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So yes, they all work the same, and it goes quicker the more Fractionaters the hydrogen passes through. Best to do so in a looping manner for just that purpose, while still having a supply of hydrogen attached to gradually replace the consumed ones.
And the faster you can shove hydrogen through a fractionator the more deuterium/min it'll generate.
The fractionators have no memory -- so each time a hydrogen enters (even if it's the dozenth time) it does a random check to see if it hit the 'lottery' and gets converted to deuterium. (That happens 1% of the time on average; or up to 2% if you've applied the highest possible proliferation)
Because this check happens each time a hydrogen enters you achieve maximum deuterium production by maximizing the number of hydrogen flowing through each fractionator. (So using faster belts and/or stacking hydrogen)
If you used, and can kept 100% full:
* a loop of Mk.I belt: 1 fractionator would average 3.6 deuterium/min.
* a loop of Mk.II belt: 1 fractionator would average 7.2 deuterium/min. (2x Mk.I)
* a loop of Mk.III belt: 1 fractionator would average 18 deuterium/min. (2.5x Mk.II)
* a loop of Mk.III belt stacked 4x: 1 fractionator would average 72 deuterium/min (4x Mk.III alone)
[And, as mentioned, adding proliferation to the hydrogen increases the default 1% conversion rate and would correspondingly increase these outputs]
So once, you unlock them, using pilers or later pile sorters to increase the throughput of hydrogen around the fractionator belt can be a major win.
Also, using multiple fractionators in a given loop will slightly reduce each one's average output unless you very carefully construct the loop to constantly replace converted hydrogen. However the space efficiency and easy of construction might outweigh the small loss of efficiency for you.