Hmm.. How is it different than the "Plastic" from air / "Oil" from air projects?
http://newlight.com/
None of this is practically new, and all of these methods require quite a huge input of energy so none of them are not really either cost or "carbon" effective...
If you're taking in CO2 and producing C (carbon nanofibers) then O2 is your by-product.
With plastics or oil you're going to need a decent source of hydrogen as well as air. A decent source of H2 is going to bump up your energy requirements.
Extracting hydrocarbons from the air seems like a puzzling move considering they are readily available in the ground.
There would be no real point in generating carbon nanofibers from the air if the over-concentration of CO2 in the air wasn't a worry in the first place. For instance, let's say CO2 goes up some more and then plateaus. Global temperatures keep increase but lag behind. Assuming environmental repercussions then projects which use up the CO2 in the atmosphere will be welcomed.
That's a given but and that's an important but it's still a crazy idea...
CO2 has a bond strength of 800 kJ/mol it's a very expensive molecule to break up using electrolysis (double the required energy of to break water).
Most of the other carbon siphoning methods such as making plastic polymers use a chemical method to combine the CO2 into complex carbohydrates and even they aren't any where close to being environmentally viable.
On top of this you need to scale this process up and start filtering air to gather CO2 which is insanely expensive on it's own, for this process to have a neutral carbon footprint on it's own all of the energy has to come from non-carbon sources.
Besides that this process needs to stand up to being competitive against other processes and most importantly it self while being fed carbon or CO2 from none-natural sources, which i have high doubts it can achieve that.
And lastly say you have managed to scale this process up made it commercially viable and environmentally sound (gl on both of those) how much carbon you going to suck in? 1000 tonnes a year? 10,000 tonnes? that's nothing a car emits on average 6-7 tonnes per year this means that a small city(10-15K residents) say 5000 cars would emit 30000 tonnes of CO2 per year do you really think this process or anything like it will have an impact on the environment on any plausible scale?
None of this is practically new, and all of these methods require quite a huge input of energy so none of them are not really either cost or "carbon" effective...