Geology Reference
In-Depth Information
This can be mathematically expressed through Shannon's entropy (Eq. (9.15)).
In fact, the scarcer an element or mineral in the crust, the more di cult it is
to find a commercially exploitable accumulation with the probability decreasing
exponentially. That said, even if a mineral or element is rare, the peculiarities
of mineralogenesis in a particular location could lead to concentrations which are
either below or above the composition of the average crust. Specifically, this phe-
nomenon depends on a given mineral's capacity to form a natural concentration,
which in turn is provoked from the various chemical or thermal inputs imparted
by the planet's internal heat or from the meteorisation caused by solar energy.
In Shannon's formula, geological and mining based knowledge plays an important
part in heightening the probability of finding a commercial concentration of a given
mineral. Pure guesswork corresponds to the greatest uncertainty in finding it.
9.4.2 Mining exploitation: declining ore grades and scarcity
As the Earth's crust is a solid solution of mixed heterogeneous substances Eq. (9.8)
applies. Should an element be scarce, x i will be very small and consequently the
minimum thermodynamic value to separate it from the crust will be very high.
This behaviour is exponential and ore grades observably decrease as mines become
exhausted, thus constantly increasing the minimum energy required for their ex-
ploitation. This is why the mining sector first picks the “low hanging fruits”, leaving
the remainder for the future with the hope that technology will improve and offset
costs.
Indeed given the ine ciency of current technology, the actual energy cost is
in reality several orders of magnitude higher than the thermodynamic minimum
which can never be superseded. Even if technology for extracting current ore grades
strongly improves in the future, the exponential character of the Second Law ex-
pressed in Eq. (9.8) gives little hope to a reduction in energy costs, particularly
when ore grades approach bare rock concentrations. Thus the absolute scarcity of
an element or mineral found in the Earth's crust can be interpreted from a ther-
modynamic perspective. This is because and as happens in the case of exploration,
technology can improve the extraction exergy costs but can never reduce the mi-
nimum exergy required in their mining- tending to infinity as the substances in a
mixture become increasingly dilute or numerous.
9.4.3 Separation processes in beneficiation, smelting and refining
As the mine steadily declines in grade, the ore must be subject to greater energy in-
puts in the stages subsequent to mining before reaching an acceptable concentration.
From a thermodynamic point of view, this refers to a set of physico-chemical pro-
cesses, namely beneficiation, followed by chemical-metallurgical operations. The
physical ones are pure separations, whilst those of a metallurgical nature are, in
fact, a combination of separations and reductions followed by a series of chemical or
 
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