From Iron Ore to Crude Steel: Mass Flows Associated with Lump, Pellet, Sinter and Scrap Iron Inputs

Abstract

This paper presents mass accounting models that trace the flow of major individual elements from iron ore through to iron lumps, pellets or sinter, the transformation of these intermediate products into pig iron (PI) or direct reduced iron (DRI), and the transformation of PI and DRI into crude steel in a basic oxygen furnace (BOF) or electric arc furnace (EAF) with the addition of scrap iron or steel or varying purity. Account is taken of non-iron oxides (gangue), addition of fluxes, the production of slag, and iron losses in slag. Simple relationships are developed giving the flux requirements for and slag production from a BF for various iron inputs, and relationships are developed giving flux requirements, the production of slag, and iron yield as a function of the proportions of PI, DRI and scrap inputs to a BOF or EAF. The mass and flow analysis presented here, and the energy flow analysis presented in a companion paper, provides a foundation for tracking the impact on energy use and iron losses of alternative pathways that might be used in the future as part of a broad-based effort to reduce energy use and associated greenhouse gas emissions.

1. Introduction

Iron ore consists of various oxides of iron (occurring as iron-containing minerals) mixed with oxides of other metals (such as Al and Si). In the production of iron and steel from iron ore, the non-iron oxide minerals are largely removed as slag and the oxygen is stripped off the iron oxides, but various other oxides (referred to as “fluxes”) must be added and later also removed as slag. This paper presents a model for the detailed accounting for the flows of iron, non-iron oxides originally present in the ore, and of fluxes added during the production of crude steel. The model accounts for iron losses as dust, sludge and slag at each step and the impact of impurities, flux addition, and reduction and oxidation reactions on the mass balance of steel production from virgin ore and scrap. Our goal is to provide a deeper understanding of the factors influencing flux requirements, slag production and iron yields using different iron and steel production processes involving virgin ores and scrap metal inputs, and in so doing, to develop simple but accurate relationships between material inputs and outputs. In combination with a parallel analysis of energy flows presented in a companion paper, the relationships developed here can be used in the construction of physically plausible and internally consistent global-scale scenarios of improved energy and material efficiencies in the future.

The layout of this paper is as follows: Section 2.1 presents mass flow models for the production of prepared iron in the form of lumps, pellets and sinter. Section 2.2 presents a procedure for computing the flux requirement, slag production, and pig iron composition given an arbitrary combination of lump, pellet and sinter inputs whose overall composition can be determined (given some reference compositions) from the mass flow model presented in Section 2.1. Section 2.3 presents a procedure for computing the slag production during the refining of an arbitrary mixture of pig iron and scrap iron of specified composition in a basic oxygen furnace, Section 2.4 presents information on the composition of direct reduced iron, and Section 2.5 presents a procedure for computing the slag production and iron yield during the refining of an arbitrary mixture of scrap, direct reduced iron and pig iron in an electric arc furnace. Section 2.6 compares results of the preceding calculation with published data. Section 3 summarizes the key relationships and potential applications of the algorithms presented here.

2. Mass Flows during Production

Figure 1 shows the flows of iron from mining of iron ore through to the production of liquid steel, along with inputs of scrap steel, that are represented here. These steps can be grouped as: (i) the production of prepared iron (lumps, pellets or sinter), (ii) the reduction of (removal of oxygen from) prepared iron to produce pig iron (PI) in a blast furnace (BF) or direct reduced iron (DRI) in a direct reduction furnace (DRF), and (iii) the refining of iron (removal of impurities) to produce steel in a basic oxygen furnace (BOF) or electric arc furnace (EAF). Initial refining is followed by more precise refining through secondary metallurgy (SM).¹

Fig. 1.

The iron and steel mass flow model developed here. BF = blast furnace, DRF = direct reduction furnace, BOF = basic oxygen furnace, EAF = electric arc furnace.

2.1. Mass Flows during the Mining and Preparation of Iron Ore

In this section, a model is presented for the computation of the amount of rock and iron ore that must be mined in order to produce a unit of iron in the form of prepared iron ore in various forms, and for computing the corresponding iron concentration. Iron ore consists predominantly of the iron oxide mineral hematite (Fe₂O₃) and magnetite (Fe₃O₄), and sometimes other iron oxides, along with non-iron-oxide minerals (consisting primarily of SiO₂, Al₂O₃ and MgO) that are referred to as gangue. Iron oxide mineral grains are largely separated from the other mineral grains by grinding the ore down to the typical size of the iron oxide grains. Iron ore is prepared for subsequent steps in three forms: as lump ore (6–30 mm size), pellets (9–16 mm), and sinter (15–25 mm).

Lump ore is used when the ore grade is relatively high, and requires no processing except crushing and screening, although some simple separation such as washing of fine particles may be done. Sintering uses a combination of ores, the majority of which are the undersized particles from the same primary source as lump ore, typically −6 mm. Primary ores which are of too low grade for direct use as lump ore or in sinter require concentrating steps, where the ore is ground to finer sizes to liberate the iron oxide particles, with the undesirable minerals (gangue) subsequently removed through flotation, magnetic separation, or other processes (described elsewhere¹⁾). The upgraded concentrate used by pelletizing and sintering needs to be agglomerated into larger particles, with pelletizing using finer particles (< 0.15 mm diameter) than sintering (0.15–6 mm). Pelletizing involves addition of balling agents (bentonite or organic binder) and fluxes (limestone, dolomite, quartzite, and olivine) to the concentrated ore, balling, and heating the mixture to a temperature of about 1300°C²⁾ to produce 9–16 mm heat-hardened pellets (with some very minor further iron loss in pellet flue gases).

Sintering involves mixing fine iron ore particles, recycled sinter fines (sinter output that broke into particles too small to be used in the blast furnace) and various iron wastes from subsequent steps in the production of iron and steel, as well as fine (< 6 mm) coke particles (called coke breeze) or coal, coking C dust (as a partial fuel source) and fluxes.⁸⁾ A gas is used to ignite the mixture, with subsequent combustion of the coke or coal providing heat to melt the mixture (at a temperature of 1100–1300°C⁹⁾), forming a porous agglomeration that is cooled and crushed to a size of about 15–25 mm.

Many blast furnaces use a combination of lump, pellet and sinter inputs. For the reader’s convenience, we reproduce in Table 1 some data on the proportions of lump, pellet and sinter inputs used in four major steel-producing regions, along with the total pig iron production in 2016. All regions use a small portion of lump input, with pellets dominant (74%) in the US and sinter dominant (70–80%) in the other regions.

Table 1. Proportions of different inputs to the blast furnace in 6 leading steel-producing countries or regions. Production amounts are from WSA.³⁾

	Input shares and year				2016 pig iron production (Mt)	Source of input data
Region	Lumps	Pellets	Sinter	Year
China	5	17 (15–30)	78 (65–80)	2007	700.7	Kurunov (2010)4)
Japan		10	90	2010	80.2	Kuramochi (2016)5)
W Europe	8	22	70	2013	75.5	IEA (2013, Table D-6)6)
Russia		10–40	60–90	2008	51.8	Kurunov (2010)4)
S Korea	17	3	80	1997	46.3	Oeters et al. (2013)1)
N America	1	92	7	2014	33.0	Kurunov (2015)7)

A typical European blast furnace might use a combination of lump, pellet and sinter inputs along with coke and coal (for energy) and further fluxes. Table 2 gives illustrative data on the amounts of these various inputs along with various outputs (dust, slag, and hot metal) and the chemical composition of the inputs and outputs. Apart from iron oxides, the inputs contain major basic gangue (CaO and MgO), major acidic gangue (SiO₂, Al₂O₃), and other gangue elements (such as S, P, MnO, K₂O, TiO₂, Na₂O and V₂O₅), as well as hydrocarbons in the coke and coal. Substantial basic flux (mainly limestone and some source of MgO such as olivine) is added to sinter. In the blast furnace the fluxes and gangue melt to form a slag with a lower density than molten iron, and so can be separated from iron, but some gangue oxides are reduced (SiO₂ to Si and MnO to Mn, for example) and so become part of the pig iron rather than removed as slag. A critical parameter is the basicity, which is the ratio of the mass of CaO to the mass of SiO₂. In the example in Table 2, the overall basicity of the inputs is about 1.0.² However, as some SiO₂ is converted to Si during the iron reduction process and appears in the hot metal rather than in the slag, the slag basicity is somewhat higher (about 1.1) than the overall input basicity.

Table 2. Representative amounts of various inputs to and outputs from a blast furnace in Europe, and typical chemical composition of inputs and outputs. HM = hot metal. Source: IEA (2013), Section D, Tables D-2, D-4 and D-6.⁶⁾

	Inputs								Outputs
	Lumps	Pellets	Sinter	Coke	Coal	Quartz	Lime-stone	Total	Undersized	Dust	Sludge	Slag	Hot metal	Total
Total mass (kg)	125	352	1120	355	152	11	13	2128	20	15	4	308	1000	1346
	Mass fractions								Absolute amounts (kg)
Fe	0.610	0.655	0.576	0.004	0.005	0.000	0.003	954.5	6.8	3.9	1.5	0.8	941.5	954.5
O in Fe oxides	0.262	0.280	0.239	0.000	0.000			399.3
CaO	0.003	0.018	0.095	0.001	0.002		0.540	120.2	0.9	0.9	0.2	118.2		120.2
MgO	0.002	0.012	0.015	0.001	0.000		0.011	21.7	0.1	0.2	0.1	21.4		21.7
SiO2	0.084	0.028	0.053	0.063	0.024	0.980	0.012	115.9	1.5	0.7	0.2	102.7		105.2
Al2O3	0.028	0.006	0.010	0.028	0.016	0.019	0.005	30.0	0.4	0.3	0.1	29.2		30.0
SiO2 reduced to Si								10.7
Si													5.0	5.0
C (in HM) or hydro-C				0.881	0.870		0.426	444.7	6.3	7.1	0.9		47.0	61.3
H				0.001	0.040			6.5		0.1				0.1
Other gangue	0.011	0.001	0.012	0.022	0.042	0.001	0.003	29.7	4.5	1.8	1.0	15.9	6.5	29.7
Gangue fraction	0.128	0.065	0.184
SiO2 fraction of gangue	0.682	0.791	0.700
Basicity	0.036	0.643	1.800					1.037				1.151

2.1.1. Lump Ore, Pelletizing and Sintering Flow Models

For the example shown in Table 2, the grade (percent of total mass as iron) is 61.0%, 65.5% and 57.8% for lumps, pellets and sinter, respectively, while gangue constitutes 12.8%, 6.5% and 18.4% of the total input mass, respectively.³ In the following, we present mass flow models for the production of lumps, pellets and sinter that allow us to obtain these mass fractions starting from iron ore of specified (but differing) grade as input for the production of lumps, pellets and sinter. The models allow us to back-calculate the mass of material that must be mined in order to produce 1.0 unit of iron in each of these prepared forms.

The flows in our models are shown in Fig. 2, where D_p is the global demand for a particular form of prepared iron (lumps, pellets or sinter); M_p is the flow of a particular prepared iron product; M_l1 and M_l2 are losses during two successive steps in each production process, and Y₁ and Y₂ are the corresponding mass yields; M_o, M_c, M_en (where n = 1 or 2) and M_fl are iron ore, ore concentrate, external input and flux mass flows, respectively; M_cb is the input of coal particles referred to as cook breeze; and M_f is the recycling flow of fine particles back to the sintering process and Y_f is the corresponding yield. For each M_i except M_fl, there is a corresponding iron mass concentration C_i.

Fig. 2.

The lump ore, pelletizing and sintering models developed here.

In the lump ore model, M_l1 is the flow of lower-grade ore particles that have been separated from the crude ore during pre-crushing, and can be discarded as tailings or added to the pelletizing or sintering process (as part of the input M_e1) at the concentrating stage (if present). The remaining flow will be of higher grade than the crude ore, and so is properly designated as a concentrated flow M_c. This flow is broken into the lump output and finer particles (M_l2) that could be part of the post-concentrator input M_e2 to the pelleting or sintering process. The equations governing the lump ore model are thus   

$$M_{l1}=\left(1-Y_1\right)M_o$$(1)

  

$$M_{l2}=\left(1-Y_2\right)Y_1{M}_o$$(2)

  

$$M_p=Y_1{Y}_2{M}_o$$(3)

  

$$M_o{C}_o-M_{l1}{C}_{l1}-M_{l2}{C}_{l2}=M_p{C}_p=D_p$$(4)

from which it follows that   

$$M_o=\frac{D_p}{C_o-\left(1-Y_1\right)C_{l1}-\left(1-Y_2\right)Y_1{C}_{l2}}$$(5)

and   

$$C_p=\frac{D_p}{M_p}=\frac{D_p}{Y_1{Y}_2{M}_o}$$(6a)

If there is no difference in average grade of fine particles (M_l2) and the lump ore product (M_p) after the crushing step, then C_l2 = C_p, and it is necessary to iterate between Eqs. (5) and (6a). However, in this case C_p can be computed instead as   

$$C_p=\frac{M_o{C}_o-M_{l1}{C}_{l1}}{M_{l2}+M_p}=\frac{C_o-\left(1-Y_1\right)C_{l1}}{Y_1}$$(6b)

which avoids the need for an iteration loop.

In the following, we derive expressions for a flow model that simultaneously incorporates all the flows collectively shown for pelleting and sintering. The various mass flows except for M_fl are given by   

$$M_c=Y_1\left(M_o+M_{e1}\right)$$(7)

  

$$M_{l1}=\left(1-Y_1\right)\left(M_o+M_{e1}\right)$$(8)

  

$$M_p=Y_2\left(M_c+M_{cb}+M_{e2}+M_{fl}+M_f\right)$$(9)

  

$$M_{l2}=\left(1-Y_2\right)\left(M_c+M_{cb}+M_{e2}+M_{fl}+M_f\right)$$(10)

  

$$M_f=\left(1-Y_r\right)M_p$$(11)

The flux input M_fl for pelletizing and sintering is computed so as to give the desired final basicity (mass CaO/mass SiO₂) of the pellets or sinter. The mass fraction of iron in ore (C_o) is equal to the mass fraction of iron oxides, F_o, times the mass fraction of iron in iron oxides (R_Fe, equal to 0.702 using a 9:1 hematite: magnetite weighting). Thus,   

$$F_o=C_o/R_{Fe}$$(12)

All the non-iron oxide minerals constitute gangue, so the mass of gangue in ore, M_go, is   

$$M_{go}=\left(1-F_o\right)M_o$$(13)

Letting F_SiO2 be the mass fraction of SiO₂ in gangue and B the basicity achieved by adding flux, M_fl is given by   

$$M_{fl}=B{F}_{SiO2}{M}_{go}=R_{fo}{M}_o$$(14)

where R_fo = BF_SiO2(1−F_o). Equation (14) neglects the acid and basic content of M_e1 and M_e2 and their impact on the required M_fl, but these are considered later when slag production is computed.

The iron mass balance equation is   

$$\begin{array}{l}{M}_o{C}_o+M_{cb}{C}_{cb}+M_{e1}{C}_{e1}+M_{e2}{C}_{e2}-M_{l1}{C}_{l1}-M_{l2}{C}_{l2}\\ =Y_r{M}_p{C}_p=D_p\end{array}$$(15)

From Eqs. (9) and (11) it follows that   

$$\begin{array}{l}{M}_f=\left({\displaystyle \frac{\left(1-Y_r\right)Y_2}{1-\left(1-Y_r\right)Y_2}}\right)\left(M_c+M_{cb}+M_{e2}+M_{fl}\right)\\ \hspace{1em}\hspace{0.5em}=R_1\left(M_c+M_{cb}+M_{e2}+M_{fl}\right)\end{array}$$(16)

where R₁ = (1−Y_r)Y₂/(1−(1−Y_r)Y₂). Substituting for M_l1 and M_l2 in Eq. (15) using Eqs. (8) and (10) and further replacing M_c and M_f with Eqs. (7) and (16), and replacing M_fl with Eq. (14), we obtain   

$${\displaystyle M_o=\frac{D_p-M_{cb}{C}_{cb}-M_{e1}{C}_{e1}-M_{e2}{C}_{e2}+\left(1-Y_1\right)M_{e1}{C}_{l1}+\left(1-Y_2\right)\left(M_{cb}+Y_1{M}_{e1}+M_{e2}\right)\left(1+R_1\right)C_{l2}}{C_o-\left(1-Y_1\right)C_{l1}-\left(1-Y_2\right)\left(1+R_1\right)\left(Y_1+R_{fo}\right)C_{l2}}}$$(17)

From Eqs. (9) and (11) we obtain   

$$M_p=\frac{Y_2\left(M_c+M_{cb}+M_{e2}+M_{fl}\right)}{1-Y_2\left(1-Y_r\right)}$$(18)

Finally, from (15),   

$$C_p=\frac{D_p}{Y_r{M}_o}$$(19)

The mass balance for concentrate iron is   

$$M_o{C}_o+M_{e1}{C}_{e1}-M_{l1}{C}_{l1}=M_c{C}_c$$(20)

from which it follows that   

$$C_c=\frac{M_o{C}_o+M_{e1}{C}_{e1}-M_{l1}{C}_{l1}}{M_C}$$(21)

2.1.2. Flow Model Results for Typical Inputs

Table 3 gives iron mass and total mass at various steps in the production of lumps, pellets and sinter, as computed by the above model for a set of inputs taken from the sources given in Table 3 and adjusted slightly so as to recover the lump, pellet and sinter iron fractions given in Table 2 (61.0%, 65.5% and 57.6%, respectively). Also given in Table 3 are gangue masses, which are computed as total mass minus iron mass minus the mass of oxygen in the iron oxides. The mass of oxygen in iron oxides in turn is computed using the O:Fe ratios derived from Table 2, which are very close to what one would expect from stoichiometry for a 90% hematite, 10% magnetite mixture.

Table 3. Relative mass flows and iron concentrations, based on the flow models shown in Fig. 2 and back-calculated from a specified final iron mass of 1.0. Among the inputs, R_r = ratio of mined rock to mined iron ore, and other terms are as defined in the main text. Pellet and sinter flux inputs correspond to basicities of 0.21 and 1.79, respectively. Sources for some input data: lump ore, Lockwood Green (2000, Appendix B);¹⁸⁾ pelletizing and sintering, Lockwood Green (2000)¹⁸⁾ and IEA (2013),⁶⁾ respectively, with details available from the author.

	Inputs chosen for:
Input	Lump ore	Pelletizing	Sintering
Co	0.600	0.500	0.502
Crw	0.149	0.169	0.169
Cl1	0.510	0.236	0.260
Cl2		0.685	0.000
Ce1		0.510	0.510
Ce2		0.475	0.458
Me1		0.000	0.000
Me2		0.041	0.212
Yc-Fe		0.807	0.807
Yc	0.900	0.589	0.610
Yp	0.900	0.915	0.910
Yr		1.000	0.800
Rr	2.530	2.530	2.530
Outputs
Component	Iron Mass	Total Mass	Gangue mass	Ci
Lump Ore
Lumps (Mp)	1.000	1.639	0.212	0.610
Loss 1 (M l1)	0.103	0.202	0.055	0.510
Loss 2 (M l2)	0.111	0.182	0.024	0.610
Iron ore (Mo)	1.214	2.024	0.291	0.600
Rock waste (Mw)	0.463	3.096	2.436	0.149
Rock (Mr)	1.677	5.120	2.727	0.300
Pelletizing
Pellets (Mp)	1.000	1.530	0.103	0.654
Loss 2 (Ml2)	0.098	0.143	0.003	0.685
External input (Me2)	0.019	0.041	0.013	0.475
Flux (Mfl)	0.000	0.056	0.056	0.000
Concentrate (Mc)	1.079	1.576	0.037	0.684
Loss 1 (Ml1)	0.260	1.102	0.730	0.236
External input (Me1)	0.000	0.000	0.000	0.510
Iron ore (Mo)	1.339	2.677	0.767	0.500
Rock waste (Mw)	0.693	4.096	3.106	0.169
Rock (Mr)	2.032	6.773	3.874	0.300
Sintering
Sinter (YrMp)	1.000	1.736	0.320	0.576
Recycled fines (Mf)	0.250	0.434	0.080	0.576
External input (Me2)	0.097	0.212	0.075	0.458
Flux (Mfl)	0.000	0.276	0.276	0.000
Concentrate (Mc)	0.902	1.375	0.098	0.656
Loss 1 (Ml1)	0.228	0.878	0.555	0.260
Ext input (Me1)	0.000	0.000	0.000	0.510
Iron ore (Mo)	1.130	2.253	0.653	0.502
Rock waste (Mw)	0.583	3.446	2.620	0.169
Rock (Mr)	1.714	5.699	3.273	0.301

As seen from Table 3, the supply of 1 tFe in lumps, pellets or sinter is estimated to entail the mining of 5.1 t, 6.8 t and 5.7 t rock, respectively (these are the M_r) values.

Iron becomes slightly more concentrated in lumps compared to the input ore (from 60.0% to 61.0%), due to the preferential removal of particles with slightly less than average ore grade during screening. Iron becomes substantially more concentrated in pellets compared to the input ore (from 50% to 65%), due to the low concentration (0.236) of iron in tailings water extracted from the concentrator, while sinter becomes more concentrated to a smaller extent (from 51% to 58%) due to the dilution of the iron content by the substantial addition of fluxes (equal to 28% of the iron mass for sinter but only 8% for pellets).

Redirecting both lump ore waste flows (M_l1 and M_l2) to pelleting or sintering only slightly reduces the rock and ore mining requirements for pelleting and sintering. If lump production is 30% of the pellet production, for example, the total iron ore flow from lump ore (M_l1 + M_l2) is only 0.12 t, which avoids 0.18 t of mined rock, compared to a base case requirement of 6.8 t for the production of pellets with 1 t of iron.

2.1.3. Changing the Iron Yield during the Concentration Step

It is of interest to know how mining requirements would change with an increase in the concentrator yield, Y₁. However, if Y₁ is changed, the concentration of iron in the waste flow (C_l1) must be changed in a consistent manner. To ensure this, we decompose Y₁ in terms of separate yields for the iron oxide and gangue components of the original ore, as follows:   

$$M_o=M_{io}+M_g$$(22)

  

$$Y_l=\frac{M_{io}{Y}_{io}+M_g{Y}_g}{M_o}$$(23)

  

$$C_{l1}=\frac{\left(1-Y_{io}\right)M_{io}}{\left(1-Y_l\right)M_o}$$(24)

where M_io and M_g are the mass of iron oxides and gangue (everything else), respectively, in the iron ore, and Y_io and Y_g are the corresponding yields (i.e., the fractions transferred to concentrate). For the pellet data given in Lockwood Greene (2000, Appendix C, Base Process DRI/EAF case),¹⁸⁾ Y_io = 0.808, Y_g = 0.043, M_io = 0.713, and M_g = 0.287, which gives Y₁ = 0.589. The maximum possible Y₁, while minimizing the transfer of gangue to the concentrate, is (M_io + M_gY_g)/M_o. As a larger initial ore grade corresponds to a larger M_io (and the M_gY_g term is small), the upper limit to Y₁ increases with increasing ore grade. Conversely, as Y₁ increases, C_l1 decreases, because the increase in Y₁ occurs through a decrease in the transfer of iron oxide to M_l1 (we also see this from Eq. (24); an increase in Y₁ is driven by an increase in Y_io, and Y_io can reach 1.0 (implying C_l1 = 0.0) whereas Y₁ cannot reach 1.0).

In Fig. 3 we show the variation of Y₁ with Y_io, and the variation of C_l1 with Y₁, both for various values of C_o. As seen from Fig. 3(a), a given iron oxide yield results in a greater overall yield the higher the iron oxide fraction (and so, the higher C_o is). As seen from Fig. 3(b), achieving a higher iron ore yield requires a lower concentration of iron in the processing waste, that is, more effective extraction of iron from the waste stream. If the iron ore has a lower grade to begin with (less iron and hence iron oxide), the iron concentration in the waste stream has to be lower in order to achieve a given output grade. Figure 3(c) shows how the mass of rock mined per tonne of prepared iron varies with Y_io and Y₂. As a quantitative illustration of the results, if Y_io could be increased from 0.808 to 0.9, Y₁ would increase from 0.589 to 0.655 while C_l1 decreases from 0.236 to 0.142, with the result that the rock mining requirement decreases from 6.1 t/tFe to 5.4 t/tFe and the pellet iron grade increases from 0.669 to 0.673.

Fig. 3.

Variation of (a) Y₁ with Y_io, (b) C_l1 with Y₁, and (c) M_r with Y_io and Y₂, all for different values of C_o. (Online version in color.)

The curves shown in Figs. 3(a), 3(b) can be closely fitted by a straight line for Y₁ vs Y_io, and by a second degree polynomial for C_l1 vs Y_io, with the coefficients in the curve fits themselves dependent on the initial ore grade. The regression equations are   

$$Y_1=a+b{Y}_{io}$$(25)

and   

$$C_{l1}=c+d{Y}_1+e{Y}_1^2$$(26)

where a = 0.04350 – 0.062C_o, b = 0.00017 + 1.42667C_o, c = 40.56 – 267.09C_o + 593.95C_o² − 448.00C_o³, d = − 78.85 + 522.50C_o – 1164.25C_o² + 898.70C_o³, and e = 33.11 – 230.26C_o + 516.52C_o² − 409.70C_o³.

It remains to be seen whether concentrating yield can be increased in practice; the analysis presented here simply shows various constraints arising from conservation of mass.

2.2. Mass Flows during the Reduction of Iron Ore in a Blast Furnace

The blast furnace mass balance shown in Table 2 involves a mixture of lump, pellet and sinter iron inputs, and also accounts for iron and slag forming materials in the coke and coal fuel inputs. In this section, we present a model for predicting the amount of slag produced and the composition of iron produced from any combination of lump, pellet and sinter inputs, including end-member cases of 100% lump, pellet or sinter input. We assume fixed inputs of per tonne of hot metal produced of 355 kg coke and 152 kg coal (as in Table 2) and – given the mass input of lumps, pellets or sinter – compute the amount of limestone (of composition given in Table 2) that must be added so as to produce a given prescribed slag basicity irrespective of the choice of iron input. In so doing, we chose the lowest possible quartz input that allows us to achieve the target input basicity.⁴ The CaO mass transferred to BF slag, M_cslag-BF, is equal to the total CaO input minus the amount M_cdBF transferred to dust, while the SiO₂ mass transferred to BF slag, M_sslag-BF, is equal to the total SiO₂ input minus dust amount M_sdBF and the amount M_sr reduced to Si. That is,   

$$\begin{array}{l}{M}_{cslag-BF}=f_{cl}{M}_l+f_{cp}{M}_p+f_{cs}{M}_s+f_{cck}{M}_{ck}+f_{ccl}{M}_{ck}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}+f_{cq}{M}_q+f_{cst}{M}_{st}-M_{cdBF}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}= M_{1c}+f_{cst}{M}_{st}- M_{cdBF}\end{array}$$(27)

and   

$$\begin{array}{l}{M}_{sslag-BF}=f_{sl}{M}_l+f_{sp}{M}_p+f_{ss}{M}_s+f_{sck}{M}_k+f_{scl}{M}_c\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}+f_{sq}{M}_q+f_{sst}{M}_{st}-M_{sdBF}-M_{sr}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{0.5em}= M_{1s}+f_{sst}{M}_{st}-M_{sdBF}-M_{sr}\end{array}$$(28)

respectively, where M_l, M_p, M_s, M_ck, M_cl, M_q and M_st are the mass inputs of lumps, pellets, sinter, coke, coal, quartz and limestone, respectively; f_cl, f_cp, f_cs, f_cck, f_ccl, f_cq and f_cst are the corresponding concentrations of CaO, and f_sl, f_sp, f_ss, f_sck, f_scl, f_sq and f_sst are the corresponding concentrations of SiO₂. M_cdBF and M_sdBF are computed as fixed fractions (α_cdBF and α_sdBF, respectively) of the total inputs of CaO and SiO₂ (respectively), while M_sr is a fixed fraction α_sr of the total input of SiO₂. That is,   

$$M_{cdBF}={\alpha }_{cdBF}\left(M_{1c}+f_{cst}{M}_{st}\right)$$(29)

  

$$M_{sdBF}={\alpha }_{sdBF}\left(M_{1s}+f_{sst}{M}_{st}\right)$$(30)

  

$$M_{sr}={\alpha }_{sr}\left(M_{1s}+f_{sst}{M}_{st}\right)$$(31)

We require that   

$$M_{CaO}=B_{sBF}{M}_{SiO2}$$(32)

where B_sBF is the specified BF slag basicity. It follows that   

$$M_{st}=\frac{B_{sBF}{M}_{1s}\left(1-{\alpha }_{sdBF}-{\alpha }_{sr}\right)-M_{1c}\left(1-{\alpha }_{cdBF}\right)}{f_{cst}\left(1-{\alpha }_{cdBF}\right)-B_{sBF}{f}_{sst}\left(1-{\alpha }_{sdBF}-{\alpha }_{sr}\right)}$$(33)

The output masses of dust, slag and hot metal are computed as follows: (1) For dust, the same fractions of the total input of each chemical compound become dust as in Table 2; (2) For slag, CaO, MgO and Al₂O₃ amounts are equal to total input minus dust (i.e., nothing goes to hot metal); SiO₂ to slag equals total input minus the dust amount minus the amount that is reduced to Si, that being 9.7% of the total input; Other amount in slag = 48.0% of total input (as in Table 2); Fe amount in slag is such that Fe is 0.3% of the total slag mass (as in Table 2 and given by Zhang et al. (2014, Table 4.4.2)¹⁹⁾); (3) For hot metal, Fe content = total input minus dust and slag amounts; Si content = amount of SiO₂ that is reduced x ratio of Si:SiO₂ molecular masses (0.467); C content is 4.7% of total hot metal; Other content =28.5% of total input (as in Table 2). The mass of prepared iron input is adjusted (and M_st is automatically updated using Eq. (33)) such the mass of hot metal produced is 1000 kg.

End-member results are given in Table 4 with a prescribed fixed slag iron concentration of 0.3%. For prepared iron inputs consisting of 100% lumps, 100% pellets or 100% sinter, the required fluxes (quartz + limestone) to the blast furnace per tonne of hot metal produced are 283 kg, 75 kg and 47 kg, respectively, while the slag production is 388 kg, 180 kg and 376 kg, respectively. The small flux for the sinter case arises because the majority of the required flux is added during the production of sinter (159 kg/t-sinter, as inferred from Table 3). The amount of slag produced increases as the ore grade decreases, as lower grade means greater SiO₂ (which becomes part of the slag) and a greater need for matching CaO (which also becomes part of the slag) in order to achieve the desired slag basicity.

Table 4. Hypothetical input mixtures (kg) to a blast furnace using only lumps, pellets or sinter, and corresponding outputs. Source: Derived assuming the same chemical composition of each input as in Table S1, subject to the slag basicity being equal to 1.10 with a fixed hot metal output of 1000 kg.

Case 1: Lumps only
	Inputs to Blast Furnace						Outputs from Blast Furnace
	Lumps	Coke	Coal	Quartz	Lime-stone	Total	Dust	Slag	Hot metal	Sum
Total mass	1538.5	354.8	152.0	0	283.2	2328.5	4.3	388.4	1000.0	1392.7
Fe	938.5	1.5	0.8		0.8	941.6	1.5	1.1	939.0	941.6
O in Fe oxides	403.3	0.0	0.0			403.3				0.0
CaO	4.6	0.2	0.3		152.9	158.0	0.3	157.7		158.0
MgO	3.1	0.2	0.1		3.1	6.5	0.0	6.5		6.5
SiO2	128.9	22.2	3.7	0	3.4	158.2	0.3	143.4		143.6
Al2O3	42.5	10.0	2.5		1.4	56.3	0.1	56.2		56.3
Si									6.8	6.8
C (or hydro-C)		312.4	132.2		120.6	565.3			47.0	47.0
Other	17.6	8.2	12.5		0.8	39.2	2.1	23.5	7.2	32.8
Ore grade	0.610			Basicity:		0.999		1.100

Case 2: Pellets only
	Inputs to Blast Furnace						Outputs from Blast Furnace
	Pellets	Coke	Coal	Quartz	Lime-stone	Total	Dust	Slag	Hot metal	Sum
Total mass	1444.3	354.8	152.0	0	75.3	2026.4	2.9	180.2	1000.0	1183.1
Fe	946.0	1.5	0.8		0.2	948.5	1.5	0.5	946.5	948.5
O in Fe oxides	403.8	0.0	0.0			403.8				0.0
CaO	26.0	0.2	0.3		40.7	67.2	0.1	67.0		67.2
MgO	17.3	0.2	0.1		0.8	18.5	0.1	18.4		18.5
SiO2	40.4	22.2	3.7	0	0.9	67.3	0.1	60.9		61.0
Al2O3	8.7	10.0	2.5		0.4	21.5	0.1	21.5		21.5
Si									2.9	2.9
C		312.4	132.2		32.1	476.7			47.0	47.0
Other	2.0	8.2	12.5		0.2	23.0	1.1	11.8	3.6	16.5
Ore grade	0.655			Basicity:		0.999		1.100

Case 3: Sinter only
	Inputs to Blast Furnace						Outputs from Blast Furnace
	Sinter	Coke	Coal	Quartz	Lime-stone	Total	Dust	Slag	Hot metal	Sum
Total mass	1630.0	354.8	152.0	45.0	1.6	2183.4	4.4	376.4	1000.0	1380.8
Fe	939.2	1.5	0.8		0.0	941.5	1.5	1.1	938.9	941.5
O in Fe oxides	390.1	0.0	0.0			390.1				0.0
CaO	154.0	0.2	0.3		0.9	155.4	0.3	155.1		155.4
MgO	24.5	0.2	0.1		0.0	24.8	0.1	24.7		24.8
SiO2	85.6	22.2	3.7	44.1	0.0	155.6	0.2	141.0		141.2
Al2O3	17.0	10.0	2.5	0.9	0.0	30.3	0.1	30.2		30.3
Si									6.7	6.7
C		312.4	132.2		0.7	445.3			47.0	47.0
Other	19.7	8.2	12.5		0.0	40.4	2.2	24.4	7.4	34.0
Ore grade	0.576			Basicity:		0.999		1.100

For any arbitrary mixture of lump, pellet and sinter inputs, the required coke, coal, quartz and limestone inputs can be computed by scaling the amounts shown in Table 4 according to the lump, pellet and sinter input amounts, as can the dust, hot metal and slag outputs. That is, the amount M_i of an input or output i is given by   

$$M_i=\left(\frac{M_l}{M_{lo}}\right)M_{il}+\left(\frac{M_p}{M_{po}}\right)M_{ip}+\left(\frac{M_s}{M_{so}}\right)M_{is}$$(34)

where M_lo, M_po and M_so are the end-member lump, pellet and sinter amounts, respectively, from Table 4; M_il, M_il and M_is are the amounts of input or output i from Table 4 for the lump, pellet and sinter end-member cases, respectively; and M_l, M_p and M_s are the amounts of lump, pellet and sinter, respectively, for a new case.⁵

2.2.1. Variable Coke: Coal Input Ratios

The above procedure can also be applied with different proportions of coke and coal as input fuel. 1 kg coal can replace 0.85–0.95 kg coke.²⁰⁾ Here, we tested the impact on required flux addition and slag production with 100% sinter input of increasing the coal injection rate from 0–200 kg/thm, with a corresponding reduction in coke using a 0.9 kg coke/kg coal replacement rate, and passing through the point 355 kg coke, 152 kg coal (from Table 2, and as used for Table 4). Coke and coal have different concentrations of SiO₂ (see Table 2), so we adjusted the quartz input so as to provide a fixed total SiO₂ input with variable coke and coal inputs, then computed the required limestone input using Eq. (33) and from that the slag production, using the procedure described above. Coal has a higher concentration of CaO than coke (Table 2), so when we increase coal relative to coke, less limestone input is required. However, as CaO is only about 50% of the limestone mass, the reduction in limestone mass is greater than the increase in slag-forming CaO in coke+coal, so there is a small reduction in the amount of slag produced when coal is substituted for coke. In particular, increasing the coal input from 0–200 kg/thm reduces the slag production from 402.8 kg/thm to 400.7 kg/thm according to this model (just below the upper end of the range given in Table 11). This variation is small enough that one can apply Eq. (34) for the full range of plausible coal injection rates with little error.

Table 11. Literature values of rates of slag production and slag iron concentration. Sources are designated as H2014,¹⁶⁾ K2011,²⁸⁾ P2016,³²⁾ R2013;²¹⁾ WSA,³⁰⁾ and Y2011.³³⁾ Table numbers in some references are given.

Source of slag		Slag production (kg/thm)	Reference	Slag Fe concentration	Reference
Blast furnace
	general	150–347	R2013 (T6.2)	0.2–0.3%	R2013 (T6.15)
	general	159–366	WSA (T10)
	general	250–421	P2016
	pellet input	160	H2014
	2:1 sinter:pellet input, 71% grade ore	210	H2014
	2:1 sinter:pellet input, 66% grade ore	260	H2014
BOF
	general	50–200	P2016
	general	85–165	R2013 (T7.3)	10–20%	R2013 (T7.12)
	general	101–206	Y2011 (T3)
EAF
	general	70–200	P2016
	general	70–343	Y2011 (T3)
	general	110–180	R2013 (T8.6)	10–63% (32% typical)	R2013 (T8.7)
	DRI input	70–150	K2011

2.2.2. Variable Ore Grade

The calculations in this section can be linked to those in Section 2.1 in order to account for variable ore grade in the following way: For alternative inputs specified in Section 2.1, compute the fraction of prepared iron consisting of iron oxides, acidic gangue, and basic gangue (flux). Then, create new contents of individual gangue components using the same proportions of acidic gangue components in the acidic gangue fraction as given in Table 4, and the same proportions of basic gangue components in the basic gangue fraction (assuming “Other gangue” to be all acidic). Finally, using these new end-member compositions, and assuming the same composition of coke, coal, quartz and stone as in Table 4, use the procedure outlined above to produce a new Table 4, which can then be used as described above to compute flux requirements and slag and hot metal outputs for an arbitrary mixture of the new lump, pellet and sinter materials.

An example of the application of this approach is shown in Table 5, which gives the variation in selected mass flows and iron concentrations associated with the production of lumps, pellets and sinter with 1.0 tFe as the ore grade is decreased. As the grade of the input ore to lump ore production and sintering decreases, the mass flows at each step (M_r, M_o, M_c and M_p) increase while the iron concentrations decrease.

Table 5. Variation of mass flows and iron concentrations during the iron preparation step, and in BF inputs (flux and prepared iron) and outputs (slag and hot metal output component) as the iron ore grade (C_o) varies using lumps, pellets and sinter prepared iron. Lump ore, pelleting and sintering mass flows are t per t of iron in the prepared iron output, while BF inputs and outputs are kg per t of hot metal produced. Also given is the mass of rock mined per t of hot metal iron.

	Lump ore			Pelleting			Sintering
Iron preparation step
Co	0.60	0.58	0.56	0.50	0.45	0.40	0.52	0.47	0.42
Mr	5.12	5.31	5.52	6.81	7.57	8.52	5.70	7.56	8.50
Mo	2.02	2.10	2.18	2.69	2.99	3.37	2.15	2.99	3.36
Mc	1.82	1.89	1.96	1.59	1.60	1.62	1.38	1.66	1.69
Mp	1.64	1.70	1.77	1.53	1.54	1.55	1.74	1.95	1.98
Cc	0.610	0.588	0.566	0.684	0.679	0.673	0.656	0.681	0.676
Cp	0.610	0.588	0.566	0.655	0.650	0.643	0.576	0.538	0.533
Mgp	0.212	0.274	0.341	0.099	0.111	0.128	0.320	0.466	0.484
Blast furnace inputs and outputs
Flux to BF	291	374	453	83	108	135	54	239	260
BF slag	410	531	645	181	209	239	399	644	670
Hot metal Fe	938	936	932	949	950	950	938	937	937
Hot metal Si	7	6	6	3	2	3	3	2	3
Hot metal gangue	8	11	14	1	1	0	1	1	0
Hot metal carbon	47	47	47	47	47	47	47	47	47
Prepared iron	1538	1592	1648	1449	1462	1478	1629	1759	1773
Mr/thmFE	5.12	5.31	5.52	6.82	7.58	8.53	5.70	7.27	8.14

The results given in Table 5 assume no effort to improve iron yield in order to compensate for falling ore grade. To increase the lump grade requires some combination of a decrease in C_l1 and increase in M_l1, that is, to produce a larger flux of more depleted lean ore after pre-crushing, thereby further concentrating most of the iron in the remaining ore. However, to separate ore with a lower mean concentration implies being more selective, which is contrary to the idea of separating a greater flux of lean ore (here, the amount of ore removed as lean ore would have to increase from 12% to 24% of the input while achieving a reduction in its grade from 0.5 to 0.4). Thus, increasing the grade of lump ore is extremely difficult and the possibilities are limited. For pellets and sinter, the reduction in C_p following a reduction in C_o by 0.100 is only 0.015 (pellets) or 0.009 (sinter). Restoring the pellet grade would require reducing C_l1 from 0.157 (its value after the ore grade decreases to 0.4) to 0.143, while restoring the sinter grade would require reducing C_l1 from 0.244 to 0.225.

2.3. Mass Flows during the Production of Steel from PI and Scrap in a BOF

The iron in PI from a BF occurs as metallic (elemental) iron, with dissolved C and some reduced non-Fe metals. In a BOF, oxygen is injected so as to remove the C and non-Fe metals through oxidation (producing CO, CO₂ and metal oxides), but at the same time some of the metallic iron is also oxidized (to FeO) and becomes part of a BOF slag (along with non-Fe metal oxides). Unless the BOF slag is recycled as input to sintering or to the BF, this represents a loss of iron. Table 6 gives a typical mass flow associated with the production of liquid steel from PI and scrap (with other minor inputs). PI but not scrap contains significant elemental Si; the Si content of PI decreases from 4.43 kg to 0.10 kg, as 4.33 kg Si are converted to 9.28 kg SiO₂ (a net gain of 4.95 kg) and added to the 1.45 kg SiO₂ in the inputs to give 10.74 kg SiO₂ in slag. Sufficient lime and burnt dolomite (containing CaO) are added to give a slag basicity of 5.6. According to Remus et al. (2013, Table 8.11),²¹⁾ the basicity of BOF slag typically ranges from 2–5, so the value given in Table 5 is high. The C content of PI decreases from 42.1 kg to 0.4 kg (0.04%) through combustion. The lower the C content after the BOF step, the greater the oxygen concentration in the steel. The C content cannot be pushed below 0.03% in a BOF without causing unacceptable oxidation of iron, but some steels require as little as 0.002–0.010%C, which requires vacuum decarburization.²²⁾ Slag production for the Table 6 case is 111 kg/tls, while dust and sludge production sum to 30 kg/tls.⁶

Table 6. Representative mass balance (kg) for the production of liquid steel primarily from pig iron (hot metal) and scrap in a BOF in Europe. Source: IEA (2013),⁶⁾ Section D, Table D-10, with slag element amounts adjusted slightly to give exact conservation of mass.

	Inputs						Outputs
	Hot Metal	Scrap	Pellets	Lime	Burnt Dolomite	Total	Liquid Steel	BOF Slag	BOF dust & Sludge	Total
Total	900.8	190	5.0	64.8	10.9	1171.5	1000.0	111.3	30.0	1141.3
Fe	848.9	187.9	3.3	0.3	0.0	1040.4	999.1	22.7	18.6	1040.4
O in FeO								6.5		6.5
CaO			0.1	59.5	4.4	63.9		60.4	3.6	63.9
MgO			0.1	1.2	6.0	7.3		6.2	1.0	7.3
SiO2			0.1	1.3		1.5		10.7		10.7
Al2O3			0.0	0.5		0.6		0.6		0.6
Si	4.4	0.0				4.4	0.1			0.1
C	41.9	0.2				42.1	0.4			0.4
Other	5.6	1.9	1.4	1.9	0.5	11.3	0.4	4.1	6.8	11.3
Basicity						43.95		5.62

The CaO mass transferred to BOF slag, M_cslag-BOF, is equal to the input from pellets (which are added in small quantity along with PI, which could itself be made from pellets), lime and burnt dolomite minus the amount M_cdBOF transferred to BOF dust, while the SiO₂ mass transferred to BF slag, M_sslag-BF, is equal to these inputs plus SiO₂ produced by oxidation of Si in the hot metal input, minus dust amount M_sdBOF. That is,   

$$\begin{array}{l}{M}_{cslag-BOF}=C_{cp}{M}_p+C_{cl}{M}_{lime}+C_{cbd}{M}_{bd}-M_{cdBOF}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}= M_{2c}+C_{cl}{M}_{lime}+C_{cbd}{M}_{bd}- M_{cdBOF}\end{array}$$(35)

and   

$$\begin{array}{l}{M}_{sslag-BOF}=C_{sp}{M}_p+C_{sl}{M}_{lime}+C_{sbd}{M}_{bd}-M_{sdBOF}-R\mathrm{\Delta }{M}_{Si}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=M_{2s}+C_{sl}{M}_{lime}+C_{sbd}{M}_{sbd}-M_{sdBOF}-R\mathrm{\Delta }{M}_{Si}\end{array}$$(36)

respectively, where M_p, M_lime and M_bd are the mass inputs of pellets, lime and burnt dolomite, respectively; C_cp, C_cl and C_cbd are the corresponding concentrations of CaO; C_sp, C_sl and C_sbd are the corresponding concentrations of SiO₂; and R is the ratio of SiO₂ to Si molecular masses. M_cdBOF and M_sdBOF are fixed fractions (α_cdBOF and α_sdBOF, respectively), of the total inputs of CaO and SiO₂ (respectively, with α_sdBOF = 0 according to Table 6), and it is assumed that M_bd is a fixed fraction α_bd of M_lime and that ΔM_Si is a fixed fraction α_Si of the total input M_Si of Si. That is,   

$$M_{bd}={\alpha }_{bd}{M}_{lime}$$(37)

  

$$M_{cdBOF}={\alpha }_{cdBOF}\left(M_{2c}+C_{cl}{M}_{lime}+C_{cbd}{M}_{bd}\right)$$(38)

  

$$\mathrm{\Delta }{M}_{Si}={\alpha }_{Si}{M}_{Si}$$(39)

We require that   

$$M_{cslag-BOF}=B_{sBOF}{M}_{sslag-BOF}$$(40)

where B_sBOF is the specified BOF slag basicity. It follows that   

$$M_{lime}=\frac{B_{sBOF}\left(M_{2s}+{\alpha }_{Si}{M}_{Si}\right)-M_{2c}\left(1-{\alpha }_{cdBOF}\right)}{\left(C_{cl}+{\alpha }_{bd}C\right)\left(1-{\alpha }_{cdBOF}\right)-B_{sBF}{C}_{sl}}$$(41)

We compute the dust and slag production and steel output for different proportions of PI and scrap input, and for different BOF slag basicities, as follows: (1) For dust, the same fractions (by component) of total input become dust as in Table 6; (2) For slag, CaO, MgO and Al₂O₃ amounts are equal to total input minus dust (i.e., nothing goes to hot metal); SiO₂ to slag equals total input minus the dust amount plus the amount that is produced by oxidation of Si, which is determined from the reduction in Si content of hot metal (see below); Other amount in slag, same proportion (52.7%) of total input as in Table 6; Fe amount in slag is such that Fe is 20.1% of the total slag mass; (3) For steel output, Fe content = total input minus dust and slag amounts; Si, C and Other amounts are reduced to the same proportion of total input as in Table 6.

With this procedure and using Eqs. (41) and (37), the proportions of pig iron and scrap input can be varied and the required lime and burnt dolomite inputs and resultant slag production and iron yield computed for any desired slag basicity. Table 7 compares the flux input, slag output, and iron yield for slag basicities of 2.0–5.0 assuming 100% PI or 100% scrap inputs to the BOF.⁷ The scrap given in Table 6, whose composition serves as a basis for computing the results given in Table 7, contains no FeO. In reality, scrap iron may contain 4% or more FeO by mass (depending on the extent of rusting). Thus, slag production amounts and iron yields for a case with 1% FeO in scrap are also given in Table 7, assuming that any FeO in scrap is passed directly into the slag (this may not always occur). As seen from Table 7, this more than doubles the amount of slag produced from scrap (the increase being 10.28 kg/tls rather than 10.0 kg/tls because 1028 kg of scrap are needed to produce 1000 kg of liquid steel). For PI input, the main contributor to BOF slag (apart from the added flux) is from the oxidation of Si in the metal input, and the higher the desired basicity, the greater the required lime input and resulting slag production. As scrap metal is assumed to contain no Si but PI is 0.5% Si, the slag production is much greater for a pure PI input than for a pure scrap input. Thus, as slag basicity varies from 2.0–5.0, lime requirements range from about 25–70 kg/tls with PI input and from 0.7–2.0 kg/tls with scrap input, while slag production ranges from about 60–120 kg/tls for PI input and from 7–9 kg/tls for scrap input with no FeO and from 18–20 kg/tls for scrap with 1% FeO (10 kg/t).

Table 7. Required lime input per tonne of liquid steel (tls) produced in a BOF, with either 100% PI or 100% or scrap as input, for the given target slag basicity, and resulting slag production and iron yield.

	Lime Requirement (kg/tls)		Slag Production (kg/tls)			Iron Yield
	Iron Input		Iron Input			Iron Input
Basicity	Pure Hot Metal	Pure Scrap	Pure Hot Metal	Pure Scrap		Pure Hot Metal	Pure Scrap
				0% FeO	1% FeO		0% FeO	1% FeO
2	25.3	0.7	56.28	7.45	17.73	0.971	0.981	0.973
3	39.1	1.1	76.27	8.07	18.35	0.967	0.980	0.973
4	53.6	1.6	97.39	8.72	18.99	0.963	0.980	0.973
5	69.0	2.0	119.73	9.39	19.67	0.959	0.980	0.973

As seen from Table 7, the computed iron yield with PI input is 96–97%, while the yield with scrap input is 98% at 0% FeO and 97% at 1% FeO. Pauliuk et al. (2017, OS)²³⁾ summarize various sources that support an assumed BOF yield of 94% (by contrast, Cullen et al. (2012, Fig. S2)²⁴⁾ indicate a global mean BOF yield of only 87.1%).

For any arbitrary proportions of PI and scrap input to the BOF with compositions as given in Table 6, the lime requirement, slag production, and iron yield can be computed as   

$$\begin{array}{l}{M}_{lime-BOF}=\left(25.33+14.45\left(B_{sBOF}-2\right)\right)f_{PI}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+(0.70+0.45\left(B_{sBOF}-2\right)f_{scrap}\end{array}$$(42)

  

$$\begin{array}{l}{M}_{slag-BOF}=\left(57.96+21.15\left(B_{sBOF}-2\right)\right)f_{PI}\\ +(9.95+10.28P_{FeO}+\left(0.647+0.0013P_{FeO}\right)\left(B_{sBOF}-2\right)f_{scrap}\end{array}$$(43)

and   

$$\begin{array}{l}{Y}_{BOF}=\left(0.971-0.004\left(B_{sBOF}-2\right)\right)f_{PI}\\ \hspace{1em}\hspace{1em}\hspace{1em}+\left(0.980-0.0076P_{FeO}\right)f_{scrap}\end{array}$$(44)

respectively, where P_FeO is the percent FeO in scrap, f_PI is the PI fraction and f_scrap is the scrap fraction. These relationships exactly replicate the results of calculations based on the procedure outlined above for basicities of 2 and 5, but become inaccurate outside the B_sBOF range of 2.0–6.0 which, however, are rarely if ever encountered.

Although not pursued here, it would be relatively straight forward to derive alternative coefficients in Eqs. (42), (43), (44) that would be applicable to hot metal with different Si and “Other” content than shown in Table 6 (due to differences in lump, pellet or sinter composition arising from differences in the initial ore grade, as traced through in Table 5, or due to changes in the proportions of lump, pellet and sinter inputs to the BF). A change in the hot metal Si content leads to a change in the slag SiO₂ content, necessitating a change in the lime input and thus, primarily, a change in the slag CaO content which, together with the change in slag SiO₂, largely determines the change in total slag production (see Table 6).

2.4. Composition of DRI

About 7% of global iron is produced as direct reduced iron (DRI) (also known as sponge iron), an alternative to the BF in which iron is reduced in the solid state by reacting lumps or pelletized iron ore concentrate with a mixture of H₂ and CO at temperatures of 800–1050°C.⁸

Unlike PI produced in a blast furnace (where the iron is fully reduced to metallic iron, Fe), about 5–8% of the iron in DRI is in the form of FeO rather than Fe. Also in contrast to PI, DRI contains significant amounts (3–6%) of gangue because there is no melting process to separate gangue materials as slag from iron minerals in the ore. Thus, relatively high quality ores are required so as to minimize the gangue content of the DRI. Another significant difference from PI is that about 30–60% of the total iron in DRI occurs as Fe₃C (cementite), compared to none in PI. Carbon in DRI occurs both in Fe₃C and as dispersed carbon particles. The amount of carbon by mass in DRI can vary from 2% to 5%, depending on the reaction conditions, with 2–3% preferred for DRI that will be used in an EAF without scrap, 3–4.5% preferred for DRI that will be used in combination with scrap, and 4.5% or more preferred for DRI that will be used as a replacement for pig iron in the BOF.²⁶⁾

Table 8 gives information on the composition of low-C (2.2%) and high-C (4.0% and 4.3%) DRI, which is relevant both to the amount of energy required to produce DRI and the amount released when it is melted in an EOF or BOF. The low-C (2.2% C) DRI is 30% Fe₃C by mass, 62% Fe° (metallic iron, which includes iron as Fe₃C), 4.7% FeO and 3.9% gangue. For high-C DRI, the Fe₃C share increases to 55–60% with a corresponding decrease in Fe°, with little change in the FeO content. Both Fe and Fe₃C are metallic forms of iron, and the metallization rate is the percentage of total iron that is in metallic form; for the cases shown in Table 8, the metallization rate is 94–96%. A common value is 94%, but best results are obtained for values of 94–96%.²⁸⁾

Table 8. Data on mass fractions of total C, Fe₃C, total and metallic iron, and gangue in DRI as produced conventionally and at two high-C plants, from Villa (2014),²⁷⁾ and various derived amounts.

	Conventional	Ternium Plant	Nucar Plant
Total C	0.022	0.040	0.043
Fe3C	0.296	0.551	0.585
Implied C in Fe3C	0.020	0.037	0.039
Implied graphite C	0.002	0.003	0.004
Implied fraction of total C in Fe3C	0.899	0.921	0.909
Total Fe	0.929	0.883	0.909
Total metallic iron	0.892	0.830	0.873
Implied metallization rate	0.961	0.940	0.960
Implied Fe as Fe3C	0.276	0.514	0.546
Implied Fe as Fe°	0.616	0.316	0.327
Implied Fe as FeO	0.037	0.053	0.036
Implied O in FeO	0.010	0.015	0.010
Gangue	0.039	0.062	0.038
Fe+C+O+gangue	1.000	1.000	1.000

2.5. Mass Flows during the Production of Steel from PI, DRI and Scrap in an EAF

Table 9 gives example compositions of scrap, DRI and PI inputs to an EAF. From the primary data we have also computed the mass of Fe as FeO and as metallic Fe, and the slag mass and iron yield corresponding to each input.⁹ Assuming that

1. all gangue (CaO, MgO, Al₂O₃ and SiO₂) in the inputs enters the slag,

2. all of the Si, Mn, P and S in the inputs are oxidized and enter the slag (in reality, trace amounts could remain unoxidized and thereby enter the liquid steel output),

3. a fraction f_r of the FeO in the input is reduced and becomes part of the liquid steel, while the balance becomes part of the slag, and

4. additional CaO is added so as to given the required slag basicity (1.75 for scrap input, 2.0 for DRI and PI inputs),

the required lime input, steel and slag output, slag iron content, and iron yield can be computed. The results can be replicated by the equations   

$$M_{lime-EAF}=0.70f_{sc}+3.50f_{DRI}$$(45)

  

$$\begin{array}{l}{M}_{steel-EAF}=\left(94.70f_{sc}+88.55f_{DRI}+92.7f_{PI}\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-\left(4.75f_{sc}+6.63f_{DRI}\right)\left(1-f_r\right)\end{array}$$(46)

  

$$\begin{array}{l}{M}_{slag-EAF}=\left(4.79f_{sc}+11.04f_{DRI}+11.11f_{PI}\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+\left(6.11f_{sc}+8.53f_{DRI}\right)\left(1-f_r\right)\end{array}$$(47)

  

$$M_{slagFe-EAF}=\left(4.75f_{sc}+6.63f_{DRI}\right)\left(1-f_r\right)$$(48)

and   

$$Y_{EAF}=1.000-\left(0.050f_{sc}+0.075f_{DRI}\right)\left(1-f_r\right)$$(49)

Table 9. Representative composition (% total mass) of scrap, DRI and PI inputs to an EAF, from Madias (2014, Table 1.5.2).²⁹⁾

Component	Input			Comment
	Scrap	DRI	PI
C	0.360	1.500	4.400
Si	0.210		1.500	Much smaller PI Si than in Table 2
Mn	0.550	0.030	0.300
S	0.040	0.020	0.020
P	0.030	0.040	0.080
Fe	94.700	88.550	92.700
O	1.360	1.950
H2O	0.680	0.500	0.100
CaO	0.820	2.500	0.600
MgO	0.120	0.790
Al2O3	0.260	1.120
SiO2	0.870	3.000	0.300
Gangue	2.070	7.410	0.900	Sum of CaO, MgO, Al2O3 and SiO2
Total	100.000	100.000	100.000
Inferred quantities
O in P2O5		0.052		All P in DRI is assumed to be in oxide form
O in FeO	1.360	1.898	0.000	Amount given above minus amount in P2O5
Fe in FeO	4.747	6.626	0.000	From stoichiometry and O amount in FeO
Metallic Fe	89.953	81.924	92.700	Total Fe minus Fe in FeO
Metallization	0.950	0.925	1.000	Metallic Fe over total Fe
Mass of new oxides produced by oxidation of reduced elements
SiO2	0.450	0.000	3.214
MnO	0.710	0.039	0.387
P2O5	0.069	0.092	0.183
Basicity	1.75	2.00	2.00
Required CaO	2.310	6.000	7.027	Computed as (pre-existing + new) SiO2 x basicity
Required flux	1.490	3.500	6.427	Required flux minus amount in input material

As f_r increases, slag production decreases and iron production (and yield) increases, because iron that would be lost in slag FeO is instead transferred to steel as metallic iron.

Slag production per tonne of liquid steel output and slag Fe concentration can be computed from the above variables, and are given in Table 10 as a function of f_r. Slag production using DRI is 2–3 times that using scrap, but the slag iron concentration is substantially less for DRI than for scrap. As there is no FeO in PI, the slag production with PI input is independent of f_r and the slag iron concentration is zero. For the cause of variable slag production considered here (variable FeO reduction), slag iron concentration increases with increasing slag production, thereby amplifying the impact on iron loss of increasing slag production. For f_r = 0.75 (thought to be a reasonable value), slag production is about 120 kg/tls, 70 kg/tls and 150 kg/tls using PI, scrap and DRI inputs, respectively, while slag iron concentrations are 0%, 19% and 13%, respectively. The corresponding iron yields (iron input/liquid steel iron output) are 1.000, 0.987 and 0.981, respectively. By comparison, Remus et al. (2013, Table 8.6)²¹⁾ indicate EAF slag production of 100–150 kg/t (and another 30–40 kg/t as ladle slag), with slag FeO mass fractions of 0.10–0.63, which implies an EAF iron yield of 0.925–0.992, which closely matches the range (0.928–0.986) given by the WSA.³⁰⁾ Apart from original FeO transferred to slag, iron can also be lost in EAF dust (1–2% loss) and, if the EAF contains supplemental fuel burners, through reaction of original Fe with the CO₂ and H₂O combustion products to produce additional FeO that is transferred to slag.³¹⁾

Table 10. Computed variation, with the fraction of input FeO that is reduced, in the amount of slag produced per tonne of liquid steel output, in the slag iron concentration, and in Fe yield for scrap, DRI and PI inputs to an EAF and target slag basicities of 1.75 using scrap input and 2.0 using DRI and PI inputs (with composition as given in Table 9). Initial FeO amounts are 6.1% for scrap, 8.5% for DRI, and 0.0% for PI. Slag Fe concentration and yield are based only on the loss of initial FeO that is not reduced.

Fraction of FeO that is reduced	kg slag/tls			Slag Fe concentration			Fe yield
	Input			Input			Input
	Scrap	DRI	PI	Scrap	DRI	PI	Scrap	DRI	PI
0.00	121	239	120	0.44	0.34	0.00	0.950	0.925	1.000
0.25	103	209	120	0.38	0.29	0.00	0.962	0.944	1.000
0.50	85	180	120	0.30	0.22	0.00	0.975	0.963	1.000
0.75	68	152	120	0.19	0.13	0.00	0.987	0.981	1.000
1.00	51	125	120	0.00	0.00	0.00	1.000	1.000	1.000

2.6. Comparison of Flux Inputs and Slag Production with Literature Values and Industry Data

Table 11 compares literature values of the amount of slag generated and the slag iron concentration at various steps. A large mass of slag is produced from a BF (160–360 kg/thm) but with very low iron concentration (0.3%); slag production from the BOF and EAF is modestly smaller (50–200 kg/thm and 70–200 kg/thm, respectively) but with a high iron concentration (about 25%). The iron content of slag (which occurs overwhelmingly as FeO) is low (< 1%) for BF slag because it is produced in a reducing environment, but it is high (12–20%) in BOF and EAF slags because they are produced in an oxidizing environment. The rates of slag production and iron concentration calculated here for BF, BOF and EAF slag fall within the range shown in Table 11.

3. Summary and Applications

In this paper, simple relationships have been developed that can be used to compute various rock, iron and slag mass flows associated with the production of iron and steel from primary ores or steel scrap, and which can be used in developing future scenarios of the global iron and steel industry. In particular, the relationships presented here allow for declining ore grade over time, changes in the composition of prepared iron inputs to blast furnaces and direct reduction furnaces for the production of PI and DRI (respectively), and shifts in the relative amounts of pig iron and scrap input to the BOF and in the relative amounts of DRI, scrap and PI to the EAF. All of these parameters are likely to change dramatically in the future, particularly if the world transitions over the coming century to a near steady-state iron and steel stock with a heavy reliance on recycling of end-of-life products.

3.1. Key Mass Balance Relationships

In Section 2.1, relationships were developed to permit calculation of the mass of iron ore mined (Eq. (17)) and the required flux input (Eq. (14)) per 1000 kg of pellet or sinter produced, and to permit calculation of the gangue content and grade of pellets and sinter, given the ore grade, the amount and iron concentration of ironworks waste inputs, the total mass and iron mass lost during pellet and sinter production, and the desired basicity of the pellets or sinter.

In Section 2.2, a relationship was developed (Eq. (34)) to permit calculation of the amount of hot metal, slag and dust produced in a BF with arbitrary proportions of lump, pellet and sinter inputs with arbitrary ore grade or gangue content (as determined in Section 2.1). It was demonstrated how the BF inputs and outputs change with a change in the grade of the original iron ore used to produce lumps, pellets or sinter.

In Section 2.3, relationships were developed (Eqs. (42), (43), (44)) to compute the required lime input and resulting slag production and yield from a BOF for arbitrary proportions of PI and scrap inputs with a given composition and for an arbitrarily prescribed fraction of metallic Si contaminant that is oxidized. These relationships could be readily modified to account for different PI content arising from differences in the original ore grade or in the proportions of lump, pellet and sinter input to the BF.

In Section 2.4, compositional data for DRI with C contents of 2.0%, 4.0% and 4.3% were presented.

In Section 2.5, relationships were developed to compute the required lime input to an EAF (Eq. (45)) and the resulting steel, slag, and slag iron outputs (Eqs. (46), (47), (48)) for arbitrary proportions of scrap, DRI and PI inputs with a given composition and for an arbitrarily prescribed fraction of input FeO that is reduced. Iron yield can also be computed (Eq. (49)). These relationships could be readily altered to reflect scrap, DRI and PI inputs with different composition (gangue and FeO content in particular).

3.2. Follow-up

In a companion paper,³⁴⁾ a parallel analysis of the energy use for each of the steps considered here is presented. Results from this paper and the companion paper will then be applied to the development of a model of mass and energy flows associated with the production of iron and steel, its transformation into end use products, and the recycling of end-of-life scrap and of scrap produced at various stages during the manufacturing of end use products. This model in turn will be applied to the development of regionally disaggregated scenarios for the elimination of greenhouse gas emissions associated with the iron and steel industry by the end of this century.

Acknowledgement

I would like to strongly thank Lawrence Hooey (Laboratory of Process Metallurgy, University of Oulu, Finland) for answering numerous questions during the writing of this paper, and for providing comments on an earlier draft. I, of course, take full responsibility for any errors.

Footnote

¹  The term “pig iron” refers to molten iron that used to be poured into metal containers called “pigs”, which is no longer the case. A more appropriate term would be “hot metal”, but as DRI is also hot metal when it leaves the DRF, the terms PI (and DRI) will be used to distinguish iron produced from a BF from iron produced in other ways.

²  Sinter has a basicity that is frequently about 1.85^10,11,12) but ranges from 1.7–2.9.⁹⁾ Pellets also contain minor amounts of flux.

³  Other workers give somewhat different pellet and sinter iron grades, but all agree that sinter has a lower Fe concentration than pellets. For example, different workers give pellet and sinter Fe concentrations of, respectively, 0.67 and 0.58,¹³⁾ 0.62 and 0.54,¹⁴⁾ and 0.65 and 0.55,¹⁵⁾ while others^16,17) indicate sinter Fe concentrations of 0.56–0.57.

⁴  A larger quartz input requires a larger limestone input, both of which increase the slag production.

⁵  Outputs calculated this way exactly match those obtained by using the calculation procedure that was used to calculate the end-member results in Table 4, but applied to the combined lump, pellet and sinter input mixture.

⁶  tls = tonnes liquid steel.

⁷  100% scrap input is not realistic, but is a useful end-member case, along with 100% PI input, for computing lime requirements and slag production for any realistic combination of PI and scrap inputs.

⁸  There are several different direct reduction technologies, which can be grouped as shaft furnaces (Midrex^®, HyL), rotary kilns (SL/RN process), rotary hearth furnaces (Fastmet^®/Fastmelt^®, Inmetco^®/RedIron^®, ITmk3^®) and fluidised bed reactors (Cercofer^®).²¹⁾ The great majority of DRI is produced using Midrex or HyL. DR processes are economical at much smaller production rates than the BF process (0.6 Mt/yr or less instead of 2–3 Mt/yr).²⁵⁾

⁹  The inferred metallization for DRI (92.5%) is a bit low.

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