What's the minimum amount of energy needed to remove CO2 from the atmosphere? I've been learning about CDR (Carbon Dioxide Removal) techniques to combat climate change. These all seem to involve extracting $\ce{CO2}$ from the atmosphere and converting to a mineral, which is then buried.
I am not a chemist, but something seems wrong about this to me.  Wouldn't the decrease in entropy need to balanced by an increase of entropy somewhere else, e.g., by using up a low entropy source of energy?
Is it possible to come up with a theoretical lower bound for the amount of energy needed to extract $\ce{CO2}$ as a proportion of the energy obtained by burning the fuel that released it in the first place?
If this is more than 100% then CDR schemes cannot possibly be an alternative to decarbonising our energy sector asap.  Even if it's less than 100% the calculation is still useful as it allows us to compare the true cost of fossil fuels with renewables, e.g., a value of 33% would indicate that the cost of fossil fuels is 50% higher than advertised (assuming we remove the $\ce{CO2}$, otherwise it's infinitely more expensive!)
(Edit)
Assume the original CO2 came from coal at 24MJ/Kg.
I’m not going to specify the mineral to which this is converted because I’m looking for a theoretical lower bound across all (scalable) technologies.
The OP is specifically interested in the efficiency of removing $\ce{CO_2}$ from ambient air, rather than from point sources like power plants.  The former is obviously less efficient because the $\ce{CO_2}$ is far less concentrated.
According to p. 50 of the the SAPEA* Evidence Review Report No. 2
(Schlögl, Robert, et al. Novel carbon capture and utilisation technologies: research and climate aspects. 2018.  Available at : https://www.sapea.info/wp-content/uploads/CCU-report-proof3-for-23-May.pdf),
&quot;the thermodynamic minimum energy required to extract CO2 from ambient air is about 250 kWh/(ton $\ce{CO_2}$).&quot;  This equals 0.99 MJ/(kg $\ce{CO_2}$).
The OP asks that we assume the $\ce{CO_2}$ came from a coal-fired plant that produces 24 MJ/(kg $\ce{CO_2}$).
Hence (assuming SAPEA's number, and the OP's, are correct), at at the theoretical maximum thermodynamic efficiency, the energetic cost of capturing $\ce{CO_2}$ from ambient air is 0.99/24 x 100 = 4% of the cost of the energy generated in producing that $\ce{CO_2}$ from a coal-fired plant.
Of course, this is not a lifecycle analysis.  One needs not only to determine the actual thermodynamic efficiency of the process, one also needs to account for the energetic costs of putting the infrastructure in place for the carbon capture, and for maintaining that infrastructure.
*For more information on SAPEA, see:
https://en.wikipedia.org/wiki/All_European_Academies