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The Exergy Indicator

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The natural capital can be evaluated from different points of view. One of them, and perhaps the most commonly known is the economic point of view. Nevertheless, standard economy is only concerned with what which being directly useful to man, is also acquirable, valuable and produce-able. For this reason, most of the natural resources, remain outside the object of analysis of the economic system. The price-fixing mechanisms, rarely take into account the concrete physical characteristics which make them valuable.

But natural capital has at least two physical features which make minerals or fresh water for example unusual: a particular composition which differentiates them from the surrounding environment, and a distribution which places them in a specific concentration. These intrinsic properties, can be in fact evaluated from a thermodynamic point of view in terms of exergy (Valero et. al. 2003 , Göran Wall 2003).

The thermodynamic value of a natural resource could be defined as the minimum work necessary to produce it with a specific structure and concentration from common materials in the environment. This minimum amount of work is theoretical by definition and is equal to the material's exergy (Riekert 1974).

A rather new discipline called Exergoecology (Valero 1998) is starting to be considered as a future rigorous tool for natural resources accounting. Exergoecology is the application of the exergy analysis in the evaluation of natural fluxes and resources on earth. The consumption of natural resources implies destruction of organized systems and dispersion, which is in fact generation of entropy or exergy destruction. This is why the exergy analysis can describe perfectly the degradation of natural capital. Other authors such as Georgescu-Roegen (Georgescu 1971) or Ruth (Ruth 1993)  have also studied and showed up the connection between economic scarcity and the entropy law.

The Exergy of the Mineral Capital

The decrease of mineral capital comes from two interrelated factors. The first and more evident one is that as demand increases, more mineral has to be extracted from the mine and hence the total available quantity decreases. The second one is that continuous extraction implies declining ore grades, meaning higher quantities of ore needed to be processed and thus more energy. The work needed to separate a substance from a mixture does not follow a linear behavior with its concentration. On the contrary, the Second Law of thermodynamics dictates that the effort required to separate the mineral from the mine follows a negative logarithmic pattern with its ore grade. 

This means that as the ore grade tends to zero, the energy needed to extract the mineral tends to infinity. Therefore dispersion, which is not considered in resource evaluations in terms of mass, is a critical factor since it will ultimately determine the value of the mineral exploitation. Furthermore, it invalidates the statement of Brooks and Andrews  that running out of minerals is ridiculous because the entire planet is composed of minerals.

Hence quantifying the decrease of mineral capital in terms of mass is not enough since it does not take into account the quality of the minerals in the mine. However the exergy indicator can overcome this deficiency because it can evaluate at the same time, composition, concentration and of course quantity, by multiplying the unitary exergies with the tonnes of the resource considered. Furthermore, exergy is an additive property within resource accounting and can be used as a global natural capital indicator.

The minimum theoretical work that nature should invest to provide minerals at a specific composition from a dissipated earth is equal to the standard chemical exergy and it can be calculated by means of the exergy balance of a reversible formation reaction (see Eq. 1).

The chemical exergy of any mineral is always proportional to its production rate.

On the other side, the minimum theoretical work needed to concentrate a substance from an ideal mixture of two components is given by Eq. 2 :


  • bc concentration exergy (kJ/kmol)
  •  xi molar concentration of substance i
  •  R gas constant (8,314 kJ/kmol K)
  •  T0 standard ambient temperature (298,15 K).

The difference between the concentration exergies obtained with the ore grade of the mine (xm) and with the average concentration in the earth crust (xc) is the minimum energy that nature had to spend to bring the minerals from the conditions in the reference state to the conditions in the mine. The concentration exergy of a mineral is not proportional to its production rate. In this case, bc increases also as the ore grade decreases.

This methodology has been already applied for assessing the exergy decrease of US copper mines in the US (download document).

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Created by aliciavd
Last modified 2015-09-10 01:19 PM
New book: Thanatia

Thanatia: The Destiny of the Earth's Mineral Resources

Thanatia: The Destiny of the Earth's Mineral Resources

A Thermodynamic Cradle-to-Cradle Assessment by (author): Antonio Valero Capilla (CIRCE — Universidad de Zaragoza, Spain), Alicia Valero Delgado (CIRCE — Universidad de Zaragoza, Spain)

Is Gaia becoming Thanatia, a resource exhausted planet? For how long can our high-tech society be sustained in the light of declining mineral ore grades, heavy dependence on un-recycled critical metals and accelerated material dispersion? These are all root causes of future disruptions that need to be addressed today.

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