I've been seen exactly this link thrown at me multiple times when discussing synthetic methane, yet it comes with a fatal flaw: It doesn't consider the process to get the CO2 in the first place.
If this is supposed to produce (close to) climate neutral methane it needs to include Direct Air Capture to gather the CO2. It also needs almost perfect avoidance of methane leaks.
Luckily none of that matters very much: Most people agree that synthetic methane isn't very useful to begin with. We can do storage and many industry applications (like steel) simply with hydrogen and avoid the whole CO2 handling and the methane handling, and the few applications that absolutely need methane can be done with biogas.
It all seems like a lot more work than just not extracting the carbon from the ground in the first place.
According to them there's enough potential for geological storage, it's just that ideally one should start now to build it (or repurpose existing natural gas storage).
My answer is: You don't.
Also, though, the cost estimates I ended up with are lower at current energy prices than the ones being offered by companies like Climeworks. Thanks to your feedback, I've restructured the comment to be less intimidating.
electricity in Germany does not cost 30 c/kWh, but roughly 7 c/kWh. the rest is taxes and fees for consumers, and the fact that the linked source makes this transparent indicates that it is deliberately mis-cited for drama.
the article severely understates the efficiency of power to gas processes and claims a maximum efficiency of 35%. however, even the 10 year old megawatt scale demonstrator in Falkenhagen Germany reaches roughly 50% efficiency [1]. modern research projects have achieved 76% efficiency in a shipping container sized prototype, and research is ongoing [2].
[1] https://www.deutschlandfunk.de/erneuerbare-energien-power-to.... [2] http://www.helmeth.eu/images/joomlaplates/documents/Publisha...