Metallurgical and Materials Transactions B

, Volume 47, Issue 6, pp 3544–3556

# A Mathematical Model for the Reduction Stage of the CAS-OB Process

• Petri Sulasalmi
• Ville-Valtteri Visuri
• Aki Kärnä
• Mika Järvinen
• Seppo Ollila
• Timo Fabritius
Article

## Abstract

This paper proposes a novel method for modeling the reduction stage of the CAS-OB process (composition adjustment by sealed argon bubbling–oxygen blowing). Our previous study proposed a model for the heating stage of the CAS-OB process; the purpose of the present study is to extend this work toward a more comprehensive model for the process in question. The CAS-OB process is designed for homogenization and control of the composition and temperature of steel. During the reduction stage, the steel phase is stirred intensely by employing the gas nozzles at the bottom of the ladle, which blow argon gas. It is assumed that the reduction rate of the top slag is dictated by the formation of slag droplets at the steel-slag interface. Slag droplets, which are generated due to turning of the steel flow in the spout, contribute mainly by increasing the interfacial area between the steel and slag phases. This phenomenon has been taken into account based on our previous study, in which the droplet size distribution and generation rate at different steel flow velocities. The reactions considered between the slag and steel phases are assumed to be mass transfer controlled and reversible. We validated the results from the model against the measurements from the real CAS-OB process. The results indicate that the model accurately predicts the end compositions of slag and steel. Moreover, it was discovered that the cooling rate of steel during the gas stirring given by the model is consistent with the results reported in the literature.

## Keywords

Mass Transfer Coefficient Sherwood Number Slag Phase Reduction Stage Refractory Lining
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Nomenclature

A

Area (m2)

a

Activity (–)

b

Generation rate of droplets (1/s)

D

Diameter of the open-eye area (m), mass diffusivity (m2/s)

d

Nozzle diameter (m)

db

Bubble diameter (m)

g

Acceleration due to gravity (m/s2)

h

Mass transfer coefficient (m/s)

j

Mass flux [kg/(m2 s)]

k

Thermal conductivity [W/(m K)]

kf

Forward reaction rate coefficient [kg/(m2 s)]

L

Characteristic length (m)

l

Streamed length (m)

m

Mass (kg)

NO

Number of O-atoms (–)

p

Pressure (Pa)

R

Reaction rate [kg/(m2 s)]

S

Reaction source term [kg/(m2 s)]

T

Temperature [K (°C)]

t

Time (s)

ub

Rising velocity (m/s)

ui

Interfacial velocity (m/s)

$$\dot{V}_{\text{G}}$$

Volumetric gas flow rate (m3/s)

X

Cation fraction (–)

x

Mole fraction (–)

y

Mass fraction (–)

## Greek Letters

α

Interaction energy (J), heat transfer coefficient [W/(m2 K)]

Γ

Binary operator

γ

Raoultian activity coefficient (–)

ε

Molar first-order interaction parameter, refers also to reaction interface

μ

Dynamic viscosity (Pa s)

ν

Stoichiometric coefficient (–)

$$\tilde{v}$$

Mass-based stoichiometric coefficient (–)

ρ

Density (kg/m3)

G

Gibbs free energy (J/mol)

ΔGconv

Conversion energy (J)

ΔH

Reaction enthalpy (J/mol)

Δh

Specific heat of reaction (J/kg)

ΔS

Reaction entropy [J/(mol K)]

Δt

Time step (s)

ΔxM

Width of the mantle (m)

ΔxR

Width of the refractory lining (m)

## Notes

### Acknowledgments

This research has been conducted within the FIMECC SIMP, a research program coordinated by the Finnish Metals and Engineering Competence Cluster (FIMECC). The authors would like to thank Leena Määttä, the specialized sampler group and the helpful operators at the CAS-OB station. The Jenny and Antti Wihuri Foundation is warmly acknowledged for financial support. The Academy of Finland (Projects 258319 and 26495) is acknowledged as well.

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© The Minerals, Metals & Materials Society and ASM International 2016

## Authors and Affiliations

• Petri Sulasalmi
• 1
Email author
• Ville-Valtteri Visuri
• 1
• Aki Kärnä
• 1
• Mika Järvinen
• 2
• Seppo Ollila
• 3
• Timo Fabritius
• 1
1. 1.Research Unit of Process MetallurgyUniversity of OuluOuluFinland
2. 2.Department of Mechanical EngineeringAalto UniversityAaltoFinland
3. 3.SSAB Europe OyRaaheFinland