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A Mathematical Model for Straight-Grate Iron Oxide Pellet Induration Furnace: Formulation, Plant Scale Validation, Implementation and Control

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Abstract

In this work, a mathematical model for the straight-grate pellet induration furnace is presented. The induration furnace is an equipment used for the efficient heat and mass transfer between the pellet bed and the flowing gas. The model includes different physicochemical phenomenon like gas-solid heat and mass transfer, drying and condensation of free surface moisture, combustion of carbon, calcination of limestone and kinetics of loss of ignition (LOI) removal from hydrated iron ore. The model is validated with the experimental and numerical data available in the literature. For the first time, an extended validation of the model against the plant scale ThermoCar (T-CAR) test is also presented. The developed model is implemented at AM/NS India pellet plants including the model assisted control to the online furnace operation. The effect of change in different furnace operating parameters on the thermal and chemical state of the pellet bed inside the furnace can be easily evaluated from the model results. The model can be used as an offline tool for optimizing the furnace parameters, increasing plant productivity, improving fired pellet properties, pilot run of new product mix, operator training purpose and as an online visualization tool for the better operational control and stability.

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Abbreviations

\(A_\textrm{s}\) :

Specific contact surface area (\(\hbox {m}^2/\hbox {m}^3\)) (\(A_\textrm{s}=6(1-\varepsilon _\textrm{b})/\phi d_\textrm{p}\))

\(C_{j}\) :

Concentration of the gas species j (\(\hbox {kmol}/\hbox {m}^3\))

\(C_{j}^{\textrm{e}}\) :

Equilibrium concentration the gas species j (\(\hbox {kmol}/\hbox {m}^3\))

\(C_{\textrm{pg}}\) :

Specific heat of gas (\(\hbox {J/kg}{\,} \hbox {K}\))

\(C_{\textrm{ps}}\) :

Specific heat of solid (\(\hbox {J/kg}{\,} \hbox {K}\))

\(D_{j}\) :

Diffusivity of the gas species j (\(\hbox {m}^2/\hbox {s}\))

\(D_{j}^{\textrm{eff}}\) :

Effective diffusivity of the gas species j (\(\hbox {m}^2/\hbox {s}\))

\(d_\textrm{p}\) :

Mean pellet diameter (m)

G :

Superficial gas flow rate (\(\hbox {kg}/\hbox {m}^2{\,} \hbox {s}\))

\(\Delta H_j\) :

Enthalpy of reaction j (J/kg)

\(h_{\textrm{gs}}\) :

Effective heat transfer co-efficient (\(\hbox {J/m}^2{\,} s{\,} \hbox {K}\))

\(K_{\textrm{H}_{2}\textrm{O}}\) :

Water mass transfer co-efficient (m/s)

\((k_{\textrm{ch}})_\textrm{c}\) :

Chemical reaction rate constant for coke combustion (m/s)

\((k_{\textrm{ch}})_\textrm{l}\) :

Chemical reaction rate constant for limestone calcination (m/s)

\(k_{\textrm{m}{\left( j\right) }}\) :

Mass transfer co-efficient of the gas species j (m/s)

\(M_{j}\) :

Molecular weight of the solid-bed species j (\(\hbox {kg}/\hbox {mol}\))

Nu :

Nusselt number (\(Nu=h_{\textrm{gs}}d_\textrm{p}/\lambda _{\textrm{g}}\))

\(P'\) :

Total pressure (Pa)

p :

Absolute gas pressure (Pa)

\(p_{\textrm{H}_{2}\textrm{O}}\) :

Water vapour partial pressure (Pa)

Pr :

Prandtl number (\(Pr=\mu _\textrm{g} \hbox {C}_{\textrm{pg}}/\lambda _{\textrm{g}}\))

\(p_{\textrm{v}_{\textrm{sat}}}\) :

Water vapour saturation pressure (Pa)

\(R_\textrm{C}\) :

Rate of coke combustion (\(\hbox {kg}/\hbox {m}^3{\,} \hbox {s}\))

Re :

Reynolds number (\(Re=Gd_\textrm{p}/\mu _{\textrm{g}}\))

\(R_{\textrm{CaCO}_3}\) :

Rate of limestone calcination (\(\hbox {kg}/\hbox {m}^3{\,} \hbox {s}\))

\(R_{\textrm{H}_{2}\textrm{O}}\) :

Rate of moisture drying/condensation (\(\hbox {kg}/\hbox {m}^3{\,} \hbox {s}\))

\(R_{\textrm{LOI}}\) :

Rate of LOI removal (\(\hbox {kg}/\hbox {m}^3{\,} \hbox {s}\))

\(R_\textrm{u}\) :

Universal gas constant (\(\hbox {J}/\hbox {mol}{\,} \hbox {K}\))

\(r_0\) :

Mean particle radius (m)

\(r_\textrm{c}\) :

Unreacted coke particle core radius (m)

\(r_\textrm{l}\) :

Unreacted limestone particle core radius (m)

Sc :

Schmidt number (\(Sc=\mu _{\textrm{g}}/\rho _{\textrm{g}}D_i\))

Sh :

Sherwood number (\(Sh=2+0.6Sc^{1/3}(Re/\epsilon _\textrm{b})^{1/2}\))

\(T_\textrm{g}\) :

Temperature of gas (K)

\(T_\textrm{s}\) :

Temperature of pellet (K)

\(T_{\textrm{rec}}\) :

Re-circulation gas temperature (K)

t :

Time (s)

\(t_{\textrm{stop}}\) :

Time corresponding to end of furnace length (s)

\(W_{j}\) :

Mass fraction of flowing gas species j (\(\hbox {kg}/\hbox {kg}\))

\(W_{\textrm{rec}}\) :

Mass fraction of recirculating gas species (\(\hbox {kg}/\hbox {kg}\))

\(Y_{\textrm{cr}}\) :

Critical moisture content in solid-bed (\(\hbox {kg}/\hbox {kg}\))

\(Y_{\textrm{H}_{2}\textrm{O}}\) :

Mass fraction of moisture content in solid-bed (kg/kg)

\(Y_j\) :

Mass fraction of solid-bed species j (kg/kg)

y :

Pellet bed height direction (m)

\(\alpha \) :

Reaction heat factor

\(\alpha _{\textrm{LOI}}\) :

LOI fraction conversion

\(\beta \) :

Factor of drying/condensation kinetics

\(\varepsilon _\textrm{b}\) :

Bed void fraction

\(\mu _\textrm{g}\) :

Viscosity of gas (\(\hbox {kg}/\hbox {m}{\,} \hbox {s}\))

\(\nu _j\) :

Stoichiometric coefficient of solid-bed reactant j

\(\rho _\textrm{g}\) :

Density of gas (\(\hbox {kg}/\hbox {m}^3\))

\(\rho _\textrm{s}\) :

Bulk density of solid-bed (\(\hbox {kg}/\hbox {m}^3\))

\(\lambda _{\textrm{g}}\) :

Thermal conductivity of gas (\(\hbox {J/m}{\,} \hbox {s}{\,} \hbox {K}\))

\(\lambda _{\textrm{s}}\) :

Thermal conductivity of solid (\(\hbox {J/m}{\,} \hbox {s}{\,} \hbox {K}\))

\(\phi \) :

Sphericity of pellet

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Acknowledgements

The authors would like to thank the management of Arcelormittal Nippon Steel India Limited (AM/NS India) for granting permission of the present model development. The authors also want to show their gratitude to AM/NS India Paradeep and Visakhapatnam pellet plants operation and instrumentation team for conducting plant scale ThermoCar testing and supporting the model implementation.

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Authors and Affiliations

  1. Research and Development, ArcelorMittal Nippon Steel India Limited (AM/NS India), Hazira, Surat, Gujarat, 394270, India

    Sagar Dave, Satyananda Patra, Yogesh Bapat, Gautam Banerjee & Sirshendu Chattopadhyay

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Correspondence to Satyananda Patra.

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Appendix: Auxiliary Equations Used in the Present Model

Appendix: Auxiliary Equations Used in the Present Model

Some correlations from the literature were used in the present model formulation to calculate temperature dependent thermodynamic and transport properties of gas and solid phases.

$$\begin{aligned} C_{\textrm{pg}}&=881+0.31T_\textrm{g}-7.98\times 10^{-5}T_\textrm{g}^2 \text {(Dash et al. [38])}{} & {} \\ C_{\textrm{ps}}&= {\left\{ \begin{array}{ll}341.6+1.324T_{\textrm{s}}-4.032\times 10^{-4}T_{\textrm{s}}^{2} &{}; T_\textrm{s}\le 950.15\\ 1111&{};950.15<T_\textrm{s}\le 1050.15\\ 999+0.0461T_\textrm{s}&{}; T_\textrm{s}>1050.15 \text {(Thurlby et al. [5])} \end{array}\right. }{} & {} \\ \hbox {CO}_{2}^{\textrm{e}}&=\frac{12.187}{T_{\textrm{s}}}\exp \left( 7.35-\frac{5211}{T_{\textrm{s}}}\right) \text {(Majumder et al. [7])}{} & {} \\ D_{\textrm{CO}_2}&=7.166\times 10^{-10}T_\textrm{g}^{1.75} \text {(Majumder et al. [7])}{} & {} \\ D_{\textrm{O}_2}&=\frac{9.45\times 10^{-5}T_\textrm{g}^{1.75}}{P'} \text {(Englund et al. [12])}{} & {} \\ \mu _\textrm{g}&=1.72\times 10^{-5}\left( \frac{T_\textrm{g}}{273.15}\right) ^{1.5}\left( \frac{386.15}{113+T_\textrm{g}}\right) \text {(Dash et al.[38])}{} & {} \\ \lambda _{\textrm{g}}&=\frac{0.00211T_\textrm{g}^{1.5}}{123.6+T_\textrm{g}} \text {(Kucukada et al. [6])}{} & {} \\ p_{v_{\textrm{sat}}}&=\exp \left( 25.541-\frac{5211}{T_\textrm{s}}\right) \text {(Patisson et al. [28])}{} & {} \end{aligned}$$

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Dave, S., Patra, S., Bapat, Y. et al. A Mathematical Model for Straight-Grate Iron Oxide Pellet Induration Furnace: Formulation, Plant Scale Validation, Implementation and Control. JOM 75, 2406–2420 (2023). https://doi.org/10.1007/s11837-023-05819-1

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