Hi kgaur,
I don’t know a lot about this subject but the driving force as I understand it is cost. The companies that are working on algal photobioreactors are trying to produce the most fuel for the least amt of $$. As for fuel, I know of three possibilities from algae—ethanol, biodiesel and hydrogen. Hydrogen is probably the least likely at this time because the other two are already in use. Diesel costs more than ethanol, so I would probably bet on that as the most likely winner in the biofuel market.
You asked which variable would be good to test so I did some googling and came up with a species of algae called Botryococcus braunii that produces high levels of hydrocarbon oils, up to 86% of its dry weight!
http://en.wikipedia.org/wiki/Botryococcus_braunii
If you could get a culture of this alga, you could grow it in liquid cultures exposed to sunlight and bubble air through it at different rates to see how this affects the rate of growth and oil production. There are other variables that affect growth rate--light intensity and duration, nutrients, pH, salinity, dilution of the culture, etc.
There is also some interest in open pond production for resource-poor countries where a bioreactor would be too expensive and apparently this alga can be grown either way. You could compare open culture methods to bioreactor methods and see which gave the fastest growth and highest yield.
There are many other species of algae that can be grown in photobioreactors, and if you are looking to produce a large amount of biomass for ethanol production by fermentation then maybe some other species would be best, but I think this process of producing oil directly in one go makes a lot of sense since the result is a primary feedstock than can be sent to refineries for making gasoline or diesel.
I hope this helps to steer your thinking about what variables you might want to look at in an experiment. This is a really good project so try to come up with a creative idea to make it your own. You may be the one to think of something that hasn't been tried yet and that's when science gets really exciting!
Good luck and keep posting and I will continue to provide suggestions and answer questions.
SciB