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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.

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    $\begingroup$ 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. $\endgroup$ – Andrew Jun 15 at 16:51
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    $\begingroup$ How about we stop cutting trees first? $\endgroup$ – Mathew Mahindaratne Jun 15 at 17:02
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    $\begingroup$ 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. $\endgroup$ – Mathew Mahindaratne Jun 15 at 17:34
  • $\begingroup$ 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. $\endgroup$ – AJKOER Jun 15 at 19:41
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    $\begingroup$ 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/… $\endgroup$ – theorist Jun 16 at 0:23
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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 $\ce{CO_2}$).

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

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  • $\begingroup$ Hi I'm a bit confused about that report. It says "Removing and concentrating CO2 from air (390 ppm) to a pure stream (> 90%) implies a greater energy input and treated gas volume than CO2capture from concentrated point sources. For example, the thermodynamic minimum energy required to extract CO2 from ambient air is about 250 kWh/tonCO2 [...] A thermal energy consumption around 2000 kWh/tonCO2 is considered". This only applies to purifying CO2 - how would storing as a mineral change the figure of 0.99MJ/Kg? Also, why do they jump from 250kWh/Ton to considering 2000kWh/Ton? Thx. $\endgroup$ – Alex Zeffertt Jun 17 at 13:43
  • $\begingroup$ From ipcc.ch/site/assets/uploads/2018/03/srccs_chapter7-1.pdf: "The best case studied so far is the wet carbonation of the natural silicate olivine, which costs between 50 and 100 US$/tCO2 stored and translates into a 30-50% energy penalty on the original power plant. When accounting for the 10-40% energy penalty in the capture plant as well, a full CCS system with mineral carbonation would need 60-180% more energy than a power plant with equivalent output without CCS". NB this isn't a theoretical minimum, and its CCS not CDR. $\endgroup$ – Alex Zeffertt Jun 17 at 14:19
  • $\begingroup$ I've accepted the answer, but now realise that my question was wrong. "Extracting" CO2 can mean just generating a pure gas, which is not particularly useful. It seems this can be done relatively cheaply (4% of original energy extracted from the fuel) but the full cost of converting it to a form that can be buried is (as the IPCC point out) vastly more expensive. $\endgroup$ – Alex Zeffertt Jun 18 at 9:38

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