Oil production seems to have two components:
1- a deterministic component based on the contribution of a few super-giant and giant fields that provides 25% to 50% of the total production;
2- a stochastic component where only a mean behavior can be derived from the contribution of thousands of small fields.
Clearly, only on the second component the central limit therorem could eventually be applied (in its convolution formulation). One consequence, is that the resulting production curve will probably be gaussian.

I try to look at that problem a while ago on PO.com:

Convergence of the sum of many oil field productions

I also agree with your conclusion that super-giant fields won't play an important role in the future. A simple Monte-Carlo simulation based on log-normal distribution for the field size and the discovery history of oil fields seems to confirm that fact:

src:A Statistical Model for the Simulation of Oil Production

We are entering now in the "tail effect" of the log-normal distribution where production from a sheer number of small fields will shape the global production curve.