Solar cells, for one thing, are not remotely sustainable. Only continuous processes have any chance of being environmentally benign, and it's widely reported that sunlight is not available for half a day on average.
The requirement for heat is a demonstration of the thermodynamic penalty of the process. There is no reference to the source of concentrated CO2 gas.
Electrolysis wastes energy. If solar electrolysis were going to happen on a meaningful scale, it would have happened decades ago; I personally have been hearing this horseshit for at least 40 years, maybe longer. The amount of hydrogen being produced on this planet using dangerous natural gas is higher than at any other point in history. This concept has been rearing it's head in the literature regularly, year after year, decade after decade. After all this talk, where is it?
It is an abuse of language to call that diagram a diagram to produce "sustainable" methane.
I grant that the word "sustainable" is abused often, which is why we hit 420 ppm of carbon dioxide in the planetary atmosphere this spring, because people look at flow charts like this and think they mean something.
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