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Numerical Modeling Simulation and Experimental Study of Dynamic Particle Bed Counter Current Reactor and Its Effect on Solid–Gas Reduction Reaction

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Mill scale is an oxide waste product of the steel mills, which contains around 70% iron and other allied impurities. In the present context, a dynamic prototype counter current reactor (CCR) has been used for experimentation and simulation of particle bed by using discrete element method (DEM). Mill scale was pulverized to ASTM mesh range 140 (106 µm)/ + 270 (53 µm), and then it was oxidized in CCR to make single oxide Fe2O3 phase by maintaining required thermodynamic conditions such as pure oxygen at 1100 °C. Then this oxidized powder was subjected to reduction reaction in CCR having gas mixture (H2:N2) ratio of 1:4 at 875 ± 5 °C for filling degree (fd) and reactor revolution (ω) ranging from 5.38 to 16.14% and 2 to 5 rpm, respectively. A creeping fluid flow condition (Re ˂ 1) and natural heat convection (Gr/Re2 ˃˃ 1) has been maintained while undergoing solid–gas reaction. Besides particle bed behavior has been quantified by Froude number (Fr) for the optimum operating window. The simulation was validated by the experimental results of reactor reaction product by X-ray diffraction (XRD) and scanning electron microscope (SEM) images. Prevailing heat transfer mechanism and reduction reaction mechanism has been established for solid–gas counter current conditions.

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\({V}_{bulk}\),\({V}_{reactor}\) :

The bulk volume and reactor volume in (mm3)

De, Ds :

Diameter of the experimental and simulation geometry (mm)

Le, Ls :

Length of the experimental and simulation geometry (mm)

\(F\_n and F\_t\) :

Inter-particle normal and tangential forces acting on the particle

\({F}_{i}\) :

Out of balance force of the particle

\({v}_{i}\) :

Translational velocity

\({\omega }_{i}\) :

Rotational velocity

m :

Mass of the particle

\({M}_{i}\) :

Out of balance contact due to momentum

I :

Rotational inertia of the particle

dt :

Time step


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The authors acknowledge Mohan S. Nainegali, CAEZEN Technologies for their EDEM software support.

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Appendix 1

*Calculation of the volume of CCR reactor and volume of bulk.

With Ref. from Table 1 and Fig. 3

Justification for scaling and calculation of number of particles for simulation:

Filling degree defined as


Calculation of the volume of CCR reactor and volume of bulk.

\({V_{reactor}={\Pi R}_e}^2{\mathrm{L}}_\mathrm{e}=10995574\text{ mm}^3.\)  

Mass of the bulk (oxidized mill scale) (ṁ) = 1 kg = 1000 g.

\({\rho }_{e}\)= experimentally calculated apparent density of the oxidized mill scale (Fe2O3) = 1.69 g/cc.

$${{V}}_{{bulk}}=\frac{\dot{\mathrm{m}}}{{\rho }_{e}} = \frac{1000 g}{1.69 g/cc}=592 cc=592000 {mm}^{3}$$
$$\mathrm{V}\;\text{single spherical particle}=\frac43\Pi\times r_e^3=0.5235{mm}^3$$
$$\text{Total number of the particle}=\frac{V_{bulk}}{V_{single\;particle}}=\frac{592000}{0.5235}=1130850$$

After performing calculations, the total number of particles for experimentation were found to be 113,850. This is a large number of particles which increase computational time and effort for simulation. Thus, both bulk and reactor volume have been scaled down 100 times from its original volume for simulation.

$${f}_{d}=\frac{{V}_{bulk}}{{V}_{reactor}}=\frac{592000\times \frac{1}{100}}{10995574\times \frac{1}{100}}=\frac{5920}{109956} = 5.38{ \%}$$
$${f}_{d}=\frac{{V}_{bulk}}{{V}_{reactor}}=\frac{5920}{109956}\times 100=5.38 \%$$

Calculation of the number of the particles in the simulation

$$\text{No of particles}=\frac{V_{bulk}}{V_{single\;particle}}=\frac{5920}{0.5235}=11300$$

Subsequent it calculated for 2 and 3 kg (Table 6),

Table 6 Calculation of the filling degree and no. of particles for simulation

Appendix 2

*Calculation of mix thermal conductivity

H2 and N2 gas containing 20 mol % of H2 and 80 mol % of N2 at temperature 1148 K. using \({K}_{{H}_{2}}=0.48\) \(W/mK {K}_{{N}_{2}}=0.05\) \(W/mK\)[32]

$${K}_{mix(H2-N2)}= \frac{\sum_{i}{X}_{i }{K}_{i }{{M}_{i }}^{{~}^{1}\!\left/ \!\!{~}_{3}\right.}}{\sum_{i}{X}_{i }{{M}_{i }}^{0{~}^{1}\!\left/ \!\!{~}_{3}\right.}}$$
$${K}_{mix(H2-N2)}= \frac{\left(0.2\right)\left(0.48\right){\left(2\right)}^{{~}^{1}\!\left/\!\!{~}_{3}\right.}+\left(0.8\right)\left(0.05\right){\left(28\right)}^{{~}^{1}\!\left/\!\!{~}_{3}\right.}}{\left(0.2\right){\left(2\right)}^{{~}^{1}\!\left/\!\!{~}_{3}\right.}+\left(0.8\right)\left(0.05\right)}$$
$${K}_{mix(H2-N2)}={K}_{f}= 0.08 W/mK$$
$${K}_{s}/{K}_{f}\gg 1$$

Thermal conductivity of H2: N2 (1:4) = 0.08 W/mK.

Thermal conductivity of FeO (wustite) = 2.2 W/mK

$${~}^{{K}_{s}}\!\left/\!\!{~}_{{K}_{f}}\right.=27.5\gg 1$$

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Jikar, P.C., Dhokey, N.B. & Shinde, S.S. Numerical Modeling Simulation and Experimental Study of Dynamic Particle Bed Counter Current Reactor and Its Effect on Solid–Gas Reduction Reaction. Mining, Metallurgy & Exploration 39, 139–152 (2022).

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