I do like the idea of limiting resources and adding additional effects for the use of certain types of energy - both of these add another layer of strategy to the game. There is even potential for additional diplomatic/geographical strategy if one considers emissions and resource deposits.
The issue I personally see with having finite Oil resources is that you are effectively limiting the natural progression of the corporation, as determined by the game mechanics:
1: Many players build with the sole goal of taking a corporation truly public, this is a fundamental part of an economic plan which affects decisions on population demographics, education, health and welfare. If oil corporations inevitably close they will become useless for this particular type of set up - IPO'ing can be fiddly and expensive, so why bother wasting time and resources on something that wont last? Not to mention the fact that you are presumably still spending the same production plant fee, and investing the same capital, that other infinite corporations require.
2. If an Oil corporation can be moved rather than closed once deposits are exhausted, we will still run into the same issue as above - relocation affects workers, welfare etc, and can easily kill a truly public corporation. And I hardly think presidents will want to move their state corporations outside of their own countries, unless the current income model is revised.
For the simple reason it makes Oil corps a bad investment for Presidents, overnight, I would imagine ample warning should be given, as well as compensation or 'free conversion' of affected corps.