jesus i am a nerd

So, when it comes to oxygen generation we all know we have a few tried and true machines which vary in effectiveness. By and large the known best conversion rate is oxyferns capable of converting water at a 98% efficiency, surpassing the electrolyzer's 88% (looking strictly at o2 values, ignoring the value of the hydrogen also generated) and as you go down the methods dead last is our old nooblet trap, the algae terrarium. Consuming 30g/s algae and 300g/s h2o to produce at best 44g/s o2 and an equally enormous 290.33g/s ph2o, clearly the bottom of the barrel. But....having been around for a long time I tend to view resources as resources just waiting for transformation. I'm no stranger to polluted oxygen gasser designs in particular, whether deodorized to clean o2 or not, it is a highly efficient 1:1 ph2o to po2 conversion rate that averages 2.4kg for every full 1 ton tile of ph2o that is exposed to oxygen or polluted oxygen so it can offgas. Because of this variability most people don't consider it a particularly useful method for o2 generation but in my experience it is a lot more effective than people give it credit for, limited only by the design of your gasser layout to maximize the surface area for bubbling.

So that being said, let us look again at our humble friend, the algae terrarium. Sure, it uses a limited resource, algae. It also uses a lot of clean water. In fact when you do the math it comes out to be that 1 gram of algae and 10 grams of clean water only nets you 1.3 grams of clean o2 and 9.7 grams of ph2o. But what if we offgas that ph2o? By having enough exposed tiles of 1 ton polluted water you can equalize the rate of evaporation to the rate of polluted water you're generating meaning you can turn that 9.7 grams into additional o2, dirty or not. That means for 1 gram of algae and 10 grams of water you are getting 11 grams of o2. Suddenly terrariums are looking pretty nice, though at the cost of duplicant interaction or automation, plus space for all the tiles.

So lets continue the math. to make a gram of algae you need 3 grams of slime. Those 3 grams also generate 2 additional grams of ph2o. When you simplify all the ratios now you're down to 1g of slime plus 3.3g of clean water giving you 3.67g o2. If you stop there you can be forgiven. That is a 111% water to oxygen ratio, which already far surpasses everything we have, though you'll need to supply your own polluted water to sustain it. But we can account for that.
The ratio of polluted oxygen to slime for a normal puft (not a prince) is 95%, or in order to get 1 gram of slime you need 1.05g of polluted oxygen. By accounting for this additional polluted oxygen cost into the produced oxygen from our previous rate we drop the simplified numbers down to…

1g slime + 3.3g h2o = Approx. 2.62g o2

Wait a minute, we suddenly jumped down to 79% water to o2 efficiency! The math doesn’t stop there though. So with all these numbers we can calculate the slime and fresh water needs to support a dupe. Simply, 25g/s and 82.5g/s water equates to your magic 100g/s oxygen needs for a duplicant. In total cycle costs, each dupe then needs 49.5kg and 15kg slime. So….about that clean water. Yeah, you can just get it from a geyser or something, but in the end you are losing water over time. But wait, we figured out earlier that you generate a lot of ph2o from slime, and all slime needs is polluted oxygen…what about if we just keep adding into that loop?

So we know that if we skim ph2o it is directly anagolous to clean h2o, meaning the amount doesn’t change between those. However, if we’re going to be taking ph2o out of slime that means we’ll be needing to convert that ph2o cost into slime, and then likewise into po2 that needs added to our previous calculations. So, to figure the slime to polluted water ratio for the distiller for a single gram, simply 1/600 for a single gram of slime, multiplied by 400, the rate of ph2o you get as that gram is processed, giving you 0.6 repeating, or 0.7 approx. We also know that every gram of slime is actually 1.05 grams of polluted oxygen, so the ratio of conversion ends up truly being 0.7 when you multiply 1.05 by 0.6 repeating. So, 49.5kg divided by 0.7?

We need an additional 70.71kg of polluted oxygen each cycle to sieve into clean water which will eliminate the water cost of the terrariums. Again, you can get this anywhere. Let us look at a good alternative source of polluted oxygen then; polluted dirt! So we need 70710g which works out to approximately 118g/s po2. To maintain this from a sublimation standpoint it is important to note that offgassing here works slightly differently. A good simple approach is for every 2500kg of polluted dirt in a storage bin you gain 10g/s po2. So using this as a jumping point we would need 12 storage bins set to and filled to this limit. Well, how do we maintain that 118g/s pdirt? By creating ethanol!

Ethanol distillery numbers get a little confusing but to make the math more straightforward let us look at what it takes to make a gram of ethanol.

2g lumber = 1g ethanol + 0.67 pdirt + 0.3g co2 – We’re already making dirt! But that ethanol has a use, too!
1g ethanol = 0.375g ph2o + 0.25g co2!

Combine it all and you get…
2g lumber = 1.045g po2 (assuming the ph2o was added to the gasser and offgassed) + 0.55g co2
So we’re getting just shy of the exact amount of po2 we need to make a gram of slime! Plus some co2, but who cares. We’re interested in making that sweet slime without needing more water cause that is the end goal! Which means that for the additional 70710g of slime we would need to make 73891.95g of po2. What is that in lumber cost? Double it! Approximately 147.8kg lumber per cycle! So what does that mean?! It means we need two wild arbor trees. A wild arbor tree is capable of generating in ideal conditions approx. 83.3kg lumber per cycle. 1.77 trees, essentially. So 2. And they’re wild so they cost you nothing at all!

However, by adding more slime needed that also means we need to account for the pufts making the slime. Just how much can a puft produce daily? 47.5kg in ideal circumstances, it turns out. We already know a single dupe is going to need 15kg, so what about all this 70.7kg? How is that gonna hit my o2 ratio? Well, it means we need two pufts, unfortunately. That takes another 1.05 from our previously calculated net o2 cost. It is now…

1g algae + 3.3g h2o = 1.57g o2…what? That isn’t the ratio I wanted….

Oh, right, WE ACCOUNTED FOR THE ALGAE AND THE WATER IN THAT CALCULATION! We generate the algae and water in the process and already removed it from our net oxygen meaning the ratio is actually…0 to 1.57.

 We actually are getting 1.57g o2 for NOTHING……except sand. The only real cost is filtration medium for purifying the water to contribute back to the o2 loop. This can be offset by the fact that deodorizers produce more clay than sand that they use, approx. 6.7kg/cycle added mass (which with coal can be made into ceramic and then granulated to sand again for the profit) after fixing the 100g/s duplicants breath, however you will need 9.9kg/cycle so adding in a pokeshell you can feed it with nearly any amount of rotting material and make up your additional 3.2kg/day sand cost.