Most of the schemes I’ve seen for “carbon sequestration” make no sense whatsoever. The ones that simply store CO2 as such seem unsafe and/or unaffordable, and most of the ones that claim to bind the CO2 chemically would violate the first and/or second law of thermodynamics. However, there is one proposal that might be in the right ballpark, maybe.
Short version: Silicate rock reacts with CO2 to form carbonate rock plus silica.
Masses and mass ratios:
I haven’t looked into it super-closely, but I suspect that Schuiling et al. might be underestimating the cost. Still, though, even if the cost is 2x higher than estimated, it’s still cheap compared to the end of the world.
In particular, they make the point that CO2 capture does not need to be done right at the smokestack. One CO2 molecule looks a lot like another, and the atmosphere is well mixed. So CO2 molecules are fungible. You can capture them wherever it’s most convenient. OTOH it seems to me there might be advantages to capturing as much as possible at the smokestack. The concentration is higher there, which might make the reaction go faster. Remember we are dealing primarily with a kinetics problem. The reaction naturally proceeds in the right direction, just too slowly.
You don’t need to take out all the CO2 overnight. A time scale of a few years is just fine, especially compared to natural processes, which require hundreds or thousands of years to remove CO2 from the atmosphere.
If this is anywhere close to right, it solves important political problems as well as operational problems. Climate deniers rely on saying either there’s no problem, or there’s nothing we can do about it (or both). It dramatically changes the discussion if there is something that can be done at a not-completely-crazy cost.
So we make a rule that says if you want to put one ton of fossil carbon into the air, you have to find enough olivine or wollastonite or whatever to compensate for at least twice that much. Maybe capture one ton at the smokestack and another ton somewhere else, perhaps by grinding it to dust and dispersing it. If this has beneficial side-effects (e.g. fertilizer), then so much the better.
I worry that the deleterious side-effects have not been fully accounted for. Olivine can turn into things like chrysotile, which is another name for asbestos, which you might not want to be dispersing in enormous quantities. You want it to end up as carbonate minerals, not asbestos.
If it works out, this is a nice free-enterprise free-market solution. Note that the definition of “free enterprise” does not mean I am free to dump my sewage into your yard. The same goes for CO2. Right now the cost of dumping CO2 is an externality; we need to make the polluters internalize this cost. If you want to burn fossil carbon, the price ought to reflect the real total cost.
The neutralization requirement would add a noticeable (but not catastrophic) amount to the price of burning fossil carbon. This makes people unhappy, but still it’s better than the end of the world. The new price, based on the newly-internalized costs, has a nifty free-market side effect, namely making renewables more competitive.
This claims to be a "techno-economic" study but IMHO skirts the central economic issue. Coal is currently selling for $35.00 per ton of coal, which produces a little over 3 tons of CO2. If you internalize the cost of carbon sequestration, coal users would have to pay an additional $240.00 to $540.00 per ton of coal. In other words, the cost of non-renewable fuel would go up by an order of magnitude or more. This would cause major disruptions. It would make non-renewable energy uncompetitive against renewables for most applications. Waaaay past the tipping point.
Berner, Lasaga, and Garrels
“The carbonate-silicate geochemical cycle and its effect on atmospheric carbon dioxide over the past 100 million years”
Shows that the general idea has been known for a long time.