquid in equilibrium with the CO 2 partial pressure in
the gas, and H is the Henry’s law constant in units of
pressure/concentration. Henry’s law is valid for dilute
solutions where the gas is sparingly soluble in the liquid. Such is the case for CO 2 dissolved in seawater.
Second, for a sparingly soluble solute, it is commonly
accepted that the solute flux is limited by the transport
of the dissolved solute across the stagnant liquid film
surrounding the bubble, i. e., the interphase mass transfer process is liquid phase controlled. Third, the partial
pressure of CO 2 remains relatively constant inside the
bubble. Fourth, the dissolved CO 2 consumption rate
is assumed to follow zero-order kinetics with respect
to dissolved CO 2 concentration, and so the volumetric
consumption rate of CO 2 is given by
Q A D
C x
Y X=CO2
:
(9.42)
Photosynthetic O 2 evolution and transfer follows the
same processes as CO 2 transfer and consumption, only
in reverse order, as illustrated in Fig. 9.24. The photosynthetically active cell is the source for O 2 , whereas
the aeration gas is the sink for O 2 mass transfer. If air is
used as the aeration gas, then typically the dissolved O 2
concentration is near its saturation value for the partial
pressure of O 2 in air.
Material Balances for CO 2 Delivery
and Consumption
Carbon dioxide limitation during growth of phototrophic cell suspension cultures in a given photobiore-
Part B | 9.4
CO 2
O 2
Gas film
Liquid film
Gas/liquid interface
Bulk liquid phase
1, 2, 3
Liquid film
4, 5
Gas Bubble
Cell
Fig. 9.24 Interphase mass transfer of CO 2 from the aeration gas bubble to the photosynthetic cell, and the concurrent
transfer of O 2 evolved by the cell to the aeration gas bubble. The interphase mass transfer and consumption of CO 2
occurs in five steps: 1) mass transfer of gas-phase CO 2 through gas film inside gas bubble; 2) dissolution of CO 2 at the
gas bubble/liquid interface; 3) mass transfer of dissolved CO 2 through the liquid film surrounding the gas bubble; 4)
mass transfer of dissolved CO 2 through the liquid film surrounding the cell; 5) consumption of CO 2 by the cell
CO 2 Transfer Processes
The transfer of CO 2 from the aeration gas stream to the
photosynthetically active cell occurs in five steps, as illustrated in Fig. 9.24:
1. Flux of CO 2 through the stagnant gas film inside the
gas bubble to the gas/liquid interface (gas film mass
transfer).
2. Equilibrium partitioning of CO 2 between the gas
and liquid at the interface (absorption).
3. Flux of dissolved CO 2 through the stagnant liquid
film surrounding the bubble (liquid film mass transfer).
4. Flux of dissolved CO 2 through the stagnant liquid
film surrounding the cell.
5. Uptake and consumption of CO 2 by the cell for photosynthesis.
Thus the aeration gas serves as the source for CO 2
mass transfer and the photosynthetically active cells
serve as the sink for CO 2 mass transfer.
Four assumptions and conditions on the CO 2 transfer processes described above are invoked to make the
system more tractable for bioprocess engineering calculations. First, the equilibrium absorption of CO 2 from
the gas to the liquid is described by Henry’s law
P A D H C A
;
(9.41)
where P A is the partial pressure of CO 2 in the gas,
C A
is the concentration of CO 2 dissolved in the liquid in equilibrium with the CO 2 partial pressure in
the gas, and H is the Henry’s law constant in units of
pressure/concentration. Henry’s law is valid for dilute
solutions where the gas is sparingly soluble in the liquid. Such is the case for CO 2 dissolved in seawater.
Second, for a sparingly soluble solute, it is commonly
accepted that the solute flux is limited by the transport
of the dissolved solute across the stagnant liquid film
surrounding the bubble, i. e., the interphase mass transfer process is liquid phase controlled. Third, the partial
pressure of CO 2 remains relatively constant inside the
bubble. Fourth, the dissolved CO 2 consumption rate
is assumed to follow zero-order kinetics with respect
to dissolved CO 2 concentration, and so the volumetric
consumption rate of CO 2 is given by
Q A D
C x
Y X=CO2
:
(9.42)
Photosynthetic O 2 evolution and transfer follows the
same processes as CO 2 transfer and consumption, only
in reverse order, as illustrated in Fig. 9.24. The photosynthetically active cell is the source for O 2 , whereas
the aeration gas is the sink for O 2 mass transfer. If air is
used as the aeration gas, then typically the dissolved O 2
concentration is near its saturation value for the partial
pressure of O 2 in air.
Material Balances for CO 2 Delivery
and Consumption
Carbon dioxide limitation during growth of phototrophic cell suspension cultures in a given photobiore-