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Computational Fluid Dynamics Simulation of the Hydrogen Reduction of Magnetite Concentrate in a Laboratory Flash Reactor

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Abstract

A three-dimensional computational fluid dynamics (CFD) model was developed to study the hydrogen reduction of magnetite concentrate particles in a laboratory flash reactor representing a novel flash ironmaking process. The model was used to simulate the fluid flow, heat transfer, and chemical reactions involved. The governing equations for the gas phase were solved in the Eulerian frame of reference while the particles were tracked in the Lagrangian framework. The change in the particle mass was related to the chemical reaction and the particle temperature was calculated by taking into consideration the heat of reaction, convection, and radiation. The stochastic trajectory model was used to describe particle dispersion due to turbulence. Partial combustion of H2 by O2 injected through a non-premixed burner was also simulated in this study. The partial combustion mechanism used in this model consisted of seven chemical reactions involving six species. The temperature profiles and reduction degrees obtained from the simulations satisfactorily agreed with the experimental measurements.

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Abbreviations

A :

Pre-exponential factor of combustion reaction

A p :

Surface area of a particle (m2)

c p :

Specific heat of species (J kg−1 K−1)

C D :

Particle drag coefficient

d p :

Geometric mean diameter of the screened particle (m)

D i,m :

Mass diffusion coefficient for species i in the mixture (m2 s−1)

D T,i :

Thermal diffusion coefficient (kg m−1 s−1)

E :

Activation energy (kJ mol−1)

E p :

Equivalent emission due to the presence of particles (W m−3)

F p,i :

Volumetric momentum exchange rate between the continuum phase and discrete phase (N m−3)

g i :

Gravitational acceleration (m s−2)

G k :

Kinetic energy generation rate due to the mean velocity gradients per unit volume (J m−3 s−1)

G b :

Kinetic energy generation rate due to buoyancy per unit volume (J m−3 s−1)

h :

Convective heat transfer coefficient (W m−2 K−1)

h g :

Sensible heat of the gas mixture (J kg−1)

I :

Radiative intensity (W m−2)

k :

Turbulent kinetic energy (J kg−1)

k b :

Backward reaction rate constant

k eff :

Effective thermal conductivity (W m−1 K−1) = k g + k t

k f :

Forward reaction rate constant

k g :

Gas thermal conductivity (W m−1 K−1)

k o :

Pre-exponential factor for the reduction reaction of concentrate by H2 (atm−1 s−1)

K e :

Equilibrium constant

m p :

Particle mass (kg)

\( m_{\text{p}}^{0} \) :

Initial particle mass (kg)

M w,i :

Molecular weight of species i (kg mol−1)

p :

Pressure (Pa)

p i :

Partial pressure of species i (atm)

Q r :

Net rate of heat addition by radiation per unit volume (W m−3)

R i :

Net rate of production of species i by chemical reaction (kg m−3 s−1)

Sc t :

Turbulent Schmidt number

S g :

Net rate of heat generation per unit volume (W m−3)

S p :

Net rate of mass addition to the gas phase per unit volume (kg m−3 s−1)

S p,i :

Net rate of addition of species i from the particle phase (kg m−3 s−1)

T :

Gas phase temperature (K)

T iso :

Isothermal zone temperature (K)

T p :

Particle temperature (K)

u i :

gas phase velocity components (m s−1)

u p :

Particle velocity (m s−1)

X :

Reduction degree

Y i :

Mass fraction of species i

ε :

Turbulence dissipation rate (J kg s−1)

ε p :

Particle emissivity

κ :

Absorption coefficient of the gas mixture (1 m−1)

κ p :

equivalent absorption coefficient due to the particle presence (1 m−1)

μ :

Gas phase viscosity (kg m s−2)

μ t :

Turbulent viscosity (kg m s−2)

ρ :

Gas phase density (kg m−3)

ρ p :

Particle density (kg m−3)

σ :

Stefan–Boltzmann constant (W m−2 K−4)

σ p :

equivalent particle scattering factor (1 m−1)

σ ij :

Kronecker delta

Φ:

Dissipation function (J kg−1 m2)

ω O,i :

The initial mass fraction of iron-bonded oxygen in magnetite concentrate particle

Ω:

Solid angle (sr)

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Acknowledgments

The technical support and resources provided by the Center for High Performance Computing at the University of Utah are gratefully acknowledged. The authors acknowledge the financial support from the U.S. Department of Energy under Award Number DE-EE0005751 with cost share by the American Iron and Steel Institute (AISI) and the University of Utah.

Disclaimer

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, expresses or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Author information

Authors and Affiliations

  1. Department of Metallurgical Engineering, University of Utah, Salt Lake City, UT, 84112, USA

    De-Qiu Fan (Graduate Student), H. Y. Sohn (Distinguished Professor), Yousef Mohassab (Research Associate) & Mohamed Elzohiery (Graduate Student)

Authors
  1. De-Qiu Fan
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  2. H. Y. Sohn
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  3. Yousef Mohassab
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  4. Mohamed Elzohiery
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Correspondence to H. Y. Sohn.

Additional information

Manuscript submitted April 1, 2016.

Appendices

Appendix A: Physical Properties of the Particle and Equilibrium Constant

Physical properties of particle:

$$ {\text{Density}}:\;\rho_{p,0} = 5170\,{\text{kg}}\,{\text{m}}^{ - 3}. $$

The specific heat for Fe3O4 and Fe are evaluated by the general expression as[37] (J kg−1 K−1)

$$ c_{{{\text{p}},{\text{Fe}}_{3} {\text{O}}_{4} \,{\text{or}}{\kern 1pt} {\text{Fe}}}} = a_{1} - a_{2} T/1000 + 100,000 \cdot a_{3} T^{ - 2} - a_{4} T^{2} /1,000,000. $$

The values of the coefficients of Fe3O4 are

  • 298 K (25 °C) < T ≤ 850 K (577 °C)

    $$ a_{1} = 2052.42,\;a_{2} = - 3773.30,\;a_{3} = - 520.52,\,a_{4} = 3458.30; $$

  • 850 K (577 °C) < T ≤ 1870 K (1597 °C)

    $$ a_{1} = 215.20,\;a_{2} = 313.27,\;a_{3} = 3695.00,\;a_{4} = 0; $$

  • 1870 K (1597 °C) < T

    $$ a_{1} = 921.59,\;a_{2} = 0,\;a_{3} = 0,a_{4} = 0. $$

The values of the coefficients of Fe are

  • 100 K (−173 °C) < T ≤ 298 K (25 °C)

    $$ a_{1} = 355.75,\;a_{2} = 393.42,\;a_{3} = - 17.79,\;a_{4} = - 57.17; $$

  • 298 K (25 °C) < T ≤ 800 K (527 °C)

    $$ a_{1} = 570.72,\;a_{2} = - 399.89,\;a_{3} = - 63.01,\;a_{4} = 717.61; $$

  • 800 K (527 °C) < T ≤ 1043 K (770 °C)

    $$ a_{1} = 16,663.82,\;a_{2} = - 25,880.11,\;a_{3} = - 19,295.30,\;a_{4} = 12,117.48; $$

  • 1043 K (770 °C) < T ≤ 1185 K (912 °C)

    $$ a_{1} = - 241,188.85,\;a_{2} = 283,943.72,\;a_{3} = 523,025.09,\;a_{4} = - 93,852.75; $$

  • 1185 K (912 °C) < T ≤ 1667 K (1394 °C)

    $$ a_{1} = 442.58,\;a_{2} = 133.64,\;a_{3} = - 30.45,\;a_{4} = 6.58; $$

  • 1667 K (1394 °C) < T ≤ 1881 K (1608 °C)

    $$ a_{1} = - 190.41,\;a_{2} = 553.94,\;a_{3} = 4927.14,\;a_{4} = - 67.88; $$

  • 1881 K (1608 °C) < T

    $$ a_{1} = 823.68,\;a_{2} = 0,\;a_{3} = \, 0,\;a_{4} = 0. $$

Equilibrium constant:

The equilibrium constant K e data was obtained from the HSC chemistry 5.11 software package[37] and was fit to a polynomial form as follows:

$$ K_{\text{e}} = b_{1} T^{7} + b_{2} T^{6} + b_{3} T^{5} + b_{4} T^{4} + b_{5} T^{3} + b_{6} T^{2} + b_{7} T + b_{8}, $$

where

  • T ≤ 1649 K (1376 °C)

    $$ b_{1} = 1.60e - 21,\;b_{2} = - 1.01e - 17,\;b_{3} = 2.54e - 14,\;b_{4} = - 3.16e - 11; $$
    $$ b_{5} = 1.90e - 08,\;b_{6} = - 3.37e - 06,\;b_{7} = - 5.88e - 04,\;b_{8} = 1.74e - 01; $$

  • 1649 K (1376 °C) < T ≤ 1811 K (1538 °C)

    $$ b_{1} = 0,\;b_{2} = 0,\;b_{3} = 0,\;b_{4} = \, 0 $$
    $$ b_{5} = 0,\;b_{6} = 7.75e - 07,\;b_{7} = - 3.43e - 03,\;b_{8} = 4.41; $$

  • 1811 K (1538 °C) < T

    $$ b_{1} = 0,\;b_{2} = 0,\;b_{3} = 0,\;b_{4} = 0; $$
    $$ b_{5} = 0,\;b_{6} = 8.89e - 08,\;b_{7} = - 6.02e - 04,\;b_{8} = 1.53. $$

Appendix B

See Table BI.

Table BI Experimental and Simulation Results of Different Runs in the Laboratory Flash Reactor
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Fan, DQ., Sohn, H.Y., Mohassab, Y. et al. Computational Fluid Dynamics Simulation of the Hydrogen Reduction of Magnetite Concentrate in a Laboratory Flash Reactor. Metall Mater Trans B 47, 3489–3500 (2016). https://doi.org/10.1007/s11663-016-0797-4

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