In the mid-1970s I taught an energy course at VPI&SU. I became interested in how minerals depletion was estimated and decided that I could do it better than had been done.
I used the least-squares-fit program of my colleague, Dr. Richard A. Arndt, to fit production-rate data for most minerals mined in the United States and the world.
Three books were published of that work:
Recently I have redone some of that work using the Solver part of Microsoft Excel to do the fits.
See Depletion Theory for a summary of the mathematics used in this research.
Verhulst Function for modeling minerals depletion.
Most recent minerals-depletion work (Data fitted for specific minerals are available upon request. Parameters of the Verhulst-function fits for specific minerals are available upon request.):
In March 2014 I redid most of the depletion calculations listed below to use many Verhulst functions to fit the small features of the data. Those small features may correspond to specific mines/wells or specific areas. Fitting the small features allow more accurate projections into the future, especially since within the last decade there have been huge increases in rates of extraction. Future peaks are always assumed to be symmetric. Instead of only one future peaks there may be more than one.