Thermodynamics of Mineral Resources - Thanatia: The Destiny of the Earth's Mineral Resources - page 280

Comminution exergy can be calculated as in Eq. (9.31):

b com = A v = = 6F r [1=d M 1=d ] 6F r =d M [J/kg] , when d M d (9.31)
where is the surface energy (J=m 2 ) obtained from Table D.2 and Table D.3. F r
is the surface roughness factor and (g=cm 3 ) the density. Both can be obtained
for a number of minerals from Table D.4.
For exergy calculations, the ideal comminution process is deemed to be one that
generates no loss of any kind, neither heat nor kinetic energy of fragments, as the
compression load is fully used in generating the new surface.
For instance, the comminution exergy of a galena fragment with a side dimension
of 100 m, would be

b com = 6 1:256 1:868 [J=m 2 ]=7:40 [10 3 kg=m 3 ]/100[10 6 m]=19.02 J/kg

This value can be compared with that of its chemical and concentration exergy
(b ch = 3,107 kJ/kg (with mol. weight 239.27 g/mol) and b c =80 kJ/kg, respectively).
Hence, galena's comminution exergy is over 10 5 times less than its chemical
one and over 4,000 times smaller than that of its concentration. This result may
however lead to the wrong conclusion because b com in Eq. (9.31) is proportional to
1=d M and the smaller the particle size, the greater the exergy needed to comminute
a given sample. Thus comminuting to micras (10 6 m) requires one thousand
times more energy than if one were solely to reduce the size to one millimeter. To
ensure that all the atoms in the crystal structure have been broken, one should
comminute all the material to the size of a nanometer (10 9 m). In which case
the comminution exergy of a material should, at least in theory, be identical to its
formation exergy. Additionally, as the cracking process starts from heterogeneities,
which are effectively defects and flaws in the structure of the feed material, the
surface tension increases as size decreases, hitting its upper limit when the grain
size reaches that of the crystal (Stamboliadis, 2004). In other words, due to its
power function behaviour, comminution is a very energy intensive process when it
comes to fine grinding and milling but is not so relevant in crushing operations and
negligible when evaluating the mineral wealth on Earth.
This is why, since the actual continental crust is markedly fractured, naturally
comminuted materials may be considered as exergy bonuses that Nature gives away
for free. However, when contemplated on a global scale this bonus is not altogether
significant especially when compared with the chemical and concentration exergies.
Additionally, the Crepuscular Earth Model presented in Chap. 10 and its accom-
panying formulas for evaluating the composition and the concentration of minerals
are not influenced by comminution exergy data either.
Hence, since comminution exergy can be effectively ignored, the total exergy
of a certain mineral can be approximated to the sum of the chemical B ch and
concentration components B c as in Eq. (9.32).
B ti = n i b chi + n i b ci + n i b comi ' B chi + B ci (9.32)