Effect of High Reactivity Coke for Mixed Charge in Ore Layer on Reaction Behavior of Each Particle in Blast Furnace

Abstract

A low coke rate operation in blast furnace is desired to decrease the carbon input and mitigate global warming problem. However, low coke rate operation tends to cause the gas permeability to deteriorate. The mixing of small-size coke (nut coke) including high reactivity coke in ore layer is considered to be a promising way to improve permeability and increase reaction efficiency in a blast furnace. Although adding a nut coke mixing to an ore layer is predicted to be empirically effective in low coke rate operation, there is little actual data on microscopic phenomena of each particle in the packed bed. In the present study, an Euler–Lagrange approach was introduced to precisely understand the influence of the packed bed structure on the reaction behavior of each particle in the three-dimensional particle arrangement.

It was observed that the heterogeneity on the reaction rate and temperature distribution was influenced by the particle arrangement. When high-reactivity coke was used at approximately 1273 K, although CO gas fraction increased, the gaseous phase temperature decreased due to the active solution loss reaction rate of the nut coke in the mixed layer. As a result, the ore reduction rate decreased. The contribution of high-reactivity coke to the ore reduction rate depends on the particle arrangement through the heat transfer and reaction heat. Accordingly, in the case of the mixed charge of the high reactivity nut coke in the ore layer, the design of the packed bed structure is important.

1. Introduction

In a blast furnace, a low coke rate operation is desired to mitigate global warming problem. Regarding the low reducing agent operation, several ideas have been proposed. Suitable application of small-size coke (nut coke) mixed charge including high-reactivity coke has received special attention because it is a promising approach to decreasing coke rate owing to the improved reaction efficiency of the blast furnace.¹⁾ Nomura et al. reported that high reactivity coke (e.g., ferro-coke) starts to react with CO₂ at a lower temperature, which lowers the temperature range of the thermal reserve zone in blast furnaces.²⁾ Then, the CO/CO₂ ratio in the gas phase equilibrated with FeO and metallic Fe changes with a decreased temperature and the utilization ratio of carbon based on the wüstite–iron reduction equilibrium increases.³⁾ Higuchi et al. confirmed that enhancing coke reactivity is effective for increasing the gas utilization ratio through the change in the thermal reserve zone temperature using BIS test furnace.⁴⁾

Although the stable operation of blast furnace in low reducing agent condition should be pursued, understanding in-furnace phenomena in blast furnace on the basis of non-empirical methods is becoming increasingly necessary. Because the microscopic phenomena that occur in a blast furnace are difficult to observe, mathematical models help in understanding the mechanism of such phenomena. As described above, the charge of nut coke and high reactivity coke is beneficial to attain low reducing agent operation, and the mechanism of chemical reaction and heat transfer must be clarified to design the favorable packed bed structure.

From the above backgrounds, the present study newly considers the effect of mixed different-reactivity cokes on the reduction of ore at the particle scale and provides information on the behavioral influence under each arrangement of different particles. In particular, this study focused on the particle arrangement of high reactivity coke in the packed bed. A large-scale direct simulation that is assumed to be of the scale of an experimental blast furnace was carried out. This approach can be used to analyze the heat and mass transfer through an actual packed bed in order to verify the reduction properties and flow characteristics, which depend on the particle arrangement.

2. Mathematical Modeling

In order to understand in-furnace gas–solid transport phenomena including momentum, heat, and mass transfers, many numerical analysis models of blast furnaces have been developed.^5,6) A suitable method according to the situation selected. Figure 1 is a schematic illustration showing the arrangement of calculated points in gas–solid flow analysis, which is available for this simulation. The Euler–Euler (E–E) method, which is also called the two-fluid model, permits steady-state analysis even if the analysis object is a large-scale system such as a huge blast furnace. At present, this method can predict the change in the melting zone from the temperature distribution.⁷⁾ Although there have been considerable researches focused on burden distribution modeling,^8,9) calculating the discrete inter-particle stress using the E–E method is too complicated. Using the Euler–Lagrange (E–L) method is much easier;¹⁰⁾ this approach can generate transport equations of an individual solid particle. Although the E–L method has a heavy computational load, current developments in computer technology has made it possible to apply it to large-scale systems.¹¹⁾

Fig. 1.

Schematic diagrams of calculation point arrangement in each numerical multiphase flow analysis.

The authors previously developed an entire blast furnace gas–solid flow analysis model using the E–L method.^12,13) The latest article discussed using the E–L method for the heat and mass transfer model and chemical reaction model.¹⁴⁾ Based on this approach, the interaction between cokes and ores under fluid flow in accordance with the movement and properties of individual particles can be directly understood in three dimensions, even if high-reactivity nut coke is used. Here, the E–L method was applied to obtain the microscopic phenomena such as reaction rate and temperature for each particle in the packed bed.

3. Governing Equations

Figure 2 shows a fixed volume element with arrows to indicate the directions of the fluxes through the surfaces by all transport phenomena in the packed bed. The gas–solid phase momentum, heat, and mass transfer and exchange are described by the following equations.

Fig. 2.

Schematic diagrams of unit cell: (a) fixed volume element through which fluid flows in a packed bed; (b) particle–particle and particle–fluid momentum transfer; (c) heat transfer; and (d) mass transfer.

3.1. Motion Equations

3.1.1. Motion of Particles¹⁵⁾

A particle’s motion depends on Newton’s second law, as shown in Fig. 2(b). Because a solid particle has a small size, the Basset term and Saffman and Magnus lift forces are neglected.   

$$m_p\frac{d{\mathit{u}}_p}{dt}={\displaystyle \sum }_{j\ne i}^{N_c}{\mathit{F}}_c+{\mathit{F}}_d+{\mathit{F}}_g$$(1)

  

$$I_p\frac{d{\omega }_p}{dt}=r_p{\displaystyle \sum }_{j\ne i}^{N_c}\left({\mathit{F}}_{cs}-{\mathit{F}}_r\right)$$(2)

where m_p is the particle mass, u_p is the particle velocity, t is time, F_c is the particle–particle contact force, N_c is the contact particle number, F_d is the particle–fluid interaction force, F_g is the gravity force, I_p is the moment of inertia, ω_p is the angular velocity, r_p is the article radius, F_cn is the normal component of the contact force, F_cs is the tangential component of contact force, and F_r is the rolling friction force. The interparticle contact force is calculated by the “soft sphere” assumption based on Hertz’s contact theory; the same approach was used in previous research.¹²⁾

3.1.2. Motion of a Fluids¹⁶⁾

The movement of a fluid is described by the continuity equation and incompressible Navier–Stokes equation, which neglect the Reynolds stress:   

$$\frac{\partial }{\partial t}\left(\mathit{\epsilon }{\rho }_g\right)+\nabla \cdot \left(\mathit{\epsilon }{\rho }_g{\mathit{u}}_g\right)=0$$(3)

  

$$\frac{\partial }{\partial t}\left(\mathit{\epsilon }{\rho }_g\right)+\nabla \cdot \left(\mathit{\epsilon }{\rho }_g{\mathit{u}}_g{\mathit{u}}_g\right)=-\mathit{\epsilon }\nabla p_g+\mathit{\epsilon }{\mu }_g{\nabla }^2{\mathit{u}}_g+\mathit{\epsilon }{\rho }_g\mathit{g}+{\mathit{F}}_f$$(4)

where ε is the void fraction, ρ_g is the fluid density, u_g is the fluid velocity, p_g is the fluid pressure, and μ_g is the fluid viscosity. ε is calculated from the proportion of the solid existing within a local cell volume.¹²⁾

3.1.3. Particle–fluid Interaction Force¹⁷⁾

To determine F_f, Ergun’s equation¹⁸⁾ is applied in the low–void fraction region (ε < 0.8), and Wen-Yu’s equation¹⁹⁾ is applied in the high-void fraction region (ε > 0.8):   

$${\mathit{F}}_f={\beta }_t\left({\mathit{u}}_p-{\mathit{u}}_g\right)$$(5)

where β_t is the particle–fluid momentum exchange coefficient. The drag force coefficient is derived from the Schiller–Naumann equation expressed as a function of the particle Reynolds number. F_d is distributed to particles as a reaction force of F_f.

3.2. Heat Conduction Equations

3.2.1. Heat Transfer of Particles

The heat transfer of particles is divided into three components, as shown in Fig. 2(c): particle–fluid heat convection Q_conv, particle–particle conduction Q_cond, and particle–bed radiation Q_rad.²⁰⁾ Furthermore, to consider the heat generation by chemical reaction Q_reac, the equation of heat transfer of a particle is as follows:   

$$m_p{C}_{p,p}\frac{d{T}_p}{dt}=Q_{reac}-\left({\displaystyle \sum }_{j\ne i}^{N_c}\hspace{0.17em}{Q}_{cond}+Q_{conv}+Q_{rad}\right)$$(6)

where C_p,p is the particle heat capacity and T_p is the particle temperature. The heat transfer resistance inside the particle is neglected. However, the particle temperature can be assumed to be a constant temperature when Bi (= h_pd_p/λ_p) is sufficiently small.²¹⁾ Here h_p is the particle–fluid heat transfer coefficient and λ_p is the particle heat conductivity. In this study, the calculation conditions were satisfied under this condition. Interparticle heat exchange between particles i and j consists of heat transfer through a contacting surface Q_ct and heat conduction through the surrounding gas layer Q_cd.^{20,21,22,23,24)} The reaction heat Q_reac is calculated from the enthalpy change in each chemical equation:   

$$Q_{reac}={\displaystyle \sum }_{l=1}^{n_r}\left[R_l\cdot \left(-\mathrm{\Delta }{H}_{R,l}\right)\right]$$(7)

where l is the reaction equation number, n_r is the total number of equations, R_l is the reaction rate of l, and ΔH_R,l is the change in enthalpy of l. The particle–bed radiation heat Q_rad is given by Stefan–Boltzmann’s law.²⁵⁾ Heat transfer to the wall is not considered. Refer to the last article for details.¹⁴⁾

3.2.2. Heat Transfer of a Fluid

The equation of heat balance for a fluid cell is written as follows:   

$$\frac{\partial }{\partial t}\left(\mathit{\epsilon }{\rho }_g{C}_{p,g}{T}_g\right)+\nabla \cdot \left(\mathit{\epsilon }{\rho }_g{\mathit{u}}_g{C}_{p,g}{T}_g\right)=\mathit{\epsilon }{\lambda }_g{\nabla }^2{T}_g+Q_p$$(8)

where C_p,g is the fluid heat capacity, λ_g is the fluid heat conductivity, and Q_p is the particle–fluid heat exchange rate. Q_p is given by the particles in a unit volume.

3.2.3. Particle-fluid Convective Heat Transfer

The particle–fluid convective heat exchange rate Q_conv is given from the relative temperatures of the particle and fluid.   

$$Q_{conv}={\beta }_h{A}_p\left(T_{p,i}-T_g\right)$$(9)

To determine the particle–fluid convective heat exchange coefficient β_h, Wakao’s equation²⁶⁾ is applied in the low-void fraction region (ε < 0.8), and Ranz–Marshall’s equation²⁷⁾ is applied in the high-void fraction region (ε > 0.8).

3.3. Mass Transfer Equations

3.3.1. Mass Transfer of Solid Species

The mass transfer of the solid phase is described by discrete particle movements considering the generation or disappearance of composition i by a chemical reaction, as shown in Fig. 2(d).   

$$m_p\frac{d{\psi }_{s,i}}{dt}=S_{s,i}$$(10)

  

$$S_{s,i}=\frac{{\nu }_{i,l}{R}_l}{M_i}$$(11)

where ψ_s,i is the mass fraction of solid species i, S_s,i is the generation rate of i, ν_i,l is the stoichiometric coefficient of i in reaction equation l, and M_i is the molecular mass of i. In the system, the solid phase consists of the following nine species: Fe₂O₃, Fe₃O₄, FeO, Fe, C, Al₂O₃, SiO₂, CaO, and MgO.

3.3.2. Mass Transfer of Gas Species

The mass transfer of the gas phase is described by a Eulerian approach that considers the convection, diffusion, and generation or disappearance of composition i.   

$$\frac{\partial }{\partial t}\left(\mathit{\epsilon }{\rho }_g{\psi }_{g,i}\right)+\nabla \cdot \left(\mathit{\epsilon }{\rho }_g{\mathit{u}}_g{\psi }_{g,i}\right)=\mathit{\epsilon }{\Gamma }_{g,i}{\nabla }^2{\psi }_{g,i}+S_{g,i}$$(12)

  

$$S_{g,i}={\displaystyle \sum }_i^{N_V}{\displaystyle \sum }_{l=1}^{n_r}\left(\frac{{\nu }_{i,l}{R}_l}{M_i}\right)$$(13)

where ψ_s,i is the mass fraction of gas species i, Γ_g,i is the diffusion coefficient of i in the mixture gas, and S_g,i is the generation rate of i. The gas phase consists of the following six species: H₂, H₂O, CO, CO₂, O₂, and N₂.

3.4. Rate of Chemical Reaction

The reaction rate of coke and the gaseous phase is described by the heterogeneous catalytic reaction model.^28,29) Hence, the reaction rate is proportional to the molar concentration C_CO2 and particle surface area A_p, as shown by   

$$R_l=k_m{A}_p{C}_{C{O}_2}$$(14)

where the overall reaction rate coefficient k_m is given from the assumed compound rate of the chemical reaction and mass transfer:   

$$k_m={\left(\frac{1}{k_d}+\frac{1}{{\eta }_e{k}_{c,l}}\right)}^{-1}$$(15)

where k_d is the mass transfer coefficient, k_c,l is the chemical reaction rate coefficient of equation l, and η_e is the catalytic effectiveness factor.

To determine k_d, Wakao’s equation³⁰⁾ is applied in the low void fraction region (ε < 0.8), and Usui’s equation³¹⁾ is applied in the high void fraction region (ε > 0.8). η_e is given by the function of the Thiele number, which is the ratio of the ideal reaction rate. Diffusion in the grain was assumed to be negligible, and the inside of a particle was assumed to have the same temperature and composition as the surface. K_c,l is given from each reaction equation l.

(a) Solution loss reaction ··· (l = 1)   

$$\text{C}\left(\text{s}\right)+{\text{CO}}_2\left(\text{g}\right)=2\text{CO}\left(\text{g}\right)$$(16)

Many catalyst reaction mechanisms are used to describe the chemical reaction rate of a solution loss. In this study, the chemical reaction rate was considered to be a Langmuir–Hinshelwood mechanism type, where molecules react through adsorption at the particle surface; the reaction rate constant of Kobayashi et al. was used.³²⁾   

$$k_{c,1}=\frac{k_{1,1}}{1+k_{2,1}{p}_{\text{CO}}+k_{3,1}{p}_{{\text{CO}}_2}}$$(17)

Here, k_1,1 = exp(18.641–36758/T_g), k_2,2 = exp(–2.578 + 6898/T_g), and k_3,2 = exp(25.901 – 35234/T_g). When high reactivity coke was used, we set k_1,1 = exp(8.1432 – 14433/T_g).²⁸⁾

For the reaction of ore, the reduction of iron oxide by CO was simply considered. The composition of iron oxide changes with the oxidation degree: Fe₂O₃ (hematite), Fe₃O₄ (magnetite), FeO (wüstite), and Fe (iron). The reaction rate between the ore and gaseous phase is given from the multi-interface unreacted core model, which assumes the porosity in ore particles is small enough to reflect the multi-stage successive reaction in the same manner as a pellet.^33,34) The reaction rate in each stage is given by the rate function of the multi-interface model; see Ref. 33) for the detailed formulation. The equilibrium constant k_e,l, chemical reaction rate coefficient k_c,l, and effective diffusion coefficient D_e,l of reaction equation l are given by Takahashi et al.³⁵⁾

(b) Reduction reaction of hematite by CO ··· (l = 2)   

$$3{\text{Fe}}_2{\text{O}}_3\left(\text{s}\right)+\text{CO}\left(\text{g}\right)=2{\text{Fe}}_3{\text{O}}_4\left(\text{s}\right)+{\text{CO}}_2\left(\text{g}\right)$$(18)

Here, k_e,2 = exp(7.255 + 3720/T_p), k_c,2 = exp(–1.445 – 6038/T_p), and D_e,2 = exp(4.135 – 14080/T_p)/p_g.

(c) Reduction reaction of magnetite by CO ··· (l = 3)   

$${\text{Fe}}_3{\text{O}}_4\left(\text{s}\right)+\text{CO}\left(\text{g}\right)=3\text{FeO}\left(\text{s}\right)+{\text{CO}}_2\left(\text{g}\right)$$(19)

Here, k_e,3 = exp(5.289 – 4711/T_p), k_c,3 = exp(–2.515 – 4811/T_p), and D_e,3 = exp(–1.835 – 7180/T_p)/p_g.

(d) Reduction reaction of wüstite by CO ··· (l = 4)   

$$\text{FeO}\left(\text{s}\right)+\text{CO}\left(\text{g}\right)=\text{Fe}\left(\text{s}\right)+{\text{CO}}_2\left(\text{g}\right)$$(20)

Here, k_e,4 = exp(–3.127 + 2879/T_p), k_c,4 = exp(0.805 – 7385/T_p), and D_e,4 = exp(0.485 – 8770/T_p)/p_g.

3.5. Reaction Heat

The reaction heat is calculated from Kirchhoff’s law, which relates enthalpy to the composition and temperature.   

$$\mathrm{\Delta }{H}_{R,l}=\mathrm{\Delta }{H}_{298K,l}+{\int }_{298K}^{T_p}{C}_{p,l}dT$$(21)

Here, ΔH_298k,l is the standard enthalpy change of formation, and ΔC_p,l is the heat capacity change of chemical equation l. ΔH_298k,l, the heat capacity coefficients, and the heats of formation are from Ref. 36).

3.6. Physical Properties

3.6.1. Gas Prperties^37,38)

ρ_g is calculated from the ideal gas equation; thus, it is a function of temperature and pressure. μ_g and λ_g are calculated from the kinetic theory of molecules using component properties calculated from the Chapman–Enskog equation.^39,40)

3.6.2. Solid Properties

The ρ_p,i of coke is assumed to be constant, and the ρ_p,i of ore is calculated from the overall reduction degree of iron oxide. The particle shape is a complete sphere; thus, the particle is represented by its particle diameter. The d_p of coke ${\psi }_{s,C}{}^{\frac{1}{3}}$ decreases relative to based on the carbon mass fraction using the shrinking core model,²⁵⁾ and the d_p of ore is assumed to be constant. In this study, each particle size was set as much as possible close to actual particle diameter. λ_p is constant. The Young’s modulus and Poisson’s ratio are the same as specified in the previous article.¹²⁾

3.7. Solution Method

The particle’s new velocity and position after time step Δt are calculated explicitly. The second-order Adams–Bashforth method was used for time marching, and the Crank–Nicholson method was used for particle movement. The distinct cell model was used for high-speed particle detection.⁴¹⁾ For fluids, the well-known Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) scheme⁴²⁾ was used to solve Eqs. (3), (4), (8), and (12) and the conservation of momentum, energy, and mass for a fluid cell. Each term was discretized with second-order accuracy. The local void fractions for a fluid cell were obtained from the particle locations.¹²⁾ Original programs written in Fortran90/95 were used in this study; these were compiled by the Intel Fortran compiler Ver. 11.1 on UNIX and then run. In order to reduce the computation time, parallel processing of the program code was performed by OpenMP because over 2000000 particles were treated in this research. The CPU was an Intel Xeon^® X5680 (3.33 GHz, 6 cores) × 2, and the amount of memory was 24 GB.

3.8. Calculation Conditions

The simulated packed bed and boundary conditions are illustrated in Fig. 3. If the blast furnace is considered to have a total inner volume of approximately 5000 m³, a huge number of particles must be treated. In order to reduce the computation load, the calculation domain was set to a 2.0 m radius and 12.0 m height and assumed to be the shaft part of a blast furnace. The initial packed bed structure was derived by calculation of the particle charging processes. Coke and ore particles were alternately charged, and the initial conditions were formed as a layered structure. Our interest was in the influence of nut coke on the reduction behavior of ores when it is mixed in an ore layer. In earlier studies, two types of initial conditions were considered to determine the influence of particle arrangement: (a) coke–mix–ore (C–M–O) and (b) coke–ore–mix (C–O–M).^43,44) These studies were at the laboratory scale, however; small experiments included several scale factors, and they sometimes emphasized differences from the actual scale. A large-scale direct simulation assumed to be the scale of a test blast furnace was carried out. In this study, the total particle number was 2373990, and the particle number ratio of coke and ore was kept to 1:1 at the mixed layer. The diameter of nut cokes particles was set to the same value of ores in order to avoid percolation. The layer thickness ratio between coke, mix, and ore was kept at 1:1:2 under the assumption of a low coke condition. Hence, the ore layer was approximately 1.2 m thick, and the coke and mix layers were approximately 0.6 m thick each. Under the assumption of a low amount of reducing agent, the coke rate was set to 249.3 kg/t, and the ore-to-coke (O/C) weight ratio was 6.37.

Fig. 3.

Schematic diagrams of three-dimensional calculation domain.

The calculation conditions are shown in Table 1. The inlet gaseous phase conditions assumed a bosh gas without moisture. In order to analyze the temperature effect on the reduction behavior, the inflow temperature T_in was set to 1273 K, and the initial temperature of the system was (T_in–20) K. The calculation was carried out up to t = 3600 s in consideration of blast furnace operation condition and computational load. The reaction rate of nut coke was based on Ref. 27).

Table 1. Calculation conditions.

Solid parameters	coke	nut coke	ore
Particle number, –	98100	351279	1924611
Particle diameter, m	0.080	0.040	0.040
Young’s modulus, Gpa	5.40	5.40	35.00
Poisson’s ratio, –	0.22	0.22	0.24
Density, kg/m3	1050	1050	3950
Friction coefficient, –	0.43	0.43	0.43
Rotational friction coefficient, –	0.30	0.30	0.30
Heat conductivity, kW/m·K	0.005	0.005	0.010
Initial temperature, K		1253
Time step, s		1.0×10–5
Initial solid compositions
mass%C	88.1	88.1	0.0
mass%Fe2O3	0.0	0.0	79.7
mass%Fe3O4	0.0	0.0	0.0
mass%FeO	0.0	0.0	5.4
mass%Fe	0.0	0.0	0.0
mass%Al2O3	3.2	3.2	1.9
mass%CaO	0.004	0.004	7.2
mass%SiO2	8.3	8.3	4.8
mass%MgO	0.0	0.0	0.008
Gas parameters	mix gas
Number of grids	60×10×60
dr, m	0.20000
Cell size    dh, m	0.20000
dθ, rad	0.10472
Inlet velocity, m/s	2.0
Top pressure, kPa	101.325
Initial temperature, K	1253
Inlet temperature, K	1273
Time step, s	1.0×10–2
Inlet gas compositions
vol%CO	30.0
vol%CO2	10.0
vol%H2	0.0
vol%H2O	0.0
vol%N2	60.0
vol%O2	0.0

4. Results and Discussions

4.1. Distribution of CO Fraction and Gas Temperature

First, we consider the effect of nut coke on the gas components and temperature distribution. Figure 4 shows the vertical cross-sectional distributions of the CO volume fraction which passes along the calculation domain center under each condition at t = 3600 s. Note that the range of this scale is from 0.26 to 0.30. The CO fraction was gradually reduced with repeated increases and decreases through repetition of the reduction and solution loss reactions. The change in gas composition was observed at the boundary between the coke and ore layers where a mass flow and different reactions coexisted. The CO fraction was approximately 2% higher in the domain of three particles from a wall surface. This is because restraining the packed particles with the wall changes the structure; this reduces the retention time of the gaseous phase in the packed bed, so the gas is rich in CO.¹⁴⁾ The inclined layer shape was also reflected by the CO fraction in the radial direction. In case of a) and b), CO fraction at the top of the packed bed was slightly increased by the use of high reactivity coke due to the increase in solution loss reaction rate, as represented in Eq. (17). If the nut coke reaction rate is same to lump coke, there is no remarkable difference in particle arrangement conditions between C–M–O and C–O–M except for the inner unit.

Fig. 4.

CO volume fraction distributions (t = 3600 s, C: coke, O: ore, M: mix).

Figures 5 and 6 shows the longitudinal gas temperature and CO fraction distribution at t = 3600 s, respectively. The temperature fluctuated with the same period as the CO fraction corresponding to the particle arrangement. The exothermic reaction of ore reduction and the endothermic reaction of coke solution loss appeared reciprocally. In case of high reactivity coke of a) and c), the temperature fluctuation became remarkable due to the intensified solution loss reaction of coke. At this time, almost the entire calculation domain reached a steady state. Therefore, this model was in a similar state as the thermal reserve zone in a blast furnace.

Fig. 5.

Gas temperature distribution under each condition (r = 0.10 m, θ = π, t = 3600 s, C: coke, O: ore, M: mix).

Fig. 6.

CO volume fraction distribution under each condition (r = 0.10 m, θ = π, t = 3600 s, C: coke, O: ore, M: mix).

Figure 5(a) shows that the gas temperature periodically varied greatly with the high endothermic reaction of high-reactivity coke. The gas temperature in the thermal reserve zone stayed around 1273 K when conventional coke was used; however, it decreased to 1240 K when high-reactivity coke was applied. The thermal reserve zone temperature has been reported to show a decreasing tendency with increased coke reactivity by the mathematical model simulations.²⁸⁾ In this study, however, the coke rate was set very low to 249.3 kg/t; thus, a remarkable temperature increase was seen due to heat from the reduction reaction. Part of the ore layer kept the initial temperature, however the temperature in the lower part of each ore layer was reduced by the heat exchange with the coke. Because the reaction heat was divided by the ratio of specific heat between the solid and gas, it mainly contributed to the temperature change of the solid. This greatly influenced the particle reaction rate, which is described in the following section.

4.2. Reduction Degree Distribution for Each Ore Particle

A detailed investigation was carried out on the ore reduction rate. Figure 7 shows the vertical cross-sectional distributions of the degree of ore reduction passing along the calculation domain center in each condition at t = 3600 s. Note that the coke particles are indicated in blue. Most particles have not moved from initial arrangement. A remarkable increase appeared near the wall due to the above mentioned wall effect.⁴³⁾ Here, the reduction degree of ore in the mixed layer was lower than that in the ore layer. Moreover, the reduction degree of the ore layer became slightly lower when high-reactivity coke was used (a, c) rather than conventional coke (b, d).

Fig. 7.

Ore particle reduction degree distributions. Coke particles are indicated by blue particles (t = 3600 s, C: coke, O: ore, M: mix).

In order to discuss the reduction rate for each particle, Fig. 8 shows a partially enlarged view of the distribution for the ore particle reduction degree. Note that the range of this scale on the reduction degree was narrow from 6.00 to 6.65. On this scale, the change in reduction degree was seen on the particle level. This heterogeneity was influenced by the particle arrangement. The reduction rate in the upper part of the ore layers was increased by the relatively high temperature; however, the upper ore showed a lower reduction rate than the mixed layer.

Fig. 8.

Ore particle reduction degree distributions at vertical cross section of 2.0 m < h < 4.5 m at t = 3600 s. Coke particles are indicated by blue particles.

When conventional coke was used (b, d), the change in reduction degree due to the arrangement was not remarkable. However, the particle arrangement greatly influenced the reduction degree when high reactivity coke was used (a, c). The reduction degree for an ore layer was higher for the arrangement shown in (c) than that shown in (a). Such a change in ore reduction degree would directly affect the behavior of the cohesive zone. Because the melting point of oxide and pig iron are influenced by the concentrations of iron oxide and carbon, respectively, the oxygen potential is correlated to liquid forming.^45,46) In the arrangement shown in (c), the solid–liquid coexistence cohesive region shifted to the lower part of the blast furnace due to the high reduction degree of the ore layer. On the other hand, it was estimated that ores with a low reduction degree in the mixed layer extend the solid–liquid coexistence cohesive region.

A comparison of Figs. 5, 6, 7 and 8 shows that because reaction heat is transported to the upper part mostly by convective heat transfer, the large endothermic reaction of high reactivity coke makes the temperature of the layer just above significantly lower. Thus, using high reactivity coke does not enhance ore reduction reaction. At 1273 K, the decrease in temperature becomes a more dominant factor with regard to the decrease in reduction degree than the increase in the CO fraction. Yokoyama et al.⁴⁴⁾ carried out a laboratory-scale reduction experiment on an ore particle bed and reported that the reduction degree increased when high reactivity coke was uniformly mixed in an ore layer or arranged to be in the lower part of the ore layer. This is because their conditions involved a high coke rate of O/C = 4.6 and a temperature that increased continuously from 1173 K to 1473 K. The change in ore reducing rate by the use of high-reactivity coke is influenced by the coke rate, and the thermal reserve zone temperature is influenced by the use of high reactivity coke. In this study, although the charge of high reactivity coke has a negative effect on the reduction rate of ore due to the intensified solution loss reaction, these phenomena could be influenced by the reducibility of ore. When high reducibility ore was used, the reduction degree would be improved owing to the change of gas composition corresponding to Fe/FeO equlibrium.

4.3. Gasification Degree Distribution for Each Coke Particle

Figure 9 shows the vertical cross-sectional distributions of the degree of coke reaction in each condition at t = 3600 s, and Fig. 10 shows a partially enlarged view of the distribution for the coke particle gasification degree. Ores are indicated as blue particles. As shown in (c), the gasification degree of lump coke notably decreased compared with the other conditions. This is because the lump coke was arranged just above a mixed layer including a considerable endothermic reaction from the high-reactivity cokes, so the temperature of the coke layer was decreased. The arrangement of (c) could keep the permeability in the lower part of the furnace by protecting the lump coke so that it keeps its strength and grain size. As described in the preceding section, it might also improve ore reduction. When using high-reactivity coke, it should be just above an ore layer and directly under a coke layer (C–O–M).

Fig. 9.

Coke particle reaction degree distributions. Ore particles are indicated by blue particles (t = 3600 s, C: coke, O: ore, M: mix).

Fig. 10.

Coke particle gasification degree distributions at vertical cross section of 3.5 m < h < 5.3 m at t = 3600 s. Ore particles are indicated by blue particles.

Figure 11 shows the time change of the average gasification degree when high-reactivity coke was used. Both arrangement conditions indicated similar gasification rates for nut coke. However, when lump coke was compared, (a) showed a linear increase with time, but (c) showed a decrease in the reaction rate with time. Based on this result, high-reactivity coke gasifies more preferentially than lump coke in (c). By protecting lump cokes, the permeability might be maintained through keeping coke slits in the melting zone.

Fig. 11.

Variation in average gasification degree of lump coke and nut coke (h > 5.0 m).

4.4. Consideration of Reaction Heat Transfer

In this study, the particle diameter was the smallest unit of spatial discretization for calculation considered for heat and mass transfer. As we noted in our last article, the reaction heat is the dominant issue for heat transfer of each particle at this temperature scale.¹⁴⁾ Therefore, in this research, the reaction heat generated on the solid surface was divided between the solid and gas phases; understanding its mechanism is important to controlling temperature distribution. This is understood at spatial scales below the particle diameter. We assumed that the particle temperature is constant, so λ_p = ∞. The reaction heat on the solid surface is transferred to the inside of particle instantly. The quantity of reaction heat that accumulates inside the particles may have been overestimated.

One of our interests is the temperature distribution inside a solid particle and at its surface. In this case, if the surface imagery can be secured by a direct numerical simulation method, as shown in Fig. 1(c), the surface temperature distribution can be considered without too much trouble. Further examination will be required for the reaction mechanism and its heat distribution at the surface between a solid and gas.

5. Conclusions

The heat and mass transport behavior through a packed bed was studied in order to verify that the reduction properties and flow characteristics depend on the particle arrangement. In particular, the influence of small-size coke was considered for low reducing agent operation. In order to analyze the discontinuous behavior of each particle, a three-dimensional packed bed analysis model based on the Euler–Lagrange approach was used to reflect discrete particle properties; the model included the simultaneous analysis of particle and fluid flow. From the calculated results, the following results were obtained.

The exothermic reaction of ore reduction and the endothermic reaction of coke solution loss influenced each other in the packed bed. Therefore, when high-reactivity coke was used, although CO fraction increased, the decrease in the gaseous phase temperature occurred due to the intensified solution loss reaction rate at the nut coke mixed layer. As a result, the ore reduction rate decreased.

When using high-reactivity coke in the order of coke–ore–mix from the bottom, the reaction rate of the ore layer became relatively higher and the reaction rate of the lump coke layer decreased. In this arrangement, high reactivity coke was preferentially gasified to lump coke. The contribution of high reactivity coke to the ore reduction rate depends on the particle arrangement through the heat transfer and reaction heat. Accordingly, in the case of the mixed charge of the high reactivity nut coke in the ore layer, the design of the packed bed structure is important.

References

• 1)   E. A.  Mousa,  A.  Babich and  D.  Senk: ISIJ Int., 51 (2011), 350.
• 2)   S.  Nomura,  K.  Higuchi,  K.  Kunitomo and  M.  Naito: ISIJ Int., 50 (2010), 1388.
• 3)   M.  Naito,  A.  Okamoto,  K.  Yamaguchi,  T.  Yamaguchi and  Y.  Inoue: Tetsu-to-Hagané, 87 (2001), 357.
• 4)   K.  Higuchi,  S.  Nomura,  K.  Kunitomo,  H.  Yamaoka and  M.  Naito: ISIJ Int., 51 (2011), 1308.
• 5)   J.  Yagi: ISIJ Int., 33 (1993), 619.
• 6)   S.  Ueda,  S.  Natsui,  H.  Nogami,  J.  Yagi and  T.  Ariyama: ISIJ Int., 50 (2010), 914.
• 7)   X. F.  Dong,  A. B.  Yu,  S. J.  Chew and  P.  Zulli: Metall. Mater. Trans. B, 41 (2010), 330.
• 8)   R.  Safavi Nick,  A.  Tilliander,  T. L. I.  Jonsson and  P. G.  Jönsson: ISIJ Int., 53 (2013), 979.
• 9)   T.  Mitra,  L.  Shao and  H.  Saxén: SCANMET IV, Vol. 2, Swerea MEFOS, Luleå, (2012), 69.
• 10)   H.  Nogami,  H.  Yamaoka and  K.  Takatani: ISIJ Int., 44 (2004), 2150.
• 11)   S.  Yuu,  T.  Umekage,  S.  Matsuzaki,  M.  Kadowaki and  K.  Kunitomo: ISIJ Int., 50 (2010), 962.
• 12)   S.  Natsui,  H.  Nogami,  S.  Ueda,  J.  Kano,  R.  Inoue and  T.  Ariyama: ISIJ Int., 51 (2011), 41.
• 13)   S.  Natsui,  S.  Ueda,  H.  Nogami,  J.  Kano,  R.  Inoue and  T.  Ariyama, Steel Res. Int., 82 (2011), 964.
• 14)   S.  Natsui,  T.  Kon,  S.  Ueda,  J.  Kano,  R.  Inoue,  T.  Ariyama and  H.  Nogami: Tetsu-to-Hagané, 98 (2012), 341.
• 15)   P. A.  Cundall and  O. D. L.  Strack: Geotechnique, 29 (1979), 47.
• 16)   J. H.  Ferziger and  M.  Perić: Computational Methods for Fluid Dynamics, Springer Japan, Tokyo, (2003).
• 17)   Y.  Tsuji,  T.  Kawaguchi and  T.  Tanaka: Powder Technol., 77 (1993), 79.
• 18)   S.  Ergun: Chem. Eng. Prog., 48 (1952), 89.
• 19)   C. Y.  Wen and  Y. H.  Yu: Chem. Eng. Prog. Symp. Series, 62 (1966), 100.
• 20)   D.  Rong and  M.  Horio: 2nd Int. Conf. on CFD in the Minerals and Process Industries, CSIRO, Melbourne, (1999), 65.
• 21)   T.  Sakurai,  T.  Minami,  T.  Kawaguchi,  T.  Tsuji,  T.  Tanaka and  Y.  Tsuji: Trans. Jpn. Soc. Mech. Eng. Ser. B, 75 (2009), 1041.
• 22)   W. L.  Vargas and  J. J.  McCarthy: Int. J. Heat Mass Transf., 45 (2002), 4847.
• 23)   K.  Kuwagi,  H.  Hirno and  T.  Takami: Jpn. J. Heat Mass Transf., 1 (2007), 49.
• 24)   Y.  Kaneko,  T.  Shiojima and  M.  Horio: Chem. Eng. Sci., 54 (1999), 5809.
• 25)   H.  Zhou,  G.  Flamant and  D.  Gauthier: Chem. Eng. Sci., 59 (2004), 4193, 4205.
• 26)   N.  Wakao,  S.  Kaguei and  T.  Funazkri: Chem. Eng. Sci., 34 (1979), 325.
• 27)   W. E.  Ranz,  W. R.  Marshall, Jr.: , Chem. Eng. Prog., 48 (1952), 141, 173.
• 28)   H.  Nogami,  T.  Yamamoto and  K.  Miyagawa: Tetsu-to-Hagané, 96 (2010), 319.
• 29)   K.  Hashimoto: Hannou kougaku, Rev. ed., Baihukan, Tokyo, (1993), 224.
• 30)   N.  Wakao and  T.  Funazkri: Chem. Eng. Sci., 33 (1978), 1375.
• 31)   T.  Usui,  M.  Naito,  T.  Murayama and  Z.  Morita: Tetsu-to-Hagané, 80 (1994), 431.
• 32)   S.  Kobayashi and  Y.  Omori: Tetsu-to-Hagané, 63 (1977), 1081.
• 33)   Y.  Hara,  M.  Sakawa and  S.  Kondo: Tetsu-to-Hagané, 62 (1976), 315.
• 34)   R. H.  Spitzer,  F. S.  Manning and  W. O.  Philbrook: Trans. Metall. Soc. AIME, 236 (1966), 1715.
• 35)   R.  Takahashi,  Y.  Takahashi,  J.  Yagi and  Y.  Omori: Ironmaking Conf. Proc., 43 (1983), 485.
• 36)   O.  Kubaschewski and  C. B.  Alcock: Metallurgical Thermochemistry, 5th ed., Pergamon, Oxford, (1979).
• 37)   C. R.  Wilke: J. Chem. Phys., 18 (1950), 517.
• 38)   F. A.  Williams: Combustion Theory, 2nd ed., Benjamin- Cummings Publishing Co., Menlo Park, (1985).
• 39)   R. B.  Bird,  W. E.  Stewart and  E. N.  Lightfoot: Transport Phenomena, 2nd ed., John Wiley & Sons, New York, (2006), 23, 274, 525, 866.
• 40)   B. E.  Poling., J. M. Prausnitz and J. P. O’ Connell: The Properties of Gases and Liquids, 5th ed., McGraw-Hill, New York, (2000), 11.6, B.1.
• 41)   H.  Mio,  A.  Shimosaka,  Y.  Shirakawa and  J.  Hidaka: Adv. Powder Technol., 18 (2007), 441.
• 42)   S. V.  Patankar: Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, (1980).
• 43)   R.  Shibasaki,  S.  Natsui,  T.  Kon,  S.  Ueda,  R.  Inoue and  T.  Ariyama: Tetsu-to-Hagané, 99 (2013), 391.
• 44)   K.  Yokoyama,  K.  Higuchi,  S.  Nomura and  K.  Kunitomo: CAMP-ISIJ, 25 (2012), 949.
• 45)   T.  Arato,  M.  Tokuda and  M.  Ohtani: Tetsu-to-Hagané, 68 (1982), 2263.
• 46)   K.  Nagata,  N.  Tsuchiya,  M.  Sumito and  K. S.  Goto: Tetsu-to-Hagané, 68 (1982), 2271.