Abstract
In the current scenario of energy requirement and the commercialization aspect of algal biofuel and biomass, it is important that means of predicting the production be available. In this paper, the mathematical models are developed for the tubular, bubble column and airlift photobioreactors to predict the productivity of the algal biomass. A modified Monod kinetic equation, incorporating the effect of nutrient and CO2 concentrations, light availability and oxygen built-up, is used to the estimate specific growth rate of the biomass. The light availability inside the reactor is defined in terms of the modified Beer–Lambert’s law as a function of distance from the surface where light is incident and the cell mass concentration. This allows a more accurate measurement of the shading effect. The equations are solved for different reactor types and their estimated productivities are successfully validated against values available in published literature. The model predicts comparatively better productivity for the tubular reactor (1.5 g/L day) than the bubble column and airlift reactor (1.42 and 1.35 g/L day respectively) because tubular reactor has shorter light/dark cycles and better light availability. The analysis is also done to identify the effect of nutrient, carbon dioxide, light and hydrodynamics on the overall productivity.
Nomenclature
Initial concentration of carbon dioxide in the gas phase (g/L)
Concentration of carbon dioxide on the surface of the cell (g/L)
Bulk concentration of carbon dioxide in the gas phase (g/L)
Bulk concentration of carbon dioxide in the liquid phase (g/L)
Initial concentration of nutrient (g/L)
Concentration of the nutrient on the surface of the cell (g/L)
Bulk concentration of nutrients in the liquid phase (g/L)
Concentration of oxygen on the surface of the cell (g/L)
Concentration of oxygen in the gas phase (mg/L)
Concentration of oxygen in the liquid phase (mg/L)
- Dg
Gas-phase axial dispersion (m2/s)
- Dl
Liquid axial dispersion coefficient (m2/s)
- Iavg
Average light available inside the reactor (μmol/m2 s)
- Io
Source light Intensity (μmol/m2 s)
Half saturation constant for carbon dioxide (mol/m3)
- kµI
Half saturation constant for average light Intensity (μmol/m2 s)
- kµN
Half saturation constant for nutrient (g/m3)
Half saturation constant for oxygen (mol/m3)
Dissolved gas to cell surface mass transfer coefficient (carbon dioxide) (s−1)
- kd
Decay rate (day−1)
- kla
Gas–liquid mass transfer coefficient (carbon dioxide) (s−1)
- kloa
Gas–liquid mass transfer coefficient (oxygen) (s−1)
Dissolved gas to cell surface mass transfer coefficient (oxygen) (s−1)
- kNap
Nutrient to cell surface mass transfer coefficient (s−1)
- n
Constant
- r
Any point along the radius of the reactor (m)
- t
Time (min)
- Ug
Gas superficial velocity (m/s)
- Ul
Liquid superficial velocity (m/s)
- X
Concentration of cell mass (g/L)
- Z
Any point along the length of the reactor (m)
- Greek notations
- α
Molar absorptivity (m2/kg)
- μg
The specific growth rate of cell mass (day−1)
- μmax
Maximum growth rate constant (day−1)
Acknowledgements
Nilanjana Banerjee is thankful to University Grant Commission (UGC), India for the Junior Research Fellowship (JRF) received from UGC during the initial phase of the work at Institute of Chemical Technology, Mumbai, India. She is also thankful to Prof. Vilas G. Gaikar for his invaluable support and guidance throughout the completion of the project and beyond.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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