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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

Abstract

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

b1,b2,b3,b4

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

CC

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

CCH4

Methane concentration (mol.m−3)

CD

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

Cp

Heat capacity of the gas (J.kg−1.K−1)

D

Reactor tube inside diameter (m)

dij,dik

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

dp

Particle diameter (m)

E

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

FB

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

FD

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

FL

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

FTh

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

gi

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

H

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

K

Constant: K=2.594

k

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

kp

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

kB

Boltzmann constant

mep

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

P

Pressure (Pa)

qr

Radiation heat flux (w)

R

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

Rep

Reynolds number of the particles: Rep=ρdpVpVμ

S0

Spectral intensity defined as: S0=216νkBTρπ2dP2CCρPρ2

Stk

Stokes number: Stk=ρpdp2V18μD

t

Time (s)

T

Fluid temperature (K)

Tp

Particle temperature (K)

ui

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

ui,uj,uk

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

uiuj

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

V

Fluid velocity vector (m.s−1)

Vp

Particle velocity vector (m.s−1)

W

Weight of the solid particles (N)

X

Solid conversion

xp

Particle position vector (m)

xi,xj, xk

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

β

Volumetric thermal expansion coefficient of fluid (K−1)

δij

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

ξ0

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

λ

The mean free path of gas molecules (m)

µ

Viscosity of the gas (Pa.s)

ρ

Density of the fluid (kg.m−3)

ρp

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

υ

Kinematic viscosity of fluid (m2.s)

Ω

Electrical resistance (ohm)

Ωk

Rotation vector

Acknowledgements

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

References

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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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