Mushroom, the parts of the North Sea where oil is a fading resource would be mainly in the area allocated to England/Wales/NI - I refuse to refer to these three as "the UK", so for brevity I'll call it 'England Etc' - in the event of Scottish independence.
There is as yet no certainty where the dividing line would be; however, the current line as regards legal matters in the North Sea runs directly east from Berwick. That is, if a trawlerman murders his skipper north of that line, he will be tried under Scots law. Others take the view that the last miles of the River Tweed, running due north-east, should indicate the direction of the trans-sea border. Whichever is chosen, 'England Etc' get the southerly and dying area.
New finds are now being revealed largely in the Atlantic, to the north and West of Shetland. 'England Etc' has no contiguity with that region whatsoever, so soon enough they would have no access to any oceanic oil.
Jomifl, perhaps you have forgotten that there are 26 Englishmen who influence legislation throughout the UK, including Scotland, with no reciprocal arrangement. That may be about half the number of Scottish MPs who vote on English matters at Westminster; however, it's still far from right that bishops of the Church of England are permitted to help create laws which affect Scottish people. Do try to recall the C of E hierrarchy next time you feel like airing the West Lothian question. If the latter is wrong, then so, indubitably, is the former!