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Data-Driven Mathematical Modeling of the Effect of Particle Size Distribution on the Transitory Reaction Kinetics of Hot Metal Desulfurization

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Abstract

The aim of this work was to develop a prediction model for hot metal desulfurization. More specifically, the study aimed at finding a set of explanatory variables that are mandatory in prediction of the kinetics of the lime-based transitory desulfurization reaction and evolution of the sulfur content in the hot metal. The prediction models were built through multivariable analysis of process data and phenomena-based simulations. The model parameters for the suggested model types are identified by solving multivariable least-squares cost functions with suitable solution strategies. One conclusion we arrived at was that in order to accurately predict the rate of desulfurization, it is necessary to know the particle size distribution of the desulfurization reagent. It was also observed that a genetic algorithm can be successfully applied in numerical parameter identification of the proposed model type. It was found that even a very simplistic parameterized expression for the first-order rate constant provides more accurate prediction for the end content of sulfur compared to more complex models, if the data set applied for the modeling contains the adequate information.

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Abbreviations

A :

Area (m2)

b i :

Regression coefficient for a variable i (-)

C d :

Drag coefficient (-)

d :

Diameter (µm)

d ka :

Average particle size by means of mass transfer (µm)

d 32 :

Sauter mean diameter (µm)

d A :

Area-based mean diameter (µm)

d mean :

Volume-based mean diameter (µm)

g:

Gas (-)

k tot :

Rate constant of the transitory reaction (1/s)

M :

Molar mass (g/mol)

\( \dot{m} \) :

Reagent feed rate (kg/s)

N :

Normal distribution (-)

p :

Particle (-)

Q :

Carrier gas flow rate (m3/s)

R :

Weight fraction of particles (-)

R :

Universal gas constant 8.3145 J/(K mol)

R 2 :

Squared Pearson correlation coefficient (-)

t :

Time (s)

t res :

Residence time (s)

u t :

Terminal velocity (m/s)

V :

Volume (m3)

x i :

Input variable i (-)

y i :

Volume fraction (-)

y :

Output variable (-)

\( \hat{y} \) :

Predicted output variable (-)

w :

Mass fraction (-)

X :

Data-matrix (-)

β :

Mass transfer coefficient (m/s)

ρ :

Density (kg/m3)

Ω:

Fraction of contacted particles (-)

θ :

Contact angle

[ ]:

Species dissolved in hot metal (-)

( ):

Species in slag phase (-)

{ }:

Species in gas phase (-)

〈 〉:

Solid species (-)

MAE:

Mean absolute error of prediction (-)

SOS:

Sum of squared errors (-)

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Acknowledgments

This work was conducted within the Flexible and Adaptive Operations in Metal Production (FLEX) research program funded by Business Finland. The authors would like to thank Dr. Aki Sorsa for constructive comments on the manuscript. Also, the work of the analysis laboratory and specialized sampling group of SSAB Europe Oy in Raahe is greatly appreciated.

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Authors and Affiliations

  1. Process Metallurgy Research Unit, University of Oulu, P.O. Box 4300, 90014, Oulu, Finland

    Tero Vuolio, Ville-Valtteri Visuri & Timo Fabritius

  2. SSAB Europe Oy, Rautaruukintie 155, P.O. Box 93, 92101, Raahe, Finland

    Sakari Tuomikoski & Timo Paananen

Authors
  1. Tero Vuolio
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  2. Ville-Valtteri Visuri
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  3. Sakari Tuomikoski
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Correspondence to Tero Vuolio.

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Manuscript submitted February 20, 2018.

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Vuolio, T., Visuri, VV., Tuomikoski, S. et al. Data-Driven Mathematical Modeling of the Effect of Particle Size Distribution on the Transitory Reaction Kinetics of Hot Metal Desulfurization. Metall Mater Trans B 49, 2692–2708 (2018). https://doi.org/10.1007/s11663-018-1318-4

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