A MODIFIED HUBBERT MODEL FOR RESOURCE RECOVERY
The recovery rate, the amount per unit time, of a finite resource, x, was modeled by Hubbert . This model, now called the Hubbert model (HM), is based on the assumption that the recovery rate, R(t), takes the mathematical logistic form, i.e., (* for equations see 'Additional Files' below). We investigate a modified (HM) for which the recovery rate has a combustion-type functional behavior, i.e., (**). For both models, we calculate the peak recovery rate, and the times to achieve this value and the value at 90% recovery of the resource. We conclude that while the general properties of the two models are similar, they differ in the details. This fact provides evidence for the general conclusion that the class of Hubbert models (***) where xmax is the maximally recovered amount, can only provide qualitative information on the actual recovery rates.  M. King Hubbert, National Academy of Sciences, Publication 1000-D (1962).
Mickens, Ronald E.
"A MODIFIED HUBBERT MODEL FOR RESOURCE RECOVERY,"
Georgia Journal of Science, Vol. 75, No. 1, Article 80.
Available at: https://digitalcommons.gaacademy.org/gjs/vol75/iss1/80