710

ISSN 0036-0295, Russian Metallurgy (Metally), Vol. 2009, No. 8, pp. 710–713. © Pleiades Publishing, Ltd., 2009.Original Russian Text © V.P. Karasev, K.L. Sutyagin, 2009, published in Elektrometallurgiya, 2009, No. 6, pp. 5–9.

The iron losses during evaporation in an electric arcare usually taken to be 1–2%. Some authors [1] believethat up to 10% of the metallic charge is lost duringevaporation and that these losses increase with the spe-cific furnace power. Iron evaporation in an electric arcalso causes additional energy consumption, since heatis directly removed from a metal pool. This importantaspect of energy and resource saving is not taken intoaccount in metallurgical literature.

Evaporation processes are mainly considered whenmetals are used as a heat-transfer agent in high-temper-ature power plants [2–4] or when solid metals are pro-cessed by high-power energy sources (laser, plasma)[5]. The data obtained allow an approximate consider-ation of the evaporation of iron under electric arcs.

First of all, we should understand the evaporationconditions in arc furnaces. In this work, we analyze theheat stages from the end of melting of wells to the endof charge subsidence in the pool. This is the longeststage of melting. An electric arc burns on the surface ofa liquid metal that is free of a slag coating or is weaklycoated with a slag. In this stage, a transformer works atthe highest secondary-voltage step and the electric-arcpower is close to the maximum power. An electric arcburns mainly in iron vapors. Average electric arc tem-perature

T

a.av

for this period can be estimated by the for-mula [6]

T

eff

= 800 ·

U

i

Fe

= 800 · 7.83 = 6264 K;

T

a.av

=

T

eff

(1/

k

j

)

0.25

= 6264 · (1/3)

0.25

= 4760 K,

where

U

i

Fe

is the single iron ionization potential and

k

j

is the coefficient that takes into account the motion ofthe electric arc column on the end of the electrode in athree-phase furnace.

The arc temperature is well above the evaporationtemperatures of iron and the oxides taking part in melt-ing (Table 1).

The authors of [3] think that iron oxide decomposesaccording to reaction (3) rather than evaporating. The

mass-spectrometric measurements of the compositionof the gas phase over FeO at 1984 K demonstrate thefollowing relative intensities of the components:Fe

+

62.9, Fe 68.6, O

2

8.8, FeO

+

3.8,and FeO 4.1. In the electric arc zone, these compo-nents do not remain inert: they interact with other gas-eous materials and form complex compounds contain-ing nitrogen, carbon, and other elements. Plasmochem-ical reactions contribute to the energetics of ironevaporation and condensation. These reactions are stillnot taken into account. The main point is that the tem-perature conditions in the electric arc zone are such thatthe surface of liquid iron can be heated to the evapora-tion temperature.

The heat flow of radiative energy from an arc to thewell walls does not cause iron evaporation. Iron andiron oxides melt and flow down to the bottom of thewell having no time to be heated to the evaporationtemperature. Evaporation mainly occurs at the lowerbase surface of the arc column. It should be taken intoaccount that the arc immerses into the metal pool todepth

Δ

h

and moves across the pool at linear velocity

v

a

. A specific funnel, which is similar to a cap with a flat

Evaporation of Iron during Steelmaking in Arc Furnaces

V. P. Karasev and K. L. Sutyagin

GOU VPO SPbGPU

Abstract

—The problems of iron evaporation during steelmaking in an arc steel-melting furnace are consid-ered. A procedure is developed for the calculation of the specific iron evaporation rate and the heat losses duringevaporation. More complete absorption of the heat of condensation by a charge and the oxidation of iron vaporsare shown to be promoted by the following factors: the presence of a slag coating, a decrease in the well diam-eter, an increase in the well depth, an increase in the electrode failure diameter, and directional supply of anoxidizer to the near-electrode zone.

Key words

: iron, evaporation, iron oxide, electric arc, arc voltage, arc power, heat losses.

DOI:

10.1134/S0036029509080084

MANUFACTURE OF FERROUS AND NONFERROUS METALS

Table 1.

Boiling temperature

T

and heat of evaporation

Δ

H

of the phase transformations in iron and some oxides [3]

Reac-tion no. Reaction

T

, K

Δ

H

, kJ/mol

1 Fe

(l)

= Fe

(g)

3145 350.0

2 FeO

(l)

= FeO

(g)

2785 544.3

3 FeO

(g)

= Fe

(g)

+ 0.5O

2

decompo-sition

703.3

4 CaO

(s)

= CaO

(l)

4460 625.3

5 SiO

2(s)

= SiO

2(g)

3223 585.8

6 SiO

2(s)

= SiO

2(g)

+ 0.5O

2

decompo-sition

810.6

RUSSIAN METALLURGY (METALLY)

Vol. 2009

No. 8

EVAPORATION OF IRON DURING STEELMAKING IN ARC FURNACES 711

bottom and edges in the form of a truncated cone, formsin the liquid metal pool under the electrode (see figure).

Table 2 gives the most important parameters of theelectric arc and the near-electrode zone in the pool. Todetermine these parameters, we assumed that the near-electrode voltage drop was

U

c-a

= 30 V, the gradient of thevoltage drop in the arc column was

β

= 0.5–1.5 V/mm, thecurrent density in the arc column was

j

= 6

×

10

6

A/m

2

, theangle between the arc column and vertical was

γ

= 16

°

[6], the coefficient of arc immersion in the pool was

k

b

= 3 mm/kA, and the alternating current frequency was

f

= 50 s

–1

.The data presented in Table 2 were calculated using

the following formulas:

L

a

= (

U

a

–

U

c-a

)/

β

;

d

eff

= 2(

I

a

/

π

j

)

0.5

;

D

w

>

D

e

+ 2

L

a

;

D

w

= 1.3

D

e

Δ

h

=

k

b

I

a

;

D

gap

= 0.75

D

e

+ 2

L

a

;

v

a

=

π

fD

gap

;

S

ca

=

π

+

π

D

gap

Δ

h

.

The electric current and the arc length were deter-mined upon constructing the corresponding electrical

Dgap2 /4

characteristics of arc furnaces. The arc length wasdetermined as a function of the accepted value of

β

.According to [6],

β

= 1.5 is characteristic of the initialarc burning on a liquid metal. At the end of melting, thearc length increases, since the thermal conditions ofvapor ionization improve (which leads to a decrease inthe gradient of

β

). The maximum diameter of the inter-electrode gap was calculated at the level of the liquidpool with allowance for the decrease induced by a 25%loss in the electrode end diameter.

After melting a well, the electric arc is shown toburn in the liquid pool and has no region freely irradi-ating onto the well walls (Fig. 1, Table 2). The arc actu-ally burns in a closed volume filled predominantly withiron vapors. Carbon sputtered from the electrode mate-rial creates a reducing atmosphere in this volume. Theformation of iron oxides in this volume is unlikely.

We agree with Ignatov [6] that, to consider thermalprocesses, it is reasonable to use interelectrode gapdiameter

D

gap

in which the arc moves rather than theeffective arc column diameter. A high velocity of arcmotion in the immersion pool favors rapid overheatingof thin surface layers of the metal to the boiling temper-

Charge in the melt

Melt

Oxidation zone

Condensation

Charge

Arc column

D

w

D

e

D

gap

zone

Δ

h

Structure of the near-electrode zone in an arc furnace.

712

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No. 8

KARASEV, SUTYAGIN

ature of iron. Under these conditions, specific ironevaporation intensity

i

i

is controlled by the heat fluxdensity incident on the metal

q.

To calculate

q

, wefound the arc power,

Pa = UaIa. The part of the arc powerreleased in the liquid metal pool Pal was calculated withallowance for shielding coefficient ks = Δh/La by theformula Pal = ksPa. We only used the minimum value ofthe shielding coefficient, and the heat flow power wasq = Pal/Sca.

The value of ii was determined by the expression

Ii = q(1 – kr)/ΔHev, (5)

where kr takes into account partial removal of energyfrom the metal evaporation surface (it was taken to be0.5) and ΔHev is the enthalpy of iron evaporation(6.27 MJ/kg). To determine evaporation rate J, we tookinto account the areas of all three arcs Sca.

We also calculated the power of heat losses for evap-oration Phl.ev taking into account both the energy lossesfor evaporation and the energy released during the con-densation of vapors and their oxidation to FeO. Theiron vapors from the arc space go up along the gapbetween the electrode and the walls of the well meltedin the charge. The iron vapors condense near the end ofthe electrode, and iron particles slightly above this zoneoxidize to form FeO. The further oxidation of ironmonoxide is likely to occur in the upper part of theworking space of the furnace or outside it, which onlyweakly affects heating of the charge. The heat of con-densation, which is equal to the heat of evaporation, ismainly transferred by radiation, reaching the electrodesurface and the well walls [2]. We assume that theassimilation of this heat by the charge is 40%, and theother part is used to heat the effluent gas.

Similarly to this assumption, 30% of the heat of oxi-dation of iron particles is absorbed by the charge. Thepercentage of heat absorption from the gas phase taken

in our calculations is close to that for bottom meltingprocesses and heating of a charge in an arc steel-melt-ing furnace by fuel–oxygen burners [7–9]. Thus, whendetermining the power of heat losses for evaporation inarcs Phl.ev, we subtract the heat returned to the chargeduring vapor condensation and oxidation (Pcond, Pox)from the heat taken from the pool during iron evapora-tion (Pev). Here, we have Pcond = Pev.

The total enthalpy of the oxidation of iron particlesby oxygen ΔHox was calculated by the procedure pro-posed in [8]. The temperatures of the componentsinvolved in the reaction were taken to be 2500 K foriron particles, 1800 K for gaseous oxygen, and 2200 Kfor the reaction product (FeO). The calculations dem-onstrate that ΔHox = 247 kJ/mol or 4.40 MJ/kg iron.When multiplying ΔHox by the evaporation rate (whichshould be expressed in kg/s), we determined the powerof the oxidation process near the arc Pox. The power ofheat losses for evaporation can be determined from theexpression

Phl.ev = Pev – 0.4Pcond – 0.3Pox.

The intermediate and final calculation data are givenin Table 3.

This procedure for the calculation of the specificiron evaporation rate and the power of heat losses forevaporation does not pretend to a high accuracy (as wellas other methods of calculating heat losses). Neverthe-less, the calculated evaporation rate in a 10-t furnace(6.5 kg/min) agrees satisfactorily with the data in [9](5 kg/min). The principle of determining the metal meltsurface area under an electrode Sca used in the calcula-tion and the assumption that iron evaporates only fromthis surface seem to be correct.

When analyzing the data in Table 3, we conclude thefollowing. The under-electrode zone in an arc furnaceshould be considered as the site of active vapor genera-

Table 2. Energy parameters of arc furnaces of various capacities and of the near-electrode zone in a pool during melting

Parameter Value of the parameter

Furnace capacity G, t 10 50 100 150

Rated transformer power S, MV A 5 35 75 135

Maximum secondary linear voltage Ul, V 250 465 706 856

Working arc current Ia, kA 10 38 75 83

Arc voltage at the working current Ua, V 90 180 387 400

Electrode diameter De, m 0.350 0.555 0.555 0.610

Arc length La, m 0.03–0.06 0.09–0.22 0.16–0.48 0.24–0.71

Effective arc column diameter deff, m 0.045 0.090 0.128 0.132

Arc motion velocity across the pool νa, m/s 45 80 90 110

Well diameter Dw, m 0.46–0.48 0.72–0.74 0.88–1.52 1.09–2.03

Arc immersion depth in the metal melt Δh, m 0.03 0.11 0.23 0.25

Maximum interelectrode gap diameter Dgap, m 0.30 0.54 0.68 0.85

Metal–arc spot contact area Sca, m2 0.09 0.40 0.60 0.85

RUSSIAN METALLURGY (METALLY) Vol. 2009 No. 8

EVAPORATION OF IRON DURING STEELMAKING IN ARC FURNACES 713

tion. To the best of our knowledge, the works dealingwith the heat transfer in arc furnaces have not discussedthe possibilities of using iron vapors for heating of acharge outside the arc burning zone. The following fac-tors will favor more complete absorption of the heat ofcondensation by a charge and the oxidation of ironvapors: the presence of a slag coating, a decrease in thewell diameter, an increase in the well depth, an increasein the electrode failure diameter, and directional supplyof an oxidizer to the near-electrode zone.

A significant portion of the evaporation products islikely not to leave the working space of the furnace.There are no reliable data on iron losses with effluentgases. It should be noted that the fraction of evaporatediron in a 150-t furnace was lower than in a 100-t fur-nace, which is likely to be caused by the high arc volt-age in a 150-t furnace at an insignificant difference inthe electric currents (Table 2). This circumstance sup-ports the tendency toward creating next-generation arcfurnaces with a high secondary voltage.

REFERENCES

1. O. M. Sosonkin and M. V. Shishimirov, “Analysis of theFactors Affecting the Metal Loss in an Arc Steel-MeltingFurnace,” Elektrometallurgiya, No. 12, 12–15 (2002).

2. M. N. Ivanovskii, V. P. Sorokin, and V. I. Subbotin, Evapo-ration and Condensation of Metals (Atomizdat, Mos-cow, 1976) [in Russian].

3. E. K. Kazenas and Yu. V. Tsvetkov, Evaporation ofOxides (Nauka, Moscow, 1997) [in Russian].

4. V. F. Prisnyakov, Boiling (Naukova Dumka, Kiev, 1988)[in Russian].

5. V. N. Kondrat’ev, “On the Mechanism of Evaporationduring the Interaction of High-Power Energy Fluxeswith Substance,” Zh. Prikl. Mekh. Tekhn. Fiz., No. 5,49–57 (1972).

6. I. I. Ignatov, “Electrical and Geometrical Parameters ofan Arc in Furnaces,” in Mathematical Simulation andCalculations of Electrothermal Equipment (VNIIETO,Moscow, 1989), pp. 32–38.

7. V. A. Kalmykov and V. P. Karasev, Electrometallurgy ofSteel: A Textbook (SPbGPU, St. Petersburg, 1999)[in Russian].

8. I. Yu. Zinurov, Yu. N. Tuluevskii, L. N. Popov, andV. S. Galyan, Electric-Energy Saving in Arc Steel-MeltingFurnaces (Energoizdat, Moscow, 1987) [in Russian].

9. K. L. Sutyagin, “Development of a Method for Predictingthe Operation Indices of Arc Steel-Melting Furnaces,”Extended Abstract of Cand. Sci. (Eng.) Dissertation,SPbGPU, St. Petersburg, 2006.

10. M. V. Shishimirov and O. M. Sosonkin, “Metal Loss duringOxygen Blowing of a Pool in an Arc Steel-Melting Fur-nace,” Izv. Vyssh. Uchebn. Zaved., Chern. Metall.,No. 3, 16–18 (2005).

Table 3. Iron evaporation intensity and the power of the heat losses for evaporation

Parameter Value of the parameter

Furnace capacity G, t 10 50 100 150

Total power of one arc Pa, MW 0.90 6.80 21.53 33.20

Shielding coefficient ks 1.00–0.50 1.22–0.50 1.43–0.48 1.04–0.35

Arc power in the metal melt Pal, MW 0.45 3.40 10.33 11.62

Specific heat flow q, MW/m2 5.00 8.50 17.22 13.67

Specific evaporation intensity il, kg/(m2 s) 0.40 0.68 1.37 1.09

Evaporation rate J, kg/min 6.5 49.0 148.0 166.8

Evaporated iron mass in 40-min furnace operation under current, t

0.28 1.96 5.92 6.67

Fraction of evaporated iron, % 2.6 3.9 5.9 4.4

Power, MW:

consumed for evaporation Pev 0.68 5.12 15.47 17.43

oxidation process Pox 0.48 3.59 10.83 12.21

heat losses for evaporation Phl.ev 0.27 1.99 6.03 6.79