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Growing algae photosynthetically in open ponds (lowest cost, lowest control)
This is the line of experimentation started by DOE. Open ponds are cheap, but must contend with invasive species. Also, water demands are high due to evaporation.
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Growing algae photosynthetically in closed bioreactors (higher cost, more control)
Algae "bioreactors" are enclosed containers exposed to sunlight. Closed bioreactors prevent contamination by unwanted species and reduce water use. But they cost more than open ponds because of the need for "photomodulation" - exposing the algae to just the right amount of light.
Bioreactor systems have another important advantage: they can capture and reuse waste CO2 from coal plants and other industrial processes. Skeptics note that when the algae are burned, they release the captured carbon into the atmosphere. But because algal fuel displaces petroleum fuel, net carbon emissions are significantly reduced.
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Growing algae in the dark through fermentation (highest cost, highest control)
This is the approach of Solazyme in San Franciso. When algae are grown photosynthetically, they manufacture their own sugar from water, air, and light. Solazyme turns off photosynthesis by growing them in complete darkness and feeding them sugar.
Feeding sugar makes the algae produce more oil. Plus the energy-dense food allows the algae to be grown in much higher concentrations, reducing costs and easing harvest. On the downside, it puts the process back in competition with food crops, undercutting one of algal fuel's unique strengths.