Actually it's not CaCO2 it's CaCO3, otherwise known as limestone.

And they're not burning it they're roasting it by putting in lots of energy to naturally drive off the CO2 content as a gas due to the high heat. Leaving you with CaO which is the chemical representation for lime.

The fly in the ointment is that the limestone is already the ideally captured form of carbon itself.

Limestone is still being heavily removed from the ground too and tonnes are being roasted into the lime that the concrete industry needs. Rather than just leaving it in the ground where it has been safely sequestered by nature for zillions of years.

More buildings could just be built directly from blocks of the limestone itself, maybe that would have significant environmental impact.

Yes, that nice white lime sure is an ideal active alkaline CO2 absorber because it naturally wants to turn back into limestone again by itself, like other alkalies do not. So the lime eventually does absorb CO2 back from the atmosphere as the cement hardens.

But each tonne of lime can only capture the same amount of carbon that was given off from the original limestone to begin with, and that was at great expense of energy.

If this could be clean energy the best you would do would be carbon neutral, unless the CO2 released from roasting the limestone could be captured at the source.

But what are you going to absorb it with if not more lime?

Plus you've got to first get it out of the ground and then back in to the ground afterward.

Thinking about things going in & out of the ground, elsewhere in the messages there is a good estimate of the density that pure compressed CO2 would have if pumped directly into supercritical storage underground. And that's about the same density as the original crude oil had so that's basically both a barrel-for-barrel and tonne-for-tonne equivalence. That means a barrel of (liquified, pressurized) CO2 needs to be put back underground for every barrel of oil removed. And a tonne of oil is basically 3 barrels but a tonne of CO2 is contained in 1600 tonnes of atmospheric air so you need to process 44000000 cubic feet of air to get one tonne of CO2 since gases are light when they're not under pressure and/or chilled/cryogenic storage. That's enough air to fill 150 Goodyear blimps. Just to get enough liquid CO2 to fill a pressure container about the size of 3 oil barrels, if your air-removal process is 100 percent efficient. Then you can break even.

If you want to truly cut back on atmospheric CO2 levels you're going to have to remove more than one barrel of CO2 for every barrel of oil produced and gas leaked worldwide.

Interestingly, many oil fields which are considered "expired" (because their production has declined below positive economic returns) still contain sizable percentages of the original oil beyond that which can be readily recovered under natural pressure or continued pumping. Still right there in the pore space of the oil-bearing rock.

These formations are also the ones that can be expected to have a barrel of storage space for every barrel of oil that had been removed, so it might be a good place to put equal quantities of CO2.

Oil companies have already injected CO2 into a central well of a once-productive field, and it uses up a lot of CO2 but the outer wells then start producing better for a while so additional salable oil is a (by)product of the procedure. But since the napkin math says it's a barrel-for-barrel equivalence they have to be able to get the CO2 way cheaper per barrel than they can sell the oil for. Or even an oil company can't afford it and they're getting more oil in the process. I'm not so sure how anybody else would fare.

As far as pressurized CO2 escaping from oil formations and oil field equipment, I don't think it would be any easier to eliminate all leaks forever than for methane, where progress is being made but we are far from there already.