Barite Depletion Including Recycling

L. David Roper
http://www.roperld.com/personal/RoperLDavid.htm
2 July, 2016

Barite (Baryte) is used in such ways that it is not easy to recycle. However, a new use may be to make ultracapacitors, from which it could be recycled. The graph below shows the cobalt extraction data for the world and two Verhulst functions fits to the data in order to extrapolate into the future.

Barite extraction rate for the world and two Verhulst functions fits to the data.

The red curve is a fit with total amount to be extracted that incorporates the latest reserves estimate (380 x 10⁶ tonnes), and the blue curve is fit with total amount to be extracted that incorporates the latest reserves-base estimate (880 x 10⁶ tonnes)..

It appears that world-barite extraction is peaking at about or before ~2050.

Taking an average extraction curve of the two fits, the crossover point at year ~2017 when the amount extracted is equal to the amount left to be extracted is shown here:

Recycling

Barite, especially the barite used to make ultracapacitors, could be recycled in the future. Assume that:

The barite-extraction curve is the average of the two curves given above.
Recycling of barite follows a hyperbolic tangent curve from 0% to 60% recycling with a break point of year 2050 and width 50 years.
The recycling is delayed by a Gaussian curve peaking at a delay of 20 years and a width of 10 years.

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

The equation for a recyling cycle is

where E_i 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 essentally zero in that time region.

Thus, under the assumptions given above, the effective amount of barite available for making items peaks at about year 2000 and falls off rapidly after that. Humans will have taken concentrated barite 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.

Minerals Depletion