they do use oil from the off bmw say normal is 1000 miles to 1 litre or oil give or take 200 miles, could use a heavy;r oil ie 5/40w also worth trying adding seafom to oil and run car for 30 miles this will clean out the piston rings if gunged up, but wont fix a worn out piston ring or worn out valve stems seals,, its one of those kill of cure moments, i have used on a engine that was like a steam train out the oil filler when running and 50 miles later was near perfect that was a honda diesel on 220,000 miles the guy drove that on until 300k and sold it where when it came in h=and add the seafoam additive added it was using a lot of oil, that car had intermittent services as well so dirty oil builds up carbon the carbon and sludge will stops rings from pressing against the bores,,,
also what can do get someone to drive your car when car is nice and hot down a steep hill revs around 4000 reves dont touch throttle until at bottom of hill then floor it if it give a puff of blue smoke then its valve stem seals and very common for them miles, if its smokes blue all the time its piston rings, if when unscrew oil filler cap when hot its like a train it rings,, like said seafoam is worth a punt,, also when ordering a cat you should also do the 02 sensors at same time i know its a pain and expensive but oil destroys them so does antifreeze as well at 114k they will be worn out, would only fit genuine ones as well.
below in link for seafoam double pack it includes a spray ie remove the spark plugs and spray in to the cylinders and leave of 24 hours to soak then crank engine no plugs in first to clear excess seafoam, then i replace the plugs and start the engine MUST REV IT FROM THE OFF IE STRAIGHT TO 3K this will clear the seafoam better its worth a punt
