Independent of Anthropogenic Global Warming assume we want to reduce the CO2 by 100 ppm. That would take the concentration in the atmosphere back to what it was in 1965. According to Wikipedia, “Each part per million by volume of CO2 in the atmosphere represents approximately 2.13 gigatonnes of carbon or 7.82 gigatonnes of CO2.”
For 100 ppm we would need to take 782 gigatonnes out of the air, 78 gigatonnes per year to get it done in ten years. Liquid CO2 is denser than water at 1.1 t/cubic meters. Or around 710 billion cubic meters or 710 cubic km of liquid CO2.
The first question that occurs to me is where do you put it? There have been a couple of events where CO2 boiled out of lakes and asphyxiated people. Lake Nyos disaster - Wikipedia A large CO2 blowout would be very rough on people downhill/downwind.
Despite the blowout problem, how about old oil fields? Oil consumption has run about 4 cubic km/year for the last 40 years. 160 cubic km of storage (less however much the formation has lost pore space) will run out in a couple of years so old oil fields will not be enough for storing CO2 though they could be used for a start.
As above, CO2 is denser than water and at modest depths, the pressure is high enough to keep it a liquid. So it is possible to store vast amounts in the ocean depths. This needs a more detailed analysis, not only of the CO2 dissolving in seawater but lighter non-polar methane dissolving into the CO2 and reducing the density. An ocean burp of a few hundred cubic km of CO2 would be a disaster.
Some people have talked about olivine. A ton of olivine (eventually) takes up a ton of CO2, so it would take mining and grinding up 78 billion tons per year. That’s a hard number to get a grasp on, around 10 tons per person for the whole population of the world every year for a decade. It’s also around 1000 times the mining of gravel in the US.
(I used to build computer interface equipment for a copper company that (at that time) ground about 22 million tons a year of hard rock to beach sand. It was an enormous operation. It would take somewhat over 3000 of these to mine and grind that much olivine.)
Just trying to put engineering numbers on the olivine proposal, not disparaging it. Olivine has a distinct advantage over pumping liquid CO2 into the ground because it will not blow out.
No matter how you slice it, it’s a big problem.