**4. Thermodynamic approach for accounting the Earth's mineral capital**

Ecological economists have learned that entropy is closely related to economics [3, 4]. It tells us about the direction to which economical fluxes (as part of the natural environment) go. However, entropy is a very difficult property to understand, and it is often used and "misused" in a metaphorical manner. In this way, we can find statements such as "mines of low entropy become mines of high entropy." However, the latter assert even if correct, does not provide much information. How can we overcome this deficiency? The answer is with exergy. Through this property, we are able to convert metaphors into real numbers. A good management of our finite concentrated mineral deposits needs to be based on reliable, objective and strong information sources, and removed away from market subjectivities.

This has been the motivation for the development of the Exergoecology approach [5, 6]. The fundamental instrument of the latter is the calculation of exergy replacement costs as a way for evaluating the "effort" that nature put into play for concentrating substances from a completely dispersed state to the concentrated conditions of the minerals found in the deposits. As the ore grade tends to zero, the exergy required to extract a mineral from the mine tends to infinity. Thanks to the fact that nature provides us with mines, the exergy needed to produce minerals is infinitely lower than if we would need to obtain them from the "bare rock." However, as extraction continues, the state of the deposits approaches to the bare rock, and future generations will have to deal with very low-grade ores, needing increasing amounts of energy for their exploitation [7]. Therefore, if we add an additional asset in the accountancy of minerals, namely the replacement costs in a "down the rainbow" view, we will consider the scarcity factor. This way, depleting high-grade ores is penalized since the exergy required to replace them with current technology would be very large. It should be noticed, that this point of view goes in the opposite direction of current practices: the larger the ore grade, the more cost-effective is its exploitation since production costs are much lower. However, this criterion enhances the depletion of high-grade ores since the future scarcity is ignored. Both aspects, replacement costs and conventional processing costs give a broader and more equilibrated vision of "sustainability" in the mining sector and closes the cycle of materials, covering the OTR and DTR paths.

Note also that these two indicators do not need speculations about the remaining mineral capital on Earth. No matter how much mineral remains to be exploited and the level of depletion, what we can assess is the "avoided" cost humanity had for exploiting the mine instead of doing it in the bare rock. These indicators also provide the exhaustion and the speed of exhaustion of all minerals we are extracting today in the planet. It is done in fully additive energy units instead of money units. Besides of that, the exergy replacement cost can easily be converted into money units since the price of each actual operation is available. That said, converting the replacement exergy into money units is senseless since the reversible processes to convert the bare rock into the mineral as in the mine are purely theoretical.

#### **4.1. Thanatia: a model of the dispersed Earth**

real consumption, and the down the rainbow is a debt we acquire with future generations. Anything that reduces the new extraction is positive: substitution, miniaturization, recycling,

Dispersion of raw materials has not been sufficiently considered in economic analyses. It has been ignored as a materials availability loss, but rather it is seen as a pollution problem. As it happens with heat in energy balances, it is obtained by difference. The dispersion is thus accounted by material balance: what is extracted minus what is recycled is equal to what is dispersed. But in reality there is no universal care in having a systematic accounting of the cycles of elements. Dispersion is the key for understanding the phenomenon of raw materials. The raw material backpack has two components: one is the overall impact of its extraction and the other, the acquired debt for avoiding dispersion. Each particular raw material has an environmental cost for dispersal. Under this light, substitution of a raw material for another would make sense if both parts of the backpack decrease. These assessments must be essentially physical. It is important to highlight that while the OTR side can be restored directly by nature in timespans of several generations - provided that our wastes should not exceed the assimilative capacity of the biosphere; the DTR side needs geological eras to naturally closing the cycle for each particular element. Restoring the planetary mines as they were before civilization would only be possible with the internal heat of Earth through volcanism. It is something beyond imagination. The "easiest" mineral resources to restore would be fossil fuels. However, fossil fuels have a formation time of the order of million years. Giampietro and Pimentel [2] gave a value

/day or 1000 kcal/0.7 m<sup>2</sup>

/year.

the efficient use of materials, and indeed the extraction efficiency.

66 Sustainability Assessment and Reporting

for fossil energy productivity of the Earth as low as 0.016 MJ/m<sup>2</sup>

**capital**

**4. Thermodynamic approach for accounting the Earth's mineral** 

strong information sources, and removed away from market subjectivities.

Ecological economists have learned that entropy is closely related to economics [3, 4]. It tells us about the direction to which economical fluxes (as part of the natural environment) go. However, entropy is a very difficult property to understand, and it is often used and "misused" in a metaphorical manner. In this way, we can find statements such as "mines of low entropy become mines of high entropy." However, the latter assert even if correct, does not provide much information. How can we overcome this deficiency? The answer is with exergy. Through this property, we are able to convert metaphors into real numbers. A good management of our finite concentrated mineral deposits needs to be based on reliable, objective and

This has been the motivation for the development of the Exergoecology approach [5, 6]. The fundamental instrument of the latter is the calculation of exergy replacement costs as a way for evaluating the "effort" that nature put into play for concentrating substances from a completely dispersed state to the concentrated conditions of the minerals found in the deposits. As the ore grade tends to zero, the exergy required to extract a mineral from the mine tends to infinity. Thanks to the fact that nature provides us with mines, the exergy needed to produce minerals is infinitely lower than if we would need to obtain them from the "bare rock." However, as extraction continues, the state of the deposits approaches to the bare rock, and future generations will have to deal with very low-grade ores, needing increasing amounts of energy for their Exergy measures the quality of systems with respect to a reference. When the system under analysis reaches the conditions of the reference, then it loses completely its distinction, i.e., its exergy [8, 9]. Therefore, the more separated the system from the reference, the more exergy it has. In the case of a mineral deposit, the more concentrated the mine, the more "quality" it has. Therefore, which should be the reference for the assessment of the mineral capital? In the end, when a mine has been completely depleted, its concentration would have theoretically reached that of the average crust. Hence, it is clear that our reference should be an Earth, where all minerals have been depleted, and all fossil fuels have been burnt. That model of Earth, that we named the "Crepuscular Planet" or "Thanatia" (from the Greek Thanatos, death), was developed by the authors and is extensively described in [10, 11]. Basically, it consists of a degraded atmosphere, hydrosphere, and continental crust. The atmosphere of Thanatia is obtained assuming that all conventional fossil fuels are burnt and all CO2 is released. As a result, it has a CO2 concentration of 683 ppm and a mean surface temperature of 17°C. The degraded hydrosphere was assumed to have the current chemical composition of seawater at 17°C (poles and glaciers melted). And for the upper continental crust, we proposed a model of bare rock defined by the composition and concentration of 324 substances in which 292 are minerals, and the remaining are mainly diadochic elements included in the crystal structure of other minerals.

As explained in [11], Thanatia should not be mixed up with the reference environment (RE), such as the one proposed by Szargut [12] for the calculation of chemical substances. In fact, both concepts constitute a reference for calculating exergies, but there are determinant differences. The assumption of assuming one substance per chemical element, which is common for all global RE, radically invalidates the use of the RE as a substitute of the model of crepuscular planet. We need a model of dispersed Earth where all commonly found substances appear.

The former only provides the chemical composition of the environment. The concentration factor is very important for assessing the mineral capital on Earth since as we explained before, the exergy of a mineral deposit increases exponentially with its ore grade. The greater the difference between the concentration of the mineral in the mine and in the dispersed crust, the more exergy (the greater value) will have the deposit. Hence, not only the composition of the "dead environment" is required, but also the concentration at which the substances are found in it.

where *kc*

CO2

**4.3. Case studies**

**4.4. Summary of the theory**

capability of social evolution.

account for the clean fossil capital on Earth [14].

is a constant called unit exergy cost and is the ratio between the real energy required

Accounting for Mineral Depletion Under the UN-SEEA Framework

http://dx.doi.org/10.5772/intechopen.77290

(3)

69

for the real process to concentrate the mineral from the ore grade *xm* to the refining grade *xr* and the minimum thermodynamic exergy required to accomplish the same process (Eq. (3)).

Since the energy required for mining is a function of the ore grade of the mine and the technology used, so it is the unit exergy cost. Then, the exergy cost of concentrating a mineral from the Earth's crust is named exergy replacement cost. Note that fossil fuels are different from non-energy minerals in that once burnt, they cannot be replaced because they have been converted mainly into

 and water. The exergy of fossil fuels is commonly accounted for through their High Heating Value (HHV). Pollutant abatement costs in exergy terms can be substracted from the HHV to

**Table 1** show results from [16] when the methodology is applied to several commodities. It has been assumed a world average ore grade for each metal shown. As can be seen, the exergy replacement costs are not insignificant and have at least the same order of magnitude than conventional mining and metallurgical costs. This way, we can give numbers to the whole cycle of materials: the over the rainbow path, through conventional mining and metallurgical

Physical measures fall within science, and a few of them transcend and become socially relevant. To cross this boundary, both the object of measurement and the units must have a set of consistent properties that facilitate understandability, universality, and measurement

In this context, the object of measurement is our global depletion of mineral resources at the planetary level. And we postulate exergy as its measurement unit. For doing that we need a theory supporting how this can be accomplished. The fundamentals of such a theory are: (1) There can be postulated an imaginary degraded Earth planet in which the crust, the hydrosphere, and the atmosphere reached a maximum level of dissipation of all its materials compatible with the Sun´s energy and the internal heat of the Earth. We name this planet Thanatia and is a crepuscular Earth where no mines exist and thus all materials are dispersed and have the composition of bare rocks commonly found in the crust; the hydrosphere contains no poles and is nearly composed by standard salt water; and the atmosphere reached the state predicted by long-term climate change models, with a high concentration of greenhouse gases coming from the complete combustion of fossil fuels. Thanatia is by no means in an equilibrium state, but in a conceivable geological steady state that can be characterized by a reasonable short set of physicochemical parameters. Thanatia is postulated as the ulti-

mate state of the present evolutionary man-induced degradation path of the Earth.

costs, and the down the rainbow path, through the exergy replacement costs.

That said it should be stated that conventional REs are still needed and constitute a tool for calculating chemical exergies. In fact, Thanatia has chemical exergy with respect to a defined RE. And as Szargut's approach is the most internationally recognized, we have adopted it with some improvements.

#### **4.2. Methodology**

Exergy measures the minimum (reversible) work required to extract and concentrate the materials from a RE to the conditions found in nature. The approach named Exergoecology [13]. allows to assess natural resources taking advantage of both thermodynamics and thermoeconomics principles. When minerals are extracted from Earth through the separation of it from the ore by means of different process like mining, beneficiation, roasting, smelting, refining, etc., the exergy associated to the mineral increases but this process requires the consumption of fuel, and other materials, whose exergy is destroyed after use.

The concentration exergy *bc* , represents the minimum amount of energy associated with the concentration of a substance from an ideal mixture of two components and is given by the following expression:

$$b\_{\circ} = -\overline{R}T\_{\circ} \left[ \ln \left( x\_{\circ} \right) + \frac{(1 - x\_{\circ})}{x\_{\circ}} \ln \left( 1 - x\_{\circ} \right) \right] \tag{1}$$

where *R* is the universal gas constant (8.314 kJ/kmol K), *T0* is the temperature of the reference environment (298.15 K), and *xi* is the concentration of the substance i. The exergy accounting of mineral resources implies to know the ore grade, which is the average mineral concentration in a mine *xm* as well as the average concentration in the Earth's crust (in Thanatia) *xc* . The value of *x* in Eq. (1) is replaced by *xc* or *xm* to obtain their respective exergies, whilst the difference between them represents the minimum energy (exergy) required to form the mineral from the concentration in the Earth's crust to the concentration in the mineral deposits.

This approach includes the irreversibility factor through the so-called exergy cost, which is defined as the total exergy required concentrating the mineral resources from the Thanatia with prevailing technologies.

The concentration of a mineral from the ore grade of the deposit to its commercial grade implies energy consumption completely different to that of concentrating the mineral from the dispersed state of Thanatia to the mine. The exergy cost of concentrating a mineral would require *kc* times the minimum concentration exergy (Eq. (2)).

$$b\_{c:i}^{\*} = k\_c \cdot b\_{ci} \tag{2}$$

where *kc* is a constant called unit exergy cost and is the ratio between the real energy required for the real process to concentrate the mineral from the ore grade *xm* to the refining grade *xr* and the minimum thermodynamic exergy required to accomplish the same process (Eq. (3)).

$$k\_c = \frac{E\_{realprovers}}{\Delta b\_{mineral\,x\_m \to x\_r}}\tag{3}$$

Since the energy required for mining is a function of the ore grade of the mine and the technology used, so it is the unit exergy cost. Then, the exergy cost of concentrating a mineral from the Earth's crust is named exergy replacement cost. Note that fossil fuels are different from non-energy minerals in that once burnt, they cannot be replaced because they have been converted mainly into CO2 and water. The exergy of fossil fuels is commonly accounted for through their High Heating Value (HHV). Pollutant abatement costs in exergy terms can be substracted from the HHV to account for the clean fossil capital on Earth [14].

#### **4.3. Case studies**

The former only provides the chemical composition of the environment. The concentration factor is very important for assessing the mineral capital on Earth since as we explained before, the exergy of a mineral deposit increases exponentially with its ore grade. The greater the difference between the concentration of the mineral in the mine and in the dispersed crust, the more exergy (the greater value) will have the deposit. Hence, not only the composition of the "dead environment" is required, but also the concentration at which the substances are found in it.

That said it should be stated that conventional REs are still needed and constitute a tool for calculating chemical exergies. In fact, Thanatia has chemical exergy with respect to a defined RE. And as Szargut's approach is the most internationally recognized, we have adopted it

Exergy measures the minimum (reversible) work required to extract and concentrate the materials from a RE to the conditions found in nature. The approach named Exergoecology [13]. allows to assess natural resources taking advantage of both thermodynamics and thermoeconomics principles. When minerals are extracted from Earth through the separation of it from the ore by means of different process like mining, beneficiation, roasting, smelting, refining, etc., the exergy associated to the mineral increases but this process requires the con-

concentration of a substance from an ideal mixture of two components and is given by the

mineral resources implies to know the ore grade, which is the average mineral concentration

between them represents the minimum energy (exergy) required to form the mineral from the

This approach includes the irreversibility factor through the so-called exergy cost, which is defined as the total exergy required concentrating the mineral resources from the Thanatia

The concentration of a mineral from the ore grade of the deposit to its commercial grade implies energy consumption completely different to that of concentrating the mineral from the dispersed state of Thanatia to the mine. The exergy cost of concentrating a mineral would

in a mine *xm* as well as the average concentration in the Earth's crust (in Thanatia) *xc*

concentration in the Earth's crust to the concentration in the mineral deposits.

times the minimum concentration exergy (Eq. (2)).

, represents the minimum amount of energy associated with the

is the concentration of the substance i. The exergy accounting of

or *xm* to obtain their respective exergies, whilst the difference

(1)

(2)

. The value

is the temperature of the reference

sumption of fuel, and other materials, whose exergy is destroyed after use.

where *R* is the universal gas constant (8.314 kJ/kmol K), *T0*

with some improvements.

68 Sustainability Assessment and Reporting

The concentration exergy *bc*

environment (298.15 K), and *xi*

of *x* in Eq. (1) is replaced by *xc*

with prevailing technologies.

require *kc*

following expression:

**4.2. Methodology**

**Table 1** show results from [16] when the methodology is applied to several commodities. It has been assumed a world average ore grade for each metal shown. As can be seen, the exergy replacement costs are not insignificant and have at least the same order of magnitude than conventional mining and metallurgical costs. This way, we can give numbers to the whole cycle of materials: the over the rainbow path, through conventional mining and metallurgical costs, and the down the rainbow path, through the exergy replacement costs.

#### **4.4. Summary of the theory**

Physical measures fall within science, and a few of them transcend and become socially relevant. To cross this boundary, both the object of measurement and the units must have a set of consistent properties that facilitate understandability, universality, and measurement capability of social evolution.

In this context, the object of measurement is our global depletion of mineral resources at the planetary level. And we postulate exergy as its measurement unit. For doing that we need a theory supporting how this can be accomplished. The fundamentals of such a theory are:

(1) There can be postulated an imaginary degraded Earth planet in which the crust, the hydrosphere, and the atmosphere reached a maximum level of dissipation of all its materials compatible with the Sun´s energy and the internal heat of the Earth. We name this planet Thanatia and is a crepuscular Earth where no mines exist and thus all materials are dispersed and have the composition of bare rocks commonly found in the crust; the hydrosphere contains no poles and is nearly composed by standard salt water; and the atmosphere reached the state predicted by long-term climate change models, with a high concentration of greenhouse gases coming from the complete combustion of fossil fuels. Thanatia is by no means in an equilibrium state, but in a conceivable geological steady state that can be characterized by a reasonable short set of physicochemical parameters. Thanatia is postulated as the ultimate state of the present evolutionary man-induced degradation path of the Earth.

(2) Exergy measures the minimum work needed to convert a thermodynamic state of a system characterized by a constant mass of constituent chemical elements into any other state of that system. Therefore, any state of the planet between the present one and Thanatia can be measured with the knowledge of the physicochemical parameters characterizing the two states. This general definition allows calculating the exergy distance between any two states of any specific mine, no matter what its chemical composition is likely to be. The same occurs when the mineral is converted into a raw material, smelted, refined, manufactured, transported, used, recycled, disposed of in a landfill, and/or dispersed.

**Values in GJ/ton of metal if not** 

**DTR path**

Aluminium-Bauxite (Gibbsite) 627 54 Antimony (Stibnite) 474 13 Arsenic (Arsenopyrite) 400 28 Barite 38 1 Beryllium (Beryl) 253 457 Bismuth (Bismuthinite) 489 56 Cadmium (Greenockite) 5898 542 Cerium (Monazite) 97 523 Chromium (Chromite) 5 36 Cobalt (Linnaeite) 10,872 138 Copper (Chalcopyrite) 292 57 Fluorite 183 1 Gadolinium-Monazite 478 3607 Gallium (in Bauxite) 144,828 610,000 Germanium (in Zinc) 23,749 498 Gold 553,250 110,057 Graphite 20 1 Gypsum 15 0 Hafnium 21,814 11,183 Indium (in Zinc) 360,598 3320 Iron ore (Hematite) 18 14 Lanthanum-Monazite 39 297 Lead (Galena) 37 4 Lime 3 6 Lithium (Spodumene) 546 433 Magnesite (from ocean) 136 447 Manganese (Pyrolusite) 16 58 Mercury (Cinnabar) 28,298 409 Molybdenum (Molybdenite) 908 148 Neodymium-Monazite 78 592 Nickel (sulphides) Pentlandite 761 115 Nickel (laterites) Garnierite 167 414 Niobium (ferrocolumbite) 4422 360 Palladium 8,983,377 583,333 Phosphate rock (Apatite) 0.35 5

**Exergy replacement costs, GJ/ton**

**OTR path**

**GJ/ton**

Accounting for Mineral Depletion Under the UN-SEEA Framework

**Mining and metallurgical costs,** 

71

http://dx.doi.org/10.5772/intechopen.77290

**specified**



(2) Exergy measures the minimum work needed to convert a thermodynamic state of a system characterized by a constant mass of constituent chemical elements into any other state of that system. Therefore, any state of the planet between the present one and Thanatia can be measured with the knowledge of the physicochemical parameters characterizing the two states. This general definition allows calculating the exergy distance between any two states of any specific mine, no matter what its chemical composition is likely to be. The same occurs when the mineral is converted into a raw material, smelted, refined, manufactured, transported, used, recycled, disposed of in a landfill, and/or dispersed.

(3) Once any two states of the system are characterized, it is possible to calculate the current exergy cost we need to invest with prevailing technologies to reach a final state from an initial one. As our technology is far from being reversible, exergy cost and minimum exergy differ in many cases in several orders of magnitude. History tells us that mining and chemical technologies have changed rather slowly over decades and hence, the exergy costs can be assumed to be constant over a not too short period of time (for some cases over decades). Exergy may be a better indicator for pure scientific purposes. In turn, exergy cost is prone for social interpretations because even if it depends on the state of technology, it is closer to societal perception of value. Both indicators are equally valid

(4) We postulate that each chemical element must have its own cycle either naturally powered by direct or indirect Sun´s energy, or geologically powered. Man-made technology can accelerate or decelerate these cycles. Thus metallic elements can be viewed to be somewhere in the geosphere or in the technosphere. One element in mine has not initiated its cycle. Once it is mined, the cycle starts. The more mineral is mined, the larger its cycle. And the shorter the residence time in the technosphere is, the greater it's dissipation. Recovering what was dispersed would require significant amounts of exergy and ingenuity that makes in many cases almost impossible closing the cycle. However, humanity will need to recover more and more elements from bare rock because of its profligate use of previously mined ones. Many rare earths and scarce elements are already obtained

(5) Under this light, we propose measuring depletion of a given mineral as the exergy cost needed to close the cycle between the compositions of the constituents in the Thanatia´s dispersed state, and the mineral in the mine at its present state. In addition, its exergy is also a complementary measure of this depletion. We named these parameters exergy replacement cost and replacement exergy, respectively. The overall process from mining to dispersion and dissipation is the well known cradle-to-grave process. This is the part everybody sees, that is why we name it as the "over the rainbow" part. However, there is an imaginary part, "down the rainbow" or grave-to-cradle approach, which can aptly explain and measure how much depletion is going on with all man activities. We have seen that all the attempts to measuring depletion "over the rainbow," either in monetary or in physical terms, collide with the impossibility to put an objective value to physical scarcity. The depletion of the mineral capital on Earth must be measured on a grave-to-

from nearly bare rocks. Technology exists accordingly.

on a thermodynamic basis.

70 Sustainability Assessment and Reporting

cradle basis.


Concerning policy relevance, a good indicator must be: (a) easy to interpret, (b) show trends over time, (c) be responsive to changes in underlying conditions, and (d) have a threshold or

Accounting for Mineral Depletion Under the UN-SEEA Framework

http://dx.doi.org/10.5772/intechopen.77290

73

Exergy as the available energy is easy to interpret since it is what laypeople call energy. As a matter of fact, we pay exergy not energy. The exergy replacement cost and the exergy cost indicators can show either aggregated or disaggregated trends over time just being responsive to any kind of variation in amounts of extraction, improvements in processes efficiency, substitution, recycling, and whatever changes in the element cycle. Finally, Thanatia as a threshold is the best provider of reference values to which evolutions on depletion can be

Concerning analytical soundness, indicators should be well supported in technical and scientific terms. It is obvious that exergy indicators are well based on the second law of

Concerning measurability, indicators should be: (a) calculated from data that are readily available or available at reasonable cost, (b) data should be documented and of known quality, and

The data for calculating exergy replacement costs must come from data provided from the physical SEEA tables. Assets providing amounts of extracted material, composition, ore grades, amounts of processed, smelted, refined chemicals, amounts of recycled material with its composition, etc., available in the PSU tables are what exergy costs need for their calculations. The data obtained for exergy replacement costs will be as reliable as the data provided by SEE accounts. And the calculations required are easily available with adequate computer programs. International agreements could be reached in order to update both data and indicators as well as improve interpretations and act accordingly. As exergy is an additive property, it has the capability of integrating and aggregating a large variety of causes of variation including how substitution, recycling, and nanotechnologies positively improve our global management of the mineral capital. Conversely, each country, company or mine could use the exergy replacement cost to account for the attained depletion level. And this cost can easily be converted into money units just by multiplying it by some previously agreed energy price. Money accounts are useful at the micro level from companies to countries, but at a global scale and throughout

time, exergy accounts may give a clearer picture far removed from economic vagaries.

**6. Concluding remarks: from SEEA to a global system of** 

**environmental-thermo-economic accounts**

Finally, the proposed indicators are complementary with others, especially with cradle-tograve indicators that close the cycles of elements. All together could provide an overall measure of "unsustainability" and its yearly variation, which could be used as a policy lever.

The depletion of a mineral should not be anymore the difference between its world price and its economic cost of production as economists propose. On the contrary, it should be assessed as the loss of reserves quantified through its replacement cost with prevailing

measured. Therefore, our indicators are policy relevant according to OECD.

reference value against, which conditions can be measured.

(c) data and indicators should be updated at regular intervals.

thermodynamics.

**Table 1.** Total exergy costs of selected metals: the OTR and DTR paths.
