CO₂ air-capture costs

David Kramer’s “A windfall for US carbon capture and storage ” (January 2022, page 22) mentions the $3.5 billion appropriated by the US government for direct air capture. I would like to point out that the energy costs of capturing carbon dioxide already diluted in the atmosphere would be prohibitive.

Methods tried so far employ a reusable absorber cycled between absorption and emission, with an input of energy required at one or both parts of the cycle. The unavoidable energy requirement for a cycle can be calculated from the entropy change ΔS of the CO₂ going from its present atmospheric concentration of about 400 ppm to a concentration needed for disposal or use, say 1 atmosphere.

Per unit mass and at room temperature T, that energy would be TΔS = RT/M ln(10⁶/400) = 4.4 × 10⁵ kJ/ton (t), where R is the molar gas constant and M the molar mass. If you assume the energy is applied electrically, and at a present US price of 12¢/kWh, the energy cost is $15/t. So far there are no reports of technologies that are anywhere close to that energy requirement or cost.

Earth’s atmosphere weighs 5.2 × 10¹⁵ t. The unavoidable entropy cost to remove just 1 ppm (by volume) of CO₂, or 7.9 × 10⁹ t, would be $120 billion. After recovery at 1 atmosphere, there are the added costs of disposal, which is complicated by the residual atmospheric gases in the recovered CO₂.

The cost could be reduced if the energy is somehow supplied directly rather than after conversion to electricity. But no energy source is free because its energy could otherwise be converted to electricity and sold.

The costs of mineralization are more difficult to estimate. The absorber is used only once, not cycled. Costs might include those for accessing, processing by crushing and dispersing, and gathering and disposing of the absorber.