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Methane >> carbon dioxide as a polyethylene/linear polymers feed stock. Double bonded oxygens are hella higher affinity than four loose hydrogens. Also as pointed out, even in a concentrated combustion effluent stack CO2 is low concentration at atmospheric pressure.

I don’t know about methane as an aromatic/hybridized ring building block. Anything is possible with chemical synthesis but is it energy feasible.

There’s always plant hydrocarbon feed stocks but I think using arable land to make plastics is dumb and also carbon intensive. (I do wear cotton clothing tho because you need to make trade offs).

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Siemens has a collaboration with Porsche are piloting already eFuel production. Cost is super high (think like $10/liter). But thermodynamically feasible.

https://www.siemens-energy.com/global/en/home/press-releases...

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That sounds like a hack from late-game Factorio: pollute enough that you can just pull iron filings right out of the air. Everyone wins! Except the meatbags who need to breathe the air …
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Assuming the damn rain does not throw your iron down to the ground before it reaches its destination. But then again you have rivers as a plan B.
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The problem with carbon capture from air is the low carbon concentration. Try to do the math for how much air you need to process to get even one barrel of oil worth of hydrocarbons from a DAC process.
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The answer to this problem as it's currently being pursued is renewable carbon feedstocks. Growing things like canola on marginal land, harvesting it and turning it into biofuels and LCLFs (low carbon liquid fuels) using renewable solar/wind energy.

It's not a solved problem, though. Truly renewable carbon feedstocks have to source their carbon from the air, not the soil, which has to be continually measured. Land selection for carbon feedstock projects has to ensure it doesn't induce land-use change in other locations due to displacing other things like food production, etc. Otherwise the emissions and environmental harm from those downstream effects have to be included in the carbon positive/negative calculations for the project.

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Remarkable amounts of carbon are available in waste streams, even if you exclude from the count plastics and other petrochemicals. Paper, cardboard, wood, natural fibers, carbon in sewage and waste food, and especially farm waste (parts of plants not otherwise consumed). Some of the latter is needed for soil conditioning, but most of that is from decay of roots, not stuff left at the surface.

All this can be extended by addition of hydrogen. Naively, if you process a carbohydrate into hydrocarbons, about half the carbon is lost as CO2. Adding hydrogen allows the oxygen to be carried off as water rather than CO2 (or, the CO2 to be converted to hydrocarbons and water in a second step.) Hydrogen currently comes from natural gas but that will have to change anyway, with the hydrogen being produced by (for example) electrolysis of water.

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