Validation of CFD–DEM model for iron ore reduction at particle level and parametric study

G Model PARTIC-1303; No. of Pages 10

ARTICLE IN PRESS Particuology xxx (2019) xxx–xxx

Contents lists available at ScienceDirect

Particuology journal homepage: www.elsevier.com/locate/partic

Validation of CFD–DEM model for iron ore reduction at particle level and parametric study E Dianyu a,b,∗ a b

International Research Institute for Minerals, Metallurgy and Materials, Jiangxi University of Science and Technology, Nanchang 330013, China Department of Chemical Engineering, Monash University, Clayton, VIC 3800, Australia

a r t i c l e

i n f o

Article history: Received 11 April 2019 Received in revised form 20 September 2019 Accepted 23 October 2019 Available online xxx Keywords: Iron ore reduction Chemical reaction Blast furnace Discrete element method Computational fluid dynamics

a b s t r a c t Iron ore reduction is a primary unit operation in current metallurgy processes and dominates the energy consumption and greenhouse gas (GHG) emissions of the iron-making process. Therefore, even a slight improvement of the energy efficiency or GHG emissions of iron ore reduction would yield considerable benefits to the cost of pig iron and, more importantly, to mitigation of the associated carbon footprint. The current study presents a discrete model that describes the iron ore reduction process for a single pellet. The transient reaction progress can be predicted and is validated against experimental measurements under various operating conditions, including different reducing gases and temperatures. The effects of pressure, isothermality, gas composition, and flow rate on reduction are investigated. The reduction rate increases significantly with increasing pressure until 5 atm, and the entire reduction process occurs more slowly under non-isothermal conditions than under isothermal conditions. This work provides a solid foundation for the development of a comprehensive particulate system model that considers both heat and mass transfer. © 2019 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

Introduction Iron ore reduction is a major unit operation in metallurgical processing, such as in the widely used blast furnace process and other novel iron-making processes, including the Corex, Finex, Midrex, and HIsmelt processes. Iron ore reduction dominates the energy consumption and greenhouse gas (GHG) emissions of the ironmaking process. In particular, the blast furnace together with the associated units, including sintering pelletizing machines and a coke oven, contribute approximately 90% of the CO2 emissions and 70% of the energy consumption in an integrated steelwork (Orth, Anastasijevic, & Eichberger, 2007; Xu & Cang, 2010). With such large ratios, even slight improvement of the energy efficiency or GHG emissions of iron ore reduction would yield considerable benefits to the cost of pig iron and, more importantly, to mitigation of the associated carbon footprint (Dong, Yu, Yagi, & Zulli, 2007). Therefore, achieving a higher efficiency of iron ore reduction has

∗ Correspondence to: International Research Institute for Minerals, Metallurgy and Materials, Jiangxi University of Science and Technology, Nanchang 330013, China. E-mail address: [email protected]

been continuously pursued in the past few decades (Naito, Takeda, & Matsui, 2015). The reduction performance can be investigated macroscopically in experimental studies, with the knowledge gained contributing to advancing our understanding of the kinetics of the reduction process (McKewan, 1960; Moriyama, Yagi, Muchi, & Tamura, 1965; Moriyama, Yagi, & Muchi, 1967; Ohmi & Usui, 1973; Yagi & Ono, 1968), which is beneficial for the development of numerical models used to examine the process in detail (Dong, Yu, Chew, & Zulli, 2010; Hou, E, Kuang, Li, & Yu, 2017; Kuang, Li, Yan, Qi, & Yu, 2014; Kuang, Li, & Yu, 2018; Peters & Hoffmann, 2016). Currently, mathematical modelling, often assisted by physical modelling, has become a promising alternative in this field. The two major numerical approaches presently being widely employed to describe such a gas–solid flow in the iron-making process are continuum approaches at a macroscopic level and discrete ones at the microscopic level. Compared with the continuum approach, the discrete method treats particles as discrete phases using the discrete element method (DEM) and the gas phase as a continuous one using computational fluid dynamics (CFD), yielding the so-called coupled CFD–DEM approach. This approach has been considered a tool for the development of a more reliable mathematical model for process control and optimization because it can generate microscopic information for individual particles without the introduction

https://doi.org/10.1016/j.partic.2019.10.008 1674-2001/© 2019 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

Please cite this article in press as: Dianyu, E. Validation of CFD–DEM model for iron ore reduction at particle level and parametric study. Particuology (2019), https://doi.org/10.1016/j.partic.2019.10.008

G Model PARTIC-1303; No. of Pages 10

ARTICLE IN PRESS E. Dianyu / Particuology xxx (2019) xxx–xxx

2

Nomenclature

Nomenclature

a Ac

Greek letters εo Porosity of iron ore, –  Labyrinth factor, – ın Relative normal displacement at contact, m Relative tangential displacement at contact, m ıt

Af Aw c cn ct Cp Cd0,i Ci,m Dm Ds l e ef E*  Ef , Ef fs ◦ H298 kfl kl kV k Kl L mij n Nc , No Pr R* rc Rl∗ Ri , Rj Ri , Rj Rij Rei Tf Tf, Ti , Tj Tlocal,I t tc vij vn ,ij vt ,ij VB V ym ∗ ym

Constant for the calculation of convective heat flux Effective surface area of coke particle for reaction, m2 Side surface area of a computational cell with unit thickness, m2 Surface area of wall, m2 Constant for the calculation of the conductive heat flux Normal damping coefficient, – Tangential damping coefficient, – Heat capacity change of a corresponding chemical reaction, kJ/(kg·K) Fluid drag force coefficient on an isolated particle i, – Concentration of m species in particle i, mol/m3 Diffusion coefficient of reducing gas m, m2 /s Intraparticle diffusion coefficient in l-th chemical reaction, m2 /s Sphere emissivity, – Fluid emissivity, – Equivalent Young’s modulus, Pa Effectiveness factors of solution-loss reactions by CO and H2 , – Reduction degree of ore particle, – Standard enthalpy change of formation, kJ/mol Gas–film mass transfer coefficient in l-th chemical reaction, m/s Rate constant of l-th chemical reaction, m/s (l = 1,2,6), m3 /(kg·s) (l = 3,4), m4 /(mol s) (l = 5) Number of particles in a computational cell, – Number of particles in a domain , – Equilibrium constant of l-th chemical reaction, – Characteristic length of wall, m Equivalent mass of particles in contact, kg Unit normal vector at contact Number of coke/ore particles in unit volume of bed, m−3 Prandtl number (cpf f /kf ), – Equivalent particle radius, m Particle–particle contact radius, m Reaction rate of l-th chemical reaction, mol/(m3 ·s) Radius of particles i and j, m Vector of the mass centre of the particle to contact plane, m Vector of the mass centre of the particles i and j at contact, m Particle Reynolds number, – Temperature of fluid, K Local temperature of fluid, K Representative temperature of particles i and j, K Environmental temperature of particle i, K Time step, s Time of particle–particle collision, s Relative particle velocity, m/s Normal relative velocity of particles i and j, m/s Tangential relative velocity of particles i and j, m/s Bed volume, m3 Volume of a computational cell, m3 Mole fraction of m-th species in gas phase, – Mole fraction of m-th species in equilibrium state, –

ıˆt ıt,max  ϕ ωijn 

ωnij

Unit vector of ıt Maximum of ıt when the particles start to slide, m Stefan–Boltzmann constant (=5.67 × 10−8 ), 2 4 W/(m ·K ) Empirical coefficient defined in Table 1, – Shape factor of solid particle, – Angular velocity of particle i, s−1 Unit vector of ωn , s−1

Subscripts Coke C D Damping E Elastic/effective/environmental F Fluid i Particle i Between particles i and j ij j Particle j l-th l m Species m Normal component n o Ore Particle p r Rolling t Tangential component w Wall Radiation rad

of empirical relations and/or assumptions. For the DEM-based discrete model, reviews on theoretical developments and major applications have been comprehensive; however, the heat and mass transfer aspects were not discussed in these reviews (Zhu, Zhou, Yang, & Yu, 2008; Kuang, Zhou, & Yu, 2019; Zhu, Zhou, Yang, & Yu, 2007). In subsequent studies, the DEM-based model was extended to study the heat transfer in a gas-fluidized bed packed with spherical particles (Hou, Zhou, & Yu, 2016; Zhou, Yu, & Zulli, 2009). Further, in a recent work, the effects of particle shape and size on the effective thermal conductivity of a packed bed were investigated using ellipsoid particles (Gan, Zhou, & Yu, 2017). Later, the mass transfer was also gradually included in the model (Kuwagi et al., 2016; Natsui, Kikuchi, & Suzuki, 2014; Natsui, Takai, Nashimoto, Kikuchi, & Suzuki, 2015; Peters & Hoffmann, 2016; Carlos Varas, Peters, & Kuipers, 2017). Further applications of the discrete model can be found in studies on the effect of the particle bed structure on the heat and mass transfer through the packed bed in an iron-making blast furnace (Natsui et al., 2014, 2015) and combustion flow in an incinerator (Kuwagi et al., 2016). In addition, CFD–DEM simulations have been used to study the interaction between mass transfer and a heterogeneous catalysed chemical reaction in co-current gas–particle flows in a riser (Carlos Varas et al., 2017). A discrete approach has also been used to predict a single iron ore reduction process as well, with a basic validation being established against experimental data (Peters & Hoffmann, 2016). Although the DEM-based model including the mass transfer has been widely applied in many particulate systems, it has not been validated more quantitatively and systematically for further applications under various operating conditions, such as under different

Please cite this article in press as: Dianyu, E. Validation of CFD–DEM model for iron ore reduction at particle level and parametric study. Particuology (2019), https://doi.org/10.1016/j.partic.2019.10.008

G Model PARTIC-1303; No. of Pages 10

ARTICLE IN PRESS E. Dianyu / Particuology xxx (2019) xxx–xxx

3

Fig. 1. Schematic illustration of one-interface unreacted shrinking core model (USCM) evolution (Amiri et al., 2015).

reducing gases and temperatures. In addition, more quantitative investigation of the effects of some of the main operating conditions on iron ore reduction is needed. For the theoretical model for iron ore reduction, the applicable model should be selected based on certain conditions. Generally, for iron oxide pellets with low porosity, the reduction proceeds topo-chemically in a macroscopic sense and distinct transitions are present among the reduction interfaces, such that the analyses based on the one-interface unreacted shrinking core model (USCM) can approximately reproduce the reaction process. Here, the USCM is adopted, as illustrated in Fig. 1 (Amiri, Ingram, Maynard, Livk, & Bekker, 2015). Further model details, such as the model assumptions and limitations, have been given in an overview of the current theoretical models applicable for the reduction of iron ore pellets (Valipour & Saboohi, 2007a, 2007b; Valipour, Hashemi, & Saboohi, 2006; Valipour, 2009). In this study, a DEM-based model that considers heat and mass transfer is developed and applied to a single iron ore particle reduction process, with the aim of capturing the reduction information at the particle scale; the model is then applied to multi-scale multiphase flow systems. The paper is organized as follows. In Section “Model description”, the mathematical model is introduced. In Section “Simulation conditions”, the simulation conditions are specified. In Section “Results and discussion”, the model validation is conducted first by comparing the predicted results with the experimental data, with the aim of establishing the applicability of this CFD–DEM model for handling chemical reactions. Next, the effect of gas film resistance under varied conditions is examined. Furthermore, the effects of some main operation parameters, including the reduction pressure, reducing gas composition, reduction isothermality, and reducing gas flow rate, are analysed. Finally, Section “Conclusions” presents the conclusions of the study. Model description This work presents a dynamic discrete model of the iron ore reduction process including a discrete solid (iron ore particle) and a continuum phase (reducing gas). It is formulated based on the combined CFD–DEM approach (Feng & Yu, 2004; Xu & Yu, 1997; Zhou, Kuang, Chu, & Yu, 2010). Heat and mass transfer models previously reported (Zhou et al., 2009) are implemented here, and major reduction reactions are adopted for the examination of thermochemical behaviours of iron ore reduction (Dong et al., 2010; Kuang et al., 2014). Governing equations for discrete solid particles The translational and rotational motions of solids are described by the DEM. The interaction between a particle and its neighbouring

particles and/or walls can occur through which the momentum and energy exchange between particles occur. At a given time t, the governing equations of the motions of particle i of mass mi and radius Ri are given by mi dvi /dt =



(fe,ij + fd,ij ) + fpf,i + mi g,

(1)

j

and Ii dωi /dt =



(Tt,ij + Tr,ij ),

(2)

j

where vi and ␻i are and rotational velocities,  the translaonal  respectively, and Ii = 2/5mi Ri2 is the moment of inertia of particle i. Here, the particle–fluid interaction force fpf,i , gravitational force mi g, and forces between particles (and between particles and walls) are involved. The forces between particles include the elastic force fe ,ij and viscous damping force fd,ij . The torque acting on particle i due to particle j includes two components: Tt ,ij , which is generated by the tangential force and causes particle i to rotate, and Tr ,ij , which is commonly known as the rolling friction torque. For possible multiple interactions of particle i, the interaction forces and torques between each pair of particles are summed. Most of the equations to determine the forces and torques are well documented in the literature as, for example, reviewed by Zhu et al. (2007). The equations used in the previous studies (Zhou et al., 2010) are adopted in the present work, as shown in Table 1. Particle i exchanges heat in three modes: by convective heat transfer with the surrounding fluid, by conductive heat transfer to other particles or walls, and by radiative heat transfer to its surrounding environment. The governing equations of energy balance and species concentration for particle i are written as mi cp,i dTi /dt =



Q˙ i,j + Q˙ i,f + Q˙ i,rad + Q˙ i,wall + Q˙ i,reaction ,

(3)

j

mi dci,m /dt = si,m ,

(4)

where Q˙ i,j is the heat exchange rate between particles i and j by conduction; Q˙ i,f is the heat exchange rate between particle i and its local surrounding fluid by convection; Q˙ i,rad is the heat exchange rate between particle i and its local surrounding environment by radiation; Q˙ i,wall is the heat exchange rate between particle i and the wall by conduction; and Q˙ i,reaction is the heating rate due to chemical reactions. Eq. (3) is the same as the so-called lumped-capacity formulation, where the thermal resistance within a particle can be neglected (Incropera & DeWitt, 2002). However, as noted by Zhou et al. (2009), Eq. (3) is established on the basis of heat balance at the particle scale and it can be applied using representative properties

Please cite this article in press as: Dianyu, E. Validation of CFD–DEM model for iron ore reduction at particle level and parametric study. Particuology (2019), https://doi.org/10.1016/j.partic.2019.10.008

G Model

ARTICLE IN PRESS

PARTIC-1303; No. of Pages 10

E. Dianyu / Particuology xxx (2019) xxx–xxx

4 Table 1 Equations to calculate the forces and torques on particle i. Force or torque Normal elastic force, fen ,ij

Equation √ 3/2 − 43 E ∗ R∗ ın n

Normal damping force, fdn ,ij

−cn (6mij E ∗

Tangential elastic force, fet ,ij

−s |fen,ij |(1 − (1 − ␦t /␦t,max )

Tangential damping force, fdt ,ij

−ct (6s mij |fen,ij | −s |fen,ij |ıˆ t



1/2

R ∗ ␦n )

vn,ij



Coulomb friction force, ft ,ij Torque by tangential forces, Tt ,ij Rolling friction torque, Tr ,ij Particle–fluid drag force, fd ,i

3/2

)ıˆ t

1 − ␦t /␦t,max /␦t,max )

1/2

vt,ij

Rij × (fet,ij + fdt,ij ) n −r,ij |fen,ij |ω ˆ ij − 2 2 0.125Cd0,i f ␲dpi εi |ui − vi |(ui − vi )εi −Vi ∇ pi

Pressure gradient force, fpg ,i

 

where 1/mij = 1/mi + 1/mj , 1/R∗ = 1/Ri + 1/Rj , E ∗ = E/ 2 1 − v2



n

 





,

ω ˆ ij = ωnij /|ωnij |, ıt = |ıt |, ıˆ t = ıt /|ıt |, R ij = Ri r j − r i / Ri + Rj , ıt,max = s ın (2 − v) / (2 (1 − v)), vij = vj − vi + ωj × R j − ωi × Ri , vn,ij = (vij · n) · n, vt,ij = (vij × n) × n, εi = 1 −



2



kV 

Vi /V , i=1

= 3.7 − 0.65 exp −(1.5 − log10 Rei ) /2 ,



2 0.5

Cd0,i = 0.63 + 4.8/Rei

, Rei = f dpi εi |ui − vi |/f .

Note that the tangential forces (fet ,ij + fdt ,ij ) should be replaced by ft ,ij when ıt ≥ ıt,max . Table 2 Heat-transfer models and equations for heat-exchange rates. Heat exchange rates

Equation

Convection

Q˙ i,f = (2.0 + aRebi Pr 1/3 )kf Ai T/dpi Q˙ f,wall = 0.037Re0.8 Pr 1/3 kf Aw T/L



Q˙ i,j = Ti − Tj



(a) (b)

rsf

2 ·

(c)

Conduction



r((

rsij

Ri2

−

r2









− r Ri2 + H /rij ) · 1/kpi + 1/kpj

 

Q˙ i,j = 4rc Tj − Ti / 1/kpi + 1/kpj





−1/2 / Q˙ i,j = c Tj − Ti rc2 tc



Radiation

 4

4 − Ti Q˙ i,rad = eAi Tlocal,i







pi cpi kpi

k˝ 

+2



−1/2 

, Q˙ f,rad = ef Af

where Tlocal,i = εf Tf,˝ + 1 − εf





+ pj cpj kpj

 4



 

Ri2 + H −

−1/2

Ri2 − r 2 /kf )

−1

dr (d) (e)

4 Tlocal,i − Tf

Tj (j = / i) /k˝

(f)

j=1

at the particle scale even for a Biot number higher than 0.1 (Hou, Zhou, & Yu, 2012). ci,m is the concentration of species m in particle i, and si,m is the reaction rate of species m with the surrounding environment. The equations for the calculation of conductive, convective, and radiative heat exchange rates in Eq. (3) are given in Table 2 (Zhou et al., 2009).

The corresponding energy equation for heat transfer can be written as

∂( f εf cpf Tf )/∂t + ∇ · ( f εf ucpf Tf ) = ∇ · (ke ∇ Tf ) + Q˙ + Q˙ reaction (7) The species transport equation for different gas components can be written as

Governing equations for gas phase

∂( f εf Cm )/∂t + ∇ · ( f εf uCm ) = ∇ · (εf m ∇ Cm ) + Rm + Sm

The continuum fluid phase is modelled similarly to the one widely used in the conventional two-fluid model. In this work, the more general Set I is used. Thus, the conservation of mass and momentum in terms of the locally averaged variables over a computational cell are given by

where u, f , p, and Ffp are the fluid velocity, density, pressure, and volumetric fluid–particle interaction force, respectively. Specifically, f is calculated from the ideal gas equation f =

∂( f εf )/∂t + ∇ · ( f εf u) = 0,

ng 

MI xI , where xI is the mole fraction of chemical species

I∈g

(5)

and

∂( f εf u)/∂t + ∇ · ( f εf uu) = −∇ p − Ffp + ∇ ·  + f εf g

Pg ⁄Rg Tg

(8)

(6)

I in the gas phase and MI is the molecular weight of I. f is thus a function of temperature and pressure.  and εf are the fluid viscous stress tensor and porosity, respectively. Note that εi is the local porosity for particle i for calculating the particle–fluid drag force, and εf is determined over a CFD cell. ke is the fluid thermal conductivity. The volumetric particle–fluid interaction force

Please cite this article in press as: Dianyu, E. Validation of CFD–DEM model for iron ore reduction at particle level and parametric study. Particuology (2019), https://doi.org/10.1016/j.partic.2019.10.008

G Model

ARTICLE IN PRESS

PARTIC-1303; No. of Pages 10

E. Dianyu / Particuology xxx (2019) xxx–xxx

5

Table 3 Key chemical reactions and equations for reaction rates. Chemical reactions 1 Fe2 O3(s) 3

+ CO(g) =

Reaction rates 2 Fe(s) 3

R1∗ =

+ CO2(g)

  yCO −y∗ /(22.4Tp )  CO 2/3

−1

  yH −y∗ /(22.4Tp ) 2 H  2 2/3

−1

d2 ϕ−1 ·273p

1/kf +0.5d0



(1−fs )−1/3 −1 /Ds1 + (1−fs )

1

1 Fe2 O3(s) 3

+ H2(g) =

2 Fe(s) 3

0 0

R2∗ =

+ H2 O(g)

k1 (1+1/K1 )

d2 ϕ−1 ·273p

1/kf +0.5d0



2

0 0

(1−fs )−1/3 −1 /Ds2 + (1−fs )

k2 (1+1/K2 )

Where kfl = Sh · Dm /d0 , Dsl = εo ·  · Dm , DCO = 6.08 × 10−10 Tp1.78 /p, DH2 = 3.71 × 10−9 Tp1.78 /p. For the low-temperature range (Tp <848 K): K2 = exp(8.883 − 8475/Tp ); when fs < 0.111, K1 = exp(4.91 + 6235/Tp ); when fs ≥ 0.111, K1 = exp(−0.7625 + 543.3/Tp ). For the high-temperature range (Tp ≥848 K): K2 = exp (1.0837 − 1737.2/Tp ); when fs < 0.111, K1 = exp(4.91 + 6235/Tp ); when 0.111 ≤fs < 0.333, K1 = exp(2.13 − 2050/Tp ); when fs ≥ 0.333, K1 = exp(−2.642 + 2164/Tp ).

Ffp in Eq. (6) can be determined as Ffp =

kV 

(fd,i + fpg,i )/V . The

i=1

volumetric heat exchange rate Q˙ in Eq. (7) is determined as Q˙ =

k V 



Q˙ f,i + Q˙ f,wall + Q˙ f,rad

/V , where Q˙ f,i is the heat exchange

i=1

rate between the fluid and particle i by convection, Q˙ f,wall is the heat exchange rate between the fluid and a wall by convection, and Q˙ f,rad is the heat exchange rate between the fluid and its environment by radiation. Q˙ f,reaction in Eq. (7) is due to chemical reactions between gas species and solid particles in the local cell, where the heat sink or source is shared by discrete and continuum phases. This work simply considers one continuum gas phase, and Cm is the concentration of species m. Rm is the source of m due to chemical reactions in the continuum phase and Sm is the source term due to the reaction between discrete and continuum phases, which is equal to the sum of si,m over all particles in a CFD cell.  m is the diffusion coefficient of species m. The iron ore is mainly reduced by CO or/and H2 . The rates for the reduction reactions considered are based on one-interface USCM, which takes into account the three reduction processes Fe2 O3 → Fe3 O4 → wustite (Fe(1− x ) O) → Fe, as shown in Table 3 (Dong et al., 2010, Kuang et al., 2014; Miyasaka, Sugata, Hara, & Kondo, 1975; Muchi, 1967; Omori, 1987; Yagi, Takahashi, & Omori, 1971). The calculation of the reduction reaction rate depends on the reduction degree (fs ) of iron ore, as follows: (a) Reduction reaction of hematite by CO fs <0.111 1/3Fe2 O3 (s) + 1/9CO(g) = 2/9Fe3 O4 (s) + 1/9CO2 (g) (b) Reduction reaction of magnetite by CO 2/9Fe3 O4 (s) + 2/9CO(g) 0.111≤fs <0.333 = 2/3FeO(s) + 2/9CO2 (g) (c) Reduction reaction of wustite by CO 2/3FeO(s) + 2/3CO(g) = 0.333≤fs 2/3Fe(s) + 2/3CO2 (g) (d) Reduction reaction of hematite by H2 fs <0.111 1/3Fe2 O3 (s) + 1/9H2 (g) = 2/9Fe3 O4 (s) + 1/9H2 O(g) (e) Reduction reaction of magnetite by H2 0.111≤fs <0.333 2/9Fe3 O4 (s) + 2/9H2 (g) = 2/3FeO(s) + 2/9H2 O(g) (f) Reduction reaction of wustite by H2 0.333≤fs 2/3FeO(s) + 2/3H2 (g) = 2/3Fe(s) + 2/3H2 O(g)

Unit: kJ/mol

Table 4 Physical properties of hematite pellet and gas. Variables

Values

Number of particles, N Particle diameter of hematite pellet, dp (mm) Particle density of hematite pellet, (kg/m3 ) Thermal conductivity of hematite pellet, kp (W/(m·K)) Specific heat of hematite pellet, cp (J/(kg·K)) Particle Young’s modulus, E (kg/(m·s2 )) Particle Poisson ratio,  Fluid thermal conductivity, kf (W/(m·K)) Inlet gas temperature, Tin (◦ C) Gas flow rate, (Nm3 /s) Pellet chemical composition (wt%) TFe/FeO/SiO2 /CaO/Al2 O3 /MgO/S

1 12.4 4,120 80 600 1 × 107 0.3 2.62 × 10−2 800/1,000/1,200 7.39–147.84 × 10−4 65.07/1.37/4.04/0.62/1.23/0.58/0.004

◦

tion, where H298 is the standard enthalpy change of formation, and Cp is the heat capacity change of a corresponding chemical reaction. ◦ Q˙ reaction = H298 +

T Cp dT.

(9)

298

Simulation conditions

◦

H298 = −2.76

◦

H298 = 5.02 ◦

H298 = −8.41

◦

H298 = 1.81

◦

H298 = 14.17

◦

H298 = 19.03

The reaction heat was calculated from Kirchhoff’s law in Eq. (9), which relates enthalpy to the heat capacity change of each reac-

In the current work, the model geometry is set with reference to that of an experimental reduction furnace (Takahashi, Yagi, & Omori, 1971), as shown in Fig. 2. The inlet gas flows through a lateral jet. Here, a two-dimensional (2D) slot model is used with the thickness of four particle diameters. During the reduction process, a hematite pellet is fixed at a pointed position. The chemical compositions of the hematite pellet, which is run to simulate the reduction process, are given in Table 4 along with other properties of the reducing gas and pellet (Takahashi et al., 1971). For the reduction process, the pellet is just heated up by the reducing gas until it reaches the desired temperature under the isothermal condition, and then, the pellet is chemically reduced by the composition of the reducing gas. Under non-isothermal conditions, the pellet with ambient temperature starts to be reduced by reducing gas at the desired temperature. Results and discussion In this part, the particle scale iron ore reduction model is systematically validated by comparing the predicted results with the previous measurements for two main iron ore reduction reactions

Please cite this article in press as: Dianyu, E. Validation of CFD–DEM model for iron ore reduction at particle level and parametric study. Particuology (2019), https://doi.org/10.1016/j.partic.2019.10.008

G Model PARTIC-1303; No. of Pages 10

ARTICLE IN PRESS E. Dianyu / Particuology xxx (2019) xxx–xxx

6

and accuracy because these two types of reactions, using CO or/and H2 as reducing gas, are the main reactions for iron ore reduction. Under the same experimental conditions, the model is used to simulate the isothermal reduction process of a hematite pellet with the physico-chemical properties, as given in Table 4. Fig. 3 compares the overall reduction rates of a hematite pellet predicted by the present model with the experimental data of previous studies (Takahashi et al., 1971; Yagi et al., 1971). Fig. 3(a) and (b) shows the comparison for H2 and CO, respectively. In Fig. 3(a), the predicted results deviate from the measured ones at higher reduction temperatures, which is likely the consequence of a lack of more accurate kinetic parameters to describe the reduction process at high temperatures, although the predictions at 859 and 960 ◦ C are almost identical to the experimental results. The same situation may be expected to be the main reason for the discrepancies in Fig. 3(b), because the theoretical calculations (Takahashi et al., 1971; Yagi et al., 1971) show a similar trend with the current model predictions when compared with the experimental results. Overall, the predicted curves and measured data can be considered to be in satisfactory agreement with each other for these two sets of data, which may be regarded as the proof of the validity of the present model.

Effect of gas film resistance

Fig. 2. Geometry of the model and the CFD mesh.

under various temperatures. Furthermore, the contribution of gas film resistance based on the USCM is examined. Finally, the effects of operation parameters, such as the pressure, gas composition, isothermality, and gas flow rate on the reduction process are discussed qualitatively and quantitatively. Model validation To obtain a comprehensive understanding of the particle-scale chemical reactions and apply the model to a practical chemical process, the model based on the above formulations is validated first. The overall reduction degree of the hematite pellet is selected as the main validation parameter. The reaction model is validated by comparing the predicted results with the previous experimental data (Takahashi et al., 1971; Yagi et al., 1971). Specifically, the model validation of hematite reduction is conducted using reducing gases CO and H2 , respectively, and one set of tests each is for adaptability

In iron ore reduction studies, the USCM is widely adopted, which normally dictates the assumption that diffusion through the gaseous film, intraparticle diffusion, and chemical reaction proceed steadily and successively during the reduction process for the heterogeneous reaction. The formulae for overall reduction rates are given in Table 3. The terms in the denominator represent the resistances of the three processes, gas film diffusion, intra-particle diffusion, and chemical reaction. Muchi (1967) suggested that the resistance of gas film diffusion may be negligible because it is very small compared with others in blast furnace conditions. However, Takahashi et al. (1971) reported that the effect of the resistance of diffusion through the gaseous film is important, particularly at a higher reducing temperature and in the initial stage of the reduction process. Consequently, the resistance of diffusion through the gaseous film should be evaluated with accuracy. Thus far, this problem has not been addressed properly. Therefore, it will be discussed here further for a better understanding and more accurate application of the model to the reduction process. First, a comparison of the reduction rate with and without gas film resistance (GFR) considered is presented in Fig. 4. A minor difference is observed depending on whether GFR is considered at higher temperature, irrespective of the type of reducing gas used. However, the variation of the average error is larger with H2 reduction than with CO reduction, which may be due to H2 reduction having a faster reduction rate, leading to a slightly higher error in even small variations. Generally, Fig. 4 reveals that although the GFR accounts for a small percentage of the total resistance, it should be considered carefully at high temperatures and for different reducing gases to improve the accuracy of the reduction calculations. Second, Fig. 5 shows the differences between the two cases, with and without GFR, under the condition of introducing the inert gas N2 to the CO reducing gas. The results illustrate that the introduction of N2 amplifies the effect of GFR, especially at high temperatures. In connection with Fig. 5, Fig. 6 shows the effect of different volume ratios of CO and N2 at a fixed reduction temperature. It is apparent that with the introduction of a larger quantity of N2 , the effect of GFR is greater. Therefore, whether GFR should be ignored depends on the specific reduction conditions. To improve the accuracy of the reduction process, it is recommended that GFR

Please cite this article in press as: Dianyu, E. Validation of CFD–DEM model for iron ore reduction at particle level and parametric study. Particuology (2019), https://doi.org/10.1016/j.partic.2019.10.008

G Model PARTIC-1303; No. of Pages 10

ARTICLE IN PRESS E. Dianyu / Particuology xxx (2019) xxx–xxx

7

Fig. 3. Comparison between predicted and experimental data on the reduction rate for the hematite pellet with (a) H2 and (b) CO.

Fig. 4. Comparison of reduction degree with and without inclusion of a gas film resistance (GFR) at various temperatures: (a) H2 reduction and (b) CO reduction.

should be considered especially in a reduction atmosphere including inert gas at high temperatures. Effect of operation parameters To better understand and further control the iron ore reduction process qualitatively and quantitatively, the effects of some important parameters, such as the reduction pressure, reducing gas composition, isothermality, and gas flow rate, which have been observed to affect iron ore reduction but have not been systematically analysed, are discussed in the following sections.

Fig. 5. Reduction at various temperatures for fixed VCO /VN2 .

Fig. 6. Reduction for different VCO /VN2 at 1000 ◦ C.

Operation pressure The effect of pressure on the reduction process is illustrated in Fig. 7(a), which shows that the reduction rate increases markedly with increasing pressure from 0.5 to ∼2 atm. However, this effect is not as pronounced at higher pressures, as indicated by the closeness of the reduction curves above 5 atm. Fig. 7(b) shows this trend quantitatively as the time taken for the reduction degree to reach 0.9 as a function of the operation pressure. A similar phenomenon has been reported in previous studies (Kurozu, Takahashi, & Takahashi, 1980; Takahashi, Koyabu, Ishii, Ishigaki, & Takahashi, 1980). The effect of reduction temperature on the reduction rate would also be similar to that of pressure. The reason for this expectation is that the resistance for gas diffusion through the product layer and the gas film outside a particle will decrease gradually at high temperatures and pressures, and the rate of gas diffusion will approach its limit in the reaction mechanism with gradually increasing pressure. Based on the analysis above, the reduction rate can be enhanced by increasing the pressure in the reduction process. Theoretically, this point can be utilized in some practical chemical reactors to improve the reduction efficiency. In practice, some chemical reactors, such as blast furnaces, have adopted this approach in practical operations. However, it should be noted that a careful assessment of how high of pressures can be used in a certain reactor should be made and its effect analysed in view of the process safety, economy, and efficiency.

Please cite this article in press as: Dianyu, E. Validation of CFD–DEM model for iron ore reduction at particle level and parametric study. Particuology (2019), https://doi.org/10.1016/j.partic.2019.10.008

G Model PARTIC-1303; No. of Pages 10 8

ARTICLE IN PRESS E. Dianyu / Particuology xxx (2019) xxx–xxx

Fig. 7. Effect of pressure on overall (a) reduction time and (b) reduction time when reduction degree reaching 0.9 at 1000 ◦ C.

Fig. 8. Reduction process of hematite pellet under different reducing gas compositions.

Gas composition The reduction curves obtained experimentally for the reduction of the experimental hematite pellets at 1000 ◦ C using H2 , H2 , and H2 O; CO, CO, and CO2 ; and mixed H2 and CO are presented in Fig. 8. Generally, it can be observed that the reduction rate is faster when using H2 compared with CO, and that of their mixed gas is in the middle, which is consistent with previously reported findings (El-Geassy, Shehata, & Ezz, 1977; Tsay, Ray, & Szekely, 1976). The hematite pellet is reduced completely in approximately 20 min by pure H2 , whereas reduction by pure CO takes almost 120 min under the current operating conditions. The reaction rate increases gradually with increasing H2 content in the mixture because of the higher reducing and diffusing capacities of H2 compared with those of CO gas (Mousa, Babich, & Senk, 2011). In other words, the decrease of the diffusion resistance increases the reaction driving force. However, it should be noted that the H2 and CO mixture ratio does not have a notable effect on the reduction rate until the ratio is less than one. This finding indicates that the hematite pellet prefers to react with H2 rather than CO under high-temperature condition and that the effect of CO existence is weak, especially under conditions with sufficient H2 for reduction. For VH2 /VH2O = 3/1 and VCO /VCO2 = 3/1, the existence of H2 O in the H2 reduction will obviously decrease the reduction efficiency, whereas the effect of CO2 on the CO reduction is more markedly observed. Essentially, the effect of CO2 gas on the reaction equilibrium is the dominating factor resulting in the negative effect of CO2 gas on the reduction process according to Le Chatelier’s principle. That is, the presence of CO2 in the reducing atmosphere decreases the power potential of CO gas for reducing the iron oxides, as does the H2 O in the H2 reducing atmosphere. The resistance of the product gas should be further discussed in the reduction process in the future.

Isothermality Fig. 9 presents comparisons of the reduction rates of the hematite pellet with H2 , CO, and their mixture under isothermal and non-isothermal reduction atmospheres at a reducing temperature of 1000 ◦ C. The curves clearly indicate that the isothermal reduction rate is higher than the non-isothermal reduction rate in all cases, which is mainly due to the reaction rate becoming higher at relatively higher temperatures for these cases at the same time, as observed previously (Valipour, 2009). As shown in Fig. 9(a) for the pure H2 reduction, a significant difference between the isothermal and non-isothermal conditions exists, which is mainly due to the temperature difference at every time step. In particular, the difference can be explained as follows: first, in the H2 reduction process, the equilibrium content of H2 decreases with increasing temperature because it is an endothermic reaction, which is attributed to the higher reducing potential at high temperature. Therefore, the reaction driving force is enhanced. Second, a higher temperature contributes to a larger mass transfer coefficient, leading to an increase of gas diffusion and a reduction in diffusion resistance. Third, the chemical reaction interface resistance decreases because of the increase of the reaction rate constant, which is consistent with the expression of an Arrhenius equation, thereby giving rise to a decrease in the overall reaction resistance. Therefore, the reduction rate is larger under isothermal condition. Interestingly, H2 /CO reducing gas has a lower reduction rate than pure H2 under isothermal conditions, whereas the opposite trend is observed under non-isothermal conditions because the driving force is smaller for H2 reduction than for CO reduction at low temperature. In pure CO reduction, as observed in Fig. 9(b), although the driving force of the reaction decreases with increasing temperature, because of the increase in the equilibrium content of CO and the reaction being exothermic, both the internal diffusion and chemical reaction interface resistances become greatly reduced, leading to an improvement in the reaction rate. Therefore, it can be deduced that the effect of temperature on the internal diffusion and chemical reaction interface resistance may exceed the reduction potential, although the extent is not significant. As a result, the reduction rate using pure CO as a reduction agent is slightly higher under isothermal conditions during the entire reduction process than under non-isothermal conditions. Therefore, the reduction rate for the mixture of H2 and CO gases is intermediate, as observed in Fig. 9(a). Reducing gas flow rate The flow rate reported in a previous work (Strangway, 1968) studying the reduction of iron ores varied from case to case. However, it is generally agreed that a relatively low critical gas velocity or critical pressure exists, above which the reaction rate is independent of the flow rate in the same reducing gas concentration.

Please cite this article in press as: Dianyu, E. Validation of CFD–DEM model for iron ore reduction at particle level and parametric study. Particuology (2019), https://doi.org/10.1016/j.partic.2019.10.008

G Model PARTIC-1303; No. of Pages 10

ARTICLE IN PRESS E. Dianyu / Particuology xxx (2019) xxx–xxx

9

Fig. 9. Comparison of isothermal and non-isothermal reduction rates for the reductions with (a) H2 and a mixture of H2 and CO and (b) CO.

Fig. 10. (a) Effect of flow rate on the reduction process; (b) pressure drop varying with flow rates; and (c) reduction time when reduction degree reached 0.9 at 1000 ◦ C.

However, this critical gas flow rate is dependent on the characteristics of the reduction apparatus and the properties of the iron ore and reducing gas. Consequently, there is a need to evaluate the critical flow rate for each set of reduction conditions and observe reduction phenomena around the value. In fact, the overall reaction degree will be limited by the flow rate because of the shortage of reducing gas quantity or/and low reaction pressure when the flow rate is below the critical value. The above concept is verified in Fig. 10. In the predicted results, the reduction rate is not accelerated gradually when the flow rate is over 59.14 × 10−4 m3 /s although the pressure drop still increases gradually, as observed in Fig. 10(b), instead of increasing step-wise, as quantitatively shown in Fig. 10(c). In other words, if the flow rate of the reducing gas is below the critical value in a certain range, the overall reduction performance is similar and closer to the numerical values. The same trend can be observed when the flow rate is above the critical value. Furthermore, it can be deduced that the same reduction degree may not be achieved using the same amount of reducing gas but flowing at a different rate.

Conclusions A particle-scale numerical model of iron ore reduction was developed and systematically validated. The USCM was embedded within the developed DEM-based multi-scale model, which was then used to discuss the effects of the GFR and operation parameters, including the pressure, gas composition, isothermality, and gas flow rate, on the reduction process. The findings can be summarized as follows:

• Comparison of the reduction rates obtained with and without considering GFR revealed a minor difference, although it was slightly larger (approximately 3% in error) when an inert gas was mixed with the reducing gas. Therefore, for simplicity, the GFR may be omitted in the study of industrial processes if the calculation error is allowed in a certain range. • The reduction rate increases significantly with increasing pressure up to ∼5 atm, beyond which it increases slightly.

Please cite this article in press as: Dianyu, E. Validation of CFD–DEM model for iron ore reduction at particle level and parametric study. Particuology (2019), https://doi.org/10.1016/j.partic.2019.10.008

G Model PARTIC-1303; No. of Pages 10 10

ARTICLE IN PRESS E. Dianyu / Particuology xxx (2019) xxx–xxx

• There is a visible difference in the reductions under isothermal and non-isothermal conditions. Under non-isothermal conditions, the entire reduction process is retarded. • There exists a critical gas flow rate, above which the reaction rate is independent of the flow rate for the same reducing gas concentration. Overall, the present work establishes a validated numerical model for describing iron ore reduction on a single particle, which can be applied to a complicated reduction process, such as that in a blast furnace. The above findings not only provide guidance for practical operations but are also a good basis from which to obtain a better understanding of the iron ore reduction process. Declaration of interest The author declares that there is no conflict of interests regarding the publication of this paper. Acknowledgments The author is grateful to the National Natural Science Foundation of China project (51904122), the Key Project of Jiangxi Provincial Research and Development (20192BBHL80016), and the Opening Research Project of State Key Laboratory of Multiphase Flow in Power Engineering for financial support of this work. References Amiri, A., Ingram, G. D., Maynard, N. E., Livk, I., & Bekker, A. V. (2015). An unreacted shrinking core model for calcination and similar solid-to-gas reactions. Chemical Engineering Communications, 202(9), 1161–1175. Carlos Varas, A. E., Peters, E. A., & Kuipers, J. A. M. (2017). Computational fluid dynamics–discrete element method (CFD-DEM) study of mass-transfer mechanisms in riser flow. Industrial & Engineering Chemistry Research, 56(19), 5558–5572. Dong, X. F., Yu, A. B., Chew, S. J., & Zulli, P. (2010). Modeling of blast furnace with layered cohesive zone. Metallurgical and Materials Transactions B, 41(2), 330–349. Dong, X. F., Yu, A. B., Yagi, J. I., & Zulli, P. (2007). Modelling of multiphase flow in a blast furnace: Recent developments and future work. ISIJ International, 47(11), 1553–1570. El-Geassy, A. A., Shehata, K. A., & Ezz, S. Y. (1977). Mechanism of iron-oxide reduction with hydrogen–carbon monoxide mixtures. Transactions of the Iron and Steel Institute of Japan, 17(11), 629–635. Feng, Y. Q., & Yu, A. B. (2004). Assessment of model formulations in the discrete particle simulation of gas−solid flow. Industrial & Engineering Chemistry Research, 43(26), 8378–8390. Gan, J. Q., Zhou, Z. Y., & Yu, A. B. (2017). Effect of particle shape and size on effective thermal conductivity of packed beds. Powder Technology, 311, 157–166. Hou, Q. F., E, D. Y., Kuang, S. B., Li, Z. Y., & Yu, A. B. (2017). DEM-based virtual experimental blast furnace: A quasi-steady state model. Powder Technology, 314, 557–566. Hou, Q. F., Zhou, Z. Y., & Yu, A. B. (2012). Computational study of the effects of material properties on heat transfer in gas fluidization. Industrial & Engineering Chemistry Research, 51(35), 11572–11586. Hou, Q. F., Zhou, Z. Y., & Yu, A. B. (2016). Gas–solid flow and heat transfer in fluidized beds with tubes: Effects of material properties and tube array settings. Powder Technology, 296, 59–71. Incropera, F. P., & DeWitt, D. P. (2002). Fundamentals of heat and mass transfer (5th ed.). New York: John Wiley & Sons. Inc. Kuang, S. B., Li, Z. Y., Yan, D. L., Qi, Y. H., & Yu, A. B. (2014). Numerical study of hot charge operation in ironmaking blast furnace. Minerals Engineering, 63, 45–56. Kuang, S. B., Li, Z. Y., & Yu, A. B. (2018). Review on modeling and simulation of blast furnace. Steel Research International, 89(1), 1700071. Kuang, S. B., Zhou, M. M., & Yu, A. B. (2019). CFD-DEM modelling and simulation of pneumatic conveying: A review. Powder Technology, http://dx.doi.org/10.1016/ j.powtec.2019.02.011 Kurozu, S. I., Takahashi, R., & Takahashi, Y. (1980). Reduction rates of iron oxide pellet with hydrogen at high pressures. Tetsu-to-Hagané, 66(1), 23–32. Kuwagi, K., Takami, T., Alias, A. B., Rong, D., Takeda, H., Yanase, S., et al. (2016). Development of DEM–CFD simulation of combustion flow in incinerator with the representative particle model. Journal of Chemical Engineering of Japan, 49(5), 425–434.

McKewan, W. M. (1960). Kinetics of iron oxide reduction. Transactions of the American Institute of Mining and Metallurgical Engineers, 218(1), 2–6. Miyasaka, N., Sugata, M., Hara, Y., & Kondo, S. I. (1975). Prediction of blast pressure change by a mathematical model. Transactions of the Iron and Steel Institute of Japan, 15(1), 27–36. Moriyama, A., Yagi, J. I., & Muchi, I. (1967). Rate-controlling steps of reduction process of iron-oxide pellet. Transactions of the Iron and Steel Institute of Japan, 7(6), 271–277. Moriyama, A., Yagi, J. I., Muchi, I., & Tamura, K. (1965). The rate-determining steps of the reduction process of iron-oxide pellet. Journal of the Japan Institute of Metals, 29(5), 528–534. Mousa, E. A., Babich, A., & Senk, D. (2011). Effect of nut coke-sinter mixture on the blast furnace performance. ISIJ International, 51(3), 350–358. Muchi, I. (1967). Mathematical model of blast furnace. Transactions of the Iron and Steel Institute of Japan, 7, 223–237. Naito, M., Takeda, K., & Matsui, Y. (2015). Ironmaking technology for the last 100 years: Deployment to advanced technologies from introduction of technological know-how, and evolution to next-generation process. ISIJ International, 55(1), 7–35. Natsui, S., Kikuchi, T., & Suzuki, R. O. (2014). Numerical analysis of carbon monoxide–hydrogen gas reduction of iron ore in a packed bed by an Euler–Lagrange approach. Metallurgical and Materials Transactions B, 45(6), 2395–2413. Natsui, S., Takai, H., Nashimoto, R., Kikuchi, T., & Suzuki, R. O. (2015). Model study of the effect of particles structure on the heat and mass transfer through the packed bed in ironmaking blast furnace. International Journal of Heat and Mass Transfer, 91, 1176–1186. Ohmi, M., & Usui, T. (1973). Study on the rate of reduction of single iron oxide pellet with hydrogen. Tetsu-to-Hagané, 59(14), 1888–1901. Omori, Y. (1987). The blast furnace phenomena and modeling. London: Elsevier Applied Science. Orth, A., Anastasijevic, N., & Eichberger, H. (2007). Low CO2 emission technologies for iron and steelmaking as well as titania slag production. Minerals Engineering, 20(9), 854–861. Peters, B., & Hoffmann, F. (2016). Iron ore reduction predicted by a discrete approach. Chemical Engineering Journal, 304, 692–702. Strangway, P. K. (1968). The kinetics of iron-oxide reduction. University of Toronto. Takahashi, R., Koyabu, Y., Ishii, M., Ishigaki, M., & Takahashi, Y. (1980). Hydrogen reduction of iron oxide pellets in laboratory scale high pressure moving bed. Tetsu-to-Hagané, 66(13), 1985–1994. Takahashi, R., Yagi, J. I., & Omori, Y. (1971). Rate of reduction of iron oxide pellets with hydrogen. Tetsu-to-Hagané, 57(10), 1597–1605. Tsay, Q. T., Ray, W. H., & Szekely, J. (1976). The modeling of hematite reduction with hydrogen plus carbon monoxide mixtures: Part I. The behavior of single pellets. AIChE Journal, 22(6), 1064–1072. Valipour, M. S. (2009). Mathematical modeling of a non-catalytic gas–solid reaction: Hematite pellet reduction with syngas. Scientia Iranica Transaction C, Chemistry, Chemical Engineering, 16(2), 108. Valipour, M. S., & Saboohi, Y. (2007a). Numerical investigation of nonisothermal reduction of hematite using syngas: The shaft scale study. Modelling and Simulation in Materials Science and Engineering, 15(5), 487. Valipour, M. S., & Saboohi, Y. (2007b). Modeling of multiple noncatalytic gas–solid reactions in a moving bed of porous pellets based on finite volume method. Heat and Mass Transfer, 43(9), 881–894. Valipour, M. S., Hashemi, M. M., & Saboohi, Y. (2006). Mathematical modeling of the reaction in an iron ore pellet using a mixture of hydrogen, water vapor, carbon monoxide and carbon dioxide: An isothermal study. Advanced Powder Technology, 17(3), 277–295. Xu, C. B., & Cang, D. Q. (2010). A brief overview of low CO2 emission technologies for iron and steel making. Journal of Iron and Steel Research, International, 17(3), 1–7. Xu, B. H., & Yu, A. B. (1997). Numerical simulation of the gas–solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics. Chemical Engineering Science, 52(16), 2785–2809. Yagi, T., & Ono, Y. (1968). A method of analysis for reduction of iron oxide in mixedcontrol kinetics. Transactions of the Iron and Steel Institute of Japan, 8, 377–381. Yagi, J. I., Takahashi, R., & Omori, Y. (1971). Study on the reduction process of iron oxide pellets in isothermal fixed bed. Tetsu-to-Hagane, 57(9), 1453–1460. Zhou, Z. Y., Kuang, S. B., Chu, K. W., & Yu, A. B. (2010). Discrete particle simulation of particle–fluid flow: Model formulations and their applicability. Journal of Fluid Mechanics, 661, 482–510. Zhou, Z. Y., Yu, A. B., & Zulli, P. (2009). Particle scale study of heat transfer in packed and bubbling fluidized beds. AIChE Journal, 55(4), 868–884. Zhu, H. P., Zhou, Z. Y., Yang, R. Y., & Yu, A. B. (2007). Discrete particle simulation of particulate systems: Theoretical developments. Chemical Engineering Science, 62(13), 3378–3396. Zhu, H. P., Zhou, Z. Y., Yang, R. Y., & Yu, A. B. (2008). Discrete particle simulation of particulate systems: A review of major applications and findings. Chemical Engineering Science, 63(23), 5728–5770.

Please cite this article in press as: Dianyu, E. Validation of CFD–DEM model for iron ore reduction at particle level and parametric study. Particuology (2019), https://doi.org/10.1016/j.partic.2019.10.008