I think i had a similar issue.The only reason I think it's the oil pump is because of information I found online such as this thread and a few others.
It does sound "impeller like" and is related to engine rpm rather than wheel speed (happens in neutral parked on the drive). I just had a new timing chain fitted and this noise existed before and after that so don't think it's the chain and a mechanic has run the car with the aux belt off which didn't affect the noise so it's not the alternator or anything aux driven.
I believe the oil pump is chain driven, not sure if anything else is? But at the moment that's my conclusion but I'm not sure about the urgency of getting it fixed other than its bloody annoying!
I described it as a somewhat faint whining or whirling noise coming from the front passenger side of the car, when revving between 2k and ~4k rpm. I could hear it get louder and louder after an oil change. Starting @ about 500 miles and getting its loudest around 2,000 miles after the oil change. 5W-40 Motul.
Does this sound like a similar description?