Assessing Long Term Sustainability of Global Supply of Natural Resources and Materials

The technological advancement of our civilization has created a consumer society expanding faster than the planet's resources allow, with our resource and energy needs rising exponentially in the past century. Securing the future of the human race will require an improved understanding of the environment as well as of technological solutions, mindsets and behaviors in line with modes of development that the ecosphere of our planet can support. Some experts see the only solution in a global deflation of the currently unsustainable exploitation of resources. However, sustainable development offers an approach that would be practical to fuse with the managerial strategies and assessment tools for policy and decision makers at the regional planning level. Environmentalists, architects, engineers, policy makers and economists will have to work together in order to ensure that planning and development can meet our society's present needs without compromising the security of future generations.


Introduction
The human population has grown exponentially over the past century and is expected to increase to nine or ten billion by the year 2050 . This growth has been accompanied by an increasing rate of consumption of natural resources (Brown & Kane, 1994, Brown, 2009a. On several key resources, the use of materials and energy has increased faster than the population growth alone. At present, humans are challenging planetary boundaries and capacities (Humphreys et al., 2003, Rockström et al., 2009. For many fossil resources (energy, most metals and key elements), the rate of extraction is now so high that it can only with difficulty be further increased (Hubbert, 1956, Pogue & Hill, 1956, Smil, 2001, Fillipelli, 2002, Arleklett, 2003, Hirsch et al., 2005, Gordon et al., 2006, Heinberg, 2007, Zittel & Schindler, 2007, Roskill Information Services, 2007a,b,c,d, 2008,b, 2010a,b,c, 2011, Strahan, 2007. In many cases, known resources are dwindling, because prospecting cannot find more. There have been several earlier warnings about the prospect of upcoming future material scarcity (Forrester, 1971, There are some important facts we need to keep in mind at all times when considering many of our essential resources. Most of them represent inheritance from past geological times, and the amounts regenerated per year are vanishingly small compared to our present use. The global commons has only a one-time allotment for all ages and generations. The amounts are finite, and if we use them all now, then we deprive future generations of many possibilities to support them selves (Norgaard & Horworth, 1991, Ainsworth & Sumaila, 2003, Heinberg, 2007, Brown, 2009b. At present, for every ton of natural resources we remove and waste irreversibly, there will be that amount permanently less in available stock on Earth for future generations.

From limits to accessibility
Around 50 different metals and elements are necessary to produce cars, computer chips, flat-screen TVs, DVD players, mobile-phone screens, hybrid cars, compact batteries, miniature machinery and cameras. For computer chips, this number has increased from around 10 different metals in 1980 to more than 40 metals and elements today. The concentrated ore deposits of these metals that can be easily tapped through mining are finite, even if -overall, the metals are in sufficient supply in the Earth's crust. But are we running out of metals that lie at the heart of our technological society? At an international conference in 2008 (Hall, 2008, Williams, 2008, experts from numerous geological surveys and mining companies claimed that many resources are yet to be mined, arguing that the key is to mine more deeply (up to 2 km) for lower-grade ores and to exploit the ocean floor (up to 7 km below sea level) (Ragnarsdottir, 2008). But deeper mining and refining of lowergrade ores will require more energy (Hall et al., 2001, Roskill Information Services, 2007a,b,c,d, 2008,b, 2010a,b,c, 2011, USGS, 2008, another precious resource. And it remains as a fact, that these views are more wishful thinking than based in any reality. Very few mines go below the 1,500 meter mark in mountains, harvesting the deep seas has not been notably successful, and there is limited technology available at present to undertake such mining. As elements go scarce and hence, expensive, mining will move to also extract from low-grade and ultra-low grade reserves. However, there are limitations to that practice. At some point, the material and energy expenditure exceeds the use that can be obtained out of the extracted resource, thus it does not pay off -usually referred to as EROI (Energy Return On Investment;Hall, 2008). One usual argument for example is that there is theoretically enough phosphorus on earth for all times. However, when we consider that what is available when phosphorus has been dissipated or lost to the sea, the energy and material expenditure to have it extracted is not economically viable. Many new technologies may end up costing too much in metals and energy to build for a mass production scale so that, at least some of them, will never cover the EROI. Even though such solutions may appear as a good idea, they are unsustainable.
Various methods have been developed to analyse material flows through socitety. Material flow analysis, MFA (or substance flow analysis, SFA) is an analytical method for quantifying flows and stocks of meterials or substances in a well-defined system. MFA is an important tool to quantify the physical consequences of human activities and needs. It is used in the field of Industrial Ecology for different spatical and temporal scales. Examples include accounting of material use by different societies, and development of strategies for improving the matrerial flow systems as material flow management Allenby, 1995, Brunner and. Life cycle assessment (LCA or life cycle analysis, www.intechopen.com Assessing Long Term Sustainability of Global Supply of Natural Resources and Materials 85 ecobalance, and cradle to grave analysis) is a technique to assess environmental impacts associated with all the stages of a product´s life from cradle to grave. The LCA includes compilation of an inventory of relevant energy and material inputs and environmental releases; the evaluation of the potential impacts associated with identified inputs and releases; and interpretation of results to help make informed decisions (e.g. Guinée, 2002). In the life cycle of a product the life cycle inventory as part of live cycle assessment can be considered an MFA as it involves system definition and balances. Cradle to cradle analysis is a specific kind of cradle to grave assessment, where the end of life disposal step for the product is a recycling process.
In this chapter, we use systems analysis and system dynamics (Forrester, 1961) as well as burnoff time and Hubbert curve representation to assess long term sustainability of global supply of natural resources and materials. Systems Analysis deals with analysis of complex systems by creating conceptual model structures with the help of Causal Loop Diagrams (CLD). CLDs make clear the cause and effect relationships and the feedbacks between different components in a system. System Dynamics is a methodology used to understand the behavior of complex systems over time. It deals with internal feedback loops and time delays that affect the behavior of the entire system. With the help of systems dynamics the conceptual model structures are transferred into dynamic numerical models, which can be then used as decision support tools, enabling the user to generate different scenarios and analyze the associated simulation results. Systems analsyis and system dynamics provides a deep insight in identifying interdependencies and feedback processes of dynamic stocks and flows of materiels, population dynamics and recycling rates. Neither MFA nor LCA encompasses these imporant components of systems analysis.

Methods of assessment
We use three different types of methods in order to estimate the time horizon of a raw material or metal resource:

Burn-off time:
We define burn-off time as known mineable reserves divided by the estimated average annual mining rate. The formula is given as: Burn-off time = reserves/mining rate [yrs] (0)

Hubbert's peak resource estimate:
An oil engineer at Shell Oil Corporation, developed what is referred to as the "Hubbert curve" (Hubbert, 1956(Hubbert, , 1966(Hubbert, , 1972(Hubbert, , 1982 in order to predict the lifetime of oil wells and oil fields. He showed, using observed production data for oil wells as well as metal and phosphate mining, that all finite resource exploitation follows a distinct pattern of the Hubbert curve 1 (Figure 1). The shape of the Hubbert curve has a scientific explanation deriving from the nature of a finite resource, as well as the fact that Hubbert could verify his model on field data several times over. The Hubbert curve is defined by: Sustainable Development -Energy, Engineering and Technologies -Manufacturing and Environment 86 where M max is the total resource available (ultimate recovery of crude oil), M the cumulative production, and the coefficients a and b are constants.
We adapted the Hubbert curve and define the annual production as: where P max is the maximum production rate, P is the production at time t, t max is the time of the peak, and the coefficient b is the curve shape constant. Available history for the source, the size of the reserve and 1 / 3 of the production curve is enough to set the a and b coefficients (Cavallo, 2004). Fig. 1. The extraction pattern for hydrocarbon follows a symmetrical curve common to extraction of all resources. This can be used with observations of production rates to estimate the time to scarcity as shown with an analysis of the Norwegian oil production. The diagram suggests that the time to scarcity for oil produced in Norway is about 15 years. By 2040, the Norwegian age of oil production from Norwegian oilfields will be over.

Systems analysis and system dynamics:
Systems analysis with the help of causal loop diagrams is essential for gaining insights into the world metal supply system. With Figure 2, we intend to show that despite the Hubbert  Hubbert (1956Hubbert ( , 1982. The system is based on two stocks, one known resource, backed by a hidden resource that can be found by prospecting for it and converting "hidden" to "known" (A). As "hidden" dwindles, "known" does get replenished until "hidden" is exhausted. As the extraction loop exhausts the "known", it gets backfilled, overlying several individual "rise and fall" curves to yield the typical Hubbert curve. The causal loop diagram is shown in (B). The resulting behavior of the components is depicted in (C). If we consider three types of resources in the system; high-grade, low-grade and ultralow-grade, we get three individual peak behavior curves (D), which may be overlaid to the final total production, expressed as profits (E). The results of using the Hubbert curve and using systems analysis and causal loop diagramming yield similar results for time to scarcity.
Sustainable Development -Energy, Engineering and Technologies -Manufacturing and Environment 88 curve being empirically determined, there is a mechanistic explanation for it. In Figure 2, a flow chart (A) is shown with the corresponding causal loop diagram (B). The system is based on two stocks, one known resource, backed by a hidden resource that can be found by prospecting and finding more resource, converting "hidden" to "known". As the hidden resource, which is finite, dwindles, the "known" resource gets replenished for a short time until the "hidden" resource is exhausted. Thus as the extraction loop exhausts the "known" resource, it gets backfilled a few times by prospecting that brings more "hidden" resource over to "known" (B, C), overlying several individual "rise and fall" curves (D) to yield the typical Hubbert curve (E). The system is driven from the profit side, as mining leads to profits and more profits drives more mining, whereas the exhaustion of the finite stocks terminates it. The diagrams show the relationship between the parameter at the arrow-head over time. The diagrams depict what happens with new resources becoming known after prospecting (D), the bottom diagram (E) shows the sum of all the small diagrams, depicting extraction as a function of time.
The basic functions of our systems dynamics simulation model philosophy are described in the causal loop diagram (CLD) shown in Figure 3. The figure shows that with increased population, the consumption of metals increases, which in turn increases the production. Emissions and waste generated from both the production and consumption of the metals lead to environmental degradation. Increased environmental degradation increases public and governmental concerns and forces society to take necessary policy actions. These actions are shown in the CLD with numbers from 1 to 4 (blue diamonds) in Figure 3. Increasing consumption and population are the two major factors for an increasing demand for metals in the world. An increase in population drives consumption, depleting markets, increasing prices and increasing supply from production to market. This allows for continued consumption augmentation as well as increased resource use. Increased resource use rate and associated waste generation leads to environmental degeneration.
Environmental degradation and declining resources have an effect on political and public awareness. This leads to the development of four different policy options. During the early 1950's, end of pipe solutions (blue diamond no. 1 in Figure 3) were used as a first response to increased concerns over environmental degradation. Instead of draining out wastewater from industrial process to rivers, we built wastewater treatment plants; or instead of emitting hazardous waste gasses into the atmosphere, we installed treatment units in such processes. During the early 90's we realised the economic value of natural resources and waste, and introduced cleaner production and pollution prevention practices (diamond no. 2) to increase the efficiency in the production processes, and thus to decrease the use of raw materials (natural resources), the waste generated and gasses emitted to the atmosphere. In the last decade, we have concentrated on sustainable consumption and production behaviour (diamond no. 3) and begun to question how we can make changes in our life style (and quality) to decrease the demand for goods and food, and consume less, which may in turn eventually decrease the environmental degradation. As a part of sustainable production policy, recycling represents a way to increase metals in the societal material cycle without depleting resources. However, as can be seen from the CLD in Figure 3 -if we trace back the main root cause for today's increasing environmental degradation, it is embedded in the increase in the world's population. We certainly need to introduce sustainable population policies (diamond no. 4) (especially in the developing countries), together with sustainable consumption and production policies (diamond no. 3) (mainly in developed countries) in www.intechopen.com  Fig. 3. Sustainability of resource use has moved over many system levels from end-of-pipe (fighting pollution) to root cause (population numbers and their behaviour). Attention has over time moved from end-of-pipe solutions (1) to more focus on clean production (2) recycling, slimmer consumption patterns and sustainable production (3). Ultimately the world must also address the consumption volume as a function of per capita use as well as the number of consumers, directly proportional to the size of the global population (4). order to decrease over population (demand) and unnecessary wasting (supply). A long-term sustainability policy for the world population will thus be needed, as a part of the total flux outrunning planetary capacities. In this context, Figure 3 presents the problem and displays the different solutions tried so far. Unsustainability in this context arises from: (a) End of pipe pollution output from the system; (b) From unsustainable production or resource use in suboptimal products; (c) From excessive volume consumption of resources; (d) and -From consumption in excess of the carrying capacity of the Earth. In order to address the problems, four different approaches were tested in this study. Potentially, it may be that a global population contraction during the next century must be planned for (Malthus, 1798, Pearson & Harper, 1945, Osborn, 1948, Ehrlich, 1968, Meadows et al., 1972, 1992, Brown, 2009a,b, Ehrlich & Ehrlich, 1990a,b, 2006, Bahn & Flenley, 1992, Brown & Kane, 1994, Daily et al., 1994. The carrying capacity of the world for population has been estimated many times, but with disparate results, primarily because of differences in fundamental assumptions (Cohen, 1995) concerning the following aspects: Sustainable population = Total resource available annually / individual annual consumption [persons] ( The equation is applied if the resource is renewable. If it is neither renewable nor substitutable, but constitutes a one-time heritage, then the annual sustainability estimate is: Total resource available annually = Total resource volume / time to doomsday [ton per year] The time to doomsday is estimated as the time to the end of our consideration, potentially the projected time of eclipse of human civilization (Gott, 1994, Leslie, 1998, Korb & Oliver, 1998, Sowers, 2002, Sober, 2003. We have previously discussed the content and meaning of a long-term time perspective, and we also made an assessment of the impacts of unsustainability of the phosphorus supply with respect to the global population ). There we arrived at the following definitions that we adopt here:  Long term sustainable perspective is when the resource is managed in such a way that a glacial gap can be bridged. Glaciation causes denudation and access to fresh strategic element bearing rock. The average time between glaciations, the room for civilization to prosper, is about 10,000 years. After that geologically large events make conditions for civilizations so fundamentally changed that no standard rules apply. The first urban societies arose 10,000 years ago, the first states emerged 5,000 years ago.  A semi-sustainable timeframe is a time equivalent to how long modern literate and democratic civilizations as we know them have persisted, more than 2,000 years. However, most societies unconsciously want to persist longer than that. The state of Denmark as an entity is about 2,000 years old.  A sustainability-oriented timeframe is the historic time that is set for 1,000 -2,000 years, the time of continuous historical records and age of the oldest surviving books.  Unsustainability in the intermediate term is 200 -1,000 years, the time perspective of many monuments and infrastructures that are well built. Unsustainability in the short term is considered to be 100-200 years. This timeframe is bordering on living memory, and often the age of a private house still lived in.  Urgent unsustainability is adopted as the term for time horizons less than 100 years.
Of note is that individual consumption is not seen as the individual physiological requirement, but that it must include efficiencies from first extraction from the deposit until it reaches the individual consumer.
Individual supply = Extracted amount per capita  product of all efficiencies in the supply chain [kg per person] The extraction steps may be many and the inefficiencies may quickly pile up. The carrying capacity of the Earth under total sustainability will be in sustainable population number ): Sustainable population = min (Sustainable population estimates (food production limitations (i))) [persons] (6) According to Liebig´s principle estimates represent the different aspects that can limit growth (nitrogen, phosphorus, water, light, essential major and trace elements, soil substrate availability). In the short run, many of those can be overrun as long as the system can deplete the available resources. However, in the long run this is impossible, as it would violate mass balance laws. Many studies have considered these resources one by one, a few have done several, but none have done them all (See Table 1 and Table 2 for an overview of different estimates). We also use a simple equation for total consumption of a resource: It is evident that we can take down total consumption by reducing the amount each consumer uses, but also by reducing the number of consumers, and both. It is important to assess the effect of recycling. An integrated assessment over all essential components is needed in the long run, as the studies of Meadows et al. (2004). Thus, what we first estimate is the supply to society, as: Where R is the degree of recycling on the flux from society. This is what is shown in Figure  4. In the calculations, we take the present mining rate, and use the present recycling degree, to estimate the present supply to society. Then, we calculate the new flow into society for other improved degrees of recycling: where we have defined six scenarios (i), including: 1. Business-as-usual, no change in recycling from today's; 2. Improved habits in the market, at least 50% recycling or maintain what we have if it is higher than 50% recycling, and improving gold recycling to 95% recycling; 3. Improve all recycling to 90%, except gold to 96% recycling; 4. Improve all recycling to 95%, except gold, platinum, palladium and rhodium to 98% recycling; 5. Improve all recycling to 95%, except gold, platinum, palladium and rhodium to 98% recycling; assume same per capita use as in 4, but assume that population is reduced to 3 billion; 6. Improve all recycling to 95%, except gold, platinum, palladium and rhodium to 98% recycling; assume one half of present per capita use as in 4, but assume that population is reduced to 3 billion. Fig. 4. Market mechanisms for metals. This causal loop diagram explains how supply and demand affect the price of a metal, and how the price feeds back on recycling and use. It can be seen from the diagram, that introduction of recycling creates a reinforcing loop, keeping material in the cycle. The enemy in the system is dissipative losses as they represent a destination for metals with no hope of return. The major driver for metal use is the population size.
Then we calculate the new net supply needed to maintain that societal supply at present level at improved recycling rates, and use that to find the new burn-off time. Figure 5 shows the flow diagram depicting what we explained above in the text, that recycling can maintain the same input to society, but decrease the input from finite resources through mining.
The real flow to society becomes amplified by recycling, because part of the outflow becomes returned to the inflow.
Burn-off time for new recycling rate = reserves /(supply to society X (1-R i ))[yrs] (11) Where R i is the recycling of scenario i. In order to get the Hubbert's methods estimate of time to scarcity, conversion from burn-off based time to scarcity is (based on our results by plotting them): Hubbert's time to 10% of peak production = 1.7 * Burn-off time + 2 (12) Fig. 5. The recycling effect. A flow diagram showing that recycling can maintain the same input to society, but decrease the input from finite resources through mining. The real flow to society becomes amplified by recycling, because part of the outflow becomes returned to the inflow.

Systems dynamics modelling of material cycles
A CLD neither demonstrates how strong each of the linkages is nor the functional form that the relationship takes. It allows us, however, to develop a better understanding of the overall system, to identify its main components as well as the cause-effect relations between these components and to trace back some main root causes of unsustainability in the system. In a fairly complex system, as the one presented here, there are substantial numbers of feedback loops, all of which result in a complex system behaviour. A model description of the CLD type does not contain all the details necessary for a full understanding of the model's behaviour, but it is possible to identify some overall reinforcing and balancing loops. We do not use neoclassical economic models in this study for analysing trends (Shafik, 1994, Turner, 2008, Goklany, 2009) as these methods do neither use mass and energy balances nor obey thermodynamic principles, thus yielding naïve results of limited value. It is important to state that neither econometricists nor economists can choose whether they believe or do not believe in thermodynamics. Time has come where we stop to be polite and tolerate their ignorance.
There is no escape from mass balance, and not internalizing this mass balance has become damaging to society, "….its validity is absolute, leaving those that disbelieve in line for complete humiliation" as Sir Arthur Eddington stated (Eddington, 1928, see Hougen et al., 1959 for further elaboration on the consequence and danger of ignoring mass balances).
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In this study, we use causal loop diagrams for finding each metal system connections, important feedbacks and system structures as a part of the generic systems dynamics procedure (Bertalanffy, 1968, Forrester, 1971, Meadows et al., 1972, 1992, Senge, 1990, Vennix et al., 1992, Sterman, 2000, Maani & Cavana, 2000, McGarvey & Hannon, 2004, Sverdrup & Svensson, 2002a,b, Cavana, 2004, Haraldsson & Sverdrup, 2004 and the learning loop (Haraldsson et al., 2002, Haraldsson 2007. The method used for constructing the system dynamics model follows a strict scheme, as well as deriving links by empirical-, experimental-and Delphi methods (Adler & Ziglio, 1996). The CLDs uniquely define the differential equations of the system, and together with a flowchart, help to build the dynamic models in the STELLA ® modelling software.
Dynamic models are developed for gold, platinum, phosphorus, rare earth elements, lithium, uranium, thorium and oil. The models are then used to estimate time to scarcity, with and without recycling for different alternative scenarios. We define the time to scarcity as the time for the known reserves of high grade and low grade to have decreased to 10% of the original amounts.
The models are constructed into several modules: 1. The global population and consumption module; 2. The mining module with reserves and prospecting; 3. The consumption and market module, including a price mechanism; 4. The recycling module; 5. The social stress module.
Each model is formulated as a series of differential equations, arranged from mass balances for the resource R: dR/dt = inputs -outflows + produced -accumulation in the system [ton per year] (13) The following 10-12 different coupled reservoirs are considered in the models through coupled differential equations, based on mass balances for a number of stocks in the system: a. Exhaustible resources (4-6 stocks): 1. High grade deposits 2. Hidden high grade deposits 3. Low grade deposits 4. Hidden low grade deposits b. Population model (simplified global) (4 stocks) (0-20 yr, 21-44 yr, 45-65 yr, 65+ yr) c. Society (2 stocks) 5. Market stock 6. Waste stock For phosphorus, gold and platinum, we also used two additional physical reservoirs, known ultralow grade and hidden ultralow grade, as well as one for social trust in the phosphorous model. The material flow chart for gold including the recycling is shown in Figure 6. The causal loop diagram given in Figure 7 shows the causal chains used in our model on global gold supply. The CLD shows the basics of the market, but for simplicity omitting the derivates trade that also belongs to the model.   Table 1 shows an overview of important metals and elemental resources for running society and human civilizations. The main sources and the main uses are listed, together with indications on the use of the reserves. Comprehensive life-cycle flow assessments are available for few substances. This is primarily a fact because many of the mining companies closely guard their data, making world reserve figures uncertain (USGS, 2008, Roskill Information Services, 2007a,b,c,d, 2008,b, 2010a,b,c,d, 2011. However, some  (Forester, 1971, Meadows et al., 1972, 1992, USGS, 2008, Graedel et al., 2004. There is lots of aluminium in solid rock, but this is so tightly bound, that it is prohibitively expensive to take them out. Large losses are to corrosion and in household trash Aluminium Guinea, USAA u s t r a l i a , C a n a d a , Russia, Norway
For platinum and palladium, there are dedicated platinum group metal mines (South Africa), but about 30% of the production is a by-product of the nickel production (Russia, Canada). Rhodium production is entirely dependent on the production of platinum and palladium, and when they stop, so does rhodium (Johnson Matthey Platinum Review, 2008). In the systems dynamic modelling output diagrams as shown in Figure 7, we can see dynamic simulations undertaken for platinum, with past and predicted future reserves in geological formations to the left and mining rate to the right. Platinum shows peak behaviour, similar to what many other materials do. Platinum is lost in several ways. Only about 20-25% of the platinum metal used for catalytic converters for cars is recycled every year. This it out of a flux of 40 ton per year, where the global production is 230 ton per year. 40-50 ton is used as catalyst in fertilizer plants; of this 10-20% is lost diffusively into the produced product (4-8 ton per year). Overall global recovery is perhaps in the range 65-75%, which needs to be improved.
Gold has a very special place amongst the metals, as it is the first metal ever used by humans. It is in every day life easy to work with and nearly indestructible. It is traded as money, but has many technical applications, the most common being decorative plating, and plating for protection against corrosion, in jewelry and electronics. It is also special in the sense that the production is well known, it has passed the peak, and we now have more above ground than in geological formations. Gold is very valuable, has always been so, and almost nothing is lost aside from small dissipative losses. It's first and most important use was as money and in prestige jewelry; this remains so to the present. In times of inflation and governmental unaccountability with issuing fiat money, gold is the resort taken by a  Table 2. Estimated burn-off times (years), time to scarcity using the empirical approach of Hubbert (1966Hubbert ( , 1982, and using integrated systems dynamics modelling for metals and elements of different classes. # represents estimates using models built by authors, * represents dynamic model assessments by Meadows et al. (1972Meadows et al. ( , 1992Meadows et al. ( , 2004 using system dynamics. Available deposit values represent the sum of estimates for high grade and lowgrade ores. majority of the world's population. Such practice becomes more prevalent in times of uncertainty. Gold world production peaked in 2005 at 2,500 ton per year, and is expected to decline further from now (now 2,100 ton per year). Overall the recycling degree of gold metal in industrial circulation is better than 92%. In modern times, significant amounts are being lost through gold plated objects and in consumer electronics dumped in landfills and burned in incinerators. Total losses are estimated at 12,000 ton over 5,000 years out of a total mined volume of 160,000 ton (7.5%). A complicating affair with gold is that much has been sold forward as paper gold to investors; this implies that the ownership is sold, but the actual physical metal has not been delivered. This is undertaken by a number of investment and hedge-fund banks that have no significant reserves of physical gold, and thus the gold they sell probably does not exist. They simply assume that they can buy it "somewhere" whenever the need should arise. For a physically limited commodity as gold, that may not be the case at all times. This situation of uncovered gold forward positions will continue to put pressure on the gold price and thus physical supply and demand for decades to come. In the systems dynamic modelling output diagrams in Figure 9, we can see dynamic simulations undertaken for gold, with past and predicted future reserves in geological formations to the left and mining rate to the right. Fig. 9. Peak gold. Systems dynamics modelling output diagrams showing past and predicted future gold reserves in geological formations (to the left) and mining rate (to the right). Figure 10 shows simulated past and future market price for platinum and gold. The metals will never become unavailable when the resource reserves dwindle, but they will become more expensive as the market availability goes down. The model was validated against observed price as well as on central banks inventory statistics in the past with good success. Fig. 10. The price-impact of metal scarcity. System dynamics modelling output diagrams showing past and future market price for platinum (to the left) and gold (to the right). The different % represents at which average rate uncovered forward and short positions are eliminated.
Silver is an important industrial metal, because of its good ductility and conductivity to electricity and heat. As with gold, significant amounts of silver have been speculatively sold forward by banks, and it is uncertain how this is to be found for physical delivery in the future when the contracts expire (OCC, 2009). Silver is lost to diffusive losses, in electronics and silver plating. Cutlery and coinage is mostly recycled. There are considerable amounts of silver stored in private homes all over the world, and a small calculation assuming that in the western world every home has 200 g silver (4 spoons, one in 20 has a full, but simple silverware set) and in the rest of the world there is 15 g silver per person (one teaspoon per household, one in 200 has a full, but simple silverware set), an estimated 400,000 tons is stored in private homes, or about 14 annual global productions.
Rare earths are always mined together as a mix; they are very difficult to separate; with them comes often Y, Sc, Ni and Ta. Figure 11 shows model outputs from simulations for the peak behaviour of rare earth metals without (left) and with (right) recycling. It can be seen that with recycling, we can keep an equal amount available in the market with less mining and that the reserves last significantly longer. With recycling, the availability of the rare earths can be brought to last up to 50 times longer, depending on the degree of recycling.
Lithium is extracted from the salt-beds of certain dried out lakes at some few locations in the world. It has great potential for making light-weight batteries for computers, mobile phones, but possibly cars are also being contemplated. However, the resource base is very small, and mass production of accumulators for cars would quickly finish it off. At present, there is no recycling, and all lithium used at present is lost.
Mining and market without recycling Mining and market with recycling Reserves without recycling Reserves with recycling Fig. 11. Peak rare earth metals. System dynamics modelling output diagrams showing rare earth metals without (to the left) and with (to the right) recycling. Diagrams on top show the supply and mining rates, where as diagrams at the bottom show reserves over time.

Recycling and replacing
In view of these findings, it is essential that we use metals like copper and zinc, platinum group elements and tantalum as well as all other scarce resources in a sustainable manner. More efficient metal use through better product design and higher durability will also help. But there are limits to recycling; zinc, for example, is used in low concentrations for galvanizing, and is difficult to recycle once it is dissipated across metallic surfaces. Where possible, therefore, scarce resources need to be replaced by more common and easily accessible ones such as aluminium or silicon. A few such technologies are already being investigated. During the past century, industrial production around the world has increased 40-fold. Virgin stocks of several metals seem inadequate to provide the modern "developed world" quality of life for all people on Earth under contemporary technology (Gordon et al., 2006). Of course, there will always be lower-grade metal to exploit, and we can also mine at deeper levels, leading some Earth scientists to reject this more pessimistic view (Williams, 2008). But the price may well prove prohibitive in practice owing to the cost of energy.
Pin-head capacitors in mobile phones that are currently made out of yttrium, tantalum or hafnium, could instead use aluminium 2 . Germanium and indium transistors can possibly be made from silicon or silicon carbide (Juang et al., 2008) or carbon nanotubes (Tans et al., 1998). Solar cells made with silicon polyvinyl chlorides are twice as efficient as thin films solar cells made from the rare metals indium and gallium. For phosphorus there is neither a substitute nor any alternative. Economists and economic theorists frequently advocate that technology and science will always develop substitutes, but for phosphorus, we know as a fact that there is none at all because nothing can replace this essential element for life, regardless of what the price might be.
Phosphorus is unique and is demanded for maintaining life in all living organisms in rigidly set proportions. Once elements and metals are dissipatively lost, the energy cost of retrieving them will normally be prohibitive, and if the need is large, the energy needed will probably not be available (Ragnarsdottir, 2007, Fillipelli, 2008. Extracting phosphorus from the seawater would be energetically unsolvable on a global supply scale. Systems dynamics outputs are shown in Figure 12. The figures show that mining rates from different sources in the longer perspective, show peak behaviour, how the production from high grade, then low grade and last the ultralow grade reserves, peaks . Fig. 12. Peak phosphorous. System dynamics modelling output diagrams showing how the mining rates from different sources peak (to the left) and how the production from high, low and ultralow grade reserves peak (to the right) in the longer perspective.

Job market is affected
It is not only price rises of metals on the world market that give an indication of scarcity: the Denver Post 3 reported in March 2008 that in mining companies, geologists were receiving higher average starting salaries than those with MBA degrees. Similar opportunities apply to skilled oil prospecting geologists and reservoir engineers. At present, these are put to work to make the system even more unsustainable, by finding more of the last hidden reserves, so that they can be finished off as well. However, as times go by and more and more resources can be shown to pass their production peak, the message will have to sink in that recycling is the new kind of mining. The new type of prospecting geologist will have to learn how to mine societal stocks to serve sustainability. Materials engineers and advanced metallurgists have also become rare (difficult subject to master well, few take on this education), and salaries for these are rising. In the near future more systems analysis and sustainability planners as well as material scientists will be needed across the world.

Convergence and contraction needs
From the estimates, using burn-off years, the Hubbert-curve estimate or systems dynamic model runs, we see that we are now challenging the planetary boundaries for supplying most of the materials humans consider necessary for serving civilization. Even metals like iron or aluminium may eventually run out in a few decades. It is of little help to point out that there exists an abundance of these in granite or in the deep crust, as long as there are no reasonable methods or technologies available for winning them. It is also evident from the systems analysis and the dynamic runs, that the market alone cannot cause the use of scarce resources to become sustainable. This is because the market is opportunistic in its function and nature, has no memory, or future vision. The rise in price when a resource becomes scarce will cause recycling to increase, but this occurs when too much of the resource has been consumed without significant recycling, and thus allows a large part of it to have become wasted. In addition to a well functioning market, strict governance and policies are needed. Governance must see to that the free market has a well-regulated arena to operate in as well as enforcing that those game rules are obeyed. This is needed to govern responsible use of resources, including starting recycling before the resource becomes scarce. Governments must make policies that look forward with responsibility for generations to come and for the preservation of society.
It is a widely spread misconception that a free market is a market without rules and regulations, with no interference from government; the opposite is the case (Smith, 1776, Friedman, 1962, Forrester, 1971, Friedman & Friedman, 1980, Sterman, 2000, Klein, 2007, Lövin, 2007, Sachs, 2008. The demand for free economy to mean no rules is nonsensical, even if it is cherished by certain political ideologies and taught at many business schools. Games without rules soon deteriorate to anarchy or rule of the strongest, and markets without rules quickly become something that has nothing to do with free markets (Friedman, 1962, Klein, 2007, Sachs, 2008, Jackson, 2009. Sustainability constraints are among some of the most important additions to free market economies if they are to be made long term stable and long term sustainable. The modern world depends on the markets systems for distribution and redistribution of goods, services and wealth, thus functioning markets are an integral part of a sustainable world.
In Table 3, we show the estimates of the maintenance supply from external sources to keep the internal society flux as in 2008, but applying a strict recycling principle. Here we have chosen scenario 4, applying 95% recycling for all elements, except precious metals that we set at 98% recycling. This is a very strict scheme, but it was chosen for the sake of example, to show how large the impact of recycling can be. Obviously, recycling is key factor in going towards metals sustainability. The required external supply can be brought down significantly, once recycling is made efficient. This, together with a contraction of the global population may bring us into the sustainability realm.
In Table 4 we show the outputs on Hubbert-estimates for time to scarcity. The scenarios are as follows; (1) Business-as-usual, no change in recycling from today; (2) At least 50% recycling or maintain what we have if it is higher than 50% recycling, and improving gold recycling to 95%; (3) Improve all recycling to 90%, except gold is improved to 96% recycling; (4) Improve all recycling to 95%, except gold, platinum, palladium and rhodium is   (1) Business-as-usual, no change in recycling from today's values, (2) Improved habits in the market, at least 50% recycling or maintain what we have if it is higher than 50% recycling, and improving gold recycling to 95% (3) Improve all recycling to 90% except gold to 96%. (4) Improve all recycling to 95%, except gold, platinum, palladium and rhodium to 98%. (5) Improve all recycling to 95%, except gold, platinum, palladium and rhodium 98%, assume same per capita use as in 4, but assume that population is reduced to 3 billion. (6) Improve all recycling to 95% except gold, platinum, palladium and rhodium to 98%, assume one half of present per capita use as in 4, but assume that population is reduced to 3 billion. improved to 98% recycling; (5) Improve all recycling to 95%, except gold, platinum, palladium and rhodium to 98% recycling, assume same per capita use as in 4, but assume that population is reduced to 3 billion; (6) Improve all recycling to 95%, except gold, platinum, palladium and rhodium to 98% recycling, assume one half of the present per capita consumption with respect to scenario 4, but assume that the global population is reduced to 3 billion (Brown, 2009. The colour code in the table shows the time to scarcity years. Degree of sustainability can be assessed as 'very unsustainable' for red and orange colours, 'unsustainable' for light orange, 'problematic for future generations' for yellow, 'approaching sustainability' for light green and 'fully sustainable' for green colours.
For fossil energy resources, we see no possibility of ever becoming sustainable, the same applies to use of thorium and uranium in conventional nuclear power stations. However, if the technological and security challenges of breeder reactor designs and fuel recycling are overcome, then the perspectives for uranium and thorium may be widened to the order of 50,000 years.
From Figure 13 we can see a comparison of the different estimates with present recycling rates as repeated to the empirically based Hubbert-estimate. Making system dynamic models and running them may take some time to do. The Hubbert-estimate is fast, providing the right historical records are available. The plot of Hubbert-estimates versus the times obtained with dynamic modelling (Figure 13) shows good correlation; this means that we can make some observations and empirical rules: 1. Burn-off times multiplied by two is a good estimate for the time to scarcity. The burnoff estimate can be made on the back of an envelope, so that it is practical for quick calculations. 2. The Hubbert estimates of time to scarcity and system dynamic modelling estimates of time to scarcity give comparable results. The Hubbert method is a quicker way to get a rough estimate of time to scarcity. 3. System dynamic modelling estimates of time to scarcity makes a more detailed overview and allows for less sweeping generalizations and more specific adaptations to the situation of the specific element and the feedbacks that affects it's fate. Dynamic modelling allows for inclusion of systemic feedbacks and sensitivity analysis, as well as lending it self to policy optimization through back-casting.
It is therefore imperative that we start on a path towards sustainable development worldwide. Whether new technologies use components that will still be available in a few decades, should be a key criterion for their development, not an afterthought. Lack of resources is a dangerous situation globally; there are many convincing examples where this is indirectly or directly the cause for social crisis and potentially also war (Hardin, 1968, Bahn & Flenley, 1992, Haraldsson et al., 2002, Diamond, 2005, Klein, 2007, Lövin, 2007, Tilly, 2007, Zhang et al., 2007, Brown, 2009b. The solutions to our sustainability problems are as much in the social domain as in the technology domain. Engineering and economics must learn to deal with the functions and mechanisms of the social machinery, and realize that people and feedbacks from social processes control and shape human behaviour. Behaviour is what controls decisions, and these are not always conscientious, nor openly rational. The notion of "the rational economic man" as a foundation for economic behaviour is a mythomania, and it has never been shown to be Sustainable Development -Energy, Engineering and Technologies -Manufacturing and Environment 108 Fig. 13. The plot of Hubbert-estimates time to scarcity (years) versus the times obtained with system dynamic modeling (years) shows good correlation. The burn-off estimates are roughly 50% of the real time to scarcity, and thus underestimates the time to scarcity.
valid. The sustainability challenge is thus a social challenge and centres around the willingness of populations to change behaviour. The use of all resources available to us at maximum rate, probably possesses a threat or significant limitation to future generations, and carries large moral and ethical problems with them (Norgaard & Horworth, 1991, Costanza & Daly, 1992, MacIntosh & Edward-Jones, 2000, Ainsworth & Sumaila, 2003.

Conclusions
Our analysis of the length that resources will last into the future allows us to make the following conclusions: 1. Society is outrunning the global resource supply rate for key resources rapidly and has struck upon the planetary boundaries for resource supply for many materials. 2. With the prevailing one way-use paradigm, implying little or no recycling, the Earth cannot feed and sustain 7-9 billion people for very long. We show that there are some important end-times within 100-200 years from now, unless some paradigm changes have occurred. 3. The paradigm change includes policy-changes involving both convergence (efficiency, reduce losses, recycling) and contraction (population contraction, less intensive resource use, smaller extraction rates). 4. It will be possible to feed and supply approximately 2.5 -3 billion people on Earth if we carefully recycle most of the resources (90-95% should be a target), making sure that we can keep enough material in the cycle, having low restocking demands, because of low losses. 5. Our bulk energy strategies are at present based on unsustainable thinking and still, inefficient use, and partly inadequate technologies.
a. We are currently in a chicken-race to consume all oil, gas and coal, with no honest thought for future generations. Many reserves are extracted very fast, involving poor recovery efficiencies. b. For air transport there is at present no substitute fuel available, nor any alternative planned for. No trials are being undertaken. No viable technical proposal is on the drawing board. There is no plan B. 6. When it comes to public policies and strategic planning for the national states, a complete rethinking must take place in order to step out of a self-destructing behaviour.
For approaching a sustainable situation in our world, recycling must be raised to levels between 80% and 95%; these are very challenging tasks both technologically and behaviourally.
It is important to realize that we cannot base any of our planning on miracles to happen in the future. When problems escalate towards crisis, we cannot assume that "someone smart" will show up with a magical solution that liberates us from all problems. Some researchers like to consider energy and material resources to be endless and unlimited, hoping for some yet undiscovered miracle. This is an inadequate attitude for future planning of sustainability, and there are many examples where such approaches failed in the past (e.g. Bahn & Flenley, 1992). At conferences we sometimes hear haggling over the exact numbers in the reserves tables, however this appears to the authors of this chapter as irresponsible, because doubling all our reserves estimates will not make the fundamental underlying problem go away. Neither does sustainability come around from talking about it; what we really need to do is to plan for real change to paradigms, social functions and human consumption patterns that allow us to become demonstrably sustainable. We must plan to become sustainable with the technologies that already exist and are available now, and with significant changes in societal and consumer behaviours. We must plan to change and set out with actions, even if it implies changing our behaviour, our lives, social standards for value, and our laws and policies. It now appears that unsustainability will soon challenge us, our daily lives and put democratic governmental form to tough tests. We need to get ready for real change, because if we do not then future generations do not have a chance to live on our Earth. The technological advancement of our civilization has created a consumer society expanding faster than the planet's resources allow, with our resource and energy needs rising exponentially in the past century. Securing the future of the human race will require an improved understanding of the environment as well as of technological solutions, mindsets and behaviors in line with modes of development that the ecosphere of our planet can support. Some experts see the only solution in a global deflation of the currently unsustainable exploitation of resources. However, sustainable development offers an approach that would be practical to fuse with the managerial strategies and assessment tools for policy and decision makers at the regional planning level. Environmentalists, architects, engineers, policy makers and economists will have to work together in order to ensure that planning and development can meet our society's present needs without compromising the security of future generations.