How to Save the World

With the recent conclusion of the recent UN Climate Change Conference, it is clear that meaningful commitments to reducing our emissions of greenhouse gases are in short supply.  Indeed, the Earth's atmosphere is victim of a tragedy of the commons.  In a time of economic uncertainty and scarce resources, it seems that nobody has the resources and will to deal with a global problem.  Something needs to be done about global warming now, before the melting of the permafrost and possibly even melting of methane clathrates releases so much carbon into the atmosphere that it doubles or even triples what is already there.  Once that carbon is released, it will be even more difficult to do something about it before the stress on Earth's ecosystems leads to catastrophe.

I will not explain the reality or physics of global warming and ocean acidification here, as that information is widely available and a mere  search away.   Instead, I want to ask this question:  If I were the leader of a wealthy country with the will to unilaterally fix the carbon problem and save the world, how could I do it?  I will explore several climate change "Apollo Program" scenarios and their feasibility.

Carbon Sequestration 

The most direct solution available would be to outright remove the carbon dioxide from the atmosphere.    Ultimately, this is what needs to happen:  even if global warming were brought under control, the twin problem of ocean acidification threatens to collapse the largest ecosystem on the planet and with it an important source of food and livelihood for humans.  First, let's determine how much carbon dioxide humans have actually put into the atmosphere.

Figure 1:  Historic parts per million carbon dioxide in the atmosphere.  Plot by NASA (2012).

A glance at figure 1 indicates that humans have increased the atmospheric carbon dioxide by about 100 parts per million by volume since the industrial revolution.  For the purpose of getting a handle on how much carbon dioxide we have to deal with, I will treat the atmosphere as an ideal gas and assume that each molecule of gas takes up about the same volume in the air regardless of type.  Then, the anthropogenic carbon dioxide (just that coming from fossil fuels) makes up about 1/1000th of the atmosphere by volume.  For an ideal gas, the volume ratio equals the ratio in moles.  In order to determine the mass of carbon dioxide in the atmosphere, then, I need to know the molar mass of the atmosphere.  I can get this from information available at Wikipedia:

Gas	%ppmv	Molar Mass (g/mol)	Contribution (g/mol)
Nitrogen	70.084	24.02	16.83
Oxygen	20.946	32.00	6.702
Argon	0.9340	39.95	0.3731
Carbon Dioxide	0.039445	44.01	0.01735
Neon	0.001818	20.18	0.0003668
Other	negligible
Total			23.92

Table 1: Calculating the Molar Mass of Earth's Atmosphere.
So, if the molar mass of the atmosphere is about 23.92 g/mol, and the atmosphere weighs 5 × 10²¹ grams, then there are 2 × 10²⁰ moles of gas in Earth's atmosphere. If 1 in 1000 of those are carbon dioxide molecules from human burning of fossil fuels, then that amounts to 2 × 10¹⁷ moles of carbon dioxide, or 9 × 10¹⁸ grams, or 9 × 10¹² metric tons of carbon dioxide.  This is just the amount that ended up in the atmosphere--the ocean has soaked up a lot of carbon dioxide that must also be dealt with, but it is more difficult to do a simple calculation to determine how much is actually there because the ocean's layers are not as well-mixed as the atmosphere's.  For now, I propose that a good sequestration scheme must ultimately be able to get rid of 10¹³ metric tons of carbon dioxide.  This carbon dioxide comes directly from the amount of carbon that we have dug out of the ground and burned.

Now let me get a handle on how much 10¹³ metric tons of carbon dioxide is.  The Great Pyramid of Giza weighs about 5.2 million metric tons, so this CO₂ weighs about as much as 2 million great pyramids!  If you froze 10¹³ metric tons of carbon dioxide into dry ice (at 1.5 g/cc), it would take up 7 × 10¹² cubic meters of space, enough to cover all of Antarctica with a layer of dry ice half a meter thick.  If you threw it all into caskets and buried them at sea, the sea level globally would go up about 2 centimeters.  Things look even worse if you propose compressing the gas in something like a giant scuba tank or mineralizing it.  A scuba tank holds gas at a pressure of about 300 bars, which amounts to only 0.5 g/cc of carbon dioxide--which means that gas stored this way would take up three times the volume of dry ice!  Alternatively, if you mineralized the carbon dioxide into calcium carbonate, it stores only 1.2 g/cc of carbon dioxide (the rest is an additional calcium or oxygen).

This enormous volume of carbon presents a storage problem.  Even if you could capture it, where do you store it?  I am uncomfortable with storage methods akin to a giant scuba tank or sarcophagi full of dry ice:  if the tank or reservoir were to break, you would be left with a gigantic Lake Nyos disaster.  I am more amenable to chemical means, such as iron seeding of the oceans, storage in undersea basalt, or chemical scrubbing.  Let's consider the feasibility of each of these options.

Iron fertilization disperses iron, a deficient nutrient, into the oceans in order to cause algae blooms that can then harness the sun's energy to consume carbon dioxide in the ocean and sequester it at the ocean floor.  A recent, successful iron seeding experiment claims to have removed 13,000 atoms of carbon from the atmosphere for each atom of iron seeded into the ocean. Then, in order to sequester our 10¹³ metric tons of carbon dioxide (2 × 10¹⁷ moles) we would need about 2 × 10¹³ moles of iron in the form of 6 × 10¹⁰ metric tons of iron(II) sulfate heptahydrate.

A search on alibaba.com indicates that iron(II) sulfate heptahydrate can be as cheaply as $50 per metric ton, and of course any buyer interested in buying 60 billion metric tons of it would definitely strain world demand and drive the price up.  Certainly, actually delivering the iron sulfate to the ocean and effectively causing the types of algal blooms necessary to sequester the iron would provide a challenging logistical problem.  Further, there is a limit to the productivity of the oceans, so this program would have to happen over a period of decades, carefully adding just the right amount of iron to achieve the optimal algal bloom.  It's also possible that there could be unforeseen environmental consequences from causing so many algal blooms which may have to be mitigated, but on the other hand there are definite environmental consequences for allowing the ocean acidity to double within the next century.  Assuming a price tag of $50 per metric ton, then the cost of saving the world with iron seeding of the oceans would be at least $3 trillion in 2012 dollars for materials alone.

Let's see if I can do better with storage in undersea basalt.  The CarbFix project seeks to inject highly carbonated seawater into basaltic lavas, leading to the mineralization and sequestration of the resultant carbonate minerals.  Currently, their prototype injects only 2200 tons of carbon into the rocks per year, and it uses nearly pure carbon dioxide taken directly from a nearby power plant.  They then mix this carbon dioxide with seawater and pump it 800 meters down into a well for reaction and mineralization. So, in order to remove our 10 trillion metric tons of carbon dioxide from the atmosphere we would have to first capture and concentrate it, then mix it with water, then drill a ready well in an appropriate geological area to capture it, then actually pump our carbonated seawater into the well.  Proponents will argue that this method is meant to capture carbon directly from the power plant, so I will ignore the energetic cost of capturing carbon dioxide from the air.  I will also assume we have a geological amount of time to mix the carbon dioxide with seawater so that the mixing will happen without any energy cost, and assume that we pump the water into the ocean at a low velocity with laminar flow in a frictionless pipe, and assume that the water immediately and without any further energy requirement dispenses 100% of its carbon dioxide load into the target strata.  In this extremely generous scenario, the amount of work per volume W/V necessary to simply pump our water down into the ocean 800 meters is:

W/V = ΔP = 78.9atm - 1atm = 77.9atm = 7.89 MPa

So, just how much carbon dioxide can our fully saturated water carry to the ocean floor?  This is a complex question, and is indeed a function of water pressure, other solutes, and temperature.  While much literature exists on this topic, it is sadly locked away from me in the vaults of scientific publishers.  I will instead use as an estimate 3.5g CO₂ per kilogram of fresh water, obtained from the engineering toolbox, which will also simplify my later calculations.  This means that each liter of water carries with it 3.5g of CO₂ to be deposited in the basalt on the sea floor.  To burn 3.5 grams of carbon at standard conditions originally released 0.080mol × 393.5 kJ/mol = 31kJ of energy, so the carbon in 1 kilogram of saturated water represents about as much energy released elsewhere.  Now finally, I can compare the energy required to pump my water to the sea floor versus the energy the carbon dioxide represents:

1L × 7.89 MPa = 7.89 kJ < 31kJ

So, within some engineering challenges, this could be a reasonable means to lock carbon away on the ocean floor.  Now suppose we have 10¹³ metric tons of carbon dioxide that we want to mix with seawater and pump into the basalt at the sea floor.  This would require us to pump 2.9 × 10¹⁸ L of water to the sea floor at a total energy cost of 2.3 × 10¹⁹ kJ, or 6.4 × 10¹⁵ kilowatt hours.  At $0.075 per kilowatt hour, then, the cost of saving the world by locking carbon dioxide in undersea basalt would be at least $480 trillion in 2012 dollars with the technology in place today.

Remember that the CarbFix project is currently a prototype and as such is meant more as a way to improve the state of the art and push prices down.  I fully support and respect their research, but this back of the envelope calculation indicates that there is a lot left to learn before undersea basalt could be considered a cost-effective carbon sequestration method.

Finally, let me consider the cost of scrubbing the air directly through chemical means.  Wikipedia outlines several possible chemistries.  The quicklime method,

CaO(s) + CO₂(g)  → CaCO₃(s)

seems like a difficult solution since quicklime is produced by heating calcium carbonate to 1000 degrees celsius, releasing a carbon dioxide.  So, the only way to truly scrub carbon dioxide from the atmosphere using this chemistry is to heat calcium carbonate to 1000 degrees, capture the released carbon dioxide, then use the produced calcium oxide to capture an atmospheric carbon dioxide and produce calcium carbonate to continue the process.  

In fact, this 2011 paper estimates that the cost of chemically capturing carbon dioxide from the atmosphere is about $1000/ton, which would mean that to remove 10¹³ metric tons of carbon dioxide from the atmosphere with chemical means would cost $10¹⁶, or 10 quadrillion dollars.

Of these three methods, iron seeding of the oceans appears to be the most plausible method by far for sequestering a huge amount of carbon dioxide on a budget.  

Global Coolants

I posit that the way forward involves both long-term implementation of a carbon-capture scheme, perhaps through iron seeding of the oceans, and a short-term implementation of a scheme to cool the earth which will prevent the release of naturally trapped carbon and methane stored under the oceans and in the permafrost.

The net anthropogenic component of global warming (or radiative forcing) is 1.5 watts per square meter.  To put this in perspective, the intensity of bright sunlight when the sun is directly above you in the sky is about 1,368 watts per square meter.  After accounting for cloud cover, reflective snow and ice, and the entire surface area of the Earth, this figure is reduced to an average of 239 watts per square meter.  So, thanks to the carbon humans have added to the atmosphere, we have increased the amount of energy retained from the Sun by about half a percent.  This is a considerable amount:  since the Earth receives about 180 terawatts of power from the sun at any time, we havc increased the rate of energy retention by an impressive 1 terawatt.

The only short-term solution available is to somehow reflect this sunlight back to space.  In order to achieve that, one might try simply shooting some foil into orbit around Earth to act as tiny mirrors.  In order to reflect 0.6% of the incident light back at Earth, we will need 0.6% × (The surface area of Earth at the edge of the atmosphere) × 2 = 6,400,000 km² of foil.  The additional factor of 2 comes from the fact that our foil will tumble around in orbit, and may not always be facing towards the sun.  If we used aluminum foil just one micron thick, this would still require 17 million metric tons of aluminum foil to be manufactured and launched into space.  Since the price tag on putting things into orbit is about $2000 per kilogram, this quickly becomes horribly prohibitive price-wise:  quintillions of dollars.

A cheaper solution would be to put sulfates into the upper atmosphere, which act as a global coolant by scattering sunlight back into space.  This paper puts the amount of power reflected back into space by sulfates at about 230 watts per gram, and if we need to send back about 1 terawatt (0.6% of 180 terawatts total), then we will need 4,347 metric tons of sulfates to be delivered into the upper atmosphere in order to cool the Earth.  This is a very promising figure, for two reasons.  First, because we don't actually need to put the sulfates into orbit.  We can just use high-altitude balloons to lift the sulfates up, then they will stay there by virtue of being a gas.  Second, because this is a remarkably small amount of gas!  Hydrogen balloons can tow a sulfate balloon into the stratosphere, then be designed to pop at altitude and release their payload. This would be extremely inexpensive yet highly effective at reducing the Earth's temperature in the short term.  

Conclusions

A long-term program of iron seeding of the oceans over a period of 50 years coupled with a short-term program of releasing sulfates into the upper atmosphere could conceivably bring the cost of saving the world down to about $50 billion per year over 50 years.  I assume that over this same 50 years that the rate at which fossil fuels are burned will drop as technology development will render carbon-based energy sources obsolete.  So, carbon-based energy sources will be replaced with nuclear, solar or wind energy.  Ultimately, the world can be saved on a wealthy country's budget without any huge sacrifice to GDP, jobs or lifestyle.  

There are a few things I note about this idea:

• It has to be implemented soon.  We are reaching a turning point where thawing of the permafrost could release an incredible amount of greenhouse gases into the atmosphere--a quantity that would increase the cost of sequestering proportionally.
• It can be implemented unilaterally.  A single nation, like the US or China, could decide to make restoring the atmosphere's carbon content to pre-industrial revolution levels into this generation's Apollo program.  This program would be expensive--perhaps $50 billion per year over 50 years--but affordable.
• There are many more ideas on how to stop global warming and ocean acidification that I have not explored that may also be tractable.  I am not a climate scientist and I don't mean to disparage anyone's work nor promote these ideas in place of peer-reviewed research, rather simply highlight ideas that I find plausible based on some back-of-the-napkin calculations.
• Finally, I may have made a mistake in my calculations here, and if you see one, please let me know so that I may correct it.