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Metallurgical and Materials Transactions B

, Volume 48, Issue 6, pp 3281–3300 | Cite as

A Gibbs Energy Minimization Approach for Modeling of Chemical Reactions in a Basic Oxygen Furnace

  • Ari KruskopfEmail author
  • Ville-Valtteri Visuri
Article

Abstract

In modern steelmaking, the decarburization of hot metal is converted into steel primarily in converter processes, such as the basic oxygen furnace. The objective of this work was to develop a new mathematical model for top blown steel converter, which accounts for the complex reaction equilibria in the impact zone, also known as the hot spot, as well as the associated mass and heat transport. An in-house computer code of the model has been developed in Matlab. The main assumption of the model is that all reactions take place in a specified reaction zone. The mass transfer between the reaction volume, bulk slag, and metal determine the reaction rates for the species. The thermodynamic equilibrium is calculated using the partitioning of Gibbs energy (PGE) method. The activity model for the liquid metal is the unified interaction parameter model and for the liquid slag the modified quasichemical model (MQM). The MQM was validated by calculating iso-activity lines for the liquid slag components. The PGE method together with the MQM was validated by calculating liquidus lines for solid components. The results were compared with measurements from literature. The full chemical reaction model was validated by comparing the metal and slag compositions to measurements from industrial scale converter. The predictions were found to be in good agreement with the measured values. Furthermore, the accuracy of the model was found to compare favorably with the models proposed in the literature. The real-time capability of the proposed model was confirmed in test calculations.

Nomenclature

\( \rho \)

Density (kg/m3)

A

Area (m2)

V

Volume (m3)

\( m \)

Mass (kg)

\( \dot{m} \)

Mass flux (kg/s)

t

Time (s)

G

Gibbs energy (J/mol)

R

Universal gas constant (J/(mol K))

T

Temperature (K)

g

Dimensionless Gibbs energy and gravitational acceleration (m/s2) in Chapter III.B

x, X

Mole fraction

\( \mu \)

Chemical potential of constituent (J/mol)

n

Molar amount (mol)

b

Mass constraint

\( a_{ij} \)

Stoichiometric matrix

F

Number of degrees of freedom

\( C \)

Number of components

\( {{\Phi }} \)

Total number of phases

\( {{\Gamma }} \)

Dimensionless chemical potential of component

J

Jacobian matrix

D

Dimensionless driving force

\( \gamma \)

Activity coefficient

\( \varepsilon \)

First-order interaction parameter

\( {{\Delta }}g \)

Gibbs energy of pair formation

\( Z \)

Coordination number

Y

Mass fraction and coordination equivalent fraction in Chapter 3.2

\( {\text{q}} \)

Gibbs energy coefficient of the pair fraction polynomial (J/mol)

\( {{\omega }} \)

Temperature independent part of the Gibbs energy coefficient (J/mol)

\( {{\eta }} \)

Temperature dependent part of the Gibbs energy coefficient [J/(mol K)]

\( {\dot{\text{V}}} \)

Volume flow rate (m 3 /s)

\( H \)

Enthalpy (J)

S

Entropy [J/(mol K)]

\( \dot{H} \)

Enthalpy flux (J/s)

\( h \)

Specific enthalpy (J/kg)

\( c_{\text{p}} \)

Heat capacity (J/(kg K))

\( \varphi \)

Enthalpy or mass source (J/s), (kg/s)

\( \alpha \)

Volume fraction

\( h_{T} \)

Heat transfer coefficient (W/(m2 K))

\( h_{Y} \)

Mass transfer coefficient (m/s)

\( k \)

Thermal conductivity (W/(m K))

\( I \)

Momentum (kg*m)/s2

\( v \)

Velocity (m/s)

\( R_{\text{p}} \)

Plume momentum ratio (dimensionless)

Subscripts

g

Gas

m

Metal

s

Slag

mix

Mixture

i, j, l, k

Generic indices

A, B, C

Components A, B, and C

RZ

Reaction zone

Liq

Liquidus

T

Temperature

IF

Interface

ref

Reference

Superscripts

ex

Excess Gibbs energy

°

Standrard state

p

Pure phase

s

Solution phase

ν

Iteration index

n

Time level

e

Equilibrium

Notes

Acknowledgments

This work was partly funded by the Finnish Funding Agency for Technology and Innovation (TEKES). The research was carried out within the framework of the DIMECC SIMP research program.

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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2017

Authors and Affiliations

  1. 1.Research Group for Materials Processing and Powder Metallurgy, Department of Chemical and Metallurgical EngineeringAalto UniversityAaltoFinland
  2. 2.Process Metallurgy Research UnitUniversity of OuluUniversity of OuluFinland

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