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Licensed Unlicensed Requires Authentication Published by De Gruyter September 21, 2018

CH4 Direct Reduction of In-Flight Fe3O4 Concentrate Particles

Bahador Abolpour, M. Mehdi Afsahi and Ataallah Soltani Goharrizi


In this study, reduction of in-flight fine particles of magnetite ore concentrate by methane at a constant heat flux has been investigated both experimentally and numerically. A 3D turbulent mathematical model was developed to simulate the dynamic motion of these particles in a methane content reactor and experiments were conducted to evaluate the model. The kinetics of the reaction were obtained using an optimizing method as: [-Ln(1-X)]1/2.91 = 1.02 × 10−2dP−2.07CCH40.16exp(−1.78 × 105/RT)t. The model predictions were compared with the experimental data and the data had an excellent agreement.

List of Symbols


Required parameters to determine the particles drag coefficient (CD) [20]


Cunningham correction to Stokes drag law, defined asCC=1+2λdP1.257+0.4e1.1dP2λ


Methane concentration (mol.m−3)


Drag coefficient of the particle [21]: CD=24Rep1+b1Repb2+b3Repb4+Rep


Heat capacity of the gas (−1.K−1)


Reactor tube inside diameter (m)


Strain tensors of fluid: dij=12uixj+ujxi,dik=12uixk+ukxi


Particle diameter (m)


Activation energy of the reaction (J.mol−1.K−1)


Brownian force (N.m1) [22]: FB=ξ0πS0Δt


Drag force vector (N.m−1)[17]: FD=18μCDRep24ρpdp2VVp


Lift force vector (N.m−1) [16]: FL=2Kυ0.5ρdijρpdpdijdik0.25VVp


Thermophoresis force (N.m−1) [23]: FTh=9πdpμ2HT2ρTp


Acceleration caused by an external physical force (m.s−2): here only the gravitational acceleration is applied in the z direction


A coefficient [23]: H=kkp+4.4λdp1+6λdp1+2kkp+8.8λdp


Constant: K=2.594


Thermal conductivity of fluid (W.m−1.K−1)


Thermal conductivity of particle (W.m−1.K−1)


Boltzmann constant


Mass of the escaped particle (kg) with conversion of Xep


Pressure (Pa)


Radiation heat flux (w)


Universal gas constant (Pa.m3.mol−1.K−1)


Reynolds number of the particles: Rep=ρdpVpVμ


Spectral intensity defined as: S0=216νkBTρπ2dP2CCρPρ2


Stokes number: Stk=ρpdp2V18μD


Time (s)


Fluid temperature (K)


Particle temperature (K)


The components of the instantaneous fluid velocity vector (m.s−1): u, v, w


The three components of the average velocity vector (m.s−1): u,v,w


Reynolds stress components (m2.s−2): uv,uw,vw,u2,v2,w2


Fluid velocity vector (m.s−1)


Particle velocity vector (m.s−1)


Weight of the solid particles (N)


Solid conversion


Particle position vector (m)

xi,xj, xk

Three components of the position vector (m): x, y, z


Volumetric thermal expansion coefficient of fluid (K−1)


Kronecker delta: δij=1i=j0ij

εikm, εjkm

Equal to 1 if i, j, k be in cyclic order, equal to −1 if i, j, k be in anti-cyclic order and equal to 0 in case any two indices are same


Zero-mean, unit-variance-independent Gaussian random number


The mean free path of gas molecules (m)


Viscosity of the gas (Pa.s)


Density of the fluid (kg.m−3)


The density of the iron concentrate (kg.m−3)


Kinematic viscosity of fluid (m2.s)


Electrical resistance (ohm)


Rotation vector


The authors acknowledge the financial support of Golgohar iron ore and steel research institute, Sirjan, Iran, under the grant number 92.2501.


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Received: 2018-07-04
Revised: 2018-08-26
Accepted: 2018-08-28
Published Online: 2018-09-21

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