ISSN 0967-0912, Steel in Translation, 2007, Vol. 37, No. 4, pp. 356–361. © Allerton Press, Inc., 2007. Original Russian Text © V.I. Kulinich, 2007, published in “Stal’,” 2007, No. 4, pp. 14–18.

Thermodynamic Modeling of the Blast-Furnace Smelting of Hot Metal V. I. Kulinich Aksusk Ferroalloy Plant, AO TNK Kazkhrom, Kazakhstan DOI: 10.3103/S0967091207040109

For the last 15 years, Aksusk Ferroalloy Plant has been vigorously investigating the physicochemical and thermodynamic processes involved in the reduction of silicon, chromium, and manganese oxides in electrofurnaces. In the present work, the goal is to improve electrosmelting on the basis of the achievements of metallurgical science and formulas established for the parameters of ferroalloy smelting as a function of the physicochemical, electrical, and spatial properties of the batch and the furnace characteristics. The scientific findings are only applicable if the relations at the atomic–molecular, physicochemical, and thermodynamic levels are compatible with technological factors such as the batch quality, the dosing conditions, the electrical and technological parameters, and the state and characteristics of the equipment. One possible approach is the creation of computer software for analysis of the state of the system, prediction of its development, and the determination of measures for increasing the efficiency. The software is based on methods developed at the plant: for calculation of the material–diagnostic balance of materials in the melt; for thermodynamic modeling of the reducing processes in nonequilibrium and equilibrium thermodynamic conditions, in open and closed systems, on the basis of the concept of a complete equilibrium process, with the determination of the enthalpic power consumption; for reproduction of the electrical conditions, in terms of the components of the active and reactive bath resistance in complex configurations (spatial electrical engineering); for calculation of the electric-arc parameters; for calculation of the energy balance of energy liberation and consumption over the zones of the bath; for calculation of other smelting parameters.

Appropriate software has been developed for the production of carbon ferrochrome, ferrosilicon, and ferrosilicomanganese, smelted in furnaces of all types (RKO, RKZ, RKG, and RKNZ furnaces) of power 16.5–80 MV A. Numerous formulas have been derived for the smelting parameters of ferroalloys as a function of quality characteristics, the physicochemical properties and composition of the batch materials, the electrical parameters, the geometric parameters of the furnaces, and other factors. In the present work, as an illustration, the application of some of these methods to blast–furnace smelting is considered. As a preliminary, the methods are tested for carbon and carbon-monoxide combustion and also for ammonia synthesis (unpublished materials, author’s manuscript). The approach is based on the calculation of the working material and thermal balances of the hot metal outlined in [1, pp. 282–306], as adapted for a Fe–O–C system of mass 100 kg [2]. In formulating the gas-dynamic and energy balances, typical operating conditions and parameters are adopted for a blast furnace of useful volume 3000 m3, according to the data of [3].

356

The blast-furnace characteristics are as follows: Shaft height, m

32.6

Ore load, kg/t of hot metal

1753

Coke consumption, kg/t of hot metal

530

Productivity, t/day

6000

Blast flow rate,

m3/min

7390

Number of tuyeres

28

Nozzle diameter, m

0.155

Blast temperature, °C

1200

THERMODYNAMIC MODELING

SIMPLIFIED MATERIAL BALANCE OF MELT The working material in the blast-furnace process may be expressed as Fe–(xO + ∂O2) – sC, where xO is the oxygen content (moles per mole of Fe) in the oxides FeOx; ∂O2 is the oxygen content (moles per mole of Fe) in the blast (or 2∂O); sC is the total carbon content (moles per mole of Fe) in the batch coke (and in the fuel introduced with the blast, which is disregarded here). Then, the spatial position (over the height zones into which the blast-furnace shaft is divided) of a particular component in the blast-furnace process is denoted by the arrows ↑ and ↓. Zone I. In the preliminary zone, T = 298–980 (±150) K. At the input to the charge hole, the working material is FeOx + sC + Σ(Mem, On). Here Σ(Mem, On) is the sum of the moles of conditionally unreduced slag-forming components of the batch. The yield of charge-hole gases ↑ is ( x – w )CO + wCO 2 + ( s – x – z )CO, or ( s – z – w )CO + wCO 2 . Zone II. This zone corresponds to transition to twothirds of the useful height at T = 980 ± 150 K. The nonequilibrium processes in an open system occur with the participation of the specified carbon FeO x + sC = ↓FeC z + ↑xCO + ↓ ( s – x – z )C fuel ; (1) ↑wCO + wO at = ↑wCO 2 .

(2)

Zone III. This corresponds to transition to the tuyere source. The input material is unenriched air blast and reduced iron, with residues of Cs as Cfuel ∂O2 + 3.762∂N2 + FeCz + (s – x – z)Cfuel. According to the material–diagnostic balance of the melt, the equilibrium process in the closed system within the tuyere zone should take the form ∂O2 + (s – x – z)Cfuel + FeCz = ↓FeCz + ↑(s – x – z)C × 2∂O: (COy), with upward energy transfer; the subscript y in Coy is equal to 2∂/(s – x – z) or, in the mixture (aCO + bCO2) to y = (a + 2b). In the tuyere source, with constant volume and pressure, there is a complete equilibrium process according to thermodynamic calculation, with the assertion that ∆G = STEEL IN TRANSLATION

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∆H – ∆ST = 0 = –RT ln Ke; the balance reactions are converted to an overall equilibrium process of the following form ↓3 ( s – x – z )Fe li ( s – x – z )C fuel = 3 ( s – x – z )Fe gas + ( s – x – fz )C fuel ∂O 2 + 3 ( s – x – z )Fe li ( s – x – z )C fuel + FeC z = ↑3 ( s – x – z )Fe gas + ↑ ( s – x – fz )CO + ↑wO at + ↑3.76∂N 2 + ↓ ( 1 – f )Fe + ↓ f FeC z + ↓Σ ( Me m O n ), where wOat is the number of moles of atomic oxygen; w = 2∂ – (s – x – fz); (1 – f )Fe + f FeCz corresponds to hot metal with a reduced carbon content. Our understanding is that a complete equilibrium process corresponds to complete transition of the system A0 at time τ0 to state A1 at time τ1, when state A0 no longer exists, i.e., the boundary of simultaneous occurrence of the processes A + B AB and AB A+B is erased. The only links between the past and present are the fundamental laws of matter conservation and energy conservation, with precise conditions of transformation at given temperature T, pressure P, and volume V. Of course, this only applies to the chemical and structural transformations and not to transformations in nuclear physics. In reversible processes, it is possible to return to the previous state A '0 , but only at time τ2, where τ0 < τ1 < τ2. The equilibrium constant Ke may change its content and magnitude in comparison with the assumptions in [4]. With gaseous A, B, and AB: system 0: (1 – x)A + (1 – x)B = xAB; the mole fractions xi: (1 – x)/(2 – x) + (1 – x)/(2 – x) + x/(2 – x) = 1; system τ: A + B (1 – x)A + (1 – x)B + xAB; the mole fractions xj on the left: 1 = 0.5 + 0.5; the mole fractions xi on the right: (1 – x)/(2 – x) + (1 – x)/(2 – x) + x/(2 – x) = 1; A0, τ0 A1, τ1. The equilibrium constants take the form x x 1 – x (2 x – 2) (3 x – 2) K e0 = ⎛ -----------⎞ ⎛ -----------⎞ P tot , ⎝ 2 – x⎠ ⎝ 2 – x⎠ x x 1 – x (2 – 2 x) –x K eτ = 4 ⎛ -----------⎞ ⎛ -----------⎞ P tot . ⎝ 2 – x⎠ ⎝ 2 – x⎠ The complete equilibrium process occurs in a closed system formed by the gas cavity of the tuyere source, with constant blast-furnace pressure and temperature. In the coke packing, consisting of (s – x – z)Cfuel, gaseous iron 3(s – x – z)Fegas enters into exothermal

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reaction with solid coke pieces, forming carbon-saturated hot metal (FeC1/3) and carbon droplets enter the gas cavity, where they burn in an O2 flux to form CO and Oat, whose coexistence is thermodynamically determined at the given P, V, Tsol in the tuyere zone. This process is confirmed in that “we know from the theory of H2, CO, C, and CH4 combustion that, with insufficient air, these materials may be in the reaction products but, with an excess of oxygen, they may also be present as a result of the dissociation of H2O and CO2. At higher temperatures, the combustion products also include atomic hydrogen and oxygen and various radicals” [5, pp. 988–995]. The iron cycle is a necessary process in the supply of Cso to the intense-oxidation zone, since coke of density d = 1000 kg/m3 and piece diameter D = 10–50 mm cannot enter a gas bubble in the tuyere zone at a pressure of 400–800 kPa, when the flux of tuyere gas with T > 1600°C leaves this zone at a velocity up to 200 m/s, with a powerful aerostatic ascent force [6]. Carbon monoxide and atomic oxygen leave the tuyere zone and are converted to CO2 in the moderate-temperature region (980 ± 150 K), with energy liberation; the CO2 enters the blast-furnace gases together with the CO from endothermal direct reduction of iron oxides by carbon, thereby ensuring energy balance of the heat liberation and consumption in the cold zone.

The material balance in the Fe–O–C system may be written in the following form (kg or wt %/mol): Input Fe Blast-furnace working 40.96/0.731 material Working material in 40.96/0.731 nonequilibrium thermodynamic process Working material in 40.96/0.731 complete thermodynamic process

O

C

37.41/2.338

21.63/1.802

16.31/1.019

21.63/1.802

21.10/1.319

9.56/0.797

Output Fe

O

C

Blast-furnace working – material – Working material in nonequilibrium thermodynamic process Working material in 40.66/0.726 complete thermodynamic process

37.31/2.332

20.05/1.671

16.24/1.014

12.06/1.005

21.00/1.312

7.98/0.665

Including

(O)sl 0.112/0.007

[C]hotmet 1.580/0.132

(Fe)sl 0.392/0.007

Calculation of the working material in 15 different blast-furnace conditions for the Commonwealth of Independent States (furnace volume 700–5500 m3), on the assumption of equal x in FeOx and equal Fetot content yields the following spread in the results: 36–44% for iron; 36–42% for oxygen; and 17–22% for carbon. The overall balance formula for the process is (moles):

CaCO3 CO2 = 0.128 ∂O2 + FeOx + Cso = [Fe + FeC1/3] + (FeOx) + CO + CO2 + ∂N2 0.662 0.731 1.802 0.332 0.394 0.005 1.010 0.660 2.490 blast-furnace gas, mole fractions, xi 0.235 0.184 0.581

Direct reduction of Fe in nonequilibrium thermodynamic conditions may be represented in the following form (x/FeOx = 1.394): ↓FeOx + ↓Cso = ↓[Fe + FeC1/3] + ↓(FeOx) + ↑CO + 0.731 1.802 0.500 0.231 0 0.996 ∆H, J –277906 0 7746 1935 0 –110134 ∆S, J/K 34.140 10.269 4.275 8.160 0 196.840

With the given mass ratios, the reaction is thermodynamically permitted with the thermodynamic-calculation temperature TTDC = 1016 K, when the energy consumption ∆H = 173727 J, or 1.152 kWh/kg of hot iron. Fegas + ↓Cfuel = ↓FeC1/3 2.16 0.72 2.16

∆HFe, J –909 758

↑CO2 + ↓Cfuel 0.005 0.720 –3726 0 2.023 4.103

To obtain only FeC1/3, TTDC = 935 K, ∆H = 1.09 kWh/kg. The processes in the coke packing and over the shaft height may be expressed as follows (moles):

CO + Oat = ↑CO + ↑CO2 0.655 0.651 0.014 0.651 STEEL IN TRANSLATION

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The complete equilibrium process in a closed system is → ∂O2 + ↓Cfuel + ↓Fe + ↓FeC1/3 = ↓Fegas + ↓[Fe + FeC1/3] + ↓(FeOx) + ↑CO + ↑CO2 + ↑Oat 0.662 ↓0.720 0.500 0.231 2.160↓ 0.332 0.394 0.005 0.666 0 0.651 → → 2.391 ←↑Fegas N2 CO Oat xi (blast): O2 = 0.21 xi (t.g.): 0.362 0.417 0.1115 0.108 ∆H, J 0 0 7746 19993 927816 5144.7 3299 –1813 –73631 0 162432 ∆S, J/K 135.8 0 4.28 84.3 448.85 2.84 13.9 0.22 131.6 0 104.96

The thermodynamic characteristics of the complete equilibrium process (CEP) are as follows ∆HCEP, J ∆SCEP, J/K ∆GCEP, J

1018648 478.02 0

TTDC, K TTDC, °C

2133.1 1860.1

Overall, per 100 kg of working material (WM), we obtain (kg) Hot metal Slag (according to the balance in [1]) Blast-furnace gas (without N2) Blast-furnace gas (with N2)

42.272 26.713 57.356 127.076

With Fe = 0 mole and Cfuel = 0.549 mol, TTDC = 2301 K on the left side of the complete equilibrium process. Note that a similar result is obtained in calculating the theoretical combustion temperature from Eq. (234) in [1], which indicates implicitly that ∆H/∆S = T when ∆G = 0. The energy and enthalpy balance of the blast-furnace process may be written in the form (kWh/kg of hot metal): Energy input 1. Blast energy Eb: potential-kinetic energy Epk = Gb(P/d + w2) enthalpic energy (t = 1200°C) Ee = GbCbt 2. Enthalpy of combustion Eco in the reaction CO + Oat = CO2 3. Exothermal reaction Fegas + Cfuel 1/3 = FeC1/3 and in column 2 after subtracting the enthalpy of Fegas formation Total

1

2

1.043 0.270

1.043 –

0.773

–

2.279

2.279

5.758 – 5.474 = 0.284

9.083

3.606

m

Σ(m )

Energy consumption

1

2

1. Direct reduction of iron FeOx + sC = (1 – f)Fe + fFeCz + xCO + (s – x – zf)Cfuel

1.142

1.142

2. Heat absorption by complete equilibrium reaction

5.474

–

3. Heating blast from Tb to TTDC

0.364

0.364

4. Enthalpy of products of complete equilibrium reaction (hot metal + slag + tuyere gas)

1.750

1.750

5. Heat losses

0.354

0.354

Total

9.084

3.610

The enthalpic energy consumption is the difference between energy-consumption items 1, 2, 3, and 4 and energy-input item 3, i.e., 1.142 + 5.474 + 0.364 + 1.750 – 5.758 = 2.971. The enthalpy for the blast-furnace process, taking account of heat losses, is 3.224 kWh/kg of hot metal. Taking into account that the complete equilibrium process occurs within the constant volume of the tuyere source, the equilibrium constant Ke is equal to the product of the mole fractions of the gas-cavity components, raised to a power equal to the number of moles on the right (>) divided by the reaction product on the left (<) and multiplied by the pressure raised to a power equal to the difference in the mole sums of the tuyere gas and the blast

m

>Πx i i Σ ( mi ) – Σ ( m j ) >Πx i i P tot i --------------P K e = ---------------------------- = = 1.0 m tot m Σ(m ) <Πx j j <Πx j j P tot j ( 2.16 + 2.49 + 0.6656 + 0.651 )

⋅ 0.1092 P tot 0.362 ⋅ 0.417 ⋅ 0.1115 -. = ------------------------------------------------------------------------------------------------------------------------------------------------------------2.49 ( 0.6619 + 2.49 ) 0.21 ⋅ 0.6619 ⋅ 0.79 P tot 2.16

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Unexpectedly, the calculation gives Ptot = 747 atm, which has hardly appeared previously in the smelting literature. However, calculation of the ferrostatic pressure of the batch column at 32.6 m gives an initial batch density of 1361 kg/m3, with an apparent density of the ore of 2.2 t/m3 (corresponding to 1752.7 kg/t of hot metal) and of the coke of 500 kg/m3 (corresponding to 529.7 kg/t of hot metal); the final density of the smelting products in the coke packing (without recycled iron) is 3057.7 kg/m3, when the densities of hot metal, slag, and fuel carbon are 6800, 3600, and 580 kg/m3, respectively. The mean density is 2115 kg/m3, which is equivalent to a pressure of 689 kPa. Within an infinitesimal time interval, when the introduction of batch, blast, and hearth gas from above may be neglected, the pressure of the batch column must be equal to the pressure in the gas cavity. This is denoted by PTDC, at a temperature TTDC in the constant Gas-dynamic calculations of the blast and tuyeresource parameters may be based on the following simplified handbook formulas: from mass conservation or the continuity equation

Gb = S1 d 1 w1 = S2 d 2 w2 , where Gb is the mass flow rate of the blast, kg/s; S1 is the cross-sectional area of the input from the collector to the tuyere pipe, m2; S2 is the cross-sectional area of the tuyere nozzle, m2; d1, d2 and w1, w2 are, respectively, the density, kg/m3, and effusion rate, m/s, of the gas in these cross sections; from energy considerations, in terms of the potential–kinetic energy of the blast P P 2 2 E pk = G b ⎛ -----1 + w 1⎞ = G b ⎛ -----2 + w 2⎞ , ⎝ d1 ⎠ ⎝ d2 ⎠ where P1 and P2 are the input and output gas pressures, Pa; from the Mendeleev–Clapeyron law P1V1 = nRT = P2V2 at TTDC = 2133.1 K, we find that PV = 380.92 atm m3 per 100 kg of the working material with a tuyere-gas mass of 219.73 kg; the pressure in the tuyere source is calculated from the equation for the mass flow rate of the blast, kg/s, at

Parameters of blast and tuyere source Parameter

Blast

Hot-metal output τ

Tuyere source beyond nozzle

42.27 kg/100 kg WM 380.9 3.152 90.89

69.44 kg/s

69.44 kg/s

69.38 kg/s

625.8 5.178 149.30

625.8 5.178 149.30

Gas volume V g , nm3

0

70.60

116.00

3 V ** g' , phys. m

380.9

3 V ** g'' , phys. m

53.14

PV = nRT, atm m3 Number of moles of gas Gas mass, kg

Deffusion, m Ssph = 0.5S **** , t.s

m2

Pressure, kPa Density, kg/m3 w of fluxes, m/s w of fluxes, m/s, from tuyere-source sphere with 0.3St.s

69.44 kg/s

14.41* kg/0.21 s

625.3 – 149.20

42.27 kg/100 kg WM 1093.3 5.967 219.74

1796.1 9.802 360.98

372.7 2.034 74.90

116.00

–

133.70

219.60

45.56

625.8

625.8

–

1093.3

1796.1

372.7

133.10

87.30

90.75

158.70

260.70

54.09

D *** tuy

D *** noz

Dt.s, m

–

0.185

0.150

–

2.212

2.610

1.545

–

–

–

–

7.686

10.700

3.750

– – –

470 1.121 176.50

716.7 1.710 176.50

689 1.644 176.50

689 1.385 20.64 34.40

689 1.385 24.36 40.60

689 1.385 69.50 115.80

* kg/0.21 s corresponds to calculation with complete removal of the gas volume in the tuyere source after 0.21 s. ** Vg' is the gas volume at TTDC and P = 1 atm; Vg'' is the gas volume at TTDC and Pact. *** At Dnoz = 0.155 m and Dtuy = 0.198 m, the pressure in the nozzle cross section is 7.696 atm and that in the tuyere source is 7.47 atm, with an effusion rate w = 154 m/s. **** 0.5St.s is the gas-permeable surface area of the tuyere-source sphere (at the top), m2. STEEL IN TRANSLATION

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some distance from the tuyere nozzle, for effusion into the medium at pressure Pt.s, Pa [7] 2k G b = S 2 K -----------P 2 d 2 k–1

P t.s⎞ ⎛ -----⎝ P2 ⎠

2/k

P t.s⎞ ( k + 1 )/k – ⎛ -----, ⎝ P2 ⎠

where k = 1.4 is the isentropic-process index (in completely isentropic retardation, all the potential–kinetic energy of the gas flux is converted to heat; retardation corresponds to zero velocity). The parameters of the blast and tuyere source are presented in the table (assuming that Dt.s = 1.55 m). In conclusion, we may note that medieval blacksmiths and metallurgists could not imagine their trade without bellows [8]. In producing iron blooms, it was necessary to draw the alloy and slag independently from the furnace. Melting entailed raising the combustion temperature of the carbon fuels. Blacksmiths raised the temperature by means of bellows, i.e., increased the pressure and effusion rate of the air blast, with increase in its potential–kinetic energy. In describing the metallurgical principles underlying the production of metals (Au, Ag, Cu, Pb, etc.) in smelting furnaces and of hot metal in blast furnaces, Lomonosov paid particular attention to the design of bellows for supplying air to the hearth [9]. Such blowers set waterwheels and later steam machinery in action. Using the experience of blacksmiths, blast-furnace specialists sharply raised the blast parameters and at the same time, to maintain efficiency and reduce batch entrainment, sharply increased the shaft height. Even in 1740, the blast furnace at Nev’yanske in the Urals was of height 12.8 m, with V0 = 72 m3; in 1908, the Clarence furnace in Scotland was of height H = 23.85 m, with V0 = 330 m3. However, the height of modern blast furnaces of useful volume 1000–5580 m3 varies only from 26 to 34 m [4, pp. 341–359]. This is associated with improved blast mechanisms. Currently, the shaft power of a K5500-41-1 compressor of productivity 5500 m3/min, with ε = 5.2, is 21800 kW; hence, with an efficiency of 0.5, 0.066 kWh of energy is consumed per m3 of furnace [7]. Analysis of the combustion conditions of carbon and carbon monoxide indicates that a temperature TTDC = 1800–2300°C is attained at pressures of 300– 400 kPa in our calculations; this corresponds to the pressure of a batch column of height 25–36 m (Pt.s – Paerost – Pfrict), with the formation of atomic oxygen; CO2 cannot exist. CONCLUSIONS 1. The main factor determining the operational efficiency of the blast furnace is the content of the working material, i.e., the Fe–O–C system and its components, in the overall balance formula STEEL IN TRANSLATION

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FeO x + sC + ∂O 2 = FeC z + xCO + ( s – x – z )C ( 2∂ )O. 2. The key parameter in the technology is the pressure in the tuyere source (Pt.s), which is determined by the spatial configuration (profile) of the blast furnace and the physicochemical properties of the batch as it is transformed over time and space (the height H0), according to the material-balance formula of nonequilibrium thermodynamics FeO x + sC = ↓FeC z + ↑xCO + ↓ ( s – x – z )C fuel . 3. The significant technological parameters are the composition and energy of the blast in the material-balance formula of the complete equilibrium reaction (without iron recycling) ∂O 2 + FeC z + ( s – x – z )C fuel = FeC z + ( s – x – z )C ⋅ 2∂O, when the pressure Pt.n in the nozzle cross section is Pt.n = Pt.s + ∆P, where ∆P > 0. 4. The energy of the blast and of carbon-fuel combustion in this material–energy balance is equal to the enthalpic energy consumption in hot-metal production plus the heat losses of the furnace. REFERENCES 1. Berman, E.F., Zherebin, B.N., Pokhvisnev, A.N., and Klempert, V.M., Metallurgiya chuguna (Metallurgy of Hot Metal), Moscow: Metallurgiya, 1989. 2. Simbinov, R.D. and Malyshev, V.P., Termodinamicheskoe, stekhiometricheskoe i eksergeticheskoe modelirovanie fazovykh ravnovesii. Metallurgicheskie protsessy (Thermodynamic, Stoichiometric, and Energetic Modeling of Phase Equilibria: Metallurgical Processes), Almaty: Gylym, 1999. 3. Volkov, Yu.P., Shparber, L. Ya., Gusarov, A.K., and Fedchenko, V.M., Ekspluatatsiya sovremennoi domennoi pechi (Modern Blast-Furnace Operation), Moscow: Metallurgiya, 1991. 4. Lupis, K., Chemical Thermodynamics of Materials (Russian translation), Moscow: Metallurgiya, 1989. 5. Kratkiya khimicheskaya entsiklopediya (Brief Chemical Encyclopedia), Moscow: GNI Sovetskaya Entsiklopediya, 1968. 6. Shchedrin, V.M., Teoriya domennoi plavki pod davleniem (Theory of Blast-Furnace Smelting under Pressure), Moscow: Metallurgizdat, 1962. 7. Teplotekhnicheskii spravochnik (Thermal-Engineering Handbook), Yurenev, V.N. and Lebedev, P.D., Eds., Moscow: Energiya, 1975, vol. 1. 8. Korotich, V.I., Naboichenko, S.S., Sotnikov, A.I., et al., Metallurgiya: ucheb. dlya vuzov (Metallurgy: A University Textbook), Yekaterinburg: Izd. UGTU, 2001. 9. Lomonosov, M.V., Trudy po mineralogii, metallurgii i gornomu delu (Works on Mineralogy, Metallurgy, and Mining), Moscow–Leningrad: Izd. AN SSSR, 1954, vol. 5.