Energy released by burning one barrel of oil: ~6 GJ. Total number of barrels consumed per year: ~100M
Total energy per year: 6 * 10^17 J
Solar flux on 10^17 J/s or 3 * 10^24
if we had a machine that could convert CO2 -> Carbon in some stable form, we would need to use 10^-7 of the earth's solar flux.
At a very high level such a machine would have two principle "knobs" (1) the efficiency and (2) percent of earth that would need to be covered. The product of the 2 must equal (or be less than) 10^7.
Some example parameters:
Efficiency : 10^-2 Area: 10^-5
This seems wildly plausible for some microbe that we design in the near future that lives in the ocean. This efficiency parameter is lower than current plants.
For those wild eyed technologists that think we can beat nature by a good amount:
Efficiency : 10^-1 Area: 10^-6
That's a couple of hundred square miles. That seems paltry for an "existential threat". Even a couple of orders of magnitude more area seem like they would be fine to sequester for this purpose.
This type of technology seems well within our grasp (or within the next 20 years). I never understand the hysteria over this topic.