Exergetic Evaluation of Natural Mineral Capital

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Exergetic Evaluation of Natural Mineral Capital (1) Reference Environment and Methodology.

Antonio Valeroa, Lidia Ranzb, Edgar Boteroc.

a,b.Centro de Investigación de Recursos y Consumos Energéticos (CIRCE), Universidad de Zaragoza, María

de Luna 3,50015 Zaragoza, Spain. c.Grupo de Investigaciones Ambientales, Universidad Pontificia Bolivariana, Circular 1 Nº 70-01, Medellín,

Colombia. Summary The series of these papers develops a methodology using the Second Law of Thermodynamics to evaluate the Earth’s mineral resources in physical units. This paper first defines a Reference Environment –R.E.- based on Szargut work [7] to evaluate the minimum energy –exergy- needed to produce all mineral resources under the physical and chemical conditions that make them useful.This reference can be assimilated to a thermodynamically dead planet where all materials have reacted, dispersed and mixed. Secondly, it is given a procedure to assess the replacement exergetic cost of a mineral, defined as the exergy resources needed to concentrate and produce it from its components in the R.E. with the current best available technology. This physical cost is measured in exergy units (GJ). With this procedure the exergy and the exergetic cost of any mine can be calculated and provides acceptable and realistic values of the energy saved for us by Nature, when she gaves for free scarce and chemically favourable minerals. 1.Introduction. Mineral resources are a natural capital that are limited in quantity and non-renewable in character, at least on a human time scale. Mineral extraction decreases the Earth’s mineral richness, which was created millions of years ago. Today these minerals are enormously important since they fuel the world economy. They provide most of the raw material to manufacture the products we consume and almost all of our primary energy (more than 95% including uranium; Adriaanse et al. [1]). Even so-called renewable energy sources use energy converters that require large quantities of mineral resources to build and maintain. According to data from the U.S. Bureau of Mines [2], the world-wide consumption of rocks and minerals is approximately 22 billion of tonnes per year. The consumption of fossil fuels is nearly 10 billion of tonnes. If we add this to all the sterile materials and wastes Naredo and Valero [3], the extraction of rocks and minerals involves about 64 billion of tonnes of materials per year and 24 billion of tonnes of fossil fuels. In addition, these figures are rising at an alarming rate. The direct human appropriation of photosynthetic products is around 10.6 billion of tonnes per year (Romano [4]). So the tonnage associated with the extraction of minerals and rocks is three times greater than the products of photosynthesis. Obviously, the predatory behaviour of our industrial civilisation is not viable in the long term. In order to channel activity towards more sustainable sources, we need to responsibly manage activities related to mineral resources. This management must also be based on the greatest possible knowledge of the mineral wealth of the territory in question and include the losses of capital which extraction periodically entails. Cleveland [5] evaluated the loss of mineral quality by studying the increase in the amount of energy to extract and separate mineral resources. If the grade of a mineral deposit decreases, the amount of energy needed to extract and separate its minerals will increase. The Cleveland indicator can be used to evaluate

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mineral resource scarcity. However, Cleveland [5] really measured the variations in energetic efficiency of extractive activities. His physical indicator depends on technical and socio-economic factors. As Chapman & Roberts [6] demonstrated, the energy to extract and separate mineral resources can be reduced by technological improvements. Even if the grade of a mineral deposit decreases, technological advances can reduce the amount of energy for extraction and separation. For this reason, we need another physical indicator that only depends on physical factors. This new indicator is the subject of our research. We evaluated mineral resource scarcity using an exergy function. The methodology developed by Szargut [7] lays the basis for a physical quantification of the Earth's mineral capital. The results could be used to inform and guide society in understanding the true physical costs of extraction and the use of mineral resources. In general terms this means ordering and classifying mineral resources into two characteristics which are largely responsible for their value: specific chemical composition and their unusually high concentration in deposits. Using the idea of exergy, we develop concrete physical criteria to evaluate these deposits. 2.Unusual Characteristics of Mineral Resources. Mineral resources are characterised by a set of properties which are mainly either intrinsic or extrinsic. Intrinsic characteristics are the mineral's own peculiarities, independently of how they are analysed. They can be divided into physical/chemical and mining/geological characteristics. The former includes composition and concentration in deposits. The minerals they contain can also be classified according to their magnetic, optical, electrical or thermal properties. Radioactivity, luminescence, density, hardness or specific weight can also be considered. Mining and geological characteristics are the result of three main processes of formation and concentration during the creation of mineral deposits: igneous, sedimentary and metamorphic. The geological features of minerals include size, geometry, mineralogical composition or geological combinations. The depth at which they are found and the lithology of the surrounding rock are also important in mineral prospecting. Extrinsic mineral characteristics are socio-economic in type including usefulness, necessity, substitutability, toxicity, economic value, etc. These properties depend on each society of consumers and are quite variable in space and time. For example, the current economic value of many mineral substances is based on the criteria of the badly-named "producers" of raw material. These criteria vary with time and are dependent on opportunities for profit at any given moment. In fact, the economic value of many metallic minerals depends on international markets. According to the World Resources Institute [8], the evolution of the pricing of metals and energetic materials has decreased markedly. However, mineral extraction is increasing each year which results in cheaper mineral resources (see Ortiz [9]). The traditional way to evaluate minerals does not consider intrinsic characteristics. A mine is an exceptional circumstance in Nature. Less effort is needed to extract its minerals compared other parts of the Earth's crust, due to its physical (concentration) and chemical (composition) aspects. The problem of mineral availability has been brought up by several authors, as well as the physical limitations (basically energetic) of exploiting minerals in low concentrations (see Bravard et al. [10], Page & Creasey [11], Kellogg [12], Cloud [13], Chapman & Roberts [6]). A lot of work has been done to analyse the energy required to concentrate from the mine grade to the stage before the refining process. But little is known about the amount of energy required to concentrate minerals from a very dispersed state in the Earth’s crust (Reference Environment) to a mine, which can be precisely associated to the physical value of a mineral.

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The value of a mineral does not only depend on concentration, but also on composition. Not all minerals with a certain element can be considered a source of that element since their chemical conditions will affect the application of different metallurgical processes. Nature also needed a certain amount of energy to provide the mineral with a specific composition, which represents the chemical value of the mineral. We performed an analysis to define the Reference Environment (R.E.), which serves as a starting point to calculate the thermodynamic value of all minerals and the yearly physical loss of exploiting resources with the best physico-chemical characteristics (with the largest exergy). 3.The Reference Environment. The thermodynamic value of a mineral could be defined as the minimal work necessary to produce the mineral with a specific structure and concentration from common materials in the environment. The process should be reversible and heat should only be exchanged with the environment. This minimum amount of work is theoretical by definition and is equal to the material’s exergy (Riekert [14]). Then, to calculate the exergy of any natural resource, including minerals, we need to define an R.E. This is to be used by convention and represents the most degraded thermodynamic state. The R.E. has resources chemically degraded and completely dispersed. We can try to imagine the entropic death of our planet, but it will probably not be like the thermal death of the universe imagined by Clausius and Kelvin. It should be something similar to what is now Venus, a planet whose atmosphere is 95 % CO2 and whose terrestrial materials are mixed and reacted until their minimal reactivity under the existing environmental conditions. In the long term and from a thermodynamic point of view, neither the pressure nor the temperature of the Earth will change significantly. The problem is the oxidation and dispersion of its resources which humankind is accelerating. After extracting mineral resources, we disperse them, provoking the oxidation of metals. We consume fossil fuels, which would have remained in a metastable state for millions of years. We consume oxygen that was formed at the same time as organic material. We dissolve materials in the sea and destroy forests. In short, we spend the Earth's chemical exergy. It is possible to consider a thermodynamically dead state where all materials have reacted, dispersed and mixed into an “entropic planet” with the three phases each one at a homogeneous composition which corresponds to the current composition of all the elements that make up the Earth's crust at environmental pressure and temperature. From this point, any substance with a higher concentration, temperature, chemical potential, pressure, height or velocity would have a greater exergy than this entropic planet. This fact can help to calculate the thermodynamic value of a resource. Some authors state the R.E. close to the actual surroundings in a hypothetical state of thermodynamic equilibrium. According to Ahrendts [15], exergies must be derived from a meaningful physical reference system that is in equilibrium with respect to a well-defined class of processes and constitutes a dead state. If the amount of different elements in the reference system is known and the temperature of the system is fixed, the quantity of each chemical compound and the value of each chemical potential is uniquely determined by the condition of chemical equilibrium. Of the subsystems on Earth that make up the stock of elements in the equilibrium reference system, Ahrendts [15] selected the atmosphere, the oceans and the layer of the Earth's crust that is accessible to technical processes (1m). He relied on the geological model in Ronov & Yaroshevsky [16]. The reference system includes only 15 elements, making up more than 99% by weight of

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the Earth’s crust. The number of chemical compounds in the model was limited to 692 by the available thermo-technical data. Ahrendts's R.E. is not suitable to evaluate mineral resource value. First of all, most of the metals cannot be evaluated because they form part of the 1% of the weight of the Earth’s crust which has been neglected. Even though their concentrations in the whole crust are very small, they can be very important locally and be extracted. Secondly, the composition of Ahrendts’s R.E. is different from the real environment. The Earth would never be similar to the calculated reference state since it is not allowed by kinetic, biological and geological factors. Finally, Ahrendts’s R.E. is not absolute. It also depends on conventions, such as the layer of the crust or the number of compounds selected. Kameyama et al. [17] proposed an artificial reference system with a reference substance for each element. The references are the most stable compounds among those with thermo-chemical data and can be integrated in the solid, liquid and gaseous environments. The criterion of chemical stability formulated by Kameyama et al. selects for very stable compounds such as nitrates, which are very rare in the environment because their formation is kinetically blocked. So the composition of this R.E. is also quite distant from the composition of the real environment, which is not integrated by the most stable substances. The exergy values in Kameyama et al. [17] do not account for differences in concentration between all the elements and compounds.Therefore, the Kameyama et al. [17] R.E. is not suitable to evaluate the scarcity of mineral resources. Szargut [7] suggests a R.E. that is more similar to the real physical environment with the most stable and abundant sources of the Earth's crust. According to Szargut, the R.E. should represent the products of an interaction between the components of the natural environment and the waste products of the processes. Therefore the most probable products of this interaction should be chosen as reference species. But Szargut also states that the compounds with the most common components of the external layer of the Earth's crust should be selected as reference substances. According to data from Taylor & McLennan [18], the upper continental crust is 32% sedimentary and 68% cratonic. Lots of minerals in the cratonic crust are compounds with the most common components of the upper continental. They should be selected but they are not very stable and do not represent the products of an interaction between the components of the natural environment and the waste products of industrial processes. They integrate the natural environment which is evolving and not stable. Szargut [7], [19] and [20] mixes abundance with stability. He assumes that the most common components of the external layer of the Earth's crust are also very stable, which is not always true. Szargut in refs. [19] and [7] mainly chooses oxides, hydroxides, carbonates, silicates, and sulfates as reference substances. Except for some silicates and oxides, the rest of these substances mainly integrate the sedimentary crust, which is only 1/3 of the upper continental crust. According to Wedepohl [21], the sedimentary crust has shales (72% volume), carbonates (15% volume), sandstones (11% volume) and evaporites (2% volume). So Szargut’s selection of the solid reference species criteria has some drawbacks and his R.E. is not very similar to the real environment. Following Szargut methodology, Ranz [22] proposes a new R.E. quite similar to the real environment. This R.E. has three phases, either solid, liquid or gas. Each of these phases has reference species (R.S.) (one for each element) in a state of maximum dispersion. The solid phase of the R.E. reproduces accurately the Earth’s upper continental crust. The solid reference species (S.R.S.) that make up this artificial environment are the same as the most abundant types to be in the Earth’s upper continental crust. Furthermore, they are found in their state of maximum dispersion. Ranz [22] provides an accurate description of the steps to choose the most suitable solid reference species, according to abundance criteria.

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The standard chemical exergy of an element calculated in this way has two components: the concentration component and the reaction component. The first provides information about the minimum amount of work needed to concentrate the reference substance of the given element from an R.E.This is very similar to the real environment, but completely dispersed. The second one tell us the minimum amount of useful energy needed to break the bonds that unite the reference substance in order to isolate the elements. The concentration component is always positive. The reaction component can be positive or negative, depending on the stability of the reference substances compared to the native elements. The reaction component of the standard chemical exergy of an element can be 100 times greater than the concentration component, so it can lead to some negative chemical exergies.For instance, elements with sulfur compounds associated as reference species have negative chemical exergies. That means that sulfur compounds are less stable than some elements they contain, but they are more abundant in the upper continental crust. In fact, most of the economic deposits of metals are integrated by sulfur compounds. The concentration exergies of the reference substances calculated by Szargut [7] are very different from the values values provided by Ranz [22]. She selected the most abundant compounds as reference substances, which decreases the minimum amount of work used to concentrate them. Thus, her concentration exergies are less than those estimated by Szargut in [19] and [7]. Her element exergies are also very different. But the differences in the concentration exergies are not the most important parameter. In this case, the choice of the most advisable reference types best explains these differences since the chemical exergy of an element informs mainly about the minimum amount of work to make it from a reference substance. In any case, a problem with the Ranz [22] proposed R.E. is that some elements show negative exergies. This is because the reference species was established as the most abundant substance containing each element. If we assign zero exergy to the most abundant substances we are decreasing arbitrarily the natural capital.This is because many abundant minerals like sulfides naturally evolute to the most stable oxides. Then, we must return to the Szargut criterion of using the most stable substance, which also is the most probable waste product in industrial processes.But, on the contrary, the R.E.proposed by Szargut [7] is, as yet said, less similar to the actual environment. In order to avoid this, we propose to improve and update the Szargut’s R.E., taking advantage of the effort done by Ranz [22] in providing more precise and coherent data. 2.1. Calculation Methodology. Following this approach, we adopted the reference species proposed by Szargut [7] for the following elements: argon, barium, bismuth, boron, bromine, cadmium, caesium, carbon, cerium, chlorine, copper, dysprosium, erbium, europium, gadolinium, gallium, germanium, gold, hafnium, helium, holmium, hydrogen, indium, iodine, iridium, iron, lanthanum, lead, lithium, lutetium, manganese, mercury, molybdenum, neodymium, neon, nickel, niobium, nitrogen, osmium, oxygen, palladium, phosphorus, platinum, plutonium, potassium, praseodymium, radium, rhenium, rubidium, ruthenium, samarium, scandium, selenium, silicon, sodium, strontium, sulphur, tantalum, tellurium, terbium, titanium, thallium thorium, thulium, tungsten, uranium, vanadium, xenon, yttrium and zinc. For the following elements we propose different reference species than Szargut: aluminium, arsenic, beryllium, calcium, circonium, chromium, cobalt, fluorine, magnesium and silver.

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2.1.1. The concentration exergy of gaseous reference species. The concentration exergy of gaseous reference species was obtained following Szargut & Dziedziniewicz [23]. Gaseous components of atmospheric air can be accepted for nine elements: C, H, O, N, Ar, Ne, He, Kr and Xe. The standard concentration exergy of gaseous reference species results from their mean partial pressures in the atmosphere,

n

noconc p

pRTb n

r

0ln−= (1)

where R is the gas constant (8.3147 J/molK), Tn is the standard normal temperature (298.15 K), pn is the standard pressure (101.325 kPa) and po n is the conventional mean partial pressure in the atmosphere (kPa). Table 1 summarises the elements associated with their gaseous reference species and the concentration exergy of the elements. 2.1.2. Reference species dissolved in seawater We used the formula proposed by Szargut & Morris [20] to calculate the standard chemical exergies of the elements with reference species dissolved in sea water. These reference species are the most commonly found in sea water.They are shown in Table 1.

]ln)(.[ γν∆ nnno

kel chkHoch

oref f

oel ch mRTpHzRT3032bbz

21Gjb

2−−−+−= −∑ (2)

where j is the number of reference ion molecules derived from one molecule of the element under consideration; ∆Go

f ref is the standard normal free energy of formation of the reference species; z is the number of the elementary positive charges in the reference ion; νk is the number of molecules of additional elements in the molecules of the reference species;

2Hochb , bo

ch el-k are standard chemical exergies of hydrogen

gas and of the kth additional element, respectively; mn is the conventional standard molarity of the reference species in seawater, γ is the activity coefficient (molarity scale) of the reference species in seawater; and pH (=8.1) is the pH of seawater. 3.1.3. The concentration exergy of solid reference species The concentration exergy of the S.R.S. is the minimum amount of work to isolate and separate each of the substances in the solid phase of the R.E. The estimation of the influence of element abundance on the concentration exergy of its reference species is only approximate. To make this calculation we supposed that the S.R.S. has the properties of the components of an ideal solution, as did Szargut [19]. To each S.R.S. we allocate what we have agreed to call its concentration exergy, which is the contribution of this substance to the total exergy of separating and isolating the substances in the R.E. The standard concentration exergy is expressed per mol of the reference substance to be separated and is given by the expression:

ii nn0conc xRTb ln−= (3)

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where xn i is the conventional mean molar fraction of the reference species in the upper continental crust. The concentration of the upper continental crust is usually expressed as elemental concentration. This will have to be converted to obtain the concentration of the S.R.S. in the R.E. Szargut [19] suggests:

oii

n Mcnl

xii 0

1= (4)

where

ion is the mean molecular fraction of the ith element in the upper continental crust (mol/g), li is the number of the atoms of the element in the molecule of the reference species, ci is the fraction of the element appearing in the form of the reference species in the upper continental crust, and Mo is the mean molecular mass of the upper continental crust. The concentration of elements in the Earth's crust used by Szargut [19], [7] was principally that of Taylor, as taken by Polanski & Smulikowski [24]. However, these values have been slightly phased out and now there are more recent and trustworthy reviews such as Taylor & McLennan [18] and [25]. As done by Ranz [22], we mainly used the data of this last revision to update the concentration exergy of the S.R.S. For some elements (bromine, carbon, chlorine, fluorine, iodine, mercury, nitrogen, and sulfur), we used the values estimated by Wedepohl [26], because they are not included in Taylor & McLennan [18] and [25]. Finally, the values of platinum, plutonium, radium, rhodium, ruthenium and tellurium were taken from Szargut [19], given that neither Taylor & McLennan [18] and [25] nor Wedepohl [26] estimated their concentration in the upper continental crust. For some elements the differences between the concentrations used by Szargut [19] and those used here for the upper continental crust (mainly from Taylor & McLennan [18]) are quite significant. For example, the Ir concentration proposed by Taylor & McLennan [18] is 51 times less than in Szargut [19]. The same occurs for Pd which was 20 times higher in Szargut [19] than in Taylor & McLennan [18]. The concentration of C in Wedepohl [26] is 15.87 times higher than in Szargut [19], and 4.88 times higher for chlorine. For the rest of the elements, concentrations in Taylor & McLennan [18] and Wedepohl [26] are not more than three times higher or lower than in Szargut [19]. These differences determine the discrepancy in the elemental exergies which are not more than 10 kJ/mol. Ranz [22] performs a more accurate comparison between the elemental concentrations we used and those of Szargut [19], together with the standard chemical exergies of the elements. The mean molecular mass of the upper continental crust estimated by Szargut [19] was Mo =135,5 g/mol. He used geochemical data from Clarke & Goldschmidt, as collected by Smulikowsky [27]. We updated the mean molecular mass of the upper continental crust, using information sources such as Wedepohl [26], Nesbitt & Young [28], Taylor & McLennan [18] or Carmichael [29]. Next we present the calculation methodology as proposed by Ranz [22]. First of all, we reviewed the relative weights of the major components (expressed as oxides) in the craton and sedimentary crust from Carmichael [29]. Then we applied the CIPW norm (after Cross, Iddings,Pirsson & Washington (1902)) to the major oxide group and obtained the norm mineral for each type of crust. The volume of the resultant norm minerals were compared with the volumes of the main rock groups in the upper continental crust (Wedepohl [26], Nesbitt & Young [28]). Then the norm minerals were modified to adjust them with the real volumes of each crust type. Finally, we calculated the mean molecular mass of the upper continental crust. The mean molecular mass of the upper continental crust was 145 g/mol (+- 10 g/mol). The chemical exergies of the elements only differed by 0,4 kJ/mol compared to Szargut [19]. The differences in

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the chemical exergy of the elements calculated in each case were not greater than 3,5 kJ/mol. This geological approach assured that the described continental crust was very similar to the real continental crust. As mentioned above, ci is the fraction of the element in each chosen specific reference. The values of this parameter in Szargut [19] and [7] are 0,05, 0,01 and 0,001 from the most to the least frequent elements. He established these values more or less intuitively, so they should be revised in detail by consulting the relevant geological sources. We present an updated ci of S.R.S. using information from Rankama & Sahama [30], Rösler & Lange [31], Taylor & McLennan [18] and Carmichael [29]. An accurate description of the calculations can be found in Ranz [22]. Table 1 summarises the reference species selected for each element, the concentration of the elements in the upper continental crust (mainly from Taylor & McLennan [18] and [25]) and their ci. 3.1.4. The standard chemical exergy of the elements The standard chemical exergy of an element can be calculated using the exergy balance of formation of the associated reference substances:

)ok-el ch

kk

0RS f

ochRS

i

0el ch bν∆G(b

d1b

2i ∑−−= ν (5)

where bo

ch RS is the standard chemical exergy of the reference species, di is the number of molecules of the element in the molecules of the reference species, ∆Go

f RS is the standard normal free energy of the formation of the reference species, bo

ch el-k is the standard chemical exergy of additional elements in the reference species, and νk is the number of molecules of the additional element in the molecule of the reference species. This equation should be applied first for elements with simple reference species (e.g. oxides) and then for more complicated ones, because the values bo

ch el -k should be known for every step of each calculation. The obtained standard chemical exergy values of the elements are shown in Table 1, as well as the values given by Szargut[7]. As can be observed, the exergy values of some updated elements are quite different, especially aluminium, arsenic, beryllium, cobalt, chromium and fluorine which range from 10 kJ/mol to 92 kJ/mol. These variations are the result of adopting less stable reference species than Szargut [7]. However, they represent with higher probability the products of interactions between the industrial compounds of the elements and the R.E. The differences in values between palladium and iridium range from 7 to 10 kJ/mol. This is mainly due to the large variation in the concentrations of these elements in the upper part of the Earth’s crust, according to estimations by Szargut [7] and Taylor & McLennan [18] and [25]. The elemental exergies of the second reference species proposed by Szargut [7] are high for calcium (8,5 kJ/mol), chlorine (9,3 kJ/mol) and iodine (9,0 kJ/mol). These values in solid references are much closer to those of dissolved substances in sea water. In the case of calcium, the 8 kJ/mol exergy difference between the species in sea water or the solid one implies that we should choose the first species instead of the second, as did Szargut [7].

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The updated exergy values of germanium, gold, hafnium, osmium, scandium, tin, titanium, vanadium and zirconium do not differ by more than 5 kJ/mol as compared to Szargut [7]. For the rest of the elements, the differences are less than 1 kJ/mol. This new proposal improves and updates the R.E. proposed by Szargut[7], however it becomes a less stable and realistic one. Also the calculated exergy values of the elements are more precise ,coherent, and all-positive. Therefore, this R.E. can be used as an idealized model of the degraded Earth, to which all substances in the planet tend to reach in the long term. Even though the effort to be precise is worth to be done, we must not forget that what we are seeking is not the thermodynamic cost (minimum cost of formation or exergy ) of the mineral capital of the Earth, but its “real” exergy cost (the calculated amount of exergy needed to compose a mine of a given mineral from this hypothetical R.E.). Therefore an additional effort is needed: that is to understand which is the general process of a mineral formation and the amount of energy involved in each of the steps. This will teach us which are the relevant stages, and propose a model to calculate the involved exergies. As it can be guessed, these exergies (and their associated errors) are far greater than those involved in considering one or another R.E..Therefore, the R.E. for a degraded Earth to be used in calculating the mineral capital can be considered sufficient for the purpose.

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Table 1 (1). Chemical exergies of the elements

CHEMICAL ELEMENT REFERENCE SPECIES CHEMICAL EL. Chemical b (kJ/mol) State

This proposal

(2001) Szargut (1989)

Element Ch.S. noi (mol/g) Rec Formula q. State z c/y solid liq. Gas ∆Gº(kJ/mol) bch (kJ/mol) bch (kJ/mol)

Aluminium Al 2.98E-03 1 Al2O3 s 0.005 16.93 -1,582.40 s 796.69 888.2 Antimonium Sb 1.64E-09 1 Sb2O5 s 0.001 56.65 -829.30 s 438.01 438.1 Argon Ar 1 Ar g 11.69 0.00 g 11.69 11.69 Arsenic As 2.00E-08 1 As2O5 s 0.001 50.45 -782.40 s 411.46 494.6

2 HasO4-2 líq -2 0.1 -94.07 -714.70 s 493.14 494.6

Barium Ba 4.00E-06 1 BaSO4 s 0.01 29.89 -1,361.90 s 774.25 775.1 2 Ba+2 líq 2 0.2 186.71 -561.00 747.71 747.7 Beryllium Be 3.33E-07 1 BeO s 0.005 37.77 -579.77 615.55 604.4 2 Be2SiO4 s 0.01 37.77 -2,033.30 s 604.48 Bismuth Bi 1 BiO+ líq 1 0.6 130.15 -146.40 s 274.56 274.5

6.80E-10 2 Bi2O3 s 0.005 54.84 -493.70 271.29 270.3 Boron B 1 B(OH)3 líq 0 1 19.80 -968.80 s 628.49 628.5 9.30E-07 2 B(OH)3 s 0.001 39.21 -969.70 648.81 648.9 Bromine Br 2.00E-08 1 Br- líq -1 0.68 -53.37 -104.00 Br2.l 101.25 101.2 Cadmium Cd 1 CdCl2 líq 0 1 58.00 -359.40 s 293.80 293.8

8.72E-10 2 CdCO3 s 0.02 49.07 -669.40 302.26 298.2 Calcium Ca 1 Ca+2 líq 2 0.21 158.99 -553.40 712.39 712.4 7.49E-04 2 CaCO3 s 0.4 7.77 -1,129.00 s 720.56 729.1 Carbon C 2.70E-04 1 CO2 g 19.87 -394.36 s.graf 410.26 410.26 2 HCO3

- líq -1 0.55 -54.91 -587.45 408.53 408.5 Cerium Ce 4.57E-07 1 CeO2 s 0.02 33.55 -1,024.80 s 1,054.38 1,054.6 Cesium Cs 1 Cs+ líq 1 0.6 122.38 -282.20 s 404.58 404.4 2.78E-08 2 CsCl s 0.01 42.21 -414.60 395.01 395.7 Chlorine Cl 1 Cl- líq -1 0.68 -69.43 -131.26 Cl2.g 123.66 123.6

1.81E-05 2 NaCl s 0.3 16.00 -384.43 127.66 136.9 Chromium Cr 6.73E-07 1 Cr2O3 s 0.005 37.74 -1,086.38 559.09 6.73E-07 2 K2Cr2O7 s 0.01 36.03 -1,882.30 s 585.55 584.3 Cobalt Co 1.70E-07 1 Co3O4 s 0.001 46.15 -772.88 270.36 312.0

1.70E-07 2 CoO s 0.001 43.43 -204.82 246.26 312.0 1.70E-07 n CoFe2O4 s 0.005 39.44 -1,032.60 315.48 312.0

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CHEMICAL ELEMENT REFERENCE SPECIES CHEMICAL EL. Chemical b (kJ/mol) State This proposal

(2001) Szargut (1989)


Copper Cu 1 Cu+2 líq 2 0.2 199.74 65.50 s 134.24 134.2 3.93E-07 2 CuCO3 s 0.05 31.65 -518.90 134.34 132.5 Dysprosium Dy 2.15E-08 1 Dy(OH)3 s 0.02 41.13 -1,294.30 s 975.32 975.9 2.15E-08 2 DyCl3·6H2O s 0.001 48.55 -2,453.60 888.24 888.9 Erbium Er 1.38E-08 1 Er(OH)3 s 0.02 42.23 -1,291.00 s 973.12 972.8 Europium Eu 5.79E-09 1 Eu(OH)3 s 0.02 44.38 -1,320.10 s 1,004.37 1,003.8 Fluorine F 3.22E-05 1 CaF2 s 0.3 16.29 -1,178.10 F2.g 482.70 504.9 Gadolinium Gd 2.42E-08 1 Gd(OH)3 s 0.02 40.83 -1,288.90 s 969.63 969.0 Gallium Ga 2.44E-07 1 Ga2O3 s 0.02 36.82 -998.60 s 514.73 514.9 Germanium Ge 2.20E-08 1 GeO2 s 0.05 38.80 -521.50 s 556.33 557.6 Gold Au 9.14E-12 1 Au s 0.5 52.39 0.00 s 52.39 50.5 2 AuCl2

- líq -1 0.6 -12.10 -151.20 15.50 15.4 Hafnium Hf 3.25E-08 1 HfO2 s 0.05 37.83 -1,027.40 s 1,061.26 1,062.9 Helium He He g 30.37 0.00 g 30.37 30.37 Holmium Ho 4.85E-09 1 Ho(OH)3 s 0.02 44.82 -1,294.80 s 979.51 978.6 Hydrogen H H2O g 9.49 -228.59 H2.g 236.10 236.1 Indium In 4.35E-10 1 In2O3 s 0.05 50.24 -830.90 s 437.59 436.8 Iodine I 1 IO3

- líq -1 0.6 34.66 -128.00 I2.s 174.76 174.7 1.10E-08 2 KIO3 s 0.01 42.79 -418.70 177.73 186.7 Iridium Ir 1.04E-13 1 IrO2 s 0.005 74.90 -185.60 s 256.53 246.8 Iron Fe 6.27E-04 1 Fe2O3 s 0.1 13.37 -742.20 s 374.81 374.3 Kripton Kr Kr g 34.36 0.00 g 34.36 34.4 Lanthanum La 2.16E-07 1 La(OH)3 s 0.02 35.41 -1,319.20 s 994.50 994.6 Lead Pb 1 PbCl2 líq 0 1 59.23 -297.20 s 232.83 232.8

9.65E-08 2 PbCO3 s 0.02 37.40 -625.50 246.69 249.3 Lithium Li 2.88E-06 1 Li+ líq 1 0.68 99.03 -294.00 s 393.03 393.0 Lutetium Lu 1.83E-09 1 Lu(OH)3 s 0.02 47.23 -1,259.60 s 946.73 945.7 Magnesium Mg 1 Mg+2 líq 2 0.23 154.69 -456.32 611.01 611.0

5.47E-04 2 Mg3Si4O10(OH)2 s 0.3 11.99 -5,543.00 s 626.12 626.1 Manganese Mn 1.09E-05 1 MnO2 s 0.1 21.70 -465.20 s 482.93 482.0

12



(2001) Szargut (1989)


Mercury Hg 1 HgCl4-2 líq -2 0.1 -83.84 -446.90 l 115.86 115.9

2.79E-10 2 HgCl2 s 0.01 53.61 -178.70 108.71 108.0 Molybdenum Mo 1 MoO4

-2 líq -2 0.1 -98.17 -836.40 s 730.29 730.3 Neodymium Nd 1.80E-07 1 Nd(OH)3 s 0.02 35.86 -1,294.30 s 970.05 970.1 Neon Ne Ne g 27.16 0.00 g 27.16 27.16 Nickel Ni 1 Ni+2 líq 2 0.2 187.10 -45.60 s 232.70 232.7 3.41E-07 2 NiO s 0.01 35.99 -211.71 245.72 242.5 Niobium Nb 2.69E-07 1 Nb2O3 s 0.01 38.30 -1,766.40 s 899.37 899.7 Nitrogen N N2 g 0.72 0.00 N2.g 0.72 0.72 Osmium Os 2.63E-13 1 OsO4 s 0.005 72.60 -305.10 s 369.76 368.1 Oxygen O O2 g 3.97 0.00 O2.g 3.97 3.97 Palladium Pd 4.70E-12 1 PdO s 0.005 65.46 -82.50 s 145.97 138.6 Phosphorous P 1 HPO4

-2 líq -2 0.1 -101.88 -1,089.30 s 861.43 861.4 2.26E-05 2 Ca3(PO4)2 s 0.1 21.61 -3,885.30 876.93 851.5

Platinum Pt 2.60E-11 1 PtO2 s 0.005 61.22 -83.70 s 140.9 141.0 Plutonium Pu 6.20E-20 1 PuO2 s 0.01 108.71 -995.10 s 1,099.84 1,100.0 Potash K 1 K+ líq 1 0.64 84.23 -282.44 s 366.67 366.6

7.16E-04 2 KCl s 0.01 17.03 -408.80 364.03 364.9 Praseodymium Pr 5.04E-08 1 Pr(OH)3 s 0.02 39.01 -1,285.10 s 964.01 963.8 Radium Ra 4.40E-15 1 RaSO4 s 0.05 77.03 -1,364.20 s 823.69 823.9 Rhenium Re 2.69E-12 1 Re2O7 s 0.01 66.84 -1,067.60 s 560.27 559.5 Rhodium Rh 9.70E-12 1 Rh2O3 s 0.005 65.38 -299.80 s 179.61 179.7 Rubidium Rb 1 Rb+ líq 1 0.6 106.48 -282.40 s 388.88 388.6 1.31E-06 2 RbCl s 0.01 32.66 -401.80 372.66 373.4 Rutenium Ru 1.00E-12 1 RuO2 s 0.005 69.29 -253.10 s 318.42 318.6 Samarium Sm 2.99E-08 1 Sm(OH)3 s 0.02 40.31 -1,314.00 s 994.20 993.6 Scandium Sc 2.45E-07 1 Sc2O3 s 0.05 34.54 -1,819.70 s 924.14 925.2 Selenium Se 6.33E-10 1 SeO4

-2 líq -2 0.1 -86.97 -441.40 s 346.49 346.5 Silicon Si 1.10E-02 1 SiO2 s 0.35 1.45 -856.70 s 854.18 854.9

13



(2001) Szargut (1989)


Silver Ag 1 AgCl2- líq -1 0.6 -21.62 -215.50 s 70.28 70.2

4.64E-10 2 AgCl s 0.02 50.64 -109.80 98.64 99.4 Sodium Na 1 Na+ líq 1 0.68 74.61 -262.05 s 336.66 336.6

1.26E-03 2 NaCl s 0.002 19.62 -384.43 342.25 342.9 Strontium Sr 3.99E-06 1 SrCO3 s 0.08 24.74 -1,140.10 s 748.63 749.8 3.99E-06 2 SrSO4 s 0.05 25.91 -1,340.60 748.97 748.9 Sulfur S 1 SO4

-2 líq -2 0.11 -127.10 -744.60 s 609.56 609.6 2.97E-05 2 CaSO4·2H2O s 0.4 15.78 -1,797.40 599.99 608.6

Tantalum Ta 1.22E-08 1 Ta2O5 s 0.01 45.97 -1,911.60 s 973.82 974.0 Tellurium Te 1.40E-11 1 TeO2 s 0.005 62.75 -270.30 s 329.08 329.2 Terbium Tb 4.03E-09 1 Tb(OH)3 s 0.02 45.28 -1,314.20 s 999.37 998.4 Thalium Tl 3.67E-09 1 Tl2O4 s 0.01 48.95 -347.30 s 194.15 194.90

2 Tl2O3 s 0.01 48.95 -311.41 177.20 Thorium Th 4.61E-08 1 ThO2 s 0.05 36.96 -1,169.10 s 1,202.09 1,202.6 Thulium Tm 1.95E-09 1 Tm(OH)3 s 0.02 47.08 -1,265.50 s 952.47 951.7 1.95E-09 2 Tm2O3 s 0.02 48.79 -1,795.80 919.32 919.0 Tin Sn 4.63E-08 1 SnO2 s 0.2 33.52 -519.60 s 549.15 551.9 Titanium Ti 6.26E-05 1 TiO2 s 0.1 17.36 -889.50 s 902.89 907.2 Uranium U 1.18E-08 1 UO3·H2O s 0.01 44.33 -1,395.90 s 1,196.19 1,196.6 1.18E-08 2 UO3 s 0.01 44.33 -1,152.70 1,191.08 1,191.5 Vanadium V 1.18E-06 1 V2O5 s 0.01 34.63 -1,419.60 s 722.15 720.4 Wolframium W 1 WO4

-2 líq -2 0.1 -85.08 -920.50 s 827.48 827.5 Xenon Xe Xe g 40.33 0.00 g 40.33 40.33 Yterbium Yb 1.27E-08 1 Yb(OH)3 s 0.02 42.43 -1,262.50 s 944.83 944.3 Ytrium Y 2.47E-07 1 Y(OH)3 s 0.02 35.07 -1,291.40 s 966.37 965.5 Zinc Zn 1 Zn+2 líq 2 0.2 191.94 -147.30 s 339.24 339.2

1.09E-06 2 ZnCO3 s 0.01 33.11 -731.60 348.50 344.7 Zirconium Zr 2.08E-06 1 ZrO2 s 0.05 27.52 -1,037.10 1,060.65 1,061.2 2.08E-06 2 ZrSiO4 s 0.4 22.37 -1,919.50 s 1,078.97 1,083.4

14

4. Thermodynamic analysis of mineral formation. We now propose to analyse the energy changes associated with the thermodynamic formation of a mineral deposit as a geological body with a high concentration of minerals. The thermodynamic value is approximated by considering a unitary vision of the energetic and entropic exchanges of grouping atoms into molecules, of these evolving into pure solid forms which then form mineral conglomerates and rocks; and finally analyse the mine as a more concentrated system of minerals than other parts of the Earth’s crust. In this global vision, a mine is an infrequent aggregate of mineralic rocks, the rocks are aggregates of minerals, the minerals are aggregates of molecular species and molecular species are homogeneous aggregates of atoms. So, the formation of a mine can be explained by the following expression: Mine=Σ rocks of a certain composition = ΣΣ minerals = ΣΣΣ molecules = ΣΣΣΣ atoms (6) Each aggregate is characterised by two properties. The first is a cohesion energy or bond that coincides thermodynamically with its formation enthalpy. The second is a mixing or formation entropy that is identified as the improbability of the corresponding aggregate. We will analyse the energies and entropies in each phase in mineral formation to compare different analogies and specificity and derive the expressions to calculate the thermodynamic value of a mineral. Stage 1. Chemical formation. Molecular, mineral and rock formations. The energy needed to form one mol of a material from its component elements in their standard states (at 1 bar and 298.15 K), is given by its formation free energy. This is a measure of the work that can be obtained from an isothermic and reversible process at constant pressure and is a direct indication of whether the reaction will take place. Equation ∆G=∆H-T∆S can be used to tabulate the standard free molar energies of formation. Since we are more familiar with energy units than entropy units, it is easier to understand the significance of ∆H o

f and ∆G of than S0.

A table of standard formation values at 1 bar and 298.15 K (see for example Pauling [32], Perry & Green [33] or Robie, Hemingway & Fisher[34]) shows some interesting relationships, including that ∆H o

f and

∆G of are on the same order of magnitude and the same sign. Its typical values range from –30kJ/mol to –200

kJ/mol for most of the sulfides; -200 to –2,500kJ/mol for most of simple compounds like sulfates, nitrates, carbonates, halides and oxides. The same considerations can be made for mineral formation as for any chemical reaction. The orders of magnitude of the energy exchange are quite variable in this stage and are generally less than the free energy of formation of the oxides from which they proceed. A typical reaction of this stage would be: molkJ 288G CaSiOSiOCaO 0

2983s2s /,)()( −=→+ ∆ (7) Multiple oxides, phosphates and different structure silicates, add these values to the free energy of formation of each component. Therefore the free energy of formation of these minerals typically range from –1,000 to even –10,000 kJ/mol.

15

Finally, a rock can be a conglomerate of pure minerals but this is rare in Nature. Commonly minerals have crystal defects as well as variations in composition. This forms a solid solution with a mixture of atoms in the atomic positions of a crystalline structure that is generally stable. The energy involved in the solid formation is several orders of magnitude less than the formation of pure minerals. Thermal interchanges are practically zero during the process of mixing. In a mix of ideal gases, the entropy of the mix can be found by the classic expression: −=S∆ [ ]2211 xnxnR lnln + (8) The same expression works for mixtures of solid or liquid solutions. Nonetheless, in the case of ideal solid solutions, x2 for the atom/molecule of substitution tends to be very small, resulting in low entropy generation. The entropy generation of a mixture never reaches the values of thermal exchanges, most frequently associated with compound formation, heating or phase change. A general conclusion of these three stages is that: the chemical exergy of a mineral is mainly due to the stages of molecular formation and in less extent to the mineralization processes. On the other side, the data concerning the values of ∆G are mostly tabulated. In the case of a mineral, the minimal chemical energy to form a compound from species in the R.E. (and from which we exploit the element of commercial interest) is given by the expression: ∑ += − mineral

0k hel ckch Gbb ∆ν (9)

This is the minimum theoretical work Nature should invest to provide minerals at a specific composition from a degraded Earth.Analysing the numbers, one finds a crucial conclusion: Since stability does not coincide with abundance in a number of cases, some minerals quite abundant in Nature, such as sulfides, have a fairly high chemical exergy that can be considered as an exergy reservoir that Earth provides us for free. This helps our technology to avoid huge amounts of commercial energy to be expended in the process of obtaining the corresponding pure element. Table 2, shows the exergy difference in kJ/mol, for those significative elements in which the most abundant mineral is not the most stable one. In other words, Table 2 shows the exergy difference for each element between the case of considering the Earth as it is (R.E. based on abundance), and a degraded Earth (R.E. based on stability, as in this paper).A key conclusion is: Sulfides are the mineral chemical wealth most important of our Planet.

16

Table 2. Exergy difference of selected elements considering either as reference species the most abundant or the most stable substances in the R.E.

Element Most abundant species

Most stable species. (As in this paper)

Exergy difference between both R.E.

(kJ/mol) Sb Sb2S3 Sb2O5 1235.58 As FeAsS As2O5 1201.32 S FeS2 =

4SO 963.63 Bi Bi BiO+ 228.88 Cd CdS CdCl2 745.75 Ce PO4Ce CeO2 258.33 Zn ZnS ++Zn 717.22 Co Co3S4 Co3O4 967.7 Cu CuFeS2 ++Cu 1423.18 Mo MoS2 −2

4MoO 1675.9 Os Os OsO4 306.81 Ag Ag2S −

2AgCl 330.65 Pt Pt PtO2 84.59 Pb PbS PbCl2 710.34 Re ReS2 Re2O7 1556.65 Ru Ru RuO2 254.82 U UO2 UO3·H2O 127.49

Stage 2. Formation of a mineral deposit. Mineral deposits are an unusual accumulation of minerals in the Earth's crust. This concentration gives rise to grades that are much higher than average. Faber [35] and many others have analysed energy and entropy exchanges. When separating the resources of a mineral deposit with N1 molecules, the resource concentration can be defined as x1=N1/N. If we extract the resource, the entropy will decrease. If it flows into another system there would be an external energy provision. The minimum energy that must be invested to proceed towards the separation per mol of the resource, is given by:

( ) ( )

−−

+−= 11

11nc x1

xx1

xRTb lnln (10)

Thus, the lower the concentration, the greater the energy needed to extract the resource. Non-fossil fuels mineral deposits are not so valuable for their chemical exergy, but because their concentration in the mine saves us energy when we extract them. We do not have to exploit all the Earth's crust where the concentration is normally hundreds of times lower.

17

Using equation (10), and given the initial concentration in the mine (Xm), it is possible to evaluate the minimum energy (Eminproc) required to concentrate a mineral in a reversible process from its concentration in the mine to a concentration required for metallurgic treatment (Xr). The latter is expressed graphically in Figure 1. The term Eminconc (Figure 1), is the minimum energy required to concentrate the element from a cortical concentration (Xc) to the concentration at which it is exploited in the mine (Xm). This is an ideal process via geological changes of concentration. This energy is the minimum needed in a reversible process to use the Earth's crust to obtain the materials used by the economic subsystem and to concentrate them to the condition they are found in the mines. In other words, this is the savings in physical exergy provided by Nature to obtain the materials, and represents the first part of their thermodynamic value. This analysis has helped to derive two expressions to calculate the thermodynamic value of a mineral. Equation (9) takes into account resource conditions and helps to evaluate the minimum energy invested to make this substance starting from the R.E. Meanwhile equation (10) helps to determine the minimum energy saved since these minerals are more concentrated than in the Earth´s crust and are the same as those that were derived from the R.E.

Figure 2. Energy requirements for concentration depending on the concentration of the element in the mixture.

5. The actual physical costs (kc and kr). Until now the proposed model of thermodynamic assessment relies on reversible physical and chemical processes. This condition can only be maintained in a “thermo-utopic” world with no friction or dissipative effects. Due to irreversibility, the actual physical costs of production are always greater than their

Concentration

Energy Requirement

Xm XrXc

Eminproc

Eminconc

18

thermodynamic costs or exergy. This physical cost is defined as the sum of all the exergy resources that would be needed with the available technology to concentrate and compose a mineral from its components in the R.E. This physical cost is measured in exergy units (GJ) rather than in monetary ones. If the sum is calculated from the cortical concentration (Xc) in the R.E. to the mine concentration (Xm), this cost will be named from now on the“exergetic cost of replacement” of a given mineral. (See for instance, the theory behind by Valero in Naredo and Valero [3]). The unit exergetic cost, k is the ratio between the actual exergetic cost of a product and its exergy. This value is dimensionless and measures the number of units of exergy needed to obtain a unit of a product. We will see in the next paper that the exergetic cost of the minerals can be one or several orders of magnitude greater than its exergetic content. This is due to irreversibilities of the processes devised by humans. Having considered this, we now need to know the actual physical costs, their variation with concentration, extraction and production technologies to obtaining mineral products. In the following section we review some of the models proposed by other authors that relate the physical and chemical mineral conditions and the real energy requirements to obtain them. And in the following paper we assess the energy invested in the metallurgic processes of extraction for the main metals. These models, along with data on real processes, help to calculate the exergetic costs associated with mineral extraction processes and treatment. Note that the exergy of a fuel practically coincides with its energy content, therefore the energy costs will coincide with the exergy costs when we sum up amounts of fuels in energy units. 5.1 Actual energetic requirements for the production of main minerals. The processes of obtaining metals and minerals can be divided into two well differentiated stages: mining and concentration (Em) on one hand, and on the other, smelting and refining the metal (Es). Several authors have analysed the energy needed to obtain minerals based on their physical and chemical conditions in the mines. Page & Creasey [11] propose the following expression:

sm

T Eg

EE += (11)

where g is concentration in percentage. Kellog [12] also proposes the existence of a relatioship between a mineral’s metallic state and the large quantities of its production energy. He proposes a model that relates tonnes of ore required to obtain one ton of metal with a concentration (g in %) and a recovery efficiency (R in %) during the concentration process :

T= 10,000/g.R (12) and define Um as the specific energy to obtain the material from the mine. It is independent of the concentration and only depends on the type of mining (underground or surface mine). The energy to physically concentrate a ton of metal is called Up. According to Kellog [12] this depends on physical-chemical characteristics and suggests that both mining and its exploitation process are affected by the decrease in ore concentration. The energy required in these processes (Um and Up) should be multiplied by factor T to obtain the total energy (U) per unit of metal produced:

19

U = ( Um + Up )10,000/g.R (13)

Both models announce a well kown fact, which is the exponential form of the relationship between the energy requirement for concentrating a mineral and its concentration, as shown in the thermodynamic behavior depicted in Fig.1. Chapman and Roberts [6] advance a little further and propose a model that relates the physical and chemical conditions of the minerals with the energetic requirements to obtain them. Unlike the above references, they take into account the efficiency of energy use in extractive metallurgic processes with respect to the minimum energy defined by the Second Law of Thermodynamics. They propose the following equation:

21

0 GgE

Fη∆

η+= (14)

where Eo is the minimum energy requirement for the exploitation and concentration processes; ∆G is the Gibbs free energy needed to transform the concentrated mineral into pure metal; η1 and η2 are respectivelly the energy efficiencies of the extraction-concentration and the refining processes.This equation shows how the energy used in the metals production depends on the initial concentration of the metal in the mine and the available technology used to obtain it. This approach centres on evaluating the energy requirements for the production of a specific metal or mineral from the mine to industry. However, the first term of Eq. (14) shows the same tendency as Eq. (10), and can be used too for calculating the quantity of energy with the actual available technology that could be spent from the Earth´s crust (i.e. the R.E.) to the mine. This can be done by calculating g, Eo from the R.E. to the mine, and the term η1 for the available technology that aplies for the case in hand. The second term ∆G/η2 is related to the chemical process cost of refining the metal. Generally, this process does not coincide with the hypothetical process of chemically converting the reference species into the resource mineral. Therefore, we must systematically analyze the energy expenses behind all metallurgical processes for a given element and estimate the approximate energy savings we get for using one or another raw material. In practical terms, we will concentrate most in the energy differences between the reduction processes of oxides and sulfides. Then, the formula we will use for assessing the replacement exergetic costs will be: k = bc * kc + bch * kch (15) Where bch is the concentration exergy, bch the chemical exergy, kc the actual physical unit cost of the concentration process and kch the chemical unit cost of converting the reference species into the mineral. Note that k´s are the inverse of the process efficiencies η´s. There are many techniques to exploit minerals and we need to systematically revise the extractive processes to determine the values of kc and kch. In the second paper of this series we present the concentration and composition exergies of mineral reserves. We also evaluate the actual costs of extraction associated with the different extractive operations for the main metals. Now, we have the complete Second Law procedure to determine the replacement exergetic costs of the mineral capital of Earth. The obtained results can be used to determine realistic values of the energy saved for us by Nature at the current state of technology. Or in other words, we have now a procedure for calculating the exergy, and the exergetic cost of any mine, which is a scarse agglomerate of materials that

20

provides mineral resources of specific composition and concentration, different from the chemically degraded and dispersed environment to which our civilization is fast forwarding. 6. Acknowlegments. Dedicated to Professor Jan Szargut and to the ironic spanish saying “ Let´s take whatever is gratis, no matter its cost”, that inspired this work. 7.References.

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[35] Faber, M. (1984). “A biophysical approach to the economy entropy, environment and resources”, In: van Gool, W.; Bruggink. J. (eds.), Energy and Time in the Economic and Physical Science. Elsevier Science Publishers B. V:, Amsterdam, pp. 315-337.

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Exergetic Evaluation of Natural Mineral Capital