What really matters is how much carbon you can capture per unit electricity used. Presumably you're going to run the carbon-capture plant on renewable electricity. If it can't capture more carbon per watt-hour than your dirtiest non-renewable power plant, you might as well just use the renewable electricity directly and junk the non-renewable plant.
>The extracted CO2 will then be piped from the collector boxes to a nearby processing facility, where it will be mixed with water and diverted to a deep underground well.
And there it will rest. Underground. Forever, presumably. The carbon dioxide captured from the Icelandic air will react with basalt rocks and begin a process of mineralization that takes several years, but it will never function as a heat-trapping atmospheric gas again.
The only use is in removing it from the atmosphere.
That's not entirely true. IIRC, climeworks have also partnered with companies who can use the CO2 directly (in carbonated drinks, or in actual greenhouses).
The majority of the CO2 in drinks will probably just end up the air again, unless some of it binds to calcium in the body or something?
Yeah that's what I suspect. Apparently some of the consumed CO2 binds with calcium, some is burped out, and some presumably comes out the other end, but I couldn't find any numbers on how much ends up where.