Thermodynamics of Mineral Resources - Thanatia: The Destiny of the Earth's Mineral Resources - page 282

necessary to perform that same action with the best available technology. Both
parameters are therefore important indicators. The first is a physical property of
matter rather than a simple indicator and does not depend on the ever changing
state of technology. It does however serve to mark the limits of technology with
the hope that Man may someday with su cient ingenuity approach them. Unfor-
tunately, today's technologies lie far from the thermodynamic limit meaning the
figures obtained in exergy calculations are extremely low and with limited appli-
cability in practice. This explains why the exergy cost indicator is exergy's ideal
counterpart.
According to the Second Law, the difference between exergy cost and exergy in a
given process is the sum of all irreversibilities occurring during that process. There-
fore, Thermodynamics provides clear clues for improving energy and materials e -
ciency. The first step to take is avoidance, where possible, of product degradation,
including oxidation, reaction, mixing or dispersion. Hence, a way to save energy
is to meticulously identify and describe all the energy dissipation mechanisms and
design a practical solution with which to overcome them.
The calculation of exergy replacement costs, B , is undertaken through
Eq. (9.33), in which the concentration, B c , and chemical, B ch , exergies are multi-
plied by the unit exergy replacement costs (k c and k ch respectively) of the processes
undertaken to obtain the mineral as in Eq. (9.33).

B t = k ch B ch + k c B c (9.33)

where k ch is the physical and dimensionless unit exergy replacement cost of refining,
calculated as the ratio between the real energy invested in the process and the
minimum chemical exergy (B ch ). And analogously k c is the unit exergy replacement
cost of concentration, calculated as the ratio between the real energy invested in
the process and the minimum concentration exergy (B c ). It must be determined for
each type of mineral with the assumption that the same technology is applied in all
concentration ranges, including those found in Thanatia and in mineral deposits.
The methodology behind is explained in detail Chap. 12.
For comminution, the exergy cost is the actual exergy, using best available tech-
nology, one saves in having a rock fragmented at the size of d M instead of that of
the barerock composing Thanatia (d ). The comminution exergy cost of a mineral
can be directly calculated with Bond's equation (Eq. (9.34)) (Valero and Valero D.,
2012b):
B com = 10W i (1= p (d M ) 1= p (d )) [kWh/t] , when d M d (9.34)

However, as with comminution exergy, the comminution exergy cost is negligi-
ble 10 when compared to a materia l's chemical or concentration exergy. For instance,
10 The cost becomes even more negligible as size increases. For instance, a galena fragment of 1
m in length requires only 0.4040 kJ/kg, which increases tenfold once the average fragmentation
decreases to 1 cm. In contrast, its exergy increases by a factor of 100 from 1:90210 3 J/kg (size
1 m) to 0.1902 J/kg (size 1cm) (Valero and Valero D., 2012b).