Abstract
During the last century, the consumption of materials for human needs increased by several orders of magnitude, even for non-renewable materials such as metals. Some data on annual consumption (input) and recycling/waste (output) can often be found in the federal statistics, but a clear picture of the main flows is missing. A dynamic material flow model is developed for the example of copper in Switzerland in order to simulate the relevant copper flows and stocks over the last 150 years. The model is calibrated using data from statistical and published sources as well as from interviews and measurements. A simulation of the current state (2000) is compared with data from other studies. The results show that Swiss consumption and losses are both high, at a level of about 8 and 2 kg/(cap year), respectively, or about three times higher than the world average. The model gives an understanding of the flows and stocks and their interdependencies as a function of time. This is crucial for materials whose consumption dynamics are characterised by long lifetimes and hence for relating the current output to the input of the whole past. The model allows a comprehensive discussion of possible measures to reduce resource use and losses to the environment. While increasing the recycling reduces losses to landfill, only copper substitution can reduce the different losses to the environment, although with a time delay of the order of a lifetime.
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Notes
In Switzerland, separation of copper from the bottom ashes of municipal solid waste incineration is currently in preparation (Jordi 2004).
References
Baccini P, Bader HP (1996) Regionaler Stoffhaushalt. Spektrum Akad.Verlag, Heidelberg
Baccini P, Brunner P (1991) Metabolism of the anthroposphere. Springer-Verlag, Berlin
Baccini P, Daxbeck H, Glenck E, Henseler G (1993) Metapolis Güterumsatz und Stoffwechselprozesse in den Privathaushalten einer Stadt. NFP „Stadt und Verkehr”, Zürich. Forschungsberichte; 34A
Bader HP, Real M, Scheidegger R (2003) Large scale implementation of Solar Home Systems in remote, rural areas. Clean Technol Environ Policy 6:18–25
Bader HP, Scheidegger R, Real M (2006) Global renewable energies: a dynamic study of implementation time, greenhouse gas emissions and financial needs. Clean Technol Environ Policy 8:159–173
Bergbäck B (1992) Industrial metabolism. The emerging immission landscape of heavy metal immission in Sweden. Dissertation, Linköping Studies in Arts and Science, no. 76
Bergbäck B, Anderberg S, Lohm U (1994) Accumulated environmental impact: the case of cadmium in Sweden. Sci Total Environ 145:13–28
Bergbäck B, Johansson K, Mohlander U (2001) Urban metal flows—a case study of Stockholm: review and conclusions. Water Air Soil Pollut 1(3–4):3–24
Binder C, Bader HP, Scheidegger R, Baccini P (2001) Dynamic models for managing durables using a stratified approach: the case of Tunja, Columbia. Ecol Econ 38:191–207
Brun R, Reichert P, Künsch HR (2001) Practical identifiability of large environmental simulation models. Water Resour Res 37(4):1015–1030
Chèvre N, Guignard C, Rossi L, Pfeifer HR, Bader HP, Scheidegger R (2010) Substance flow analysis as a tool for urban water management: the case of copper in Lausanne, Switzerland. Water Sci Technol (accepted)
Daigo I, Hashimoto S, Matsuno Y, Adachi Y (2009) Material stocks and flows accounting for copper and copper-based alloys in Japan. Resour Conserv Recycl 53(4):208–217
Erdmann L, Handke V, Klinski S, Behrendt S, Scharp M (2002) Nachhaltige Bestandsbewirtschaftung nicht erneuerbarer knapper Ressourcen Handlungsoptionen und Steuerungsinstrumente am Beispiel von Kupfer und Blei ITZ: Institut für Zukunftsstudien und Technologiebewertung Berlin
Faller M (2001) Metallabtrag und Metallabschwemmung von Metalldächern: Untersuchungsergebnisse der Freibewittersversuche in der Schweiz. BAUMETALL 4:52–59
Fisher JC, Pry RH (1970) Simple substitution model of technological change. General Electric Company’s Research and Development Center report 70-C-215, Schenectady, NY
He W, Wallinder IO, Leygraf CA (2001) Comparison between corrosion rates and runoff rates from new and aged copper and zinc as roofing material. Water Air Soil Pollut 1(3–4):67–82
Hedbrant J (2003) Structuring empirical knowledge on environmental issues. Dissertation, Linköping Studies in Arts and Science, no. 283
Hug F, Bader HP, Scheidegger R, Baccini P (2004) A dynamic model to illustrate the development of an interregional energy household to a sustainable status. Clean Technol Environ Policy 6:138–148
Iverfeldt A (ed) (2001) Metals in the urban and forest environment. Water Air Soil Poll Focus 1(3–4):1–476
Johnstone IM (2001a) Energy and mass flow of housing: a model and example. Build Environ 36:27–41
Johnstone IM (2001b) Energy and mass flows of housing: estimating mortality. Build Environ 36:43–51
Jolly JWL, Edelstein DL (1989) Copper in: minerals yearbook. US Department of Commerce, Bureau of Mines, Washington, pp 339–386
Jordi B (2004) Recycling - die Rohstoffquelle der Zukunft. BUWAL UMWELT 1/04, Bern, pp 35–38
Kohler N, Hassler U, Paschen H (1999) Stoffströme und Kosten in den Bereichen Bauen und Wohnen. Springer Verlag, Berlin
Lichtensteiger T (Hrsg) (2006) Bauwerke als Ressourcennutzer und Ressourcenspender in der langfristigen Entwicklung urbaner Systeme. vdf Hochschulverlag AG an der ETH Zürich
Lohm U, Bergbäck B, Hedbrandt J, Jonsson A, Svidén J, Sörme L, Östlund C (1997) Databasen. Stockholm. Flöden och ackumulation av metaller i Stockholms teknosfär. Linköping University, Tema Vatten Rapport 25
Metallgesellschaft AG (1992) Metallstatistik 1982-1992, vol 80 (also vols 70, 60, 50, 30, 10). Metallgesellschaft AG, Frankfurt am Main
Müller D, Bader HP, Baccini P (2004) Physical characterization of regional timber management for a long-term scale. J Ind Ecol 8(3):65–88
Nilarp F (1994) Omsättningen av koppar i Sverige i ett bärkraftighetsperspektiv. Chalmers University of Technology and Gothenburg University, Department of Physical Resource Theory
Pfister F, Bader HP, Scheidegger R, Baccini P (2005) Dynamic modelling of resource management for farming systems. Agric Syst 86(1):1–28
Schaffner M, Bader H-P, Scheidegger R (2009) Modelling the contribution of point sources and non point sources pollution to Thachin River. Sci Total Environ 407:4902–4915
Schmid Neset T, Bader HP, Scheidegger R (2006) Food consumption, nutrient flows: nitrogen in Sweden since the 1870 s. J Ind Ecol 10(4):61–75
Schmid Neset T, Bader HP, Scheidegger R, Lohm U (2008) The flow of phosphorus in food production and consumption Linköping, Sweden, 1870-2000. Sci Total Environ 396(2–3):111–120
Sigg L, Behra R, Boller M, Eggen R, Meier W, Sulzberger B, Xue HB (1999) Relevance of copper inputs in natural waters. EAWAG News 46E:9–11
Sörme L (2003) Urban heavy metals stocks and flows. Dissertation, Linköping Studies in Arts and Science, no. 270
Sörme L, Lagerkvist R (2002) Sources of heavy metals in urban wastewater in Stockholm. Sci Total Environ 298:131–145
Spatari S, Bertram M, Fuge D, Fuse K, Graedel H, Rechberger TE (2002) The contemporary European copper cycle: 1 year stocks and flows. Ecol Econ 42(1–2):27–42
Spatari S, Bertram M, Gordon RB, Henderson K, Graedel TE (2005) Twentieth century copper stocks and flows in North America: a dynamic analysis. Ecol Econ 54(1):37–51
Tarr J, Ayres R (1990) The earth as transformed by human action: global and regional changes in the biosphere over the past 300 years. In: Turner BL et al (eds) The Hudson-Raritan River basin, 1790–1980. Cambridge University Press, New York, pp 623–640
van der Voet E, Guinée Jeroen B, de Haes U, Helias A (eds) (2000) Heavy metals: a problem solved? Methods and models to evaluate policy strategies for heavy metals series: environment & policy, vol 22. Kluwer Academic Press, London
Von Arx U (1998) Kupfer in der Schweiz (Standortbestimmung). BUWAL, Bern
Wang T, Mao J, Johnson J, Rack RK, Graedel TE (2008) Anthropogenic metal cycles in China. J Mater Cycles Waste Manage 10:188–197
Wittmer D (2006) Kupfer im regionalen Ressourcenhaushalt – Ein methodischer Beitrag zur Exploration urbaner Lagerstätten. Dissertation ETH Zürich, vdf Hochschulverlag AG ETH Zürich; 16325
Wittmer D, Lichtensteiger Th, Baccini P (2003) Copper exploration for urban mining. In: Lagos GE, Warner AEM, Sanchez M (eds) Proceedings of Copper 2003. Health, environment and sustainable development, vol 11, pp 85–101
Xue HB, Oestreich A, Kistler D, Sigg L (1996) Free cupric ion concentrations and Cu complexation in selected Swiss lakes and rivers. Aquat Sci 58(1):69–87
Zeltner C, Bader H-P, Scheidegger R, Baccini P (1999) Sustainable metal management exemplified by copper in the USA. Reg Environ Changes 1:31–46
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We would like to thank an anonymous reviewer who made very helpful suggestions.
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Appendices
Appendix A1: Model equations for buildings
For the explanation of the equations below, see “Mathematical model” section.
Buildings
Balance equation for stocks:
Abrasions/corrosion:
Input into buildings:
Copper stock in buildings:
Copper import into buildings:
a Build(t) is a parameter function describing the specific abrasion and corrosion rate per stock unit per year. k ImpBuild(t) is the fraction of copper imported into buildings.
Envelope of buildings
Balance equation:
Copper stock:
Renewing:
P outer(t) is the copper stock in the OuterBuild. k outer(t,t′) is the transfer function or lifetime distribution of copper installed in the OuterBuild at a time t′.
Interior of buildings
For M Inner(t), I Inner(t) and O Inner(t) similar equations to (8)–(10) apply.
Recycling:
k Rec(t) is the fraction of recycling in the total output of dismantling/demolition.
Appendix A2: Calibration of the parameter functions
Stock for buildings P Inner, P Outer
Time series for the past of these stocks were compiled in Wittmer (2006) on the basis of the data sources mentioned above.
These time series show growth behaviour which is typical for all kinds of stocks. Logistic or sigmoidal curves are simple and turned out to describe growth adequately Fisher and Pry (1970). Logistic growth curves, and in particular linear-logistic and double logistic growth curves, were therefore fitted to these time series.
Logistic growth is exponential at the beginning, linear in the middle of the growth phase and decreasing towards the end until saturation is reached. Linear-logistic growth shows a linear pattern at the beginning of the growth period, followed by logistic growth. The derivation is continuous at the transition point.
This growth behaviour can be described mathematically as follows:
t 0 is the initial point of the growth, a 1 the slope of the linear growth, p init the initial value of the logistic part in the distant past t → −∞, p sat the saturation value in the far future t → −∞, α is proportional to the maximum growth rate and t turn is the turning point of the growth curve respectively.
The linear-logistic curve was chosen for buildings and mobiles because it proved to be more appropriate to the data than a simple logistic curve. An important parameter of the growth curves is the growth rate α, since typical values of this parameter are known for industrial or economics processes. The results of the non-linear fit for α are α InnerBuild = 0.069 and αOuterBuild = 0.057, respectively. These values are lower or comparable to typically observed growth rates for industrial products up to 0.15, see Bader et al. (2006). The results are presented in Fig. 6.
Lifetime distribution: k Inner, k Outer
The lifetime distribution can be described by a transfer function k(t Op, k Ip) in the two variables t Op and t Ip describing the amount of input at time t Ip which leaves the balance volume at time t Op.
The following two-parameter Gauss function was used as the lifetime distribution:
N 0: Normalisation factor; τ(t′), σ(t′): average lifetime and widths of the lifetime distributions of copper inputs at input time t′. Note that τ and σ are the values of the maximum and width of the lifetime distribution rather than the average and standard deviation, respectively. This is because the lifetime distribution is a truncated normal distribution. For the usual cases where σ ≤ τ/2, however, the difference between these quantities is small, namely, 2.9% for σ = τ/2 and 0.1% for σ = τ/3, etc. We therefore refer to τ and σ as the average and standard deviations of the lifetime distribution.
This lifetime distribution was discussed in detail in Baccini and Bader (1996) and applied in many case studies (Zeltner et al. 1999; Müller et al. 2004; Binder et al. 2001; Bader et al. 2006).
Estimates for τ and σ were obtained as follows. Since no time series data are available, we assume τ and σ to be a constant function of time in the sense of a first approximation.
Buildings: k Inner, k Outer: τ and σ are obtained from the experience of experts and tradesmen.
The estimated parameters τ and σ are listed in Table 4.
Abrasion/corrosion coefficients: a Build
The abrasion/corrosion was assumed to be proportional to the surfaces exposed. For the infrastructures and buildings, the relevant surfaces of cables and sheets were related to the corresponding masses. The specific abrasion and corrosion rates were found in the literature [von Arx (1998): abrasion rate: 0.0036/year, Faller (2001): corrosion rate: 1.8 g/(m2 year), He et al. (2001): corrosion rate for Sweden 1.3 g/(m2 year)].
Appendix A3: Adaptation of the model to specific scenarios
Scenario: Copper ban in the envelope of buildings
The adaptation of the model is very simple: Eq. 9 for the copper stock of the building envelope has to be changed as follows:
Copper stock:
t (Outer)Ban is the time at which the copper ban begins for the envelope of the buildings.
Scenario: Copper ban + copper dismantling in the envelope of buildings
In addition to the modification equation (9a) above, Eq. 10 must also be adapted.
Renewal and dismantling:
where
O (Renew)Outer (t) and O (Dism)Outer (t) are the copper outputs of OuterBuild due to renewing and dismantling, respectively. P (Dism)Outer (t) is the specific dismantling rate per stock unit per year. t Ou(t) is the age (relative to the initial time 0) of the oldest copper in OuterBuild that has not yet been removed due to renewing and dismantling. For t Ou(t), the following ordinary differential equation applies:
where
is the rest of the copper output into OuterBuild at a time t′ and not renewed until a time t.
Equations (10a) are a generalisation of the relevant equations in Müller et al. (2004) and Bader et al. (2006). For reasons of simplicity in Eq. 10a, it was assumed that the copper ban and forced dismantling have the same onset time.
However, this is not a restricting assumption. Note that Eq. 10c is a possible but reasonable approach to the dismantling flow O (Dism)Outer , representing a dismantling process that is proportional to the stock.
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Bader, HP., Scheidegger, R., Wittmer, D. et al. Copper flows in buildings, infrastructure and mobiles: a dynamic model and its application to Switzerland. Clean Techn Environ Policy 13, 87–101 (2011). https://doi.org/10.1007/s10098-010-0278-4
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DOI: https://doi.org/10.1007/s10098-010-0278-4