Generally the final energy demand of the industry is simulated as a function of changes in population, in economic activity and in energy intensity. We simplify and consider the demand for energy to be a function of 3 groups of parameters and processes: 1) activity data, i.e. population, income and more explicit, bottom-up, activity indicators such as steel productions;2) processes that determine the intensity of use, such as structural change (SC), autonomous energy efficiency improvement (AEEI) and price-induced energy efficiency improvement (PIEEI) and, finally, and 3) price-based fuel substitution i.e. the choice fuels on the basis of their relative costs.

**Heavy industry model: Steel and Cement**

The demand for raw materials can be described as a function of per capita income levels (Groenenberg, 2002; Neelis and Patel, 2006; Roberts, 1996; Tilton, 1996; van Vuuren et al., 1999). Empirically, it has been observed that the general form for resource intensity often follows an inverted U-shaped curve. The inverted U shape can be explained in terms of superposition of three different trends: transition, substitution and technological development (van Vuuren et al., 1999). There are a number of possible formal descriptions that can be chosen that are able to describe an inverted U-shape. Based on discussion in Roorda (2006) and Neelis and Patel (2006) we use:

In which *IU* = Intensity of Use (kg/$), *GDPpc* = Gross Domestic Product per capita (2005 PPP$),*α* = Maximum total consumption per capita (PCC) and β = GDP per capita level with the maximum IU

To account for changes in the maximum per capita consumption due to increased material efficiency, an additional constant θ was introduced, which can be interpreted as the annual material efficiency improvement factor.

The total consumption per capita (PCC), is then:

We used regression analysis to parameterize the PCC function to historic data, deriving values for α, β and θ in the formulas above (see Neelis and Patel, 2006; Roorda, 2006). Cement is based on a single global regression --that is in a second step adjusted for each region. For steel demand, instead, we used regression analyses for major individual regions, to reflect different consumption patterns in these regions (Neelis and Patel, 2006). We use a Gompertz curve to smooth out deviations between historic data and the PCC curve:

In this, Δ_{2005} is the deviation between actual and estimated per capita consumption and μ and ϕ are Gompertz parameters, with values chosen to remove the deviation over a period of 40-50 years.

The scenario factor Ω allows for more or less material intensive future scenarios. This factor acts as a multiplier on the PCC values, and its values extrapolate linearly between 2005 and 2100 to 0.9 for material extensive scenarios and 1.1 for material intensive scenarios. Using historical data on steel and cement consumption a regression analysis was performed to derive values for the parameters α and β.

In the model, we assume that all demand for steel and cement is fulfilled, either through domestic production or trade with other regions. We use a vintage capital stock model to simulate the development of the steel and cement producing capital stock over time. In case of declining demand, it is possible that there is too much production capacity compared to the actual demand and production is scaled back proportionally for all plants.

Investment costs are a relatively large part of production costs of steel and cement plants. Therefore, it is usually cheaper to use an existing facility than building a new one. Hence, we assume that all factories are used until the end of their technical lifetime (assumed 40 years), which brings clear inertia into the model.

For each cement and steel production technology, we assume a specific energy consumption (SEC): the amount of energy that is needed to produce a ton of the respective material. This SEC is assumed to improve over time. For future projections, we split the SEC in two components: 1) the minimum energy use for each technology assuming zero losses and the 2) additional energy required due to inefficiencies in the technology. We make assumptions on the future rate of efficiency improvement based on literature (Gielen et al., 1998; Groenenberg, 2002; IEA, 2009b; Neelis and Patel, 2006) and generalize this function as follows:

where β = Minimal energy needed (in gigajoules (GJ) per tonne of material), ε = Efficiency improvement every year (%/yr), α = Total inefficiency in the year 2005 (GJ/t), t = year for which SEC is calculated

The TIMER model simulates historic energy use for all sectors and regions from 1971 to 2007, before calculating scenarios forward into the future. To replicate historic energy use, we assume that factories have a marginal energy intensity (SEC) at the moment of being built that equals the observed average historic SEC of the entire capital stock fifteen years later. The model has been run with this assumption and the average energy use of the total stock in the model was within 10% of the historic data.

The SEC values used in this study represent only energy use in the factory, defining the system boundaries of SEC values as factory gate-to-factory gate. This excludes energy use related to the production of raw materials, which could be relevant due to gradually decreasing ore quantities. For copper, Harmsen et al. (2013) show that in the case of ambitious implementation of renewable energy, the cumulative energy use across the process chain increases by a factor of 2 to 7 depending on technological progress, the recycling rate and the future electricity demand. Although the Reserve / production (R/P) ratio of iron is three times as large as that of copper, it is quite possible that, in the longer term, lowering ore grades will result in higher GER of primary steel.

In the scrap model, we assume three types of scrap: metal that is lost during the production of the metal itself (circulating scrap), metal that is lost during the production of goods (prompt scrap) and scrap that is available after the lifetime of the goods (obsolete scrap). We actually assume circulating scrap to be part of the steel production process, because nearly all of it is recycled and it never leaves the system boundaries of the steel plant. We assume that prompt scrap is available for recycling immediately, with a recycle rate of 70%. Obsolete scrap is determined by identifying 4 types of steel uses, each with a typical lifetime in society. After steel in certain functions has reached the associated lifetime (starting from the production year), it is available again to be recycled. Representative examples for each of the four product groups are 1) construction, 2) machinery, 3) cars and 4) soda cans. Table 3 gives more information of the product groups and Figure 4 shows the availability for recycling of the different product groups in the years after they have been produced. The recycle rate of metal that becomes available to use as obsolete scrap is assumed 70% (Neelis and Patel, 2006). Scrap is not traded internationally in this model. One reason is that it would require determining a regional scrap price – for which we did not find enough information to include this in the model.