The Exergy Replacement Costs of Mineral Wealth - Thanatia: The Destiny of the Earth's Mineral Resources - page 360

consumption as a function of ore grade suggest relationships varying from x 0:2
m

to

x 0: m (Valero D. et al., 2013).
With this last step, the authors have now all the components required for asses-
sing the exergy replacement costs of the minerals analysed. This is done using the
procedure shown in Fig. 12.1. Note that from all the energy data of Table 8.3 de-
rived from various different references, only one value 2 per category and metal has
been used (for mining & conc. and for smelting & refining).
Table 12.2 shows a summary of the replacement, mining, concentration and re-
fining costs of the minerals considered. The exergy replacement costs are expressed
as “bonus” in the table. It has been assumed, that each substance is extracted
from only one mineral ore (detailed in parenthesis). The crustal average mineral
concentration of the deposits and pre-refining average grades are represented by
x c , x m and x r , respectively. For those substances where no data was found con-
cerning average refining grades, the authors have assumed a value of x r =0.9. The
energy consumption trend as a function of the ore grade E(x m ) requires that the
ore grade is expressed in mass percentage of the metal considered, if not otherwise
specified. With Eq. (12.4), the unit exergy replacement costs k(x c ) and k(x m ) are
obtained, assuming that the same energy trend applies for the whole concentration
grade (from x c to x r ). Finally, the mineral bonus is obtained with Eq. (12.3) 3 . As
stated in Chap. 4, the bonus (replacement costs) represents the natural exergy of
the deposit which is gradually being lost when the mine is exploited. To the latter,
one needs only to add the conventional mining & concentration and refining costs
as presented in the Table 12.2.
One can extract some conclusions from Table 12.2. As aforementioned, unit
exergy costs are calculated as the ratio between the real energy required for mining
and concentrating a substance and the minimum thermodynamic energy (exergy)
required to achieve the same process. This means that they provide a measure for
the irreversibility (or technological ignorance) of the process. The closer the k-value
is to 1, the less irreversible the process and hence, the lower the quantity of energy
required. But k is also a function of the ore grade. The smaller it is, the greater
the mineral's unit exergy cost.
For instance, gold has the highest k(x = x m ) value of the metals analysed, at-
tributable to its low concentration in mines and the amount of energy needed to
concentrate it. Besides, the actual ore grade in mines is close to that in Thana-
tia. Contrasting examples are silicon or lime which have a lower k(x = x m ) value
ascribed to their high ore grade.

2 With the most reasonable value being taken considering all information sources.
3 Here, only the concentration term is considered since Thanatia contains all minerals evaluated
but at a lower concentration. This effectively means that there would be no need to produce them
as they are already available with the same chemical structure.