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Mathematical modeling of the argon-oxygen decarburization refining process of stainless steel: Part I. Mathematical model of the process

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Abstract

Some available mathematical models for the argon-oxygen decarburization (AOD) stainless steelmaking process have been reviewed. The actual situations of the AOD process, including the competitive oxidation of the elements dissolved in the molten steel and the changes in the bath composition, as well as the nonisothermal nature of the process, have been analyzed. A new mathematical model for the AOD refining process of stainless steel has been proposed and developed. The model is based on the assumption that the blown oxygen oxidizes C, Cr, Si, and Mn in the steel and Fe as a matrix, but the FeO formed is also an oxidant of C, Cr, Si, and Mn in the steel. All the possible oxidation-reduction reactions take place simultaneously and reach a combined equilibrium in competition at the liquid/bubble interfaces. It is also assumed that at high carbon levels, the oxidation rates of elements are primarily related to the supplied oxygen rate, and at low carbon levels, the rate of decarburization is mainly determined by the mass transfer of carbon from the molten steel bulk to the reaction interfaces. It is further assumed that the nonreacting oxygen blown into the bath does not accumulate in the liquid steel and will escape from the bath into the exhaust gas. The model performs the rate calculations of the refining process and the mass and heat balances of the system. Also, the effects of the operating factors, including adding the slag materials, crop ends, and scrap, and alloy agents; the nonisothermal conditions; the changes in the amounts of metal and slag during the refining; and other factors have all been taken into account.

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Abbreviations

A rea :

total reaction interface, cm2

a i :

activity of i component

c p,i :

specific heat of i substance at constant pressure, J·g−1·K−1

D C :

diffusion coefficient of carbon in molten steel, cm2·s−1

d b :

average diameter of bubble, cm

f i :

Henrian activity coefficient of component i in molten steel

ΔG i :

Gibbs free energy for oxidation reaction of i element, J·g−1

g :

acceleration due to gravity, cm·s−2

H b :

rising height of bubble, cm

ΔH i :

oxidation enthalpy of i element, J·g−1

[pct i]:

mass percent concentration of i solute in molten steel, mass pct

[pct i] e :

equilibrium concentration of i solute in molten steel at reaction interface, mass pct

(pct j):

mass percent concentration of j component in slag melt, mass pct

K i :

equilibrium constant for indirect oxidation reaction of i solute in molten steel

K Cr-C :

equilibrium constant of [C](Cr2O3) reaction

k C :

mass transfer of carbon in molten steel, cm·s−1

M i :

mole mass of i substance, g·mole−1

N j :

mole fraction concentration of j component in slag

n b :

total number of bubble

n i :

mole flow rate of i component, mole·s−1

P CO :

partial dimensionless pressure of carbon monoxide

P i :

total dimensionless pressure in AOD vessel

p i :

average absolute pressure in AOD vessel, atm

Q :

total gas flow rate, cm3·s−1

Q ph :

physical heat of lime melting and dissolving in molten slag, J·g−1

Q ch :

chemical heat of lime dissolving in slag melt, J·g−1

Q i :

flow rate of i gas, cm3·s−1

Q sub :

total flow rate of inert gas, cm3·s−1

q 1 :

heat loss by conduction from bottom of the vessel, J·s−1

q 2 :

heat loss by conduction from the lower of the vessel, J·s−1

q 3 :

heat loss by conduction from the upper of the vessel, J·s−1

q 4 :

heat loss by conduction from top of the vessel, J·s−1

q 5 :

heat loss absorbed by refractory lining of the vessel during bath rising temperature, J·s−1

q u :

uncertain heat loss of the system, J·s−1

R:

gas constant (=8.314), J·mol−1·K−1

r b :

mean radius of bubble, cm

r eq :

mean equivalent radius of bubble, cm

T :

bath temperature, K

T g , T g0 :

temperature of gas and its initial value, K

u b :

velocity of bubble, cm·s−1

W alloy :

mass of alloy agents added, g

W CaO :

mass of lime added, g

W m :

mass of liquid steel, g

W s :

mass of slag, g

x :

distribution ratio of oxygen for i component in liquid steel

γ :

Raoultian activity coefficient of j component in slag melt

η :

utilization ratio of oxygen

λ :

heat conductivity of i material, W·cm−1·K−1

ρ :

density of i material, g·cm−3

as :

asbestos board

cl :

clay brick

Mg-Al:

alumina-magnesite brick

Mg-Cr:

chrome-magnesite brick

Mag:

magnesite

m, s, l :

metal, slag phase and lining, respectively

sh :

shell

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Author notes

  1. De-Ping Zhu (Graduate Student, Engineer)

    Present address: the Department of Metallic Materials, Shanghai University, 200072, Shanghai, People’s Republic of China

Authors and Affiliations

  1. the Department of Metallic Materials, Shanghai University, 200072, Shanghai, People’s Republic of China

    Ji-He Wei (Professor)

  2. Shanghai Wensi Sorftware Limited Company, USA

    De-Ping Zhu (Graduate Student, Engineer)

Authors
  1. Ji-He Wei
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  2. De-Ping Zhu
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Additional information

[]—metal phase; ()—slag phase; {}—gaseous phase; and 〈〉—solid phase

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Wei, JH., Zhu, DP. Mathematical modeling of the argon-oxygen decarburization refining process of stainless steel: Part I. Mathematical model of the process. Metall Mater Trans B 33, 111–119 (2002). https://doi.org/10.1007/s11663-002-0091-5

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  • DOI: https://doi.org/10.1007/s11663-002-0091-5

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