The Exergy Replacement Costs of Mineral Wealth - Thanatia: The Destiny of the Earth's Mineral Resources - page 356

12.3 Technological development and the theory of learning curves

There are two opposing trends influencing the energy required for mining: the
ore grade x m , which increases energy requirements, and improvements in energy
e ciency, which subsequently decreases it. This means that changes in ore grade
cannot be directly translated into changes in fuel use since there are also changes
in technology which affect fuel use (Chapman and Roberts, 1983).
It is a fact that in the mining industry, technology has always played an im-
portant role in transforming mineral resources into mineral wealth and useful end
products. Nevertheless, technological breakthroughs of mineral extraction had been
relatively slow until the Industrial Revolution. The spiraling demand of core com-
modities such as iron and copper found in this period led to even greater techno-
logical advances that even now remain in operation: flotation, the blast furnace,
railways, geophysics, drilling, trucks and transport and so on - all of which permitted
the mining of ever lower ore grades.
A way to assess the evolution of technological development is through the the-
ory of learning curves. These are used to analyse a well observed fact. Through
experience, mankind becomes increasingly e cient. As experience is acquired, costs
decline, e ciency and quality upgrades and waste is reduced. Technical change is of
course a gradual process that entails not only technical knowledge and investment,
but also an increase in material and energy e ciency. Both material and energy
e ciency increase independently and changes can stem from the learning by doing
concept (Ruth, 1993). Technical change is introduced by implementing technology
learning rates, which specify the quantitative relationship between the cumulative
experiences of the technology and cost reductions (Söderholm and Sundqvist, 2007).
The simplest and most frequent representation of learning curves in energy tech-
nology studies is Wright's log-linear model (Yelle, 1979):
Y x = Y 0 x l (12.8)
where Y x represents the energy required to produce the x th unit, Y 0 is the theoretical
energy of the first production unit, x is the sequential number of the unit for which
the energy is to be computed and l is a constant reflecting the rate of energy demand
reduction from year to year (learning index). S is the energy slope expressed as
a decimal value (learning rate), while (1-S) is defined as the progress ratio which
expresses the fraction to which energy requirements are reduced with cumulated
production. It is calculated as:

l = lnS
ln2

(12.9)

However there is a limit on the energy use to ore production that cannot be ex-
ceeded i.e. b c (the minimum theoretical energy required to concentrate a substance
from an ideal mixture of components): even with increased experience as explained
by (Ruth, 1995):

Y b c = Y 0 x l (12.10)