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Development of Single Pellet Induration Model for Magnetite Pellet: A Holistic Approach

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Abstract

Evolution of the internal state of magnetite pellet during induration is defined by the kinetics of physico-chemical transformation it undergoes owing primarily to oxidation [< ~1273 K (1000 °C)] and sintering [> ~1273 K (1000 °C)] phenomena, along with the associated heat transfer. In the pursuit to simulate such evolution and properties of the magnetite pellet during induration, the respective oxidation and sintering kinetic models have been developed independently in previous studies. Oxidation model, which was built on the principles of grain model is capable of simulating the progress of oxidation at particle as well as at pellet scale, where kinetics of particle oxidation is suitably described by the Avrami mechanism. Similarly, sintering models at pellet scale were formulated by incorporating the deduced kinetic parameters for probable presence of both the phases—oxidized magnetite and non-oxidized magnetite. Subsequently, these independent models are integrated in a pertinent way to develop the single pellet induration model (SPIM), whose approach and formulation has been presented in this study. The methodology adopted will enable to simulate the internal state at any time during induration at pellet as well as particle scale for varying raw material mixes and the process parameters, such as temperature, O2 content and flow rate of the oxidizing gas. Thus, it can assist in optimizing the thermal and gaseous profiles in order to achieve the desired pellet properties, such as oxidation extent, type of reaction front, strength, etc.

Graphical Abstract

Simulation from the single pellet induration model (SPIM) predicting the evolution of internal state of magnetite at pellet a well as particle scale, when the temperature and O2 content in oxidizing gas is varied.

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Change history

Abbreviations

\(\Delta H\) :

Heat of reaction

\(N\) :

Number of cells

\({T}_{1\to n}\) :

Temperature from 1st to nth cell in the pellet

\({pO}_{2, 1\to n}\) :

Partial pressure of O2 from 1st to nth cell in the pellet

\({\gamma }_{1\to n}\) :

Shrinkage from 1st to nth cell in the pellet

\({V}_{1\to n}\) :

Volume of pellet from 1st to nth cell in the pellet

\({\varepsilon }_{1\to n}\) :

Porosity of pellet from 1st to nth cell in the pellet

\({\dot{{N}N}}_{{\text{O}}_{2}}\) :

Diffusion flux of O2

\({D}_{eff}\) :

Effective diffusivity of the oxidizing gas

\({D}_{{O}_{2}-{N}_{2}}\) :

Diffusion coefficient of gas comprising of O2 and N2, i.e., air

\({X}_{{O}_{2}}\) :

Mole fraction of O2

\(C\) :

Molar concentration of oxidizing gas

\({N}\epsilon\) :

Porosity of pellet

\({N}\tau\) :

Tortuosity of pellet

\(r\) :

Radius of pellet

\(\dot{G(r)}\) :

Number of moles of O2 consumed at any radial location \(r\) per unit volume of pellet per unit time

\({N}_{p}\) :

Number of particles/grains per unit volume of the pellet

\({N}{\delta }_{M,{Fe}_{3}{O}_{4}}\) :

Molar density of Fe3O4

\(f\) :

Fraction of conversion by oxidation for the concentrate

\({d}_{p}\) :

Diameter of pellet

\(t\) :

Isothermal time

\(a\) :

Avrami rate constant

\(n\) :

Avrami time exponent

\(K\) :

Arrhenius reaction rate constant

\({K}_{0}\) :

Pre-exponential factor

\(Q\) :

Activation energy

\(R\) :

Ideal gas constant

\({N}\rho\) :

Density

\({C}_{p}\) :

Specific heat capacity

\({k}_{eff}\) :

Effective conductivity

\({H}_{Gen}\) :

Heat generation corresponding to local rate of oxidation

\({N}\sigma\) :

Staffan-Boltzmann constant

\({N}\varepsilon\) :

Emissivity

γ :

Sintering extent

\({{N}\gamma }_{total}\) :

Total sintering extent

\({{N}\gamma }_{hem}\) :

Sintering extent of hematite phase

\({\gamma }_{mag}\) :

Sintering extent of magnetite phase

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Acknowledgments

Authors thank the Hjalmar Lundbohm Research Centre (HLRC) for financially supporting the development as part of Ph.D. project, and thereafter the funding from Centre of Advanced Mining and Metallurgy (CAMM) and the strategic innovation program Swedish Mining Innovation (SMI), a joint venture by Vinnova, Formas and the Swedish Energy Agency to support the continued development is highly appreciated. Authors would like to extend their gratitude towards Ola Eriksson and Daniel Marjavaara, LKAB and Anders Dahlin, Alteco System (formerly LKAB) for their technical inputs in planning the experiments and developing the model. Appreciation are also due to Christer Stenström, Staffan Hedvall and Hamid Sefidari of LKAB Metlab, Lulea, Sweden for sample preparation for the microstructural evaluation.

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Authors and Affiliations

  1. Research and Product Development, Luossavaara Kiirunavaara Aktiebolag (LKAB), Luleå, Sweden

    T. K. Sandeep Kumar & A. Eriksson

  2. Mineral and Metals Processing Research Laboratory, Lulea University of Technology, Luleå, Sweden

    N. N. Viswanathan, A. Eriksson, C. Andersson & H. Ahmed

  3. Metallurgical Engineering & Materials Science, Indian Institute of Technology Bombay, Mumbai, India

    N. N. Viswanathan

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Sandeep Kumar, T.K., Viswanathan, N.N., Eriksson, A. et al. Development of Single Pellet Induration Model for Magnetite Pellet: A Holistic Approach. Metall Mater Trans B 54, 2951–2964 (2023). https://doi.org/10.1007/s11663-023-02879-1

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