*3.3. Modeling Pathways*

The annual energy consumption for steel production (*Qt*,*<sup>i</sup>*) in year *t* for Pathway *i* is calculated by applying the specific energy consumption of fuel and reducing agen<sup>t</sup> combined with total annual crude steel production:

$$Q\_{t,i} = \sum\_{j} \sum\_{r} s\_{r,j} \mathbf{x}\_{t,i,r} P\_{\prime} \quad t \in T\_{\prime} \quad i \in I \tag{1}$$

where *sr*,*j* is specific energy consumption of fuel and reducing agen<sup>t</sup> *j* in the technology *r* (kWh/t). *P* denotes total annual crude steel production (tonne) and *xt*,*i*,*<sup>r</sup>* represents the share of the production from the technology *r* in year *t* for pathway *i* (%).

For each pathway, the annual CO2 emissions from the steel production *Et*,*<sup>i</sup>*(tonne CO2) in year *t* are given by:

$$E\_{t,i} = \sum\_{r} c\_{r} \mathbf{x}\_{t,i,r} P\_{r} \quad t \in T\_{\prime} \quad i \in I \tag{2}$$

where *P* denotes total annual crude steel production (tonne), *er* is CO2 emissions intensity of the steelmaking technology *r* (tonne CO2), and *xt*,*i*,*<sup>r</sup>* represents the share of the production from the technology *r* in year *t* for pathway *i* (%).

The CO2 emission intensity of the steel production *er* is expressed as:

$$\mathbf{e}\_r = \sum\_j f\_j \mathbf{s}\_{r, j\prime} \quad r \in \mathcal{R} \tag{3}$$

where *fj* denotes CO2 emission factor of fuel and reducing agen<sup>t</sup> *j* (kg CO2/kWh), *sr*,*j* is specific energy consumption of fuel and reducing agen<sup>t</sup> *j* in the technology *r* (kWh/t).

The steel production costs, *CTr* , for each of the steel production technologies *r* are calculated as:

$$\mathbf{C}\_{r}^{T} = V\_{r} + F\_{r} + A\_{r}, \quad r \in \mathbb{R} \tag{4}$$

where *Vr* is the variable operating cost, *Fr* is the fixed operating costs and *Ar* is the annualized capital costs which are calculated as:

$$A\_r = \frac{\mathbb{C}APEX\_r \left(1 + i\right)^n i}{\left(1 + i\right)^n - 1}, \ t \in T, \ r \in \mathbb{R} \tag{5}$$

where *i* is the interest rate assumed to be 5%, *n* is the economic lifetime assumed to be 20 years and *CAPEXr* is the capital cost of the steel production technologies *r*.
