Tim Kruger at Cquestrate has an idea for sequestering large amounts of CO2: dump quicklime (CaO) in the ocean.
The basic idea is to convert limestone (CaCO3) and CO2 into calcium bicarbonate (Ca(HCO3)2).
CaCO3 + energy -> CaO + CO2 Burn limestone into quicklime
CaO + H2O -> Ca(OH)2 Dissolve quicklime in ocean to make calcium hydroxide
Ca(OH)2 + 2CO2 -> Ca(HCO3)2 Calcium hydroxide absorbs CO2 to make calcium bicarbonate
CaCO3 + H2O + CO2 + 178 kJ/mol -> Ca(HCO3)2
The problem is the amount of energy required. Let's say it comes from coal. Typically, you can get 30 MJ/kg out of coal. To get your 178 kJ above, you'll produce a half mol of CO2 just burning coal, assuming perfect efficiency. That's half your benefit gone right there.
But, it's a high temperature reaction (840 C). That means you have to get the reactants (calcium carbonate, coal and coal oxidizer, e.g. air) up to that temperature, react them, then drop the reaction products back down to normal temperature. To get perfect efficiency, all of the heat from the cooling products has to be transferred to the reactants. There is going to be some loss.
Let's say you lose 25% of the coal heat, and 75% goes to making quicklime. Then, for every 2 kg of coal burned, you will eventually absorb the CO2 that was produced by burning another kg of coal somewhere else.
Bottom line: we'd have to triple the rate at which we burn coal to get carbon neutral with this scheme. That's not practical. It'll get better if we use natural gas or oil, but it won't change the basic calculation that we'd have to multiply our existing consumption of fossil fuels to get carbon neutral.
Now, if someone wants to tell me about a scheme in which limestone is burned in a solar furnace to make cement, I'm all ears. CO2 sequestration from such cement manufacture makes more sense than it does from coal-fired powerplants, because limestone burning (no air) releases pure CO2, whereas coal burning releases CO2 mixed with lots of nitrogen from the air. However, there are lots of other problems.
Sigh. We're not getting out of this mess easily.