The theoretical minimum energy requirement to keep atmospheric CO₂ concentrations below 450 ppm by 2100 under the "carry on as usual" RCP 8.5 scenario is 1479 EJ, equivalent to more than 98x the total electrical energy supplied in the United States in 2019. When efficiency losses are taken into account, this energy requirement balloons to approximately 195x - 1258x the total electrical energy supplied in the United States in 2019.

Summary

To limit atmospheric CO₂ to 450 ppm by 2100, massive carbon removal would require unprecedented energy investments. Under the worst-case RCP 8.5 scenario (900 ppm CO₂), even theoretical minimum energy needs equal 1479 EJ - 98 times the US's 2019 electricity production. Real-world efficiencies dramatically increase requirements: at 7.8% efficiency (current DAC technology), RCP 8.5 would need 1258x US annual electricity output. Less extreme scenarios still demand staggering investments: RCP 4.5 requires 24x-309x US electricity, while RCP 2.6 needs 36x-467x. These calculations assume constant 2019 energy levels and perfect CO₂ capture, highlighting DAC's impracticality without massive emission reductions. The analysis reveals thermodynamic limits constrain carbon removal as a standalone solution, especially under high-emission pathways.

Previously, we calculated that the theoretical minimum energy required to capture one kg of CO₂ is between 397.55 kJ and 440.75 kJ, depending on the concentration of CO₂ in the atmosphere. But how do these numbers translate to the real-world requirements for carbon dioxide removal and, more specifically, Direct Air Capture (DAC)?

Carbon dioxide to be removed from the atmosphere to keep the concentration of CO₂ at 450 ppm by 2100 under the Representative Concentration Pathways (RCPs)

For this, we can utilize the International Panel on Climate Change (IPCC) Representative Concentration Pathways (RCPs). The Representative Concentration Pathways (RCPs) are a set of scenarios developed by the IPCC that describe future global emission pathways. The RCPs are critical in understanding future climate scenarios as they don't simply describe a final state such as "net zero" by 2100, but instead, they describe possible trajectories of emissions and concentrations of CO₂ in the atmosphere.

To recap, three of the four main RCPs are:

• RCP 2.6: This is the pathway that is consistent with the goal of limiting global warming to between 0.9°C and 2.4°C by the end of the century with a CO₂ concentration of 400 ppm in 2100. RCP 2.6 is considered an extremely ambitious scenario (and at this point wishful thinking) given the recent emission trends and stalled progress on mitigation efforts ^{1 2 3}.

• RCP 4.5: This pathway is consistent with the goal of limiting global warming to between 1.7°C and 3.3°C above preindustrial levels by the end of the century with a CO₂ concentration of 525 ppm in 2100 ^{1 2 3}.

• RCP 8.5: This pathway is consistent with the goal of limiting global warming to between 3.2°C and 5.7°C above preindustrial levels by the end of the century with a CO₂ concentration of above 900 ppm in 2100 ^{1 2 3}.

Previously, we also calculated the amount of carbon dioxide that would need to be removed from the atmosphere to meet the RCP 2.6 pathway, as well as the amount of carbon dioxide that would need to be removed in the RCP 4.5 and RCP 8.5 pathways to achieve our stated goal of "limiting the atmospheric concentration of CO₂ to 450 ppm by 2100" shown in table 1 below.

Table 1: Atmospheric CO₂ removal required to achieve 450 ppm or less for each RCP scenario

Scenario	Projected 2100 CO₂ concentrations (ppm)	Estimated average global temperature Rise Range (°C)	CO₂ Removal required (Gt)
RCP 2.6	400	0.9 – 2.4	1300
RCP 4.5	525	1.7 – 3.3	866.4
RCP 8.5	900	3.2 – 5.7	3522.6

Minimum energy requirements

Using the idealized calculations for Gibbs free energy, we can calculate the minimum energy requirements for each of the RCPs to meet our stated goal of 450 ppm by 2100.

Assuming that:

• The capture process will be operating at an unrealistic 100% efficiency.
• We will assume that the energy requirement to capture one kg of CO₂ is 420 kJ, which is the average of the calculated high and low values. We are doing this because the efficiency of capture decreases as the atmospheric concentration of CO₂ decreases. So as more CO₂ is removed from the atmosphere, the energy requirement will increase.
• This is a back-of-the-envelope calculation. A more accurate calculation would take into account the efficiency of the capture process as the concentration of CO₂ in the atmosphere changes.
• The final concentration of the captured CO₂ is 100% pure.

$$\begin{align*} \text{Energy}_{RCP \space 2.6} &= 1300 \text{Gt} \times 420 \text{kJ/kg}\\ &= 1300 \times 10^{12} \text{ kg} \times 420 \text{ kJ/kg}\\ &= 5.46 \times 10^{17} \text{ kJ}\\ &= 546 \text{ EJ} \end{align*}$$ $$\begin{align*} \text{Energy}_{RCP \space 4.5} &= 866.4 \text{Gt} \times 420 \text{kJ/kg}\\ &= 866.4 \times 10^{12} \text{ kg} \times 420 \text{ kJ/kg}\\ &= 3.639 \times 10^{17} \text{ kJ}\\ &= 363.9 \text{ EJ} \end{align*}$$ $$\begin{align*} \text{Energy}_{RCP \space 8.5} &= 3522.6 \text{Gt} \times 420 \text{kJ/kg}\\ &= 3522.6 \times 10^{12} \text{ kg} \times 420 \text{ kJ/kg}\\ &= 1.479 \times 10^{18} \text{ kJ}\\ &= 1479 \text{ EJ} \end{align*}$$

How do these numbers translate to current energy production?

In 2019, the International Energy Agency (IEA) estimated that the world's total energy supplied (including energy generation and the use of fossil fuels in industry and transport) was 606 exajoules (EJ) where one EJ is equivalent to $10^{18}$ joules, while the global electricity generation was equal to 26,932 TWh or 96.96 EJ ⁴. For the United States, total energy supplied was equal to 92.64 EJ, while the electricity generation was equal to 4,186 TWh or 15.07 EJ ⁴.

We can therefore summarize for each of the three analyzed RCPs, in order to reach our goal of below 450 ppm by 2100:

• RCP 2.6: 546 EJ of energy required to remove 1300 Gt of CO₂ from the atmosphere. This is equivalent to approximately 90.10% of the world's total energy supply in 2019, more than 5x the world's total electricity generation in 2019 and more than 36x the total electrical energy supplied in the United States in 2019.

• RCP 4.5: 363.9 EJ of energy required to remove 866.4 Gt of CO₂ from the atmosphere. This is equivalent to approximately 60.05% of the world's total energy supply in 2019, more than 3x the world's total electricity generation in 2019 and more than 24x the total electrical energy supplied in the United States in 2019.

• RCP 8.5: 1479 EJ of energy required to remove 3522.6 Gt of CO₂ from the atmosphere. This is equivalent to approximately 244.06% of the world's total energy supply in 2019, more than 15x the world's total electricity generation in 2019 and more than 98x the total electrical energy supplied in the United States in 2019.

This energy would not need to be supplied in a single year, but instead would be spread out over the rest of the century. If we were to assume that the world's electrical energy supply was to remain constant at 2019 levels (in reality, energy supplied increases over time), for the RCP 4.5 scenario which requires the least amount of CO₂ removal, approximately 5% of the global yearly electrical energy supply would need to be diverted to DAC.

Accounting for real-world capture efficiencies

As we have already stated, the following analysis was for calculating the theoretical minimum energy requirements for carbon dioxide removal. However, no real-world process is 100% efficient, especially in thermodynamic processes which are highly susceptible to losses. The efficiency of a gas separation process is highly dependent on the relative concentrations of gas that you are trying to separate, known as the concentration factor ⁵.

In general, the lower the concentration factor, the greater efficiency can be achieved. The concentration factor is the ratio of the gas before separation to after separation. If you were trying to separate CO₂ from a mixture that was 50% CO₂ into pure CO₂, the concentration factor would be 1 divided by 0.5 = 2. If you were trying to separate CO₂ at 450 ppm in air into pure CO₂, the concentration factor would be 1 divided by 0.00045 ≈ 2222.22. Analysis of industrial gas separation processes has shown that even when gas separation processes are at high concentrations (low concentration factors of between 1 and 10) the efficiencies rarely exceed 40% and are usually closer to 10%-30% ⁵.

For the contemporary state-of-the-art liquid sorbent DAC plant that is currently being built in the United States with an estimated capture capacity of 1 Mt of CO₂ per year, the calculated thermodynamic efficiency is just 7.8% ⁶.

Applying these efficiencies to our analysis:

RCP 2.6

• At 50% efficiency, the energy required to remove 1300 Gt of CO₂ from the atmosphere is 1092 EJ, which is equivalent to more than 11x the world's total electricity generation in 2019 and more than 72x the total electrical energy supplied in the United States in 2019.
• At 7.8% efficiency, the energy required to remove 1300 Gt of CO₂ from the atmosphere is 7038 EJ, which is equivalent to more than 72x the world's total electricity generation in 2019 and more than 467x the total electrical energy supplied in the United States in 2019.

RCP 4.5

• At 50% efficiency, the energy required to remove 866.4 Gt of CO₂ from the atmosphere is 728 EJ, which is equivalent to more than 7x the world's total electricity generation in 2019 and more than 48x the total electrical energy supplied in the United States in 2019.
• At 7.8% efficiency, the energy required to remove 866.4 Gt of CO₂ from the atmosphere is 4665 EJ, which is equivalent to more than 48x the world's total electricity generation in 2019 and more than 309x the total electrical energy supplied in the United States in 2019.

RCP 8.5

• At 50% efficiency, the energy required to remove 3522.6 Gt of CO₂ from the atmosphere is 2958 EJ, which is equivalent to more than 30x the world's total electricity generation in 2019 and more than 196x the total electrical energy supplied in the United States in 2019.
• At 7.8% efficiency, the energy required to remove 3522.6 Gt of CO₂ from the atmosphere is 18962 EJ, which is equivalent to more than 195x the world's total electricity generation in 2019 and more than 1258x the total electrical energy supplied in the United States in 2019.

Conclusion

Thermodynamic analysis of the theoretical minimum energy requirements for atmospheric carbon dioxide removal can shed light on the enormous energy requirements of the technology. When including still unrealistic efficiency figures such as 50% and a more realistic efficiency of 7.8%, these numbers are even more staggering. What this analysis does reveal is that carbon dioxide removal and more specifically DAC cannot be a viable climate mitigation strategy without also including heavy cuts to emissions. By looking at the energy requirements of the RCP 8.5 scenario where no significant cuts to emissions are made and fossil fuel utilization increases, more than the total electricity generation of the United States in 2019 would need to be diverted to DAC every year for the remainder of the century to keep the atmospheric concentration of CO₂ at 450 ppm by 2100.

Note: The calculations in this section were inspired by Prof. David Kipping of the Cool Worlds Lab at the Department of Astronomy, Columbia University ⁷.

Sources

Footnotes

1. Intergovernmental Panel on Climate Change (IPCC). (2023). Climate change 2023: Synthesis report. Contribution of Working Groups I, II, and III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (Core Writing Team, H. Lee, & J. Romero, Eds.). IPCC. https://doi.org/10.59327/IPCC/AR6-9789291691647 ↩ ↩² ↩³

2. Dooley, J. J., & Calvin, K. V. (2011). Temporal and spatial deployment of carbon dioxide capture and storage technologies across the representative concentration pathways. Energy Procedia, 4, 5845-5852. https://doi.org/10.1016/j.egypro.2011.02.583 ↩ ↩² ↩³

3. IPCC. (2019). Summary for policymakers. In H.-O. Pörtner, D.C. Roberts, V. Masson-Delmotte, P. Zhai, M. Tignor, E. Poloczanska, K. Mintenbeck, A. Alegría, M. Nicolai, A. Okem, J. Petzold, B. Rama, & N.M. Weyer (Eds.), IPCC special report on the ocean and cryosphere in a changing climate. In press. ↩ ↩² ↩³

4. International Energy Agency. (2021). Key world energy statistics 2021. IEA. https://www.iea.org/reports/key-world-energy-statistics-2021 ↩ ↩²

5. House, K. Z., Baclig, A. C., Ranjan, M., van Nierop, E. A., Wilcox, J., & Herzog, H. J. (2011). Economic and energetic analysis of capturing CO₂ from ambient air. Proceedings of the National Academy of Sciences of the United States of America, 108(51), 20428-20433. https://doi.org/10.1073/pnas.1012253108 ↩ ↩²

6. Long-Innes, R., & Struchtrup, H. (2022). Thermodynamic loss analysis of a liquid-sorbent direct air carbon capture plant. Cell Reports Physical Science, 3(3), Article 100791. https://doi.org/10.1016/j.xcrp.2022.100791 ↩

7. Cool Worlds. (2023). How thermodynamics holds back negative carbon tech [Video]. YouTube. https://youtu.be/EBN9JeX3iDs?si=zgxvSbJIoemJRW9b ↩