re: Even though we have infinite reserve growth, we will still see peak oil in a few years time. Has that sunk in?

Agreed. Reserve growth is great material for spin-doctors! you can actually claim to have a forever growing URR which of course is mostly irrelevant to the problem of increasing flow rates.

I have limited growth to a maximum of 95 years (see Figure 6) but you're self-limiting parabolic growth could be a good substitute.

It's not hard to analytically solve the power-law forms (unlimited growth) but the self-limited foms need numerical solutions. In lieu of solving numerically, I have had good success modeling this limiting behavior with two damped exponentials, which essentially mimics the hM(t) and hG(t) terms that you have in Eq. 7. The following is an impulse response to a delta discovery @ T=1900:


from http://mobjectivist.blogspot.com/2006/02/decomposing-reserve-growth.html

It looks like this when put on top of a real reserve growth curve:

Whether this is worth doing, and whether this is mathematically valid, I have to ponder a bit. But since you essentially came up with this idea independently of me, I think it is worth pursuing.