**3. Closing material's cycles: the view "down the rainbow" (DTR)**

An important problem in valuation is the frequent fluctuation of the market price of mineral commodities while operating costs are quite foreseeable. Consequently, the resource rent may be composed of a quite volatile time series. Mineral exploration and evaluation costs are treated as a form of gross fixed capital formation. Moreover, decommissioning costs reduce

The physical extraction rate is usually constant along the life of the resource if there are no reappraisals. However, as resources approach depletion, there will be a decline in the ore grades and the environmental and energy costs associated with extraction will increase, thus avoiding extraction of yearly constant quantities. Even the central framework of SEEA warns that there is no reason why the extraction rate should necessarily be constant. In practical terms an important physical fact is ignored: the extinction of the mine is not constant along

We find two main objections to the SEEA. First, dividing nature into assets does not reflect all interactions among natural systems themselves. For instance, converting a forest into a stock of timber does not reflect other benefits coming from it, like floods protection, clean air, being a life-supporting system, or even its recreational purposes. Numbers will never reflect causality and may provoke greed for rapid exploitation of natural resources. For the SEEA central framework, the whole is exactly the sum of its parts. It resigns holism in favor of reductionism. Second, SEEA and SNA are firmly based on market price methods. Even if money has the power of easy comparisons among different issues, it reflects social values rather than objective values. They vary with time and from nation to nation. Money reflects the purchasing power of man in society. We pay people, not nature, and if nature claims nothing for its services, the monetary accounting system will only reflect present man´s interests. The implicit paradigm behind is: if we could extract and use all present environmental capital and convert it into money, it would be better than having physical assets not yet exploited. This is an absurd reductionism, and only the impossibility of having enough money to extract and convert nature into money inhibits that insanity. On the other hand, if everything is converted into money, the value of money itself would depreciate. Therefore, those that have retained their resources would become the wealthiest. The willingness to pay weakens with abundance and strengthens with scarcity. Yet the lack for a better numéraire excuses the use of money.

In fact, an important problem in SEEA is that it uses physical accounts without homogeneity in units or specificity in the type of mineral/material. This makes very confusing the trace of physical flows throughout its life cycle since materials react, mix, and decompose. Converting these units into exergy values would facilitate materials trace analyses through Sankey diagrams.

That said, the SEEA constitutes an impressive initiative for putting numbers to the man-nature interactions in a rational and global way. Universally organized statistics is perhaps the main value of the SEEA, and economists have developed well established procedures to rely on them. In what follows, we present an alternate method for assessing natural non-renewable resources

the resource rent earned by the extractor over the operating life of the extraction site.

the extraction period but follows the law of diminishing returns.

**2.3. Final comments on the SEEA**

64 Sustainability Assessment and Reporting

from a thermodynamic perspective.

We have seen in the previous section that SEEA accounts for physical flows in a cradle-to-grave perspective. However, in the cradle-to-grave path, there is information that these accountancy systems will never supply: depletion. Neither the economic nor physical accounting systems are efficient enough to assess the depletion of natural resources.

Something lacks in a global view: the mineral endowment and the non-renewable resources of the Earth are constantly decreasing. Each time non-renewable resourcesare extracted and not replaced we lose them irreversibly. And the only thing we can measure is its yearly decrease, not its lost value. There is no way of appraising what valuable things mankind is losing forever. Scarcity and the effort needed to replace non-renewable resources is absent in conventional accounting methodologies. Indicators for Materials recycling, substitution and consumption decrease also lack in the credit list. It could be argued that having an indicator of scarcity per chemical element could be enough to solve the problem. However, the myriad of inorganic products we can extract from mine Earth and the huge amount of chemical products that these materials can be converted into, makes impossible to have a decent accounting of the material cycles of all chemical elements.

In our view, there is a lack of theory rather than a lack of indicators. Partial or total cradleto-grave assessments are the half part of the cycle. We name them "over the rainbow" (OTR) accounting methodologies. They lack the other side: the grave-to-cradle assessment. In the same way that imaginary numbers can hardly be explained in the real space, some phenomena like depletion may be better explained in the "down the rainbow" (DTR) approach [1].

The planet works in cycles driven by solar energy: carbon, oxygen, nitrogen, phosphorus, sulfur, and water have their cycles but, to our knowledge, there are no postulated cycles for metals and chemical elements in general. Those elements related with life have short closing cycle times even if they have reset times measured in geological scale times. However, such elements that do not form part of biological life will hardly be reset. They are constituents of our exosomatic organs, and they are in danger of being scarce for future organs because of dispersion. In practical terms, both types of chemical elements must have their own cycle. And the human being must allocate a major effort to close and accelerate their closure. Sustainable development requires the closing of all chemical elements in the planet either for endo or for exo-somatic organs. Their closing cycle velocity, and the effort required must be a function of how intense is their use with respect to their physical scarcity. If man alters the cycles, closing them corresponds to man.

By extracting the ore from a mine, the exergy (i.e. physical utility) of the ore increases, even though we spent a lot of exergy (i.e. useful energy) to remove it. From the standpoint of future generations having the raw material in a store instead of having it in a mine would be a good inheritance. All environmental costs would be a matter of the past. This is something similar to leaving for the future the pyramids or the cathedrals. Clearly, if we use this raw material and then recycle it, we would be using it temporarily.

The problem arises with dispersion. What is dispersed and, of course, the increase in demand needs to be replaced with more extraction. That increases the size of the cycle to be closed, and the energy debit increases over and down the rainbow. The over the rainbow part is a 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, the efficient use of materials, and indeed the extraction efficiency.

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

Accounting for Mineral Depletion Under the UN-SEEA Framework

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

67

the mining sector and closes the cycle of materials, covering the OTR and DTR paths.

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

result, it has a CO2

of other minerals.

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.

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

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

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.

concentration of 683 ppm and a mean surface temperature of 17°C. The

is released. As a

obtained assuming that all conventional fossil fuels are burnt and all CO2

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 for fossil energy productivity of the Earth as low as 0.016 MJ/m<sup>2</sup> /day or 1000 kcal/0.7 m<sup>2</sup> /year.
