The Exergy Replacement Costs of Mineral Wealth - Thanatia: The Destiny of the Earth's Mineral Resources - page 359

200

Real data set

180

y = 23.81x -0.35

Concentration Energy [GJ/t]

160

140

120

100

80

60

40

20

0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Ore Grade[%]

Fig. 12.3 Energy requirements for copper production in function of ore grade. Adapted from

Mudd (2010a)

Fig. 12.3 shows the trends for an ore grade range including the average value re-
ported by Cox and Singer (1992).

12.5 The exergy replacement costs of the minerals on Earth

From energy data, one can subsequently calculate the unit exergy costs of the dif-
ferent minerals studied. As stated above, empirical energy data for mining and
concentration processes, as a function of ore grade E(x m ), could be found for only
four minerals: gold, copper, nickel, cobalt and uranium. For the rest of the com-
modities where no empirical data was known to exist, the general formula applied
to energy consumption as a function of the ore grade follows the exponential curve
given by Eq. (12.11).

E(x m ) = Ax m 0:5 [x m , metal concentration %] (12.11)

Coe cient A is determined for each mineral since the average ore grades x m
(Table 6.10) and the energy required for concentrating and extracting the mineral
at that specific grade E(x m ) is known (Table 8.3). It should be noted that x m
values are expressed in Eq. (12.11) as a mass percentage of the element under
consideration.
The latter is a very rough approximation and is derived by observing the trends
of commodities where empirical values are readily available. The empirical data
found for the minerals gold, copper, nickel, cobalt and uranium suggest that the
energy required for mining grows exponentially with the ore grade (Fig. 12.2,
Fig. 12.3). This observed fact which is in accordance with the Second Law, allows
for a general approximation of the exponential energy trend with the ore grade for
those minerals where no empirical data was available. Empirical data of energy