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Figure 29.5 Model results, 1900-2100: (a) consumption; (b) secondary production fraction; (c) price; (d) ore grade; (e) energy consumption

Figure 29.5 (cont.)

model has the option to scale down future metal demand from the IU curve, for example to simulate the effect of technology transfer. Finally, demand in the model is also influenced by metal prices, for which we have used a simple elasticity function. The calibration of the IU function, based on the regional use trends, produced the IU curves shown in Figure 29.4.

Metal Production

The model distinguishes between primary production and recycling (see Figure 29.1). Their market shares are calculated on the basis of relative costs: that is, if costs are equal, market shares are also equal; if relative costs rise, the market share declines (for more details, see de Vries and van den Wijngaart 1995). In contrast to the demand formulation, we have assumed that, since metal ores and commodities are traded globally, most of the production dynamics included in the model can adequately be described at the one-world level. A one-world production model also avoids the need to describe the complex dynamics of regional metal production and trade.

Primary production

Primary production in the model encompasses all processes from mining and milling to smelting and refining. With respect to its dynamics (see Figure 29.2), two main loops can be distinguished: the long-term loop describing the trade-off between depletion and learning dynamics, and the short-term demand-investment-production-price loop. Here, we focus on the first, since it is more relevant given our model objective.

Long-term loop: learning and depletion

We have defined the issue of (potential) depletion completely in terms of quality, that is, ore grade. Assuming that resources of the highest quality are exploited first, further exploitation always leads to quality decline. Such a decline can lead to increased energy requirements and production costs per unit of primary metal if not offset by further technological development. In the past, technological development has been extremely important. Considering steel, for instance, in this century we have seen the introduction of the Bessemer production process, open hearth steel production, oxygen steel production, continuous casting processing and electric arc steel production - each time reducing energy requirement and production costs. Several authors have found that technology development can be described well by a log-linear relationship between cumulative production and the efficiency of the process ('learning-by-doing'). The more frequently a process has been performed, the more knowledge has accumulated to improve its efficiency. The progress ratio of such curves (defined as one minus the factor with which production per unit of capital or energy improves on a doubling of cumulative output) generally varies between 0.65 and 0.95 (Chapman and Roberts 1983; Argote and Epple 1990; Weston and Ruth 1997). Based on historical data, a progress ratio of 0.8 is used in the metals model (Chapman and Roberts 1983).

Ore grade decline by itself has received considerable attention from geologists in terms of quantity-quality relationships. The relationship chosen for the metals model is that of Lasky, describing ore grade as a function of the cumulative tonnage of ore produced. (In fact, this empirical relationship can be looked upon as the high grade end of a log-normal distribution. Log-normal distribution of elements is often assumed to be a fundamental law of geochemistry.) Lasky-type relationships should be used with care (Brinck 1979; Singer and Mosier 1981). Deffeyes and MacGregor (1980) have derived several depletion constants for such curves that are also used in the metals model. Parameters for the capital -output ratio (COR) and energy intensity (EI) equations are based on de Vries (1989a) and Chapman and Roberts (1983).

Secondary Production

In principle, recycling limits waste flows to the environment and reduces energy requirements since the energy-intensive mining and concentration stages are avoided. The main factors influencing the recycling rates are (a) scrap availability, (b) relative processing costs of scrap and virgin metals, and (c) possibility of cost-effective scrap collection (Duchin and Lange 1994).

We distinguish between two types of recycling in the model: (i) old scrap recycling, that is, direct recycling of metal products after their use (p = 2 in Figures 29.1 and 29.2); and (ii) dumped scrap recycling, that is, recycling of metal products after disposal (p = 3 in Figure 29.1). Secondary production in the literature sometimes also includes 'home scrap' and 'process scrap' recycling, which refers to recycling within the metal industry. These types of recycling have not been modeled explicitly as they are considered as part of the primary production process.

Dynamics of secondary production

The main difference between the model dynamics for recycling and those for primary production is that the costs for old scrap recycling are assumed to depend on the quality of the material to be recycled. As easily recyclable fractions will normally be recycled first, recycling will become more expensive if a higher fraction of old scrap is recycled (Gordon et al. 1987). For both capital and energy intensity we have used the relationship of Gordon et al. (1987). The energy intensity of recycling of the metals included in this study is, on average, about one-fourth to one-third of primary production (Chapman and Roberts 1983; Frosch et al. 1997).

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