The concentration of carbon dioxide gas in today’s atmosphere is 417ppm (parts per million). There are 10^44 gas molecules in the entire atmosphere (78% diatomic nitrogen, 21% diatomic oxygen, 1% everything else), so 1ppm is equivalent to 10^38 gas particles. The 417ppm of CO2 represents a total of 4.17×10^40 molecules.
Some people hope for new technology to remove carbon dioxide gas from Earth’s atmosphere, and then forestall the advance of global warming, or even completely eliminate it. I see this as improbable because I think any such technology would be extremely inefficient at CO2 removal, and be energy intensive as well. The process of gaseous diffusion, as with the release of CO2 into the atmosphere, requires no energy; the gases just mix, spread and dilute, and the entropy of the atmosphere increases. It is an “irreversible process” in the parlance of chemical thermodynamics. This means that the spontaneous un-mixing of gases and their re-concentration into separate volumes has never been observed. Energy must be invested to effect any such desired separation of component gases in a mixture. To explore the possibility of CO2 removal, I have quantified my sense of improbability about it, and describe that here.
Consider a hypothetical CO2 removal machine that is a tube with a filter box in the middle. Air is fanned into the tube, flows into the filter box where some of its CO2 is removed, and then flows out of the tube to rejoin the atmosphere and to slightly reduce the global average concentration of CO2. Energy is supplied to entrain air into the device, and energy is supplied to power the unspecified process that effects the CO2 removal within the filter box. The machine would operate continuously so that over time all the atmosphere would be filtered and de-carbonized.
This would be a very large machine, and most likely be a large array of identical or similar units all over the world that would comprise a composite machine. I will describe this composite as if it were a single tube. 
This machine has a filter cross-sectional area of 10,000 km^2 (10^10 m^2) into which air is fanned through at 1meter/second (2.24mph). Producing that continuous mass flow from still air requires 16GW of power, assuming an efficiency of 40% (from raw power into moving air). The filtration process is assumed to consume 40GW (1% of the power used by the United States) and be 1% effective at CO2 removal. The anthropogenic emission of CO2, at its current rate of 35.5GT/year (giga metric tons per year), is assumed to continue indefinitely (the economy!), with the oceans absorbing 29% of those emissions (10.4GT/y).
At the end of 10 years of continuous operation Machine #1 would have cleared 3.26ppm of CO2 from Earth’s atmosphere, at a cost of 1.77×10^19 Joules of energy (4.92×10^12 kilowatt-hours). Reducing the CO2 concentration to the pre-industrial level of 280ppm would require 507.6 years.
Clearly, improvements are required for Machine #1. So, we assume that 10% efficiency of CO2 removal can be effected by investing 400GW (10% of the power used by the United States) into the filter box. Now, the power consumption is 416GW for Machine #2. After 10 years of continuous operation 31.5ppm of CO2 would be removed from the atmosphere (bringing the concentration down to 386ppm), at an energy cost of 1.31×10^20 Joules (3.64×10^13kWh). Reducing the atmospheric concentration of CO2 back to 280ppm would require 51 years. This might seem promising except for the fact that the assumed 10% efficiency is pure fantasy.
Machine #3, All Earth’s Lands
To regain a sense of reality, consider the actual performance of the entire land surface of the Earth (1.489×10^14 m^2) acting as a CO2 removal filter. This was the case in the clearing of 2500ppm of CO2 from the atmosphere over the course of 200,000 years during the geologically brief episode of explosive global warming 55.5 million years ago, known as the Paleocene-Eocene Thermal Maximum (PETM). I described the PETM and cited numerous public-access scientific references to it in .
Using the same rate of CO2 removal (the e-folding time) as occurred during the PETM, in my formulation of CO2 removal machines, it transpires that the efficiency of removal by the Earth-filter (rock weathering reactions in the long term) is 8.6×10^-8 (0.0000086%). After 10 years, this Earth-machine would clear 0.42ppm of the atmospheric CO2 (bringing the level down from 417ppm to 416.6ppm). That level would be reduced to 280ppm in 3,984 years.
Hope in technology springs eternal for some, so maybe our Machine #2 even with a realistic efficiency can better the clearing-time set by the Earth, natural Machine #3. We accept an efficiency of 1.474×10^-7 (0.00001474%), invest 1.31×10^19 Joules of energy every year at a rate of 416GW of continuous power, and after 10 years find 0ppm of CO2 removal! in fact however long we run this machine there will always be 0ppm of CO2 removal, because the rate of technological removal is equalled by the rate of anthropogenic emissions. Reaching 280ppm is literally infinitely far away.
Maybe by some technological breakthrough the efficiency can be raised by a factor of 100, to 1.474×10^-5 (0.001474%). Then in 100 years Machine #5 would have cleared 0.0478ppm of atmospheric CO2 (reducing the level from 417ppm to 416.95ppm) for an investment of 1.31×10^21 Joules (3.64×10^14kWh). Achieving 280ppm would require 348,577 years. It’s hard to beat the Earth at its own game.
Best Course of Action
It should be obvious by now that our best course of action is to apply our energy resources to the betterment of our many societies and the equalization of living standards worldwide, and to the transformation of our economic activities for minimal CO2 emissions. The current catch-phrase for this transformation is “degrowth.”
During this pandemic year of 2020, the U.S. GDP shrank by 33%, and the CO2 emissions by the United States also shrank by the same proportion. Worldwide CO2 emissions shrank by 17%. Zero emissions require zero GPD, as we now know it.
Global warming will advance and its consequences will add great stresses to many human, animal and plant populations. This geophysical process could be experienced as “the collapse of civilization,” or it could be taken as a collective challenge to advance human civilization by bonds of solidarity, and the restoration of its reverence for the natural world. If we put our energy into fashioning that imperfect utopia, we would live through global warming with a justifiable sense of pride, and even have fun.
 Stream Tube CO2 Removal Machine
8 August 2020
 Ye Cannot Swerve Me: Moby-Dick and Climate Change
15 July 2019