There is some push to use the Logistic equation solution to model oil depletion. It's one of those ideas that draws from questionable premises: "do oil molecules multiply?, is there a carrying capacity for oil?", etc. I would be interesting to either counter or support this claim by deconstructing the equation for oil. (I have my own theories that I can contribute).
The other interesting feature of the Logistic solution is that it has the same structure as the Fermi-Dirac distribution function, although the derivation is completely different.
This leads one to think that the Logistic can have other origins, not related to solutions of the Logistic equation. I have my own derivation that I can contribute, drawing from dispersion mechanisms.