The Exergy Evolution of Mineral Wealth - Thanatia: The Destiny of the Earth's Mineral Resources - page 375

Fig. 13.2 Evolution in gold price throughout the 20th century. Data obtained from USGS (2010)
for the methodology) were strongly influenced by the need to make assumptions.
Results today are more reliable given that the curve can be defined through many
more points and there is better estimations for mineral reserves. Bardi and Pagani
(2008) for example examined the world production of 57 minerals reported in the
USGS database and came to the conclusion that the bell-shaped curve can be used
globally and for most minerals, not only for fossil fuels.
In the authors' opinion the bell-shaped curve is better suited to non-fuel minerals
than fuels if exergy is plotted against time instead of mass over time. This is because
whilst fuel quality remains near constant with extraction, non-fuel mineral quality
degrades as time goes on (as long as mining continues). Therefore exergy is a
better unit of measure than mass, since it accounts not only for quantity but also
for ore grades and composition. Accordingly, in this topic the exergy replacement
cost associated with the extraction of a certain commodity over time is represented.
With a least squares procedure, the points are adjusted to fit the curve given by
Eq. (13.5). It should be noted that using either exergy, B, or exergy replacement
costs, B , vs t is not particularly important given that the peak value remains the
same — the unit exergy replacement costs having been considered to be constant
throughout the period of time assessed.
Presenting the Hubbert Peak Model in terms of exergy replacement cost holds
a further advantage: all curves can be shown within a single diagram, given that
the orders of magnitude are similar. This will be known from now on as “Exergy