- Energy requirement: BIG
According to Wikipedia https://en.wikipedia.org/wiki/Photosynthetic_efficiency , the maximum theoretical photosynthetic efficiency of plants using sunlight is 11%, but due to reflection and transmission is more typically 3-6%. Similar figures are presented for algae in https://www.sciencedirect.com/topics/chemistry/photosynthetic-efficiency#:~:text=Photosynthetic%20efficiency%20of%20microalgae%20is,microalgae%20biomass%20produced%20by%20photosynthesis
The free energy to convert a mole of CO2 to glucose and O2 is 114 kcal (0.13 kWh).
The ISS uses 0.84 kg of oxygen per person per day, or 26 moles. At, say, 4.5% efficiency this would require 77 kWh per day, or 3.3 kW continuously.
If this power is produced by solar cells (at 15% efficiency), it would require about 21 square meters (or 1/10th of a tennis court) while ISS is in direct sunlight. In LEO it would require twice that panel area (plus batteries) due to nocturnal eclipsing.
But LEDs are only 35% efficient at converting electricity to light, so adjust accordingly.
- Algae Growth:
For efficiency, the algae need to be constantly held at the optimum combination of temperature, nutrient concentration and algae density. This means a continuous process of adding nutrients and removing algae, not a batch process. If the bioreactor is producing 26 moles a day of oxygen, it would also be producing about 750 g per day of glucose, protein and oils. This would be about a person’s normal caloric intake… but only if you can choke down grass-clipping smoothies which you know contain your own excrement.
An algae bioreactor initially seems like a great idea for space travel. It is very elegant to turn waste CO2 and astronaut poop into oxygen and food. Unfortunately, the device’s mass and energy requirements make it impractical for voyages in the inner solar system.
Because of resupply difficulties, it will likely be mandatory for interstellar travel.