Epilogue - Thanatia: The Destiny of the Earth's Mineral Resources - page 511

countdown considering the upper limit reveals that in the majority of cases, the
peak will be reached before the end of this century with the exception of lead, iron,
manganese, vanadium, chromium, coal and potash.
It is worth reiterating that the Hubbert Peak Model is more an academic exercise
than a faithful description of reality. That said, it helps to construct scenarios based
on “business as usual”, thereby providing food for thought as to the importance of
resource conservation.
17.4 The spiraling tree of the elements
In the writing of this topic the authors have confirmed that rather than cycles the life
of mineral resources behave forming spirals. As in the case of the Global Cycles of
carbon, nitrogen, phosphorous and other elements in the geobiosphere, a Global Life
Cycle for each metal in the technosphere has been proposed in the literature (see for
instance, the cradle to cradle concept by McDonough and Braungart (2002) or Du
and Graedel (2011)). Specifically, Du and Graedel (2011) quantitatively described
the cycles of fifteen rare earth elements (for the year 2007) going from their mining to
their in-use stocks, end-of-life and lastly the scrap recycling steps. When one thinks
of cycles one automatically assumes that there is a closing of circles. However, an
integrated thermodynamic view widens this perspective by contemplating the cycles
of all the elements over the crust by classifying the actions into two generic branches:
constructive including mining, stockpiling, manufacturing, fabrication, stocking in
use and recycling and destructive, reactions such as dispersion, mixing, rebound and
backfire effects. Consequently cycles can never be circles but spirals. Such spirals
are progressively disappearing into nothing because dispersion is the opposing and
ultimately winning force to recycling. This can be conceptually represented by the
spiralling tree shown in Fig. 17.1. This tree is a typical fractal analogous to the
recursive structures, common to many natural systems (Kelleher, 2007).
Accordingly, the authors propose that the life route for each chemical element
follows a Grand Natural Fractal Tree involving all processes related to elements, be
they natural or manmade. An atom of a given element in a mine has yet to initiate
its cycle. Only once it is extracted does the spiral start. The more an element
(mineral) is mined the thicker its cycle. The cycle continues with manufacturing,
fabrication, use, end-of-life, landfill and dissipation. Dissipation into the crust,
hydrosphere or atmosphere is the last step. The spirals never truly end, they will
sooner or later find their way to Thanatia.
Mines represent the tree trunk with each branch implying a different use of an
element. Stock-in-use is indicated by the volume a tree occupies in the techno-
sphere. If its branch has a large radius, a given use has a greater longevity leading
to an extended life of that element. Each stage produces wastes that can be re-
cycled or downgraded to subsequent life-phases. Recycling can be done within the
same branch of application or grafted into another branch. Following a number