EXERGY EVOLUTION OF THE MINERAL CAPITAL ON EARTH

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1 Mechanical Engineering Ph.D. Thesis EXERGY EVOLUTION OF THE MINERAL CAPITAL ON EARTH By Alicia Valero Delgado July 2008 Directed by: Antonio Valero Capilla, Ph.D. Department of Mechanical Engineering Centro Politécnico Superior University of Zaragoza

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3 Exergy evolution of the mineral capital on earth Alicia Valero Delgado Thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy University of Zaragoza, Spain Abstract The 20th century has been characterized by the economic growth of many industrialized countries. This growth was mainly sustained by the massive extraction and use of the earth s mineral resources. The tendency observed worldwide in the present, is that consumption will continue increasing, especially due to the rapid development of Asia, the desire for a higher living standard of the developing world and the technological progress. But the physical limitations of our planet might seriously restrain world economies. In fact, many mineral commodities such as oil or copper are already showing signs of scarcity problems, and consequently their prices are increasing sharply. Our society is based on an inefficient use of energy and materials, since there is a lack of awareness of the limit. If resources are limited, their management must be carefully planned. But it is impossible to manage efficiently the resources on earth, if we do not know what is available and at which rate it is being depleted. Therefore, the aim of this PhD has been the assessment of the physical stock on earth and the degradation velocity of our mineral resources due to human action. This has been accomplished through the exergy analysis under the exergoecological approach. This way, the resources are physically assessed as the energy required to replace them from a complete degraded state to the conditions in which they are currently presented in nature. The main advantage of its use with respect to other physical indicators is that in a single property, all the physical features of a resource are accounted for. Furthermore, exergy has the capability of aggregating heterogeneous energy and material assets. Unlike standard economic valuations, the exergy analysis gives objective information since it is not subject to monetary policy, or currency speculation. i

4 Accordingly, in this work three imperative activities were carried out: A systematic analysis of the main chemical components and the mineral resources on earth has been accomplished. Furthermore, the first composition in terms of minerals of the upper continental crust has been developed, through a procedure that assures chemical coherence between species and elements. The integration of all these data has provided a global overview of the geochemistry of our planet with special attention to the substances that compose the earth s outer spheres and to that part of the substances useful to man: the mineral resources. The thermodynamic tools required for the physical assessment of natural resources and particularly for minerals have been provided. This way, the standard thermodynamic properties of the earth and its constituents (enthalpy, Gibbs free energy and exergy) have been calculated. Additionally, the exergy of the mineral resources of the earth (of fuel and non-fuel origin) has been obtained and compared to that of other energy resources. With the help of different scarcity indicators developed in this PhD, an analysis of the state of our mineral resources has been accomplished. For that purpose the mineral exergy degradation throughout the 20th century has been studied. This has allowed to estimate when the peak of production of the main mineral commodities is reached. Additionally, an outlook of the scarcity degree of our mineral capital in the 21st century has been undertaken. The results of this study reveal that the exergy analysis of minerals could constitute a universal and transparent prediction tool for assessing the degradation degree of non-renewable resources, with dramatic consequences for the future management of the earth s physical stock. ii

5 To my beloved grandfather iii

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7 In the end we will conserve only what we love; we will love only what we understand; we will understand only what we have been taught Baba Dioum. Senegalese Environmentalist v

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9 Acknowledgements The work with this dissertation has been exciting, instructive, and fun, although moments of hardship and frustration have also existed. Without help, support, and encouragement from a great number persons, I would never have been able to finish this PhD. In this long ride of almost 5 years, I have had the opportunity to meet exceptional people around the world. In the scientific field, many researchers have unselfishly supported me. I should start to acknowledge the Russian geochemist N.A. Grigor ev, that I discovered by chance investigating the literature about the geochemistry of the earth. Through a quite complicated communication procedure (via ordinary post and in Russian language), Grigor ev generously shared with me his not yet published results about the mineralogical composition of the earth s crust. Thanks to the translations of the Russian teacher in the University of Zaragoza Helena Moradell, Grigor ev s exceptional and pioneer work has been the base of the model of continental crust developed in this PhD. A deep debt of thanks is also owed to Gavin Mudd from the Institute for Sustainable Water Resources in Monash University (Australia), who kindly made available and prior to publication, his excellent and also pioneer study about average mineral ore grades in his country. Thanks to Mudd s work, a comprehensive case study of the mineral exergy degradation of a nation was possible. This thesis has required a high level of geological and geochemical knowledge. Therefore, my chemical engineering background had to be reinforced with earth science s fundamentals. Of essential help was the continued support of Javier Gómez, from the department of petrology in the University of Zaragoza. From the very beginning, he became my unofficial advisor in the geological field and his point of view has been very valued for this work. I should also thank the Instituto Geológico y Minero de España - IGME, and in particular Miguel Ángel Zapatero, for making available IGME s information and mineral statistics. Decisive for the accomplishment of this PhD, was my 3-month stay at the British Geological Survey (BGS), one of the most renowned geological institutions in Europe. Not only the exceptional library and data bases of BGS were crucial for this work, but also the good advice of many of its premium researchers. I would like to express my deepest gratitude to the BGS s director, John Ludden, who immediately accepted me in the organization and gave me access with no exception to all BGS available information. Thanks go also to Andrew Bloodworth, head of the Mineral s UK department and to all his team, for their warm welcome and for treating me as one more of the group. I cannot forget Tim Colman, who was always willing to help me and from which I learnt so many things. I have met at BGS many good friends that surely will remain in the future. vii

10 The thermochemistry part of this PhD was strongly reinforced with the reviews of Philippe Vieillard, probably the best European expert in the field of geothermochemistry, from the University of Poitiers. In these few lines, I want to express my gratitude for the many hours that Vieillard spent in teaching me patiently the different estimation methods for the calculation of the thermodynamic properties of minerals and in reviewing the results obtained. I would like to thank prof. Jan Szargut and Wojciech Stanek from the Institute of Thermal Technology in the Silesian University of Technology. It has been an honor to interact and discuss with my Polish friends the different exergy approaches used. Very useful were also the advices of the Spanish renowned economist José Manuel Naredo. He has been and is being a fundamental piece in the integration of the exergoecological approach used and further developed in this PhD, into the economic thinking. I should not forget Juan Ignacio Pardo, from the department of physical chemistry and M a Cruz López de Silanes, from the department of applied mathematics, both in the University of Zaragoza, who were always willing to help me. If Javier Gómez was my geology advisor, César Torres, expert of thermoeconomics and collaborator of the CIRCE Foundation, was doubtless my mathematics and L A TEX advisor. When I got stuck in a mathematical problem, he was the one in finding the best solution. In the same way, he has solved most of my numerous doubts with L A TEX. In fact, he is the author of the layout of this PhD. Thank you very much indeed for your invaluable help and time. I wish to acknowledge the CIRCE Foundation for its financial support and for the excellent working environment. All its members, starting from the administration staff, teachers, students and researchers make the work very pleasant. Special thanks are owed to my managers and fellows Javier Uche, Luis Miguel Romeo and Inmaculada Arauzo, who have giving me every facility in the accomplishment of this PhD. Thanks to their generosity and that of my CIRCE friends Amaya Martínez and Francisco Barrio, I could dedicate most of my time in the last year in finishing this work. I would also like to thank all my friends from Zaragoza, and from other parts of Spain for the great moments that I have shared with them. viii

11 This PhD is dedicated to my beloved grandfather, who has always believed in me and has supported and encouraged me. As you see I finally finished the work that you were impatiently waiting for. In the same way, I want to deeply thank my grandmother, for her endless care and affection. And of course I cannot forget my uncles, aunts and cousins, which all constitute an important part of my life. I am totally indebted to Stefan, who left family, friends and work in Germany for living with me in Spain. Probably I will never be able to reward the huge sacrifice you have made for me. I just hope that in some way, it has been worth. Thanks for your love, patience and understanding. Thanks also for helping me in the programming of the calculation tools used in this PhD, which has resulted in the first scientific web portal devoted to exergoecology. The great success of the "Exergoecology Portal", which every day gains supporters around the world, is due to your effort and your well-doing. You are not only a good professional, but an excellent person and I am very lucky to have you by my side. My beloved mother, your wise advise, love and care are an essential support in my personal and professional life. Your firm and sincere personality has affected me to be steadfast and never bend to difficulty. You have taught me many indispensable things of life that have helped me to face fearlessly important challenges and decisions in my life. I reserve my most grateful thanks to my father and supervisor Antonio Valero. To be honest, at the beginning I was not sure whether this combination would work. Today I am sure that it was worth and that you have been the best PhD director that I could ever had. Obviously you have been very demanding with me, probably more than with other of your students. But you have also been there many evenings, week-ends and holidays, motivating me to work harder and to do my best. You are an inspiration for me as a scientist, teacher, entrepreneur and most importantly as a father. It has been a great pleasure to work with you. When the next one? ix

12 Contents Contents x 1 Starting point, objectives and scope Introduction Economic growth and the consumption of natural resources Scarcity indicators Exergy and the assessment of natural resources The Exergoecology approach Scope, objectives and structure of this PhD Scientific papers derived from this PhD I The earth and its resources 17 2 The geochemistry of the earth. Known facts Introduction The bulk earth The composition of the earth The atmosphere The composition of the atmosphere The hydrosphere Seawater The composition of the sea Renewable water resources: surface and ground waters Stream, river and lake waters Ground waters Ice caps, ice sheets and glaciers The composition of glacial runoff The continental crust The chemical composition of the upper continental crust Summary of the chapter The mineralogical composition of the upper continental crust x

13 3.1 Introduction The classification of minerals The silica minerals The feldspar group The pyroxene group The amphibole group The olivine group The mica group The chlorite group Grigor ev s mineralogical composition of the crust A new model of the mineralogical composition of the earth s crust The mass balance The mass balance applied to the continental crust Aluminium Antimony Arsenic Barium Beryllium Bismuth Boron Bromine Cadmium Calcium Carbon Cerium Cesium Chlorine Chromium Cobalt Copper Dysprosium Erbium Europium Fluorine Gadolinium Gallium Germanium Gold Hafnium Holmium Indium Iodine Iridium Iron xi

14 Lanthanum Lead Lithium Lutetium Magnesium Manganese Mercury Molybdenum Neodymium Nickel Niobium Nitrogen Osmium and Iridium Palladium Phosphorous Platinum Potassium Praseodymium Rare Earth Elements: Praseodymium, Samarium, Europium, Gadolinium, Terbium, Dysprosium, Holmium, Erbium, Thulium and Lutetium Rhenium Rhodium Rubidium Ruthenium Samarium Scandium Selenium Silicon Silver Sodium Strontium Sulfur Tantalum Tellurium Terbium Thallium Thorium Thulium Tin Titanium Uranium Vanadium Wolfram xii

15 Ytterbium Yttrium Zinc Zirconium Mathematical representation Results Discussion of the most abundant minerals Discussion of the most relevant minerals Discussion of the aggregated composition Drawbacks of the model Summary of the chapter The resources of the earth Introduction Natural resources: definition, classification and early assessment The energy balance Energy from the solid earth The Geothermal energy Nuclear energy Tidal energy Energy from the sun Solar power Water power Wind power Ocean power Ocean thermal gradient Ocean Waves Biomass Fossil fuels Coal Oil and natural gas Unconventional fossil fuels Summary of the results of energy resources Non-fuel mineral resources The economic classification of minerals Mineral s average ore grades Mineral s abundance Summary of the chapter xiii

16 II The thermodynamic properties of the earth and its exergy evolution Thermodynamic models for the exergy assessment of natural resources Introduction The reference environment Selection of the best suitable reference environment Partial reference environments Comprehensive reference environments Abundance criterion Calculation methodology: standard chemical exergy of the chemical elements Standard chemical exergy of chemical compounds Gaseous reference substances Solid reference substances Reference substances dissolved in seawater Update of Szargut s R.E Update of the standard chemical exergy of chemical compounds Update of the gaseous reference substances Update of the solid reference substances Update of the liquid reference substances The updated reference environment. Results Drawbacks of Szargut s R.E. methodology The exergy of mineral resources The energy involved in the process of formation of a mineral deposit The exergy of non-fuel mineral resources The chemical energy and exergy of fossil fuels The exergy costs Prediction of Enthalpy and Gibbs free energy of formation of minerals Calculation of H 0 or G 0 from s f f The ideal mixing model Assuming G r and H r constant Thermochemical approximations for sulfosalts and complex oxides The method of corresponding states The method of Chermak and Rimstidt for silicate minerals The O 2 method The O 2 method for hydrated clay minerals and for phyllosilicates The O 2 method for different compounds with the same cations xiv

17 5.4.6 Assuming S r zero Assuming G r and H r zero The element substitution method The addition method for hydrated minerals The decomposition method Summary of the methodologies Summary of the chapter The thermodynamic properties of the earth and its mineral resources Introduction The properties of the earth The thermodynamic properties of the atmosphere The thermodynamic properties of the hydrosphere The thermodynamic properties of the upper continental crust The chemical exergy of the earth An approach to the chemical composition of the crepuscular earth The exergy of the mineral resources The exergy contained in fossil fuels Coal Oil Natural gas The exergy of non-fuel mineral resources The exergy of the natural resources on earth Summary of the chapter The time factor in the exergy assessment of mineral resources Introduction The exergy distance The tons of mineral equivalent The R/P ratio applied to exergy The Hubbert peak applied to exergy The exergy loss of mineral deposits due to mineral extraction. The case of copper in the US Copper mining features Chemical exergy Concentration exergy Total exergy Exergy costs The R/P ratio and the depletion degree of the deposits The Hubbert peak model Summary of the results The exergy loss of a country due to mineral extraction. The case of Australia Non-fuel minerals xv

18 Gold Copper Nickel Silver Lead Zinc Iron Fuel minerals Coal Oil Natural gas Summary and discussion of the results Conversion of exergy costs into monetary costs Summary of the chapter The exergy evolution of planet earth Introduction The exergy loss of world s mineral reserves in the 20th century Non-fuel minerals Fuel minerals The exergy loss of world s fossil fuel reserves due to the greenhouse effect The carbon cycle and the greenhouse effect Scenarios The fossil fuel exergy decrease A prediction of the exergy loss of world s mineral reserves in the 21st century Hubbert scenario The IPCC s B1 scenario The IPCC s A1T scenario The IPCC s B2 scenario The IPCC s A1B scenario The IPCC s A2 scenario The IPCC s A1FI scenario Summary of the scenarios Final reflections The Limits to Growth to be reconsidered? The need for global agreements on the extraction and use of natural resources The need for an accountability theory of mineral resources. The Physical Geonomics Summary of the chapter Conclusions xvi

19 9.1 Introduction Synthesis of the PhD Scientific contributions of the PhD Perspectives A Additional calculations A.1 Input data. Mineralogical composition of the earth s crust A.2 Calculation of average mineral ore grades A.3 Calculation of the R.E A.4 Calculation of the chemical exergy of gaseous fuels A.5 Estimation of the thermodynamic properties of minerals A.5.1 Chermak s methodology A.5.2 Vieillard s methodology for hydrated clay minerals A.5.3 Estimated values of the enthalpy and Gibbs free energy of minerals A.6 Exergy calculation of the mineral resources A.7 Australian fossil fuel production A.7.1 Coal A.7.2 Oil A.7.3 Natural gas A.8 World s fuel production A.8.1 Uranium A.8.2 Coal A.8.3 Oil A.8.4 Natural gas A.9 The Hubbert peak applied to world production of the main non-fuel minerals A.10 Fuel consumption in the 21st century Nomenclature, Figures, Tables and References 413 Nomenclature List of Figures List of Tables References xvii

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21 Chapter 1 Starting point, objectives and scope 1.1 Introduction The aim of this first introductory chapter is to provide an overview of the fundamentals on which this PhD is based and to outline the main objectives and scope of the study. Since this work is focused on the assessment of earth s resources, the most relevant studies concerned with the depletion of natural resources are reviewed. The former studies reveal the urgent need for information about our natural capital and for appropriate indicators for its assessment. Accordingly, the most common scarcity indicators are outlined and compared to the indicator used in this PhD: the exergy indicator, based on the second law of thermodynamics. Subsequently, an overview of the different existing approaches connecting the entropy law with the consumption of resources is provided. The latter are compared to the exergoecology approach, which is the methodology applied in this PhD for the assessment of mineral resources. Finally, the specific questions that this work tries to answer are outlined, together with its scope. 1.2 Economic growth and the consumption of natural resources The earth s continental crust is the source of the main goods essential for industrial civilization. Fuels, metals and non-metallic minerals are the fundamental basis for the technological development of any country. As Dunham [78] states, although the whole continental crust is composed by rocks as solid solutions of minerals, these 1

22 2 STARTING POINT, OBJECTIVES AND SCOPE are not in practice recoverable. Only when a combination of natural processes has worked together to produce an enrichment, is an ore to be found. And these complex processes operate very slowly when compared with the whole life-span of our species so far. Hence, it is clear the non-renewable nature of mineral resources, at least from a human perspective. The 20 th century was marked by great technological innovations leading to the consumption and further dispersion of huge amounts of mineral resources previously concentrated in natural deposits. This fact pushed up the economies of industrialized countries, but also raised the concern about resources scarcity. Probably, the possibility of running out of energy resources has provoked the most worries, especially due to the sharp rise of fuel prices. However non-fuel resources are also being exhausted very rapidly, as shown by Morse [230]: only in the US, over the span of the last century, the demand for metals grew from a little over 160 million tons to about 3,3 billion tons. The general attitude that has governed in the past was that the earth is nothing more than resources to be used. Adam Smith s invisible hand [321] has been a guiding principle for those who believe that free trade or market will ultimately lead to a natural order of things. Nevertheless, in the early seventies the first Arab oil embargo, the peaking of oil production, together with the studies of the Club of Rome (Forrester [96] and Meadows et al. [218]), started the alarm bells ringing regarding resources scarcity as the limit to economic growth [221]. In fact, the theory that economic growth is irrevocably constrained by the finiteness of natural resources came at least 1 a century before with the British economist Thomas Malthus [206]. The theory of Malthus was that the efforts of an expanding population to produce food on a limited land base would suffer diminishing returns, and if reproduction was not checked through moral restraint it would be checked by famine, war and pestilence. Malthus contemporary David Ricardo relativized the Malthusian s absolute scarcity of land. He showed that an expanding competitive economy could always turn to lower-quality land, thereby increasing the required labor to produce food and driving up its cost [302]. But classical economists were mainly focused on land and did not really faced the problem of depletion of minerals and other non-renewable resources. It was not until the beginning of the 20 th century, that the US conservation movement feared that progress would end because the rapacious present generation would consume the next of its needed natural resources. In the 1930s, Harold Hotelling [145] put numbers to the not very rigorous statements of the conservationists. According to Hotelling, resources would be depleted at a declining rate, and their price would rise at a rate equal to their owners opportunity rate of interest. In the seventies, the Club of Rome came into being and the first attempt at a global model by J. Forrester was pubilshed in World Dynamics [96]. The limits to Growth wealth. 1 The French physiocrats came to the conclusion in the XVIII century that land is the source of all

23 Economic growth and the consumption of natural resources 3 by Meadows et al. [218] followed in 1972, receiving great publicity. The works of Meadows et al. in 1972 and later updates in 1993 [217] and 2004 [219], argue that the current exponential growth cannot longer be supported as natural goods become depleted. Through the World3 computer model, different scenarios of resources consumption, pollution, population, policy, etc. were developed. The study claimed that if no immediate actions are undertaken, an economical collapse is foreseeable in the near future. The truth is that even if the consumption of natural capital has increased dramatically, evidence until to date has not really supported the idea that natural resources depletion has stopped economic growth. Some authors such as Barnett and Morse [20] or Scott and Pearse [302] appealed to the role of technological progress in improving the efficiency of extractive processes and redefining available resources. They stated that there is no evidence for the hypothesis that natural resources will lead to reduction of economic growth. Solow [326] argued that substitution of capital goods of natural resources in production processes reduces resource requirements and, in general, technical change may overcome limits imposed on economic activities in the environment. On the contrary, Costanza and Daly [65], Ayres and Nair [17] or Cleveland and Ruth [59], believe that technology will not overcome resource scarcity and environmental degradation, since human capital ultimately is derived from and sustained by energy, materials and ecological services. Until now, natural capital has been treated as a free good, but nowadays it is becoming the limiting factor in development. Champan and Roberts [53] argue also that resource substitution might be valid in the short term, but will fail in the long term when there is equal resource scarcity on all substitutable materials. Some attempts have been made to measure the economic costs of depletion and degradation and use them to correct standard measures of economic welfare such as GDP (see for instance Ahmad, El Serafy and Lutz [2]; Daly and Cobb [70]; Costanza [64]; Van Dieren [75]). Although the debate on how national accounting should be extended towards environmental accounting is still open, all approaches reflect that when depletions of natural capital, pollution costs, and income distribution effects are accounted for, the improving of the economy is seriously questioned. As we face the new century, the question of whether resource scarcity will constrain economy is still in the air. But the rapid economic development of Asia and the desire for a higher living standard in the developing world demands an even greater consumption of natural resources together with rapid technological progress to prevent increasing scarcity of the different commodities. Our society is based on an inefficient use of energy and materials, since there is a lack of awareness of the limit. If resources are limited, their management must be carefully planned in order to be consistent with the sustainability doctrine. But for that purpose, we need to know how many resources are available on earth and at which rate they are being consumed. A responsible management can only be based thus on a comprehensive

24 4 STARTING POINT, OBJECTIVES AND SCOPE information source. As Faber [91] claimed, the true intertemporal scarcity of environmental goods must be analyzed and appropriate indicators for the scarcity of these goods must be found. In this PhD, we have dived in data bases of many different institutions, organizations, universities and journals, searching for global numbers of the mineral capital on earth. For someone that never faced that task, it is surprising the lack of existing information about our resources not only in the past, but also in the present. This is a clear indicator of the little importance that humankind has placed in investigating the resources that nature gives us for free. Generally, the institutions owning information about resources do not interpret the compiled values. And ironically, many studies claiming the end of natural resources are rarely based on the physical statistics provided by the formers. More resources data bases, better global statistics, the opening of global information channels and impartial and serious interpretations of the information are key factors for transformation to sustainability. And the data interpretation must be undertaken with the help of appropriate indicators. This PhD has tried to fill with physical content some of the sociological messages about resource scarcity published elsewhere. This has been accomplished by making a rigorous analysis of the global minerals on earth through an indicator based on the second law of thermodynamics. The next section provides an overview of the different available scarcity indicators with its capabilities and drawbacks, so as to compare them to the indicator chosen in this PhD. 1.3 Scarcity indicators Consideration of scarcity and its measurement requires clarification of what we mean by scarcity. As Zwartendyk et al. [414] argue, physical scarcity refers to the relative rarity of an element or mineral substance in nature; it has nothing to do with human effort. Economic scarcity has very much to do with the interests and needs of humans. It reflects that work is required to obtain mineral products and that we are willing to pay a price for them. Generally, the greater the physical scarcity of a mineral, the costlier it will be to obtain, so its economic scarcity may be greater as well. The scientific community has already started to study this issue and some physical and economic indicators have been proposed. In the renowned work Scarcity and Growth 2 (1963) of Barnet and Morse [20], extraction costs were used as scarcity indicators. Extraction cost is computed as the amount of labor and capital required to produce a unit of output. The same indicator 2 Scarcity and Growth was the first systematic empirical examination of historical trends.

25 Scarcity indicators 5 was used until the update of that work: Scarcity and Growth Reconsidered [325]. This measure is founded on the classical economics view that with diminishing marginal returns and finite natural resources, the cost of natural resource extraction should increase as demand increases and depletion occurs. Krautkraemer [188] argued in Scarcity and Growth Reconsidered that extraction cost is an inherently static measure; it does not capture future effects that are important for indicating natural resource scarcity. In addition, extraction cost captures information about only the supply side of the market. If demand is growing more rapidly than extraction cost is declining, then extraction cost will give a false indication of decreasing scarcity (the opposite is also possible). Probably the most used indicator nowadays is price. Price incorporates information about the demand for the resource and possible expectations about future demand and availability. According to Fisher [95], the resource price would summarize the sacrifices, direct and indirect, made to obtain a unit of the resource. Naredo [237] claims though that standard economy is only concerned with what being directly useful to man, is also acquirable, valuable and produce-able. For this reason, most of the natural resources, remain outside the object of analysis of the economic system. And the price-fixing mechanisms, rarely take into account the concrete physical characteristics which make them valuable. Ruth [294] states that for prices to subsume all required information to make an intertemporally optimal choice about material and energy and the level of production, markets must be efficient, and preferences of current and future generations have to be anticipated. Additionally, current and future technologies must be fully described. In contrast, prices rather reflect the incomplete description of current technologies, preferences of present generations, and current institutional settings. Though non renewable resources are becoming more and more scarce, prices have not followed the same trend. According to Hotelling [145], prices should raise with scarcity, since low cost resources normally would be used first and quantities of extraction normally would decrease over time. On the contrary, historical statistics show that costs of extraction and prices have mostly decreased over time [313]. This apparent contradiction is due to technological innovation but also to the lack of information about scarcity. Reynolds [277] states that true scarcity is only revealed through prices towards the end of exhaustion. Physical indicators are usually based either on mass or energy. Generally, all energy resources are assessed in terms of its energy content, what allows a direct comparison between them. On the other hand, non-fuel minerals are usually physically and individually assessed in terms of tonnage and grade. It is obvious that mineral resources evaluated in that way cannot be easily compared, and a global number for the mineral s capital on earth cannot be given, as mass and grade are not additive. Furthermore, assimilating such a great amount of information for each resource is not always easy and not very useful for decision makers.

26 6 STARTING POINT, OBJECTIVES AND SCOPE Odum [245], [246] proposed an original physical unit of measure for assessing resources and products based on the solar emergy joule (sej). Emergy analysis is a technique of quantitative analysis which determines the values of resources, services and commodities in common units of the solar energy it took to make them. One of its fundamental organizing principles is the maximum empower principle. It is stated as systems that will prevail in competition with others, develop the most useful work with inflowing emergy sources by reinforcing productive processes and overcoming limitations through system organization. To derive solar emergy of a resource or commodity, it is necessary to trace back through all the resources and energy that are used to produce it and express them in the amount of solar energy that went into their production [42]. The solar emergy per unit product or output flow is called solar transformity, with units of sej/j. Solar transformities have to be obtained for each commodity. Most transformities cannot be considered as universal, as the processes involved in the formation of the commodities differ, depending on the period of time and place considered. The emergy analysis owns two fundamental capabilities that we think are required to be used as a scarcity indicator: 1) it is based on the physical characteristics of the resource and 2) all resources are measured with a single unit. Generally, the emergy analysis can be successfully applied for renewable resources. However it is very questioned the applicability of this approach for mineral resources, where the sun has not played a central role in their creation. No matter how much solar energy is received from the sun, the quantity of gold or iron for instance on earth, will not change. Consequently, the rigorousness of the transformities for mineral resource assessment is doubtful. Hence, the emergy analysis is not suitable for the purpose of this PhD, which is the assessment of mineral resources. The physical features that make mineral resources valuable are: a particular composition which differentiates them from the surrounding environment, and a distribution which places them in a specific concentration. And these intrinsic properties can be in fact evaluated from a second law of thermodynamics point of view in terms of a single property: exergy. As it happens to emergy and unlike standard economic valuations, the exergy analysis gives objective information since it is not subject to monetary policy, or currency speculation. Furthermore, all natural resources can be assessed in terms of exergy and can be summed up. Exergy is a property of the resource and as such, the calculation methods are physically and mathematically supported, as opposed to emergy. As explained in the next section, exergy is based on the notion of a reference environment, in which the quality and quantity of substances is fixed. Hence the analysis places value to resources depending on the level of departure from the defined reference environment. And, as opposed to the emergy analysis, whether the substances in it were created through the energy of the sun or through other processes is irrelevant and does not affect the final results.

27 Exergy and the assessment of natural resources 7 The exergy method is chosen in this PhD for assessing the evolution of mineral scarcity. In the next section, an overview of the different existing approaches connecting the entropy law with the consumption of resources is provided. 1.4 Exergy and the assessment of natural resources A fundamental law of nature (the first law of thermodynamics), tells us that energy and matter can be neither created nor destroyed. The second law places additional limits on energy transformations and reflects qualitative characteristics. It states that energy can only be transformed by the consumption of quality. Locally, the quality can be improved, but this can only occur at the expense of a greater deterioration of the quality elsewhere. The level of quality deterioration or disorder is measured through the property entropy. Hence, the second law of thermodynamics can be formulated as follows. In all real processes of energy transformation the total entropy of all involved bodies can only be increased or, in an ideal case, unchanged. Beyond these conditions, the process is impossible even if the first law is fulfilled [39]. The combination of both laws indicates that it is not a question of the existent amount of mass or energy, but on the quality of that mass or energy, or in other words on its exergy content. Technically, exergy is defined as the maximum amount of work that may theoretically be performed by bringing a resource into equilibrium with its surroundings by a sequence of reversible processes. The exergy of a system gives an idea of its evolution potential for not being in thermodynamic equilibrium with the environment. Unlike mass and energy, exergy is not a conserved property. It is an extensive property, with the same unit as energy. In all physical transformations of matter or energy, it is always exergy that is lost. Exergy analysis is a powerful tool for improving the efficiency of processes and systems. This leads to less resources to be used and the emission of less wastes to the environment. However it is a much more useful concept, and can be applied for resource accounting. All materials have a definable and calculable exergy content, with respect to a defined external environment. The consumption of natural resources implies destruction of organized systems and pollution dispersion, which is in fact generation of entropy or exergy destruction. Furthermore, exergy has the capability of aggregating heterogeneous energy and material assets. This is why the exergy analysis can describe perfectly the degradation of natural capital. For that reason, an increasing number of scientists, such as Szargut and coworkers [344], [338], [339], Brodianski [39], Wall [393], [394], [395], Rosen [289], [290], Dincer [76], Sciubba [299] or Ayres et al. [14] believe that exergy provides useful information within resource accounting and can adequately address certain environmental concerns. Additionally, different renowned studies have shown up the connection between economic scarcity and the entropy law. Some notable examples are briefly outlined next.

28 8 STARTING POINT, OBJECTIVES AND SCOPE Georgescu-Roegen was one of the first authors in realizing the links between the economic process and the second law of thermodynamics. In his seminal work The Entropy Law and the Economic Process [111], he states that the entropy law itself emerges as the most economic in nature of all natural laws [...] and this law is the basis of the economy of life at all levels. Georgescu-Roegen stresses the importance of the variable time in economic activity, which is clearly shown in the irreversibility of the exploitation of resources. This author even postulated the Fourth Law of Thermodynamics, the entropy law of matter. According to this law, matter and not energy is the limiting factor in economic growth. Georgescu-Roegen s Fourth Law has been criticized by a number of analysts in economics and physical sciences. It has been pointed out that on a fundamental physical level, there is no such law. In principle, it is always possible to use high quality energy to trace, collect and reassemble the dissipated elements [59]. The theoretical flaws of the Fourth Law, have lead some to dismiss Georgescu-Roegen s ideas or deny their significance. Faber et al. [92] developed a model integrating thermodynamic considerations into a model of optimal resource use and environmental management. They analyzed the relationship among resource use in the economic system, capital formation, resource concentration and entropy production. Ayres and Nair [17] state that the second law of thermodynamics has certain consequences for the production process which are not adequately reflected in the standard economic model. Among these consequences are that the exergy of the total output of a sector must be less than the exergy of the inputs and overall entropy is increased through the production of waste materials and heat. Ayres and Miller [16] developed a model that treats natural resources, physical capital and knowledge (measured in terms of negative entropy or negentropy) as mutually substitutable inputs into the production process. In 1988, Ayres [13] used the model for the calculation of optimal investment policies and simulation of optimal time paths and substitution pattern for the world primary energy sources from the year 1869 to Recently, Ayres [15], calculated the exergy performed in the US economy during the twentieth century. One of the conclusions of his study was that growth in exergy consumption have had an enormous impact on past economic growth. The increasing efficiency of the production in primary work tended to result in lower costs, which triggered increasing demand that often resulted in greater exergy consumption. This fact is known as Jevons paradox. Ruth [294] stated that use in economic production processes must consider thermodynamic limits on material and energy use in order to be optimal in the long-run. And economic decisions must consider the finiteness of the resources available, the interconnectedness of the economic system with other ecosystem components, the time preference of consumers and producers and the technologies with which materials and energy are transformed in the production process. He developed a model of nonrenewable resource use. As an example, Ruth determined the optimal extraction path and production of iron ore at each period of time, taking into account thermodynamic limits on material and energy efficiency, the treatment of endoge-