This post was going to be about copper, which is not my favourite metal, but at least it has character (

Apparently there is lots of the stuff around---so much that, unlike gold, it is difficult to see the end of mining it. This is great--I need a new fridge.

I have a copper nugget somewhere among my personal effects in Canada. I had thought I had a photo of it to post here, but no such luck--just a copper coin.

This is the best I can come up with--a smashed open vesicle from a basalt I found in the Rae-Richardson river system ages ago, filled in with what might be a copper mineral. The penny is copper, too.

My interest today concerns long-term forecasts of metal production. In an earlier posting, I discussed estimates of the total amount of gold remaining to be mined (on Earth). My comments today concern Hubbert linearization in the application to forecasting the amounts of oil, gold, copper, and other minerals that have yet to be found.

The linearization approach can be viewed as a technical approach whereby in the graph of annual production/cumulative production vs cumulative production, the extension of the linear line towards the cumulative production axis gives the maximum cumulative production. Alternatively, one can attempt to plot the logistic curve, of P vs Q, and look to fit the total plot to a parabola, where annual production falls to zero when the total amount of the resource has been extracted.

Oil was a classic example--but in the graph above we see a little wrinkle in the plot. The current fracking phenomenon in oil shales has caused the US to re-enter the climbing production phase (for as long as it lasts). If this climbing phase is no more than a small blip, then it will only result in a small change in the final estimate of total oil production (somewhat shy of 250 billion barrels). If it continues, however, then we can make no estimate of final production.

Copper, for instance, is still in the climbing production phase, so it turns out to be impossible to use this method to estimate the total amount to be mined. The problem is that the current slope of the graph is positive, so the line will not extrapolate to the cumulative production axis.

Scanning around the interwebpipes for estimates of the total amount of gold expected to be mined here on Earth leads to estimates ranging from about 250,000 t to around 390,000 t (much larger amounts considered possible mainly by lunatics).

But perhaps I am among them. The method by which these estimates turns out to be highly sensitive to estimates of historical production (generally prior to 1850, for which records are incomplete) but is also highly influenced by the recent historical production. In particular, where relative production is declining, we can use Hubbert linearization to predict a final cumulative resource.

But for this method to give a reasonable estimate, the history of production has to be relatively smooth. And this is something we do not see. Mining tends to occur in cycles--gold for instance.

For gold, some of these cycles are tied to discoveries--South Africa, for instance, or California, and the Yukon, are all visible on the chart. Large cycles may also be driven by finance, especially the current cycle, which is the result of the rise in price through the late 1970s into 1980.

Permitting of mines is taking a long time, and it would not be unreasonable to assume that another peak in production may occur in response to the rise in gold prices since 2000. Any resulting increase in production will have a sharp impact on the estimate of the total amount of gold to be mined in future.

Another potential cause of production increase is technological change. Such change can lower the price of extracting resources, making otherwise uneconomic deposits economic. More importantly, technological change can reduce the energy cost, which may greatly increase the resources that may be extracted.

As an example, the relatively recent development of heap leaching has made a host of near-surface, low-grade deposits mineable. What would a miner in 1885 think if you told him we would one day mine gold deposits with grades of 0.01 oz/ton?

*i.e*., is not grey).Apparently there is lots of the stuff around---so much that, unlike gold, it is difficult to see the end of mining it. This is great--I need a new fridge.

I have a copper nugget somewhere among my personal effects in Canada. I had thought I had a photo of it to post here, but no such luck--just a copper coin.

This is the best I can come up with--a smashed open vesicle from a basalt I found in the Rae-Richardson river system ages ago, filled in with what might be a copper mineral. The penny is copper, too.

My interest today concerns long-term forecasts of metal production. In an earlier posting, I discussed estimates of the total amount of gold remaining to be mined (on Earth). My comments today concern Hubbert linearization in the application to forecasting the amounts of oil, gold, copper, and other minerals that have yet to be found.

The linearization approach can be viewed as a technical approach whereby in the graph of annual production/cumulative production vs cumulative production, the extension of the linear line towards the cumulative production axis gives the maximum cumulative production. Alternatively, one can attempt to plot the logistic curve, of P vs Q, and look to fit the total plot to a parabola, where annual production falls to zero when the total amount of the resource has been extracted.

*P/Q linearization for US oil production. Data from EIA.*

Oil was a classic example--but in the graph above we see a little wrinkle in the plot. The current fracking phenomenon in oil shales has caused the US to re-enter the climbing production phase (for as long as it lasts). If this climbing phase is no more than a small blip, then it will only result in a small change in the final estimate of total oil production (somewhat shy of 250 billion barrels). If it continues, however, then we can make no estimate of final production.

Copper, for instance, is still in the climbing production phase, so it turns out to be impossible to use this method to estimate the total amount to be mined. The problem is that the current slope of the graph is positive, so the line will not extrapolate to the cumulative production axis.

Scanning around the interwebpipes for estimates of the total amount of gold expected to be mined here on Earth leads to estimates ranging from about 250,000 t to around 390,000 t (much larger amounts considered possible mainly by lunatics).

But perhaps I am among them. The method by which these estimates turns out to be highly sensitive to estimates of historical production (generally prior to 1850, for which records are incomplete) but is also highly influenced by the recent historical production. In particular, where relative production is declining, we can use Hubbert linearization to predict a final cumulative resource.

But for this method to give a reasonable estimate, the history of production has to be relatively smooth. And this is something we do not see. Mining tends to occur in cycles--gold for instance.

For gold, some of these cycles are tied to discoveries--South Africa, for instance, or California, and the Yukon, are all visible on the chart. Large cycles may also be driven by finance, especially the current cycle, which is the result of the rise in price through the late 1970s into 1980.

Permitting of mines is taking a long time, and it would not be unreasonable to assume that another peak in production may occur in response to the rise in gold prices since 2000. Any resulting increase in production will have a sharp impact on the estimate of the total amount of gold to be mined in future.

Another potential cause of production increase is technological change. Such change can lower the price of extracting resources, making otherwise uneconomic deposits economic. More importantly, technological change can reduce the energy cost, which may greatly increase the resources that may be extracted.

As an example, the relatively recent development of heap leaching has made a host of near-surface, low-grade deposits mineable. What would a miner in 1885 think if you told him we would one day mine gold deposits with grades of 0.01 oz/ton?

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