Magnesium Depletion and Recycling

L. David Roper
2 July, 2016

Magnesium is used in batteries, paints and plastics. The graph below shows the magnesium extraction data for the world and a Verhulst function fit to the data in order to extrapolate into the future.

Magnesium extraction rate for the world and two Verhulst function fits to the data.

Since there is a large reserves for magnesium, there will probably be one or more future peaks for magnesium extraction. Magnesium can also be obtained from sea water.


Assume that:

The effective magnesium available for making items after the first ten recycling cycles is shown in the following graph, along with the effective magnesium available for each cycle:

The equation for a recyling cycle is


where Ei is the amount available from the previous cycle. Here is an example of the Excel coding:

{=(($J$2+$I$2)/2+(($J$2-$I$2)/2)*TANH((A27-$K$2)/$L$2))*SUM($I$27:I27*(EXP(-1*((A27-$A$27:A27-$N$2)/$O$2)^2/2))/$O$2/SQRT(2*PI()))} (The curly bracket surrounding the term makes it into an array; it must be entered by holding down the SHIFT & CTRL keys while pressing the ENTER key.)

The Excel spreadsheet is set up to make it easy to calculate with different recycling assumptions.

Minerals Depletion