Thermodynamics of Mineral Resources - Thanatia: The Destiny of the Earth's Mineral Resources - page 279

In addition to concentration exergy, the binding forces in the formation of a
crystal (the comminution exergy) should be accounted for. This is because minerals
in the crust are commonly embedded in a silicate matrix and its cohesian exergy is
its comminution exergy, i.e. the minimum exergy needed to comminute the mineral
between two given sizes. An analysis of this is undertaken in the following section.
9.5.2.3 Comminution exergy
Historically, the authors have maintained that the main features characterising a mi-
neral resource are its composition and concentration (Valero D. et al., 2008; Valero
and Valero D., 2010). If this were really the case, Eq. (9.30), would account for the
exergy required to concentrate the substance from the degraded state of Thanatia
to the conditions currently found in mineral deposits. However, strictly speaking,
Eq. (9.30) is only valid for ideal gas mixtures where collisions among molecules are
elastic. In reality, a cohesion energy is always present in any mineral, preventing
its spontaneous conversion into the gaseous state. Thus Eq. (9.30) would only ap-
ply to the exergy of a mixture and not to that needed to break the binding forces
among solids such as hydrogen, hydration, ionic and/or covalent bonds. Such forces
are su ciently strong enough to require the involvement of physical comminution
processes like crushing, grinding and milling. Therefore and investigated by Valero
and Valero D. (2012b) there is an important factor missing in the physical char-
acterisation of a mineral, namely its comminution exergy. This exergy identifies
the minimum energy required to bind solids from a given dispersed state to a more
cohesive one.
The energy needed to separate a solid particle from others smaller in size depends
on different physical aspects such as hardness or surface area. Some expressions
have been developed to link particle size to the energy input needed in grinding,
such as Kick's law or Bond's law. Both indicate that the energy used increases
exponentially as particle size decreases. These empirical formulas explain the actual
costs but not the minimum cost or exergy, leading to an intensive study by the
authors on the comminution exergy for minerals or rocks as a function of their
comminuted size (Valero and Valero D., 2012b) 9 . What follows is a short description
of the comminution exergy formula with respect to a large size fragmented rock in
Thanatia.
In order to obtain the comminution exergy of a given rock in a mine, one must
first define its state of initial fragmentation, characterised by the geometrical mean
size d M . Such fragments will be composed by ore and gangue with a specific surface
energy per unit mass. At the same time, one needs to assume that the size of the
barerock in Thanatia is d , meaning that its surface per unit volume is negligible
in comparison to fragments contained in a mine. Subsequently, one can define a
mineral's comminution exergy as the exergy one saves in having this rock fragmented
to d M instead of the size of the barerock composing Thanatia (d ).
9 The publication of Valero and Valero D. (2012b) is predominately based on the work of Tromans
and Meech (2002a, 2004).