# 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.

• Suggestion - remove the "proportion of energy obtained" part of the question, since that is dependent on the fuel source and so is highly variable. You can decide yourself what fuel source(s) you want to do the proportion calculation for. Also, please specify the final form of the CO2. If mineral, what mineral and how do you account for the energy cost of supplying the other reactant (eg CaO). Maybe pure room temp CO2 gas would be a better final state? That can be pumped into underground caverns or reacted with something to mineralize. Jun 15, 2020 at 16:51
• How about we stop cutting trees first? Jun 15, 2020 at 17:02
• I wasn't kidding about trees: To achieve negative emissions, the study recommends using forestry and agricultural practices that increase the carbon-sucking ability of soil and trees, with the goal of pulling 100 gigatons of carbon out of the atmosphere. Jun 15, 2020 at 17:34
• Per a source: "Like any other plant, algae, when grown using sunlight, consume (or absorb) carbon dioxide (CO2) as they grow, releasing oxygen (O2) for the rest of us to breathe. For high productivity, algae require more CO2, which can be supplied by emissions sources such as power plants, ethanol facilities, and other sources." Link: allaboutalgae.com/benefits/…. So, not only remove CO2, make O2 and some algae are even a fuel source. Green technology that is itself green. Jun 15, 2020 at 19:41
• Yes, the energetic cost of the carbon capture can't exceed the energy produced in forming the CO2. And, in general, it doesn't -- the net energy production, even with carbon capture technologies, is positive (they wouldn't make any sense otherwise). So the question becomes: What are the energetic and economic costs, compared to other alternatives? This article, from 2019, provides a comprehensive analysis: nature.com/articles/… Jun 16, 2020 at 0:23

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),
"the thermodynamic minimum energy required to extract CO2 from ambient air is about 250 kWh/(ton $$\ce{CO_2}$$)." 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 $$\ce{C}$$) or 6.55 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 0.99/6.55 x 100 = 15% 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.