Following up comment #2 above, even though the idea of compartmental modeling is well-known in epidemiology, here's evidence of how little it is applied to fossil fuel depletion.
Google Scholar citations for "compartmental models" & "oil depletion"
The only hit shown refers to our work, and by expanding the keyword search, Google returns this:
> Herrero, C., García-Olivares, A. and Pelegrí, J.L., 2014. Impact of anthropogenic CO2 on the next glacial cycle. Climatic change, 122(1-2), pp.283-298.
The way that Herroro et al apply a compartmental model is to model the compartments as oil, atmospheric CO2 from combustion of the oil, and sequestering of that CO2 in the ocean. We also model this compartmental flow in [Chap 9](https://agupubs.onlinelibrary.wiley.com/doi/10.1002/9781119434351.ch9).
So it's an interesting intersection of a model used both for Green Math (epidemiology) and for earth/climate sciences.