The US navy is planning on introducing the ability to generate jet fuel from seawater on its nuclear aircraft carriers in the 2020s. The process works, it just takes a tremendous amount of energy (hence the nuclear carrier part) and it requires a lot of water to create a gallon of jet fuel (20,000 gallons I believe for a singe gallon of jet fuel).

The toughest part, however, is that the process would release methane gas into the air. So it's unclear if it's really greenhouse-gas neutral.

In theory, though, if you could trap the methane and then sequester the hydrocarbons you made, you'd have a way to pull CO2 out of the atmosphere.