The large unit in the foreground was used to remove water from main engine fuel, one of the smaller units would do the same for generator fuel and the third one would be used for cleaning lubricating oil.
No these are to separate water etc from either Heavy oil , diesel oil or Lube oil before going into the engine system, she should have a OWS in the bilge system to remove the oil from water before discharge overboard.
The separators were connected in series in heavy oil operation. Purifier and clarifier. They separated heavy incombustible parts from the fuel and of course the water.
These filtered out parts landed in the mud tank, and at my time of sailing they were pumped out by pumping or with compressed air into the sea.
Environmental protection was not yet the order of the day.
In parallel, the lubricating oils of the main engine and the auxiliary diesel would be continuously cleaned equally by other separators.
An oil change was not necessary. Only the oil loss was constantly being supplemented
I should add that the sludge discharged from the separators usually ended up in a tank located beneath the machines and this was pumped out as required, The lub oil separators would have their own separate tank and in the event of a broken water seal the oil could be recovered ,cleaned and put back into the system.
Diesel generators would have self contained filtration systems fitted as only relatively small amounts of oil in use Thinking of Streamline Filters using compressed paper discs as the filter medium but other designs were available.
Water is cheaper than fuel. The unseparated Bunker C heavy oil contains a lot of natural water. Even before separation, tank drainage is still necessary in the settling tank and after separation in the day tank.
With lubricating oil it is different. They are high-quality oils and without water. However, water could get into the lubricating oil through leakages in the engine cooling water. Emulsions are then formed.
By the way, the separators on the photo are from ALPHA LAVAL