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 (see further). 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, Δ2005 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 in eqn. 4) 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.
The TIMER model uses a multinomial logit for market allocation of new investments (to determine the share of different competing technologies:
- Si = the share of option i
- pi = price of option i in $/tonne (or $/GJ for energy carriers)
- λ = Logit Factor
- n = the number of options
This equation basically assigns the largest share in investments to options with relatively lowest costs. The logit factor λ represents the cross-price elasticity and determines how “strong” the function responds to price differences between options. The larger the value of λ the stronger impact price differences have on the market allocation. The value of λ is based on historical price differences and market allocations.
The allocation of energy carriers and production technologies takes place in two steps of nested multinomial logit formulations. First, the share of energy carriers for each production technology is determined. For steel and cement production technologies without preference for certain energy carriers, such as cement kilns, we assume the allocation of energy carriers to each technology is only based on energy prices. Other technologies, however, are restricted to certain energy carriers, such as an EAF for steel production that require a minimum share of electricity. For these technologies, minimum shares of certain energy carriers are prescribed, whereas the remaining share is filled by cost-based allocations. After allocating energy carriers, the costs of production from each technology can be determined, and market allocation is done for technologies. The iron and steel production model includes seven technology options and cement production includes four (both sectors contain options with CCS).
Second, the total costs for production technologies are determined, including energy costs (based on the energy carrier allocation above), annualized investment cost, O&M cost and in case of cement potentially carbon taxes for process emissions. Production technologies are allocated based on the total costs to produce a tonne of steel or cement.
Assumed share in Steel Consumption
Assumed average Lifetime
Assumed standard deviation
Technologies and assumptions for producing steel and cement
The iron and steel production model includes seven technology options:
- Standard Coal Blast Furnace (BF) + Basic Oxygen Furnace (BOF)
- Efficient Coal BF + BOF
- Efficient Coal BF+ BOF + CCS
- Direct Reduced Iron (DRI) + Electric Arc Furnace (EAF)
- DRI EAF + CCS
- Scrap EAF
- COREX smelt reduction + BOF
- COREX smelt reduction + BOF + CCS
The cement production model includes four technologies:
- Standard dry feed rotary kiln\[\|file:///Y:/ontwapps/Timer/ADVANCE/model%20documentation/WIKI/WIKItemplate.docx#_ftn2\]
- Efficient dry feed rotary kiln\[\|file:///Y:/ontwapps/Timer/ADVANCE/model%20documentation/WIKI/WIKItemplate.docx#_ftn3\]
- Efficient dry feed kiln with on-site-CCS
- Efficient dry feed kiln with oxy-combustion CCS
\[\|file:///Y:/ontwapps/Timer/ADVANCE/model%20documentation/WIKI/WIKItemplate.docx#_ftnref2\] This means: a raw mill, a pre-heater, a pre-calciner, a rotary kiln and a cooler, with simple exhaust heat recovery and fuel preparation.