《I don't think Titan has rocks. Its all ice.》
I'll expand my comment a little bit to adress some hurdles, as it seems there is a necessity for general picture here.
"Based on its bulk density of 1.88 g/cm3, Titan's composition is half water ice and half rocky material."
"Titan is probably partially differentiated into distinct layers with a 3,400-kilometer (2,100 mi) rocky center"
Yes there is some depth to reach it, but hey aren't you looking for epic challenges to overcome, lol. It part of that titanic endeavor. You need to turn the thing inside out to do what you describe.
Indeed 900km down to reach basalt and stuff, seems a but too much, even if it is "just" ice on top of it which one can melt, and lower gravity on that body.
But a problem is that any global changes on a scale like this one, even if it just a moon, even if it looks not so significant like just adding 20 percent something of oxygen, and removing 5 percent methane, it still quite a big task, not something which can be done with a fortpost in a reasonable time.
How much efforts or something it requires, I do not know at the moment, but let us see, some measurable things we can deduce, just a portion of required activity.
Observations from the Voyager space probes have shown that Titan's atmosphere is denser than Earth's, with a surface pressure about 1.45 atm. It is also about 1.19 times as massive as Earth's overall
That already speaks volume, but what it means in practical reality, in things we can have a more palpatable subjective percepton.
Total mass of Titan atmosphere is about 6e18 kg, and for 20 percent oxygen we need to add around 1/5 of that but let's go with 1.3e18 kg
- not try to be precise with numbers and there are hidden assumptions and maybe some mistakes as well, just wish calculus to be easier on me in this case, as I interested in order of magnitudes of those results.
Assuming your installations blow out somwhat warm air, for whatever reason there is enough of those, then it means the process has to release about 1e18 cubic meters of oxygen, or about 1e9 cubic km of oxygen.
Assuming you have 1 square km crossection pipe to blow that oxygen out, at speed of 100 m/s, it will take about 317 years to finish the job.
Sooo, 317 such installations can do that in a year, and if speed of expelling air is 10 m/s which seems less demanding and more realistic, then it is 3170 such installations.
- Okay, I have to admit it way much better than I have expected.
If each of those installations takes 10x10km square, for other equipment and such, then overal it just 0.5 percent of surface of Titan, to have the result in a year.
what order of energy it takes
According to wiki industrial processes take about 50 kWh per kg of hydrogen, which means 8 kg of oxygen, so about 6kWh per kg of oxygen.
According to our number 1.3e18kg oxygen required, we need about 8e18 kWh to finish the job, and with our 1 year timeframe it requires about 913,242,009 GW power for electricity production.
For comparison, industrial countries as of today here on earth produce electricity in hundreds of GW numbers, 50 to 300 something like that, per country. (Total energy production and consumption per country is about 6 times of that, if I recall it correctly)
- Sooo energy requirement are quite good, as expected, satisfied to guess at least something right.
So even if we extend time frame to 10 or a 100 years, it still, beats the total energy production consumption on that planet, like in a hundred or thousand times.
That is just one energy consumption activity, but it needs more, scrubbing air for methane, extracting amonia from water so it won't be released in your freshly created athmosphere. And I have to stress it, solution of water and NH3 is half of the planet, and seen it 8 percent of mass(or something, won't reread those wikis) and that we talking up to 1e22kg of material to process(total mass of Titan is 1.34e23 kg), at least some portion of it which is on top of the new waterworld, it may be a fraction of total but it still humongous. Maybe even not in a sense of energy required to extract, but in a sense how much movement of mass you have to create, to be able to extract stuff.
Waste hydrogen can be converted in to ammonia, at the same time removing some nitrogen from athmospnere to decrease pressure (maaan the whole moon will start to bubble, will be epic), and then it can be stored at some depths of the ocean thing, it does not require that much pressure to convert it to a liquid.
Electrolysing rocks - waste products will be metals and Si, they are easier to store and can be useful in constructions, but yeah it may be quite deep, to get a free access to it, if there aren't some sticking out mountains at bottom of ocean. Option which depends on technologies available and situation on the grounds.
better options, alternatives
In comments there was a siggestion to use some moons which do not have athmosphere, it may be a better choice indeed, from a perspective for things to remain more clean and controlable. There are no poisonous gases to mix with your newly created athmosphere.
I understand the desire to paint a grand picture, express idea, but it not always goes along with what makes sense to do.
Those dome like constructìns in Expanse series, they are actually not a bad alternative for a full conversion.(on ganimede if I recall correctly)
Probably one of the things which you may miss importance and implicatiins of it, is that sun as light energy source there is basically non existant at that place. Meaning just making air does not give that much benefits for Titane moon without that free sun energy which we are so used to. You have to create artificial sun for the whole moon to take advantage of that atmosphere, or no plant life will grow and athmosphere will be near to be pointless.
Build space habitats in orbit, do what you need that Titan for, do it remotley, via machines and satelite network like StarLink, enjoy full gravity, grenery of plants fresh air and other good working conditions, and let robots to suffer for their ai overlord to come.
Do it for all the moons, conver them all in to space habitats and battleships or whatever. The stuff you try to have fantasy about is outdated and direct hello from 70's - not cool, not epic. Or if things are just backdrop, then just handwave and make a good story instead. If activity in space is one of the bones for the story or main line then take a red pill and convert to space habs which is the way to make good environment in any place you go. And welcome remote operated equipment and robots, which are a thing of today, in mining(mature enough) and other places(maturity varies).