silver extraction rate for the world and two Verhulst function fits to the data.
L. David Roper
http://arts.bev.net/RoperLDavid/
20 March, 2010
Silver has been used for making currency coins for many millennia. In the minds of many people it is still the basis for an international monetary standard. Since about 1980 is has been used extensively in electronics manufacturing, because it is very ductile and malleable and is a good conductor of electricity and heat
The graph below shows the silver extraction data for the world and Verhulst function fits to the data for two different amounts of eventual extraction in order to extrapolate into the future.
silver extraction rate for the world and two Verhulst function fits to the data.
The red curve is obtained by restricting the total extraction (1350x103 tonnes) to the amount already extracted (about 1100x103 tonnes) plus the estimated reserves of about 270x103 tonnes; the blue curve is obtained by restricting the total extraction (1650x103 tonnes) to the amount already extracted (about 1100x103 tonnes) plus the estimated reserves base of about 570x103 tonnes.
It appears that average world-silver extraction will peak somewhere between 2000 and 2010.
Taking an average extraction curve of the two fits, the crossover point at year 1993 when the amount extracted is equal to the amount left to be extracted is shown here:
Undoubtedly there is much recycling of silver, especially since many people and nations hold silver as a "currency". By the term "recycle" I refer to silver that is resold for storage as well as to be used to make items.
Assume that:
The effective silver available for purchase after the first ten recycling cycles is shown in the following graph, along with the effective silver available for each cycle for the average of the two extraction cases described above:
The equation for a recycling 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.)
Of course, the recycling could be extended to more cycles, skewing the curve further into the future. However, the peak and fall off after it will not change because further cycles are essentially zero in that time region.
Thus, under the assumptions given above, the effective amount of silver available for making items peaks before 2100 and falls off rapidly after that. Humans will have taken concentrated silver deposits and scattered them across the surface of the earth.
The Excel spreadsheet is set up to make it easy to calculate with different recycling assumptions.