*2.4. Iron Ore Dissolution*

Some steel shops also add iron ore before or during the blow to cool down the metal bath and meet the desired end point temperature. Since the mass of iron ore added is usually small compared to the amount of scrap, a rather simple model is used to account for the cooling effect of iron ore.

Iron ore composition can vary greatly according to the region but the predominant element is usually Fe followed by oxygen. For the current model all Fe in the iron ore is assumed to be in the form of magnetite (Fe3O4) that is reduced to iron oxide by carbon in the metal bath according to Equation (7). Furthermore, the iron ore melting point *Tm* is considered to be equal to the FeO melting point (1644 K). Reduction of magnetite and melting of the formed iron oxide are assumed to happen concomitantly. The iron ore particles are assumed to be spherical and to have uniform temperature, therefore the total heat transfered to the surface of an iron ore particle can be calculated using Equation (34):

$$Q\_{conv,ore} = 4\pi r\_{or}^2 h\_{area} (T\_s - T\_{orc}) \tag{34}$$

where *Tore* is the iron ore temperature, *hore* is the heat transfer coefficient, *rore* is the radius and *Ts* is the slag temperature. It is assumed that a fraction *Tore*/*Tm* of the total heat *Qconv*,*ore* contributes to melting of the iron ore and the remainder is used for sensible heating. A similar approach was used by MacRosty and Swartz [25] and Bekker et al. [26] to model scrap melting in electric arc furnaces. At the beginning of the process *Tore* << *Tm* and most of the heat is used to heat up the iron ore. As *Tore* approaches *Tm*, the fraction of the total heat used for melting increases. An energy balance for a single iron ore particle yields:

$$\mathcal{W}\_{\text{ore}}\mathbb{C}\_{P,\text{ore}}\frac{dT\_{\text{ore}}}{dt} = (1 - T\_{\text{ore}}/T\_{\text{in}})Q\_{\text{conv},\text{ore}}\tag{35}$$

where *Wore* is the mass of a single iron ore particle and can be obtained from Equation (36):

$$\mathcal{W}\_{\text{ore}} = \frac{4}{3} \pi r\_{\text{ore}}^3 \rho\_{\text{ore}} \tag{36}$$

In the above, *ρore* is the iron ore density and *CP*,*ore* is the iron ore heat capacity. A heat balance at the interface of the iron ore particle gives Equation (37) for the rate of dissolution of an iron ore particle:

$$A\_{\rm ore} \rho\_{\rm ore} (\Delta H\_{\rm ore} + \text{C} \, p\_{\rm FeO} (T\_{\rm s} - T\_{\rm ore})) \frac{d r\_{\rm ore}}{dt} = - (T\_{\rm ore} / T\_{\rm m}) Q\_{\rm conv, \alpha \nu} \tag{37}$$

where Δ*Hore* is the latent heat of melting of FeO, *CP*,*FeO* is the heat capacity of iron oxide and *Aore* is the area of the interface, here equal to the surface area of a sphere of radius *rore*.

The heat consumed to reduce magnetite to iron oxide is given by:

$$Q\_{rel,ore} = \frac{y\_{Fe,ore}}{3M\_{Fe}} \dot{W}\_{ore,melt} \Delta H^{rxn} \tag{38}$$

where *yFe*,*ore* is the mass fraction of Fe in the iron ore, Δ*Hrxn* is the heat for the reaction defined in Equation (7), *MFe* is the molar mass of iron and *W*˙ *ore*,*melt* is the melting rate of iron ore given by:

$$
\dot{W}\_{ore,melt} = -4\pi\rho\_{ore}r\_{ore}^2 \frac{dr\_{ore}}{dt} \tag{39}
$$

The total heat consumed by iron ore melting and reduction is given by:

$$Q\_{IO} = n\_{ore}(Q\_{conv, \rho re} + Q\_{red, \rho re})\tag{40}$$

where *nore* is the number of iron ore lumps.
