5x over the current baseline cost of fuel. The only studies I could find of doing this were using large scale bulk solar and not counting financing costs into the equation.
They found that if avoiding fossil fuel use (natural gas is the cheapest easily available Hydrogen source right now), and cracking water to get it, end to end energy efficiency is between 44-56% (as in electrical efficiency to theoretical available chemical energy in the fuel). Burning said fuel for energy (turbines being one of the most efficient ways) then varies from 40-63% efficiency, rockets can hit up to 70% efficiency (varies immensely by many factors).
So, getting what they need from a fossil fuel is up to 70% efficient. Getting what they need from a Sebatier process? 28-41% efficient (combined). Add in extra capital costs and maintenance of acquiring and running the equipment, about 5x more expensive fossil fuel evens out.
It’s potentially worse than that of course when you factor in potential increases in electrical rates if fossil fuels did get 5x, but there is nothing saying that would for sure happen. They presumably could run it during oversupply from a large solar plant, but that is already factored into those studies. If you’re doing it at scale, that ‘free energy’ won’t be free for long.
