> This is basic thermodynamics: if you can burn fossil fuels to get energy/electricity, then putting the CO2 byproduct back into an inert form will cost exactly as much (or more; courtesy of the second law) as it would have to get that energy from a different source in the first place.

> There is no technology - now or ever - that will make "scrubbing" CO2 more economical than simply leaving the oil in the ground, and using renewable energy sources.

This is not true.

There is no thermodynamic reason that the energy of splitting C(n)H(2n+2) + 2O(2) into water and carbon dioxide should have any connection to the energy of moving molecules of CO2 from location A to location B. If you were talking about carbon sequestration by turning it back into a hydrocarbon fuel, then yes. For carbon capture and storage, this line of thinking is wrong. Most of the CO2 sequestration strategies either rely on pressurization/containerization (PV energy is paltry compared to bond energy) or the formation of some carbonic acid ion (ionic bond energies are paltry compared to covalent bond energies).

Now, there is an issue that CO2 is severely diluted by putting it into the atmosphere. The entropic effects of dilution have to be overcome to concentrate CO2. A back-of-the-envelope estimate puts the entropy of mixing CO2 (400 ppm) into air at around 0.62 J/K, so roughly 20.4 kJ/mole CO2 are required, at least, to return it to a pure state (just taking about 3820 moles of air + CO2 and turning it into 3819 moles of air + 1 mole of pure CO2). Burning a mole of methane will produce approximately 810 kJ of energy and 1 mole of CO2 (and 2 moles of water).

So the energy produced by creating CO2 will be approximately 800,000 J/mole, while the energy required to separate CO2 at 400 ppm from the atmosphere will be approximately 20,000 J/mole. You could have a natural gas-fired CO2 concentrator (the Carbon Engineering process requires heat to regenerate their chemical absorbers, so you could get pretty high utilization of the heat of combustion) and it wouldn't be an issue. Again, this is because there's a huge difference in collecting CO2 versus breaking and forming chemical bonds. That implies that 1 mole of methane can be used to sequester less than 39 moles of CO2 from the air. Now, we assumed that we could direct energy 100% to CO2 capture (maybe not a bad assumption for a chemical "free energy" process like LiOH scrubbing), but I think it's safe to say at least that 1 mole of methane could power a plant that sequesters all of the CO2 it produces (1 mole) plus some extra.

Now, I don't work in CO2 capture, but I work with membranes and liquid separation processes, which experience similar issues when you're trying to concentrate a dilute product. I expect that it's not the energy of the separation that's an issue, but rather the capital expense required to scale a CO2 capture plant to the desired CO2 capture rate (I would guess it'd have to be tonnes per day or higher) and maintaining sufficient air flow (about 2500 tonnes of air at average global CO2 concentration are required to produce 1 tonne of CO2, or about 2.1 million m^3 of air -- 1 tonne/day => 24.6 m^3/second/(tonne/day), which is quite a lot) to the capture media that makes the process expensive. There are plenty of chemical processes (maybe fifty trillion different amine scrubber chemistries/processes, hydroxides, zeolites, base-functional polymers and membranes) to work with. For reference, a 1 tonne/day plant would be equivalent to about negative 61 cars per year.

So, it would be far more efficient to capture CO2 at the power plant than free-floating in air (this is what, e.g., chemical looping combustion attempts to achieve). That I'm aware, the two ways you could achieve this are by removing nitrogen on the inlet (N2-O2 separation, or O2 adsorption/desorption onto a selective adsorber), or removing nitrogen on the outlet (N2-CO2 separation).

So while there are practical issues in CO2 capture which might be hard to overcome, the thermodynamics of CO2 capture does at least pass the "sniff test".