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Our intrepid interstellar crew arrive in a new solar system. The find a planet in the Goldilocks zone. However the planet has no life, but is otherwise earth like*. The atmosphere is 80% nitrogen, 20% carbon dioxide. Give or take.

If the crew were to drop say 50 canisters of 1kg of algae in to the seas:

  • How long would the algae take to spread through the whole planet's sea?
  • How long to convert the atmosphere to be breathable?

*For argument sake, it is the exactly same as earth; apart from no life and consequently a different atmosphere. (Unless there is a good or interesting reason why it would be different)

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  • $\begingroup$ I feel like this question needs more detail: 1) How far apart are you dropping these canisters? 2) Do the canisters have an effective mechanism to spread the algae after falling into the sea? 3) How salty is the sea? 4) How warm is the water? etc. etc. $\endgroup$ – Tony Sep 30 '16 at 5:35
  • $\begingroup$ Voting too broad. It all depends on how engineered your algae is, and what nutrients are available for it - things you didn't specify. Also, why algae and not cyanobacteria? $\endgroup$ – Mołot Sep 30 '16 at 9:21
  • $\begingroup$ @Tony 1. I am thinking spreading the canisters even-ish around the planet would be a good idea?! 2. Having the canisters to release their content would be a good idea?! 3. I don't know earth like perhaps?! 4. I don't know earth like perhaps?! $\endgroup$ – DarcyThomas Sep 30 '16 at 9:37
  • $\begingroup$ @Molot I'm looking for a reasonable answers. So something reasonable for a hard sci-fi. So reasonable GE. Nutrients perhaps like what you would find on an earth with no life, like in the question :p Cyanobacteria vs Algae good call had not thought about Cyanobacteria whichever would work better. Although Cyanobacteria tend to be toxic (I think), so may not be the best in the long term; as the crew are probably gonna want to do more than just create oxygen. $\endgroup$ – DarcyThomas Sep 30 '16 at 9:48
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How long would the algae take to spread through the whole planet's sea?

Algae have to float, so this depends on ocean current. The fastest sustained speed of any current on earth is probably the Antarctic circumpolar current at around 4 km/h. Lets divide the circumference of the earth by that to estimate $ \frac{40000 \text{km}}{4 \text{km/h}} = 10000 \text{h} = 417 \text{days}$. Different speed currents and different continental geometries,matter; since most currents aren't that fast around 2 years is probably a good estimate.

How long to convert the atmosphere to be breathable?

So first off, there are two separate processes at work here. CO2 is converted to organic carbons, like carbohydrates, and water is converted to oxygen, in separate steps of the photosynthetic process. So when the 20% CO$_2$ is gone, that doesn't mean that 20% O$_2$ as been created, or vice versa.

This site suggests the world's ocean primary productivity is 3.8 Pg per month. And here we have an estimator of 47.5% by mass C in vegetation, consistent across all kinds of vegetation. To finish this calculation, we need the mass of 20% of the CO$_2$ in the atmosphere. To make things simple, we'll say O$_2$ and N$_2$ are about the same molecular weight. Its a $\frac{14}{32}$ molecular weight ratio between the carbon part of CO$_2$ and O$_2$, so 20% of a $5.15\times 10^{18} \text{kg}$ atmosphere gives us $ 0.2 \cdot 5.15\times 10^{18} \text{kg} \cdot \frac{14}{32} = 4.5\times10^{17} \text{kg}$ of carbon that needs to be removed from the atmosphere. Putting it all together:

$$\frac{4.5\times10^{17} \text{kg}}{0.475 \frac{\text{carbon}}{\text{biomass}} \cdot 3.8\times10^{12} \text{kg}\frac{\text{biomass}}{\text{month}}} = 249653\, \text{months} = 20804\, \text{years}$$

20 millenia, that seems crazy fast!?! Well if there are no other lifeforms respirating, there is not much of a carbon cycle. It comes from the atmosphere, gets turned into algae, sinks to the ocean floor.

In an alternate calculation, this paper suggest you can get up to 30g per m$^2$ per day of biomass production on algae farms designed to capture carbon. If you use the entire surface of the ocean ($3.6\times10^{14}\text{m}^2$ as your farm you would get

$$\frac{4.5\times10^{17} \text{kg}}{0.03 \frac{\text{kg}}{\text{m}^2\cdot\text{day}}\cdot 0.475 \frac{\text{carbon}}{\text{biomass}} \cdot 3.6\times10^{14}\text{m}^2} = 87719\, \text{days} = 240\, \text{years}.$$

So you can probably remove all the CO$_2$ in a couple centuries with carefully optimized algae plan.

On to Oxygen. During the Great Oxygenation Event; there were alot of chemical reactions going on. A naive calculation like above will be particularly unrealistic because O$_2$ is such a reactive compound that it will react with just about anything lying around. Particularly, apparently there used to be lots of elemental iron just hanging around on the earth's surface. Over hundreds of millions of years it all oxidized into the rusty deposits we mine today.

This paper (on page 9) estimates that current oxygen levels would be reached in 2000 years at today's rates of photosynthesis. But there would be a significant loss of oxygen to free iron and sulfur and other easily oxidized minerals present in seawater and in the exposed bare rocks on the land. This page has some facts and figures. In geological history, it took perhaps 10-100 million years to fill all available oxygen sinks.

The way around this is oxygen production rate. Lets say that just as we could crank up the rate of oxygen production by a factor of 100 like we did with the CO$_2$ in algae farms. Now we are making an atmosphere's worth of oxygen every 20 years. This might be faster than geological processes can absorb the free oxygen. So lets say that we get another factor of 10 slowdown due to oxygen sinks, and bam, we're right at 200 years to oxygenate the atmosphere again. A little hand-wavy, but I can't find any data on the rate of oxygen absorption by the rocks on early earth, so we'll stick with it.

Conclusions

Algae would fill the earth's oceans in a few years, so quickly as to be irrelevant to the terraforming process.

Using natural processes and a few cans of algae, it would take 20,000 years to get rid of the CO$_2$, and tens of millions of years to add enough oxygen to fill all oxygen sinks.

Using specially selected/engineered algae and concentrated effort, you could replace CO$_2$ with O$_2$ in as little as 200 years.


Edit to double-check for science.

Assume incident sunlight averages $6 \frac{\text{kWh}}{\text{m}^2}$. Multiply by the area of the ocean and that works out to $$6 \frac{\text{kWh}}{\text{m}^2}\cdot 3.6\times10^{14}\text{m}^2=2.8\times10^{24}\frac{\text{J}}{\text{year}}.$$

Photosynthesis costs 478800 J per mol of CO$_2$ removed (I'm only going to measure the carbon side here), and 0.014 kg of carbon are removed for every mol removed. That gives us:

$$\frac{2.8\times10^{24}\frac{\text{J}}{\text{year}}}{478880\frac{\text{J}}{\text{mol}}} \cdot 0.014\frac{\text{kg}}{\text{mol}} = 8.3\times10^{16}\frac{\text{kg}}{\text{year}}.$$

That means about 5 years to remove all the CO$_2$ in the atmosphere capturing every J of energy incident on the oceans, and using it at 100% efficiency. If you consider that photosynthesis can use about 45% of incident energy, at 30% efficiency, then if every J of incident energy struck a choloroplast, it would take about 37 years to remove all the CO$_2$ in the atmosphere.

So 200 years is 19% efficient compared to max theoretical with photosynthesis, or put another way, if you can get 19% of the incident sunlight on the ocean to be utilized by algae, you will remove all CO$_2$ from the atmosphere in 200 years.

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  • $\begingroup$ Good answer thanks. What do you think would be the absolute lower bound. ( 100% solar energy conversion efficiency * Sea area / energy conversion cost) $\endgroup$ – DarcyThomas Sep 30 '16 at 9:59
  • $\begingroup$ @DarcyThomas I think that 200 years is the lower bound. Photosynthesis doesn't have 100% solar energy conversion efficiency. As long as you are talking about algae, and not some other engineered micro-organism, I don't see how you can get much more efficient than the calculation above. $\endgroup$ – kingledion Sep 30 '16 at 12:00
  • $\begingroup$ I was thinking more as a way of double checking what would be reasonable. If the absolute lower bound came out as 100 years, then 200 years would be 50% efficiency which would very high efficiency. But if it was 2 years, then 200 years would be 1% efficiency which would be quite reasonable. Get what I mean? $\endgroup$ – DarcyThomas Sep 30 '16 at 18:38
  • $\begingroup$ @DarcyThomas Challenge accepted, check the edit. $\endgroup$ – kingledion Sep 30 '16 at 19:10
  • $\begingroup$ Hmm ... if 200 years is our lower bound (and that assuming super-algae and nobody trying to clean up all that gross algae), then this would be hard to weaponize against the evil SeeOhTwo-ites. (Not unexpectedly, considering we're trying to change the entire atmosphere!) That said, I imagine that the huge, rapid influx of O2 would create very strange effects -- including massive wildfires -- which the SeeOhTwo-ites might find very distracting. If I were fighting their planet, it'd be worth it to drop a few algae cannisters in their ocean betimes. $\endgroup$ – akaioi Aug 29 '17 at 23:42

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