The Improbability of CO2 Removal from the Atmosphere


The Improbability of CO2 Removal from the Atmosphere

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. [1]

Machine #1

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.

Machine #2

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 [2].

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.

Machine #4

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.

Machine #5

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.


[1] Stream Tube CO2 Removal Machine
8 August 2020
Stream Tube CO2 Removal Machine

[2] Ye Cannot Swerve Me: Moby-Dick and Climate Change
15 July 2019


From Caesar’s Last Breath To Ours

After the career: books donated in 2019.


From Caesar’s Last Breath To Ours

Human Life is a sexually transmitted planetary disease, Climate Change is the disinfectant that will cure it. (I’ll explain myself on this later.)

Sam Kean’s concluding 5 paragraphs, on CO2 in the atmosphere, from his book Caesar’s Last Breath (And Other True Tales of History, Science, and the Sextillions of Molecules in the Air Around Us, 2017, Back Bay Books, Little Brown & Co) are interesting, being a series of statements of long-known physical quantities. Since I studied “gas physics” for my graduate studies (in the 1970s), and I developed an interest in climate change at least by 2004 (when I published my first article on climate change), I’ve known the basic facts Kean commented on for quite some time.

In one of my technical books on gas physics (Introduction to Physical Gas Dynamics, by Walter G. Vincenti and Charles H. Kruger, 1965, John Wiley & Sons, NY) an example is given in which the authors illustrate the physical phenomena of gaseous diffusion by showing that the last breath expelled by Julius Caeser will have taken years to fully disperse in a homogenous manner throughout the earth’s atmosphere, and so each person ‘today’ would likely breath in, on average, 5 molecules of that last breath. One amazing feature of the example is that it shows just how many molecules there are in each cubic meter of air (at sea level and ‘normal’ temperature), 2.69×10^25 per meter^3 = 2.69×10^19 per cm^3. Vincenti and Kruger quote the following from James Jeans’ 1940 book An Introduction to the Kinetic Theory of Gases (Cambridge University Press):

“…, a man is known to breath out about 400 c.c. of air at each breath, so that a single breath of air must contain about 10^22 molecules. The whole atmosphere of the earth consists of about 10^44 molecules. Thus one molecule bears the same relation to a breath of air as the latter does to the whole atmosphere of the earth. If we assume that the last breath of, say, Julius Caesar has by now become thoroughly scattered through the atmosphere, then the chances are that each of us inhales one molecule of it with every breath we take. A man’s lungs hold about 2000 c.c. of air, so that the chances are that in the lungs of each of us there are about five molecules from the last breath of Julius Caesar.”

The average spacing between air molecules (at sea level, or “standard temperature and pressure” = STP) is about 3.3×10^-7 centimeters. Since air molecules travel at an average speed of 5×10^4 centimeters/second (at STP), and each such molecule travels an average distance of 6×10^-6 centimeters before colliding into another molecule (obviously whizzing by many others between collisions), the frequency of collisions per molecule is about 10^10 collisions/second, or about 10 collisions per nanosecond.

Each such collision will deflect the colliding molecules into new directions of travel, so it can take them a very long time to actually transport from Point A to Point B separated by global distances. One number bandied about by commentators on climate change (who at least halfway know what they’re talking about) is that it takes “30 years” for local CO2 emissions to begin having a “global effect” as part of global warming. This is basically the timescale of atmospheric homogenization by diffusion of the locally emitted plumes, because of course the individual CO2 molecules of such plumes are quite ready to absorb infrared radiation, and lose it as heat released to other air molecules during collisions (the actual mechanics of global warming) from the instant those CO2 molecules are formed.

A different indicator of atmospheric trace gas homogenization is that a uniform (independent of geographical location) quantity per unit mass of radioactive fallout absorption/take-up by trees was first measured (recently, from tree corings) to have occurred in late 1965. Radioactive fallout was first created in 1945, and the greatest number of atmospheric (and any) nuclear explosions, by far, occurred in 1962. Some geologists have now proposed labeling the beginning of the Anthropocene from late 1965, and calling that year the end of the Holocene (which is/was the current geological epoch, which began with the last glacial period/retreat approximately 11,650 years ago). “Anthropocene” because it is the first epoch in which human activity (anthropo) has a global geophysical impact; such impacts being worldwide nuclear fallout (as in the 1957 book and 1959 movie On The Beach), and anthropogenic CO2/greenhouse gas-driven global warming.

When I first wrote about global warming/climate change, it was out of this perspective as a gas physicist trying to explain the technical details to a lay audience. I soon learned that the audience was not only laying, but snoring. I was trying to prod “people” into action to forestall climate change by “greening” energy technology, since I was also an engineer focused on “energy” and “efficiency.” Plus I was hoping a huge public shift in this direction would open up some nice ($$$) job opportunities for me. But the snoozing audience just wants consumerism at the lowest common denominator level, and the Big Bosses just want bombs (and money for themselves). So no sweet high-tech green-physics job for me, but more firepower for the ‘criminalated’ psychopaths who are our guiding self-worshipping self-imagined Olympians, more gargantuan Black Friday tsunamis of electro-plastic garbage consumerism for the ‘amnesiatariat,’ and as a result giga-tons more carbonation of the atmosphere and acidification of the seas, and less viability for our planet with its growing human population.

Since “the human element” (mental inertia, ego, tribalism) always controls and limits the actualization of any technical enterprise by a group of people — like greening away from fossil fuels — it was quickly obvious to me that though most “solar energy” technologies were ancient and well-understood “we” were not going to give up fossil fuel convenience, wealth-generation and enablement-of-political-power in favor of green energy, and so consequently global warming could only increase. And it has, and will. So I write about climate change “for the art of it” and for personal satisfaction, in particular to put my views “on the record” for my children. But I can only fantasize, without belief, that such writing will have any practical political effect — of course I’d like it to, but I’m a realist. Happily, it’s always nice to hear every now and then from someone who already agrees with my views, that something I’ve written has given them some encouragement.

And that is where the arc of my climate change consciousness — from the science to our society — has brought me to today: human connection. Given that fossil fueled humanity is intransigent, and now the advance of climate change is implacable (“tipping points”), I see the best focus for most people’s limited energies beyond their immediate survival and family needs to be the developing of a consciousness of climate change and political reality, and a commitment to acting toward others at a minimum with benign neutrality and better yet with compassion, honesty and solidarity, so human society is generally improved and economically more leveled, regardless of the geophysical conditions under which it exists at any given time. For a society that is as deeply humane as I’ve suggested (and vastly different than today’s) then if and when we really do enter a rapidly accelerating “end time” our individual exits would be as decently humane as possible because they would be occurring within a societal death-with-dignity of a society of broad solidarity. I suppose this is kind of glum thinking, but maybe that’s an inevitable result of my growing ‘old’ in these times.

All this has been a rather prolix introduction to a video about climate change I thought you might enjoy. The Age Of Stupid is a 90 minute British documentary from 2009 (five years in the making) that remains brilliantly cogent about the “human element” driving the climate change geophysics, and is also refreshingly accurate about the physical details of that geophysics. [1] The Age Of Stupid Revisited is a 15 minute look back on the original documentary, from today. [2] Nothing has changed for the better; for the worse yes. Reflecting on this documentary, on the arc of my climate change consciousness, and on my belief (which I wish future reality would contradict) that there will never be any significant collective action to stop anthropo-exacerbation of climate change, and to also end poverty and to economically level national and world societies, I arrived at the rather tart characterization that: human life is a sexually transmitted planetary disease, and climate change is the disinfectant that will cure it.


[1] The Age of Stupid

[2] The Age of Stupid revisited: what’s changed on climate change?
15 March 2019