This is a great article in so many ways. You cannot imagine how many social gatherings I go to with my wife, and no one wants to discuss the thermodynamics of DAC with me! ;)
But this article has a weakness. This statement needs to be reconsidered. "Because Gibbs free energy is a state function, it doesn’t matter exactly how you get from mixed to unmixed."
You have analyzed DAC as being one endpoint and one strategy and attribute the results to all endpoints and strategies. For this article, the endpoint is compressed, pure CO2 sequestered underground and under great pressure. The energy required to accomplish this is high because the choices are poor.
Now, I understand that this is the leading DAC solution being pursued by the US DOE. The energy required is actually higher as your analysis has not included losses attributed to transportation. That captured and compressed CO2 is going into a pipeline and transported to somewhere (Wyoming?) to be sequestered. There will be energy considerations associated with the friction of transport.
The point that needs to be considered is that different endpoints can have different energy requirements. And different strategies for an endpoint can influence the necessary energy as well. For an understanding of how strategy influences energy considerations, review Lackner's analysis of Sherwood's rule, Passive Direct Air Capture and his support for mechanical trees.
The major problem with traditional DAC is that it is a process that concentrates very dilute CO2 into a pure gas stream, compresses and transports that stream and then stores all that CO2 and all that energy in a geological formation. This process requires a great deal of energy because it is designed by chemical engineers who optimize processes for mass transport and deal with the energy consequences later.
DAC needs to be defined as any process that removes CO2 from the air and renders that CO2 inert to the atmosphere. This broader definition of DAC will provide a greater variety of solutions to be considered.
All around us, living organisms capture CO2 directly from the air while using much less energy. They don't ever create a pure concentration of CO2. And they never compress that captured CO2. Why? Too much damn energy.
I am not a nature-based CO2 kinda guy. I am firmly in the engineered CO2 capture/sequester camp. I see nature providing us with insights as to how to better design engineered CO2 capture and engineered CO2 sequestration solutions.
And the key to all this is to optimize for energy rather than mass transport. That is a whole 'nuther discussion.
Hi Andrew -- I share your skepticism about direct air capture. In 2019 I spent a summer writing a commissioned report reviewing the literature on the many social and political challenges in developing, deploying, and scaling direct air capture. The link below is to a column I wrote for Issues in Science and Technology summarizing my analysis and conclusions. Among the key takeaways related to your analysis is the immense land footprint / land use required to scale direct air capture considering that each plant needs its own power source either in the form of renewables, nuclear, or in the nearer term natural gas. And that you have to build a massive pipeline system to transport the captured CO2 to geographic locations where it is possible to be buried. https://issues.org/sciences-publics-politics-carbon-removal/
That's an interesting article. I didn't even get into the infrastructure requirements, which will be vast. We know how much infrastructure it takes to release 40 GtCO2 into the atmosphere and I suspect it will take a similar amount to pull it out of the atmosphere, which will be a herculean task. And I haven't really thought about the land requirements.
I enjoyed this post, so I'll confess to nerdery. I'm far from qualified to check your math, but doesn't this imply that all solutions that rely on large-scale atmospheric carbon capture are not just undemonstrated, but wildly implausible?
But what about other approaches? How about capturing carbon from power plant or other industrial exhausts? I assume the CO2 would have much greater concentrations here, so how much lower could energy requirements go?
capturing carbon at the plant does indeed require less energy because of the higher concentration of CO2 in the air, but it's not that much less energy because ∆S goes as the log of the volume ratio. I think it's yet to be determined what role DAC can play in our climate response.
I've wondered, but not enough to do the math, how CCS "doesn't work" while DAC "works" but i suppose there are many assumptions built into the works/doesn't work conclusion and an implied time frame, i.e. CCS has to 'work' now economically while DAC has to have a glide path to a future 'works' state.
Several facilities for capturing CO2 from power plant and other industrial effluent streams have already been built. It may seem paradoxical, but the entropy is actually larger for a 20%CO2/80%Other mixture than for a .042%CO2/99.958%Other mixture, as you can verify for yourself using the formula in the post. However, capture at the source has the huge advantage of requiring handling only ca 1/500 as much gas. Sequestration costs could be similar, depending on the availability of suitable deep geological features near the plant.
This analysis fails to include the free energy costs of manufacturing and maintaining the enormous amount of infrastructure and equipment to do any significant amount of DAC. Once the energy and material costs (real ones, not ideal, thermodynamically reversible one) of mining the metals, manufacturing the plastics, making the concrete, transporting them, supporting the large number of people and robots required to build and maintain a million DAC facilities, etc. are honestly included, as well as the fact the basic processes of isolation, compression, and sequestration of carbon dioxide must be carried out irreversibly, it will become apparent that the free energy cost of DAC will equal or exceed the useable work obtained from burning the fossil fuels in the first place. DAC is simply not thermodynamically feasible.
Isn't part of Zeke's job at Stripe related to funding startup carbon capture companies, i.e. trying to drive the energy requirements closer to the thermodynamic limit?
This is a safe zone for nerds, so welcome fellow traveler. Yes, Zeke's day job is to fund promising carbon dioxide removal schemes. This would include DAC, but also other things like BECCS that would not directly require such massive energy inputs.
Any and all methods of decreasing atmospheric CO2 require energy, it is just a question of sources and pathways. BECCS and other photosynthesis based methods require sunlight, nutrients and water for carbon fixation so the comparison isn't "lots of energy for DAC, little for BECCS" but "Lots of solar panels for DAC, lots of area and inputs for BECCS." As you nicely put it, thermodynamics exists and can't be ignored.
The polluter should not only pay for the carbon capture but offer proof of capture.
Given that capture is possible now then the polluter pays philosophy should start now.
Facing up to the costs of carbon capture after pollution has caused 2 degs of warming will be far more difficult than facing up to the costs now. It will also be no easier to get rogue countries to engage in carbon capture after 2 degs warming than it is now. Those who operate carbon capture will be paying for the rogues.
This is a great article and should be a required read for everyone who thinks DAC is going to be "the solution". If you do the math it's just not workable.
Does it get easier if the air is liquified first? CO2 is densest, would it just pool at bottom of a tank?
Reason I ask is that you see companies like HydroStor, building CAES systems that rely on compression/liquification to provide energy storage. What if you could catch&release the N2/O2 each day, but sequester the CO2 (hand wave here).
i.e. their whole business is going to be compressing and decompressing gases all day long, in the service of buffering intermittent energy sources. Can you get two birds with one machine ?
Thanks for this - it's an important point which we need to keep making in the face of those who want to delay climate action. Every angle of science we look at says there's no way we can fix climate change without massive reductions in overall emissions. We can't put all our hope in somehow offsetting emissions by extracting CO2 either industrially or by planting trees.
Apologies if these are the wrong units but am I converting ~correctly to kwh if I am getting ~210kwh/t as theoretical thermodynamic minimum? (139kwh for separation + a little under half of that for compression) This assumes passive i.e. no air handling?
I don’t have a chemistry or physics background, but how does this square with the Project Vista olivine DAC method discussed in the link below? Is it that the energy was stored in the olivine by the volcanos creating it?
I think for that to work, there's already enough CO2 in seawater/air, so there's no separation or compression that we have to do. And I'm guessing the weathering reaction either releases heat or increases entropy so Gibbs free energy is negative/it happens spontaneously
That's a good question. Most studies assume that we'll inject it deep underground (which is why you need to compress it). I doubt the volume of the gas will be an impediment. I think the energetic and expense of building the infrastructure will be the main issues.
You are correct. At depths greater than about 800 meters, CO2 is In a supercritical liquid state. BTW, I did the entropy and Gibbs free energy calculations a while back, motivated by a letter to the editor in the February issue of Physics Today, only using non-CO2 constituemts from the 1976 Standard Atmosphere, and got results close to yours. Interestingly, the aspirational goal of the DAC community is $100/ton, which means they will need to be highly efficient. In setting their goals I doubt that they priced in the massive expansion in power production capacity needed to power DAC at gigaton/year scales.
At a minimum, the bright and shiny CDR future depends on relatively inexpensive sustainable energy collection at availability and price points below current fossil fuel costs (to accommodate the end of coal, oil and fossil gas) and inclusive of the need for CDR and MRV, as well as something like doubling the energy per person in total to accommodate increasing the global middle class over the same time. Lots of energy at a very low price point with continuing decreasing effort to build and maintain. Good news, is as the system equilibrates and the need for CDR decreases, the energy sources for CDR can be transitioned into other pursuits.
Something like moderate temp geothermal primarily for district heating, but since that is not needed (most) of the time, or not at full rates, use the available heat for solid sorbent DAC.
Then you have a geothermal energy system that doesn’t need the power conversion hardware, and high utilization.
Maybe can even use the same hole (or a different depth one?) to putnthenCO2 down?
Don't burn coal to remove O2 from the air? Pretty obvious. And if you can use almost zero marginal cost energy from wind or solar or nuclear or geothermal, capture and sequestration should be on the menu for optimizing the CO2 content of the atmosphere.
This is a great article in so many ways. You cannot imagine how many social gatherings I go to with my wife, and no one wants to discuss the thermodynamics of DAC with me! ;)
But this article has a weakness. This statement needs to be reconsidered. "Because Gibbs free energy is a state function, it doesn’t matter exactly how you get from mixed to unmixed."
You have analyzed DAC as being one endpoint and one strategy and attribute the results to all endpoints and strategies. For this article, the endpoint is compressed, pure CO2 sequestered underground and under great pressure. The energy required to accomplish this is high because the choices are poor.
Now, I understand that this is the leading DAC solution being pursued by the US DOE. The energy required is actually higher as your analysis has not included losses attributed to transportation. That captured and compressed CO2 is going into a pipeline and transported to somewhere (Wyoming?) to be sequestered. There will be energy considerations associated with the friction of transport.
The point that needs to be considered is that different endpoints can have different energy requirements. And different strategies for an endpoint can influence the necessary energy as well. For an understanding of how strategy influences energy considerations, review Lackner's analysis of Sherwood's rule, Passive Direct Air Capture and his support for mechanical trees.
The major problem with traditional DAC is that it is a process that concentrates very dilute CO2 into a pure gas stream, compresses and transports that stream and then stores all that CO2 and all that energy in a geological formation. This process requires a great deal of energy because it is designed by chemical engineers who optimize processes for mass transport and deal with the energy consequences later.
DAC needs to be defined as any process that removes CO2 from the air and renders that CO2 inert to the atmosphere. This broader definition of DAC will provide a greater variety of solutions to be considered.
All around us, living organisms capture CO2 directly from the air while using much less energy. They don't ever create a pure concentration of CO2. And they never compress that captured CO2. Why? Too much damn energy.
I am not a nature-based CO2 kinda guy. I am firmly in the engineered CO2 capture/sequester camp. I see nature providing us with insights as to how to better design engineered CO2 capture and engineered CO2 sequestration solutions.
And the key to all this is to optimize for energy rather than mass transport. That is a whole 'nuther discussion.
Hi Andrew -- I share your skepticism about direct air capture. In 2019 I spent a summer writing a commissioned report reviewing the literature on the many social and political challenges in developing, deploying, and scaling direct air capture. The link below is to a column I wrote for Issues in Science and Technology summarizing my analysis and conclusions. Among the key takeaways related to your analysis is the immense land footprint / land use required to scale direct air capture considering that each plant needs its own power source either in the form of renewables, nuclear, or in the nearer term natural gas. And that you have to build a massive pipeline system to transport the captured CO2 to geographic locations where it is possible to be buried. https://issues.org/sciences-publics-politics-carbon-removal/
That's an interesting article. I didn't even get into the infrastructure requirements, which will be vast. We know how much infrastructure it takes to release 40 GtCO2 into the atmosphere and I suspect it will take a similar amount to pull it out of the atmosphere, which will be a herculean task. And I haven't really thought about the land requirements.
I am a nerd.
"Heat is work and work is heat" https://www.youtube.com/watch?v=Mw-brvKO-Z0
(link goes to the Flanders and Swann song, "First and Second law" about . . . the first and second law of thermodynamics)
I enjoyed this post, so I'll confess to nerdery. I'm far from qualified to check your math, but doesn't this imply that all solutions that rely on large-scale atmospheric carbon capture are not just undemonstrated, but wildly implausible?
But what about other approaches? How about capturing carbon from power plant or other industrial exhausts? I assume the CO2 would have much greater concentrations here, so how much lower could energy requirements go?
capturing carbon at the plant does indeed require less energy because of the higher concentration of CO2 in the air, but it's not that much less energy because ∆S goes as the log of the volume ratio. I think it's yet to be determined what role DAC can play in our climate response.
I've wondered, but not enough to do the math, how CCS "doesn't work" while DAC "works" but i suppose there are many assumptions built into the works/doesn't work conclusion and an implied time frame, i.e. CCS has to 'work' now economically while DAC has to have a glide path to a future 'works' state.
Several facilities for capturing CO2 from power plant and other industrial effluent streams have already been built. It may seem paradoxical, but the entropy is actually larger for a 20%CO2/80%Other mixture than for a .042%CO2/99.958%Other mixture, as you can verify for yourself using the formula in the post. However, capture at the source has the huge advantage of requiring handling only ca 1/500 as much gas. Sequestration costs could be similar, depending on the availability of suitable deep geological features near the plant.
This analysis fails to include the free energy costs of manufacturing and maintaining the enormous amount of infrastructure and equipment to do any significant amount of DAC. Once the energy and material costs (real ones, not ideal, thermodynamically reversible one) of mining the metals, manufacturing the plastics, making the concrete, transporting them, supporting the large number of people and robots required to build and maintain a million DAC facilities, etc. are honestly included, as well as the fact the basic processes of isolation, compression, and sequestration of carbon dioxide must be carried out irreversibly, it will become apparent that the free energy cost of DAC will equal or exceed the useable work obtained from burning the fossil fuels in the first place. DAC is simply not thermodynamically feasible.
Nerd. Guilty as charged.
Isn't part of Zeke's job at Stripe related to funding startup carbon capture companies, i.e. trying to drive the energy requirements closer to the thermodynamic limit?
This is a safe zone for nerds, so welcome fellow traveler. Yes, Zeke's day job is to fund promising carbon dioxide removal schemes. This would include DAC, but also other things like BECCS that would not directly require such massive energy inputs.
Any and all methods of decreasing atmospheric CO2 require energy, it is just a question of sources and pathways. BECCS and other photosynthesis based methods require sunlight, nutrients and water for carbon fixation so the comparison isn't "lots of energy for DAC, little for BECCS" but "Lots of solar panels for DAC, lots of area and inputs for BECCS." As you nicely put it, thermodynamics exists and can't be ignored.
The polluter should not only pay for the carbon capture but offer proof of capture.
Given that capture is possible now then the polluter pays philosophy should start now.
Facing up to the costs of carbon capture after pollution has caused 2 degs of warming will be far more difficult than facing up to the costs now. It will also be no easier to get rogue countries to engage in carbon capture after 2 degs warming than it is now. Those who operate carbon capture will be paying for the rogues.
This is a great article and should be a required read for everyone who thinks DAC is going to be "the solution". If you do the math it's just not workable.
There is a way, but you aren't going to like it.
https://richardcrim.substack.com/p/the-crisis-report-40
Does it get easier if the air is liquified first? CO2 is densest, would it just pool at bottom of a tank?
Reason I ask is that you see companies like HydroStor, building CAES systems that rely on compression/liquification to provide energy storage. What if you could catch&release the N2/O2 each day, but sequester the CO2 (hand wave here).
i.e. their whole business is going to be compressing and decompressing gases all day long, in the service of buffering intermittent energy sources. Can you get two birds with one machine ?
Thanks for this - it's an important point which we need to keep making in the face of those who want to delay climate action. Every angle of science we look at says there's no way we can fix climate change without massive reductions in overall emissions. We can't put all our hope in somehow offsetting emissions by extracting CO2 either industrially or by planting trees.
Apologies if these are the wrong units but am I converting ~correctly to kwh if I am getting ~210kwh/t as theoretical thermodynamic minimum? (139kwh for separation + a little under half of that for compression) This assumes passive i.e. no air handling?
Yeah, 210 kWh/t is what I get for the theoretical limit.
Slightly (10%) higher than the Lackner calculation (who [I think] gets 0.45Gj / 125kwh per t for separation)? Is there a layperson-legible explanation for difference of approach? https://www.researchgate.net/publication/257177020_The_thermodynamics_of_direct_air_capture_of_carbon_dioxide
I don’t have a chemistry or physics background, but how does this square with the Project Vista olivine DAC method discussed in the link below? Is it that the energy was stored in the olivine by the volcanos creating it?
https://www.technologyreview.com/2020/06/22/1004218/how-green-sand-could-capture-billions-of-tons-of-carbon-dioxide/
I think for that to work, there's already enough CO2 in seawater/air, so there's no separation or compression that we have to do. And I'm guessing the weathering reaction either releases heat or increases entropy so Gibbs free energy is negative/it happens spontaneously
What’s the lowest possible cost per ton of captured CO2?
Isn't there potentially another problem to solve? What is the volume of all that compressed CO2? Where will it all go?
That's a good question. Most studies assume that we'll inject it deep underground (which is why you need to compress it). I doubt the volume of the gas will be an impediment. I think the energetic and expense of building the infrastructure will be the main issues.
You are correct. At depths greater than about 800 meters, CO2 is In a supercritical liquid state. BTW, I did the entropy and Gibbs free energy calculations a while back, motivated by a letter to the editor in the February issue of Physics Today, only using non-CO2 constituemts from the 1976 Standard Atmosphere, and got results close to yours. Interestingly, the aspirational goal of the DAC community is $100/ton, which means they will need to be highly efficient. In setting their goals I doubt that they priced in the massive expansion in power production capacity needed to power DAC at gigaton/year scales.
At a minimum, the bright and shiny CDR future depends on relatively inexpensive sustainable energy collection at availability and price points below current fossil fuel costs (to accommodate the end of coal, oil and fossil gas) and inclusive of the need for CDR and MRV, as well as something like doubling the energy per person in total to accommodate increasing the global middle class over the same time. Lots of energy at a very low price point with continuing decreasing effort to build and maintain. Good news, is as the system equilibrates and the need for CDR decreases, the energy sources for CDR can be transitioned into other pursuits.
Something like moderate temp geothermal primarily for district heating, but since that is not needed (most) of the time, or not at full rates, use the available heat for solid sorbent DAC.
Then you have a geothermal energy system that doesn’t need the power conversion hardware, and high utilization.
Maybe can even use the same hole (or a different depth one?) to putnthenCO2 down?
Don't burn coal to remove O2 from the air? Pretty obvious. And if you can use almost zero marginal cost energy from wind or solar or nuclear or geothermal, capture and sequestration should be on the menu for optimizing the CO2 content of the atmosphere.