Estimation of Particle Segregation Behavior in Ore-coke Mixed Layer Using Screening Layer Model

Abstract

To achieve low RAR operation by coke mixed charging, it is important to control coke segregation behavior in mixed layer at blast furnace top. In this study, a numerical simulator based on screening layer model was developed to estimate the distribution of mixed coke ratio in mixed layer. The results are summarized as follows:

(1) The parameters required for the screening layer model to estimate the segregation behavior of the burden materials were determined by PIV test and numerical fitting.

(2) The screening layer model containing parameters obtained by experiments and fittings was taken into the blast furnace burden distribution simulator. The simulation results showed that the distribution of mixed coke ratio of the small coke in the ore can be accurately estimated under the charging conditions of the actual furnace.

(3) The influence of the difference in tilting direction of the rotating chute on the distribution of mixed coke ratio was evaluated. In the reverse tilting, the radial distribution of the mixed coke ratio became more uniform as compared with the forward tilting charging. Therefore, it is considered that reverse tilting is more effective for carrying out coke mixed charging.

1. Introduction

In recent years, reduction of CO₂ emissions has become an important issue from the viewpoint of global warming prevention. In the steel industry, further promotion of low reducing agent ratio (RAR) and low coke ratio operation to reduce CO₂ emission is required in future blast furnace operation. In order to reduce RAR, the preferential reduction of lump coke is required, however in this case, the ore-to-coke ratio (O/C) increases, and this causes various problem such as a decrease in gas permeability in the furnace due to enlargement of the cohesive zone. Coke mixed charging in the ore layer is known as one of operational improvement at such a high weight ratio of ore. At Nippon Steel’s Hirohata Works, under-size coke (small coke) was initially applied to coke mixed charging for effective utilization of energy.¹⁾ Next, small coke mixed charging at ratio of 28 kg/t-pig and 50 kg/pig was carried out at Nippon Steel’s Kimitsu and Oita Works, respectively^2,3) and improvement of gas permeability in the furnace bottom and reducibility were reported. Watakabe et al. studied the effect of coke mixing on the high temperature properties of the ore-coke mixed layer by an under-load-reduction test,⁴⁾ finding that the gas permeability in the cohesive zone clearly increased. In addition to that effect, it has been suggested that coke mixed charging also improves reducibility by decreasing the gasification temperature of the coke. This is based on the principle that the reduction equilibrium point of FeO–Fe can be controlled by decreasing the thermal reserve zone temperature in the blast furnace by lowering the gasification temperature of coke.⁵⁾

In order to maximize the effect of coke mixed charging, in addition to evaluation of the effect on the blast furnace, including the gas permeability of mixed coke,⁶⁾ a technique the realizes high controllability of the mixability of burden materials of different particle diameters and densities is also needed. This is because the burden materials are granular, and ore and coke tend to separate during charging due to segregation caused by the difference in their particle diameters and densities. Some experimental results and quantitatively arranged models have been reported in this connection. For example, Okuno et al.⁷⁾ developed a model that considers the change in particle size segregation caused by the deposition of burden materials based on the results of experiments and measurements in a blast furnace. Segregation has also been quantified by numerical simulations using the discrete element method (DEM),^8,9,10) in which the trajectories of the individual particles in granular materials are calculated based on Newton’s equation of motion. DEM is a promising method because it is possible to reproduce the behavior unique to granular materials, but is computationally intensive because it targets all particles in the granular material. This is a problem in actual blast furnace operation, in that the segregation behavior of the burden materials must be estimated quickly and reflected in operation at an early stage. Based on the above, in order to propose appropriate burden distribution corresponding to changes in operating conditions and material properties and to apply it to operation at an early stage, the segregation phenomena of small coke from the ore layer was estimated, and a model that can easily calculate the distribution of the mixed coke ratio in the blast furnace radial direction was developed. In addition, improvement of operational efficiency by effective utilization of small coke was also investigated by using developed model.

2. Development of Model of Coke Segregation in Mixed Layer Using Screening Layer Model

2.1. Outline of Screening Layer Model

In this paper, the screening layer model proposed by Shinohara¹¹⁾ was used to estimate the segregation behavior of coke in ore. As described above, the segregation phenomena of granular materials are roughly classified into particle size segregation caused by particle diameter difference and density segregation caused by density difference. The screening layer model can describe these phenomena in a unified manner. The outline of the screening layer model is explained below.

When granular materials consisting of mixed particles with different physical properties such as particle diameter and density are supplied to a deposition surface, they flow down the deposition surface while forming an angle of repose. Segregation occurs in the flowing particle layer, and the low fluidity particles (small particles) pass from the top to the bottom in the flow layer. The small particles reaching the lower deposition surface are delayed by the upper layer while being dragged by the upper layer. At this time, as shown in Fig. 1, three layers are formed in the flowing layer, consisting of a “Remained layer” with segregated particles (large particles), a “Segregating layer” composed of a mixture of large and small particles, and a “Separated layer” in which the small particles are separated from the mixed components. It is assumed that the small particles which are transferred to the separation layer are further packed in the lower stationary layer (“Static layer”).

Fig. 1.

Concept of screening layer model. (Online version in color.)

By taking the mass balance of small particles in each layer, the following Eqs. (1), (2), (3) and (4) are obtained:   

$$\frac{\partial h_r}{\partial t}=-\frac{\partial (h_r\cdot v_r)}{\partial x}+\frac{Q\cdot cos\varphi }{1-{\epsilon }_r}\frac{1-M_i}{M_i},$$(1)

  

$$\frac{\partial h_{rs}}{\partial t}=-\frac{\partial (h_{rs}\cdot v_r)}{\partial x}-\frac{Q\cdot cos\varphi }{M_i(1-{\epsilon }_{rs})},$$(2)

  

$$\frac{\partial h_s}{\partial t}=-\frac{\partial (h_s\cdot v_s)}{\partial x}+\frac{Q-P}{(1-{\epsilon }_s)}cos\varphi ,$$(3)

  

$$\frac{\partial h_{sp}}{\partial t}=-\frac{P\cdot cos\varphi }{1-{\epsilon }_s}.$$(4)

Where, Q is the moving velocity of small particles per unit cross section in the vertical direction from the “Segregating layer” to the “Separated layer” [m³/(m²·s)] , P is the moving velocity of small particles per unit cross section in the vertical direction from the “Separated layer” to the “Static layer” below [m³/(m²·s)], h is the thickness of each layer [m], t is time [s], v is the velocity of particles along the deposition surface in each layer [m/s], x is the distance along the deposition surface from the feed point of the particles [m], M_i is the mixed ratio of initial small particles on a volume basis [–], ε is the void fraction of each layer [–], and ϕ is the angle of repose of the mixed powder of coke and sinter ore particles [rad]. The subscripts r, rs, s and sp denote the “Remained layer”, the “Segregating layer”, the “Separated layer” and the “Static layer”, respectively. The following assumptions are made in solving Eqs. (1), (2), (3) and (4). First, since the angle of repose, ϕ, formed by granular materials while flowing down the slope is constant, the downflow layer always flows down with a uniform thickness, h_t, in order to maintain this angle. When the ratio of the particle velocity of the “Separated layer” to that of the “Segregating layer” is R, R directly corresponds to the physical properties of the particles and seems to be unrelated to the operating conditions in the experiment,¹³⁾ and it is assumed to be constant under the two - component system of coke and sintered ore. Namely, the following Eqs. (5), (6) and (7) are considered:   

$$h_r(t,x)+h_{rs}(t,x)+h_s(t,x)=h_t,$$(5)

  

$$\frac{\partial h_t}{\partial t}=0,$$(6)

  

$$\frac{v_s(t,x)}{v_r(t,x)}=R.$$(7)

The moving velocity of the small particles to the “Static layer” is 0 (P = 0). Equations (1), (2) and (3) are added, and by considering Eqs. (5), (6) and (7), the following equation is obtained:   

$$\begin{array}{l}{\displaystyle \frac{\partial \left\{v_r(h_r+h_{rs}+h_s\cdot R)\right\}}{\partial x}}=\\ {\displaystyle \frac{Q}{M_i}}\left({\displaystyle \frac{1-M_i}{1-{\epsilon }_r}}-{\displaystyle \frac{1}{1-{\epsilon }_{rs}}}\right)\cdot cos\varphi +{\displaystyle \frac{Q}{1-{\epsilon }_s}}\cdot cos\varphi .\end{array}$$(8)

The void fractions of each layer were assumed to be constant while the granular materials were flowing,¹⁴⁾ and the respective values were assumed to be ε_r = 0.4, ε_rs = 0.35 and, ε_s = 0.4.¹⁴⁾ By differentiating and numerically solving Eq. (8), the thicknesses of each layer in the downward flow direction of the granular materials at an arbitrary time are calculated, and the distribution of the mixing ratio based on the volume can be estimated. However, since the ratio R of the particle velocity of the “Separated layer” to that of the “Segregating layer” and the velocity Q of the ore in Eq. (8) are unknown values, it is necessary to determine these values by some method. Because it is assumed that lump coke is mixed⁴⁾ in addition to small coke when coke is mixed and charged into sintered ore, it is desirable that R and Q are values which can correspond to the change of particle diameter. The procedure for determining R and Q will be explained below.

2.2. Measurement of Velocity Ratio R Using PIV

2.2.1. Experimental Method

The velocity ratio R, which was conventionally treated as a parameter,^11,12,13,14) was measured in this paper by directly observing the motion of particles in the layer. Figure 2 shows a schematic diagram of the experimental apparatus. Sintered ore which is actually used in blast furnace and pumice simulating coke were used as samples. (For convenience, pumice is called coke below.) Table 1 shows the particle diameter of each sample. The particle diameter of the sintered ore was kept constant and the particle diameter of the coke was changed, and the effects of changes in the particle diameter ratio D_p,Coke/D_p,Sinter on the velocity ratio R were investigated. D_p,Coke and D_p,Sinter were the arithmetic mean diameters of the coke and sintered ore, respectively. First, sintered ore and coke were charged from the upper part of an acrylic rectangular vessel with dimensions of 50 mm in depth and 300 mm in width to the vessel end. The charging rates of the sintered ore and coke were 515 g/s and 22 g/s, respectively. Next, the behavior of the sintered ore and coke flowing down the surface of the deposited layer during charging was photographed using a high-speed camera at a photographing speed of 500 fps. PIV (Particle Image Velocimetry) processing was applied to the moving image photographed by the high-speed camera. The velocity distribution of the particles in the surface layer was calculated when the deposit layer was formed and the motion of the burden materials reached the steady state. Here the steady state is defined as the time when the angle (angle ϕ in Fig. 2.) formed at the bottom of the deposit layer converges to a constant value. The velocity distributions of 70 frames were measured after reaching the steady state, and their average values were taken as the velocity distributions in each case (Case 1, 2, 3) in Table 1. The measurement position of the velocity distribution was the surface layer of the midpoint between the deposit layer skirt position and the burden falling position, and the measurement direction was the direction perpendicular to the sedimentary layer slope. The velocities of the “Separated layer” and the “Segregating layer” were obtained from the obtained velocity distribution, and their ratio was defined as R.

Fig. 2.

Schematic diagram of experimental apparatus. (Online version in color.)

Table 1. Particle diameter of the sample used in PIV test.

		Case 1	Case 2	Case 3
Particle diameter [mm]	Sinter		0.8–1.4
	Coke	1.4–1.7	2.4–2.8	3.3–4.0
Particle diameter ratio [–]		1.4	2.4	3.3

2.2.2. Experimental Results

Figure 3 shows an example of a PIV-processed image for a moving image taken at the time of charging. It was confirmed that the velocity distribution of the burden materials in the surface layer can be estimated appropriately by PIV treatment. Figure 4 shows the velocity distribution of the burden materials on the surface layer for each case in Table 1. The velocity of the burden materials decreased from the top to the bottom in each case. At the same layer height, the burden material velocity in each case increased with increasing particle diameter ratio. A similar tendency was observed in the velocity distribution in the layer in all cases shown in Fig. 4. As shown in Fig. 5, the velocity of the burden materials decreased from the top of the layer to the bottom at a constant gradient (region AB), and then decreased at a constant gradient (region BC) through an intermediate inflection point (point B). Therefore, in this paper, the “Remained layer” and the “Segregating layer” after the separation of ore and coke correspond to region AB in Fig. 5, and the “Separated layer” mainly composed of ore particles corresponds to region BC. Then, the average values of the velocities in each region were defined as v_r and v_s in Eqs. (1) and (3), and the velocity ratio R shown in Eq. (7) was calculated. Figure 6 shows the velocity ratio R for each case in Table 1. The velocity ratio R decreased with increasing particle diameter ratio. The angular velocity of the particles rolling and flowing down the slope increases with increasing particle diameter.¹⁵⁾ It is considered that the increase of R is caused by the increase of the moving velocity of the large particle side with the increase in the particle diameter ratio, that is, the increase in the particle diameter of the large particle side.

Fig. 3.

Image of PIV analysis. (Online version in color.)

Fig. 4.

Distribution of velocity of burden materials in the height direction of deposition layer.

Fig. 5.

Definition of high and low speed area in layer.

Fig. 6.

Velocity ratio of separated layer to segregating layer for each particle diameter ratio. (Online version in color.)

From the results shown in Fig. 6, a linear relationship was observed between the particle diameter ratio and the velocity ratio R. Based on the values of the particle diameter ratios shown in Table 1 and the results in Fig. 6, the velocity ratio R was used as a function of the particle diameter ratio as shown in the following Eq. (9):   

$$R=-0.0575\left(\frac{D_{p,Coke}}{D_{p,Sinter}}\right)+\mathrm{0.6177.}$$(9)

2.3. Determination of Moving Velocity Q of Sintered Ore

2.3.1. Measurement and Calculation Method

Next, the moving velocity Q of the sintered ore from the “Segregating layer” in Eq. (8) was determined. A simulation by the model described later was carried out under the same condition as the experiment described below, and this parameter Q was obtained by trial and error so that the result by the simulation approached the experimental result. The experiment was carried out using blast furnace charging model equipment (scale ratio: 1/17.8 of Fukuyama No. 5 blast furnace) which simulated the charging system of a bell-less top blast furnace. A schematic diagram of the experimental apparatus and the experimental conditions are shown in Fig. 7 and Table 2, respectively. The experimental conditions and the sample particle diameter were determined according to the scale ratio of the charging equipment.¹⁶⁾ The particle diameter of the sample particle was made to be 1/17.8 of that of the actual furnace in accordance with the scale ratio. The Froude number was fitted to the actual system. In the experiment, the slope angle of the coke deposit layer was set to 30° in advance. Then, ore and coke packed in different bunkers were simultaneously charged onto the coke deposit layer surface via a rotating chute. The angle (hereinafter referred to as tilting angle) between the rotating chute and the furnace center during charging of the sintered ore and coke was fixed at 52°, and the number of rotations was 8. Next, the mixed coke ratio at each position in the radial direction of the burden deposit layer was measured after charging was completed. A circular tube with an inner diameter of ϕ30 mm was inserted from the surface at various points in the radial direction of the deposit layer, and the sintered ore and coke were sampled in the circular tube. After sampling, the sintered ore and coke were separated by specific gravity using a sodium iodide aqueous solution, and their respective weights were measured. The mixed coke ratio was defined by the following Eq. (10):   

$$Mixed\mathrm{\hspace{0.17em} }Coke\mathrm{\hspace{0.17em} }Ratio=\frac{W_{Coke,i}}{W_{Coke,i}+W_{Sinter,i}}.$$(10)

The mixed coke ratio at each position in the radial direction was calculated from the obtained weight. In Eq. (10), W_Coke,i and W_Sinter,i represent the coke and sintered ore weight [kg] at each radial sampling point i (i = 1, 2, 3,..., 6), respectively. According to the definition in Eq. (10), the set value of the mixed coke ratio in this experiment is 0.44/(10 + 0.44) = 0.042 because the total weight of coke is 0.44 kg and the total weight of sintered ore is 10 kg according to Table 2.

Fig. 7.

Schematic diagram of experimental apparatus. (Online version in color.)

Table 2. Experimental conditions.

Angle of burden surface	[°]	30
Particle diameter ratio	[–]	0.3, 0.8, 1.7, 3.4
Tilting angle of rotating chute	[°]	52
The number of rotation	[–]	8
Rotation speed	[rpm]	42
Charged sinter weight	[kg]	10
Charged mixed coke weight	[kg]	0.44

Next, the distribution of the mixed coke ratio in the radial direction obtained by the experiment was fitted by the model, and the moving velocity Q of the sintered ore in Eq. (8) was determined. The velocity ratio R shown in Eq. (9) obtained by the above experiment was substituted into Eq. (8) as a function of the particle diameter ratio of sintered ore and coke. A subroutine to calculate the radial mixed coke ratio distribution by differentiating Eq. (8) was newly incorporated into the existing burden distribution estimation model.¹⁷⁾ This model is capable of estimating the falling trajectory of the burden from the rotating chute and the layer thickness and particle diameter distribution of the sintered ore and coke in the radial direction after charging in a bell-less top blast furnace. The simulation was carried out under the same condition as the experiment using this model, and the results were compared with the measured result obtained in the experiment.

2.3.2. Measurement and Calculation Results

Figure 8 shows the distribution of the mixed coke ratio in the radial direction obtained by the experiment. In this experiment, the falling position of the burden is constant (r/R₀ ≒ 0.7) because the burden is charged while the tilting angle is constant, and a deposition shape with skirts on the furnace center side and peripheral side (wall side) of the falling position is formed. Therefore, as the distance in the radial direction from the falling position increased, coke segregated and the mixed coke ratio increased. As the particle diameter ratio decreased, coke segregation was suppressed and the distribution of the mixed coke ratio became uniform, approaching the set value (0.042). Figure 9 shows the results of calculation of the mixed coke ratio distribution in the radial direction by the burden distribution estimation simulator. The calculation results show that the moving velocity Q is fitted to the experimental results for each particle diameter ratio. As can be seen from Fig. 9, the calculation results by this simulator can express the experimental results that coke segregates and the mixed coke ratio increases with increasing distance from the falling position. Figure 10 shows the value of the moving velocity Q determined by fitting at each particle diameter ratio. It is found that the fitted moving velocity Q increases with increasing particle diameter ratio, and coke, which is a large particle, and sintered ore, which is a small particle, separate more easily. In order to introduce the moving velocity Q obtained by fitting into the burden distribution estimation simulator, Q was defined as a function of the particle diameter ratio of large particles and small particles from the results in Fig. 10, as shown in the following Eq. (11):   

$$Q=0.0033ln\left(\frac{D_{p,Coke}}{D_{p,Sinter}}\right)+\mathrm{0.0065.}$$(11)

Fig. 8.

Radial distribution of mixed coke ratio (Experiment). (Online version in color.)

Fig. 9.

Radial distribution of mixed coke ratio (Calculation).

Fig. 10.

Fitted penetration rate of segregating component for each particle diameter ratio. (Online version in color.)

3. Validation of Model

The velocity ratio R and the moving velocity Q determined by the experiment and fitting were introduced into the burden distribution estimation simulator, and the estimation accuracy of the distribution of the mixed coke ratio in sintered ore was verified by the developed model. First, using a blast furnace charging apparatus model simulating a bell-less top blast furnace as in the previous section, samples were charged in a pattern similar to the charging pattern of the burden in an actual blast furnace, and the distribution of the mixed coke ratio in the radial direction was measured. Table 3 shows the charging amount and charging time of each sample used in the experiment. Charging of the total amount of sintered ore and coke was divided into two times for both the ore and the coke; first, the coke was charged twice, after which the sintered ore was charged twice. This was defined as one charge, and a total of three charges were carried out. Table 3 shows the charging amount and charging time of lump coke (Coke 1, 2), small coke mixed in sintered ore (Small coke 1, 2) and sintered ore (Ore 1, 2). The rotating velocity of the rotating chute was 42 rpm, as described above. Figure 11 shows the particle size distribution of each sample used in the experiment. The particle diameter of each sample was adjusted to the particle diameter of coke and sinter ore used in the actual furnace at the same scale ratio as the experimental apparatus. The tilting angle of the rotating chute was adjusted sequentially during rotating according to the operation. In this paper, the experiments and burden distribution estimation simulator calculations were carried out for two cases: Case 1 (conventional tilting), in which the tilting angle θ gradually decreases during sintered ore charging in a given charging pattern and charging is performed from the peripheral side in the radial direction to the center side, and Case 2 (reverse tilting) in which the tilting angle θ gradually increases and charging is performed from the center side to the peripheral side. In both Case 1 and Case 2, the tilting range of the rotating chute was 50° to 28.5°. In addition, it is confirmed by visual observation that the flow down and segregation of the sample have been completed on the same sedimentary surface before the next charge after the completion of charging in each rotatings.

Table 3. Charged weight and charged time.

	Charging weight [kg]	Charging time [s]
Coke 1	2.4	17
Coke 2	2.4	24
Ore 1	19.2	23
Small coke 1	0.8	23
Ore 2	10.3	13
Small coke 2	0.43	13

Fig. 11.

Particle size distribution of sinter, coke and small coke.

Figure 12 shows the experimental results of the mixed coke ratio of small coke in the radial direction at the top sedimentation surface and the calculation results by the burden distribution estimation simulator. The calculation results for both Case 1 and Case 2 reproduced the experimental results well. As a result, it was confirmed that the simulator with the screening layer model can estimate the distribution of the mixed coke ratio of small coke with high accuracy even under the charging conditions of an actual furnace, and the simulator can cope with cases in which the charging condition changes drastically, such as from conventional to reverse tilting. In the experimental and calculation results, the mixed coke ratio in the furnace center increased during the conventional tilting charging of Case 1. This is because the burden materials flow into the furnace center due to the fact that the burden is charged from the peripheral side to the center side, and as a result, small coke, which has a larger particle diameter than that of sintered ore, segregates and is concentrated in the furnace center. On the other hand, in the reverse tilting charging of Case 2, the mixed coke ratio in the furnace center decreases, showing a value close to the set value (67 kg/t) at a non-dimensional radius of less than 0.2, and had a comparatively uniform distribution in comparison with the conventional tilting charging of Case 1. This is because the burden materials are charged from the center side to the peripheral side in reverse tilting charging, and as a result, the inflow of the sintered ore to the center during charging is suppressed and segregation is difficult. Since the uniformity of the mixed coke ratio in the radial direction and the decrease of the mixed coke ratio in the furnace center are expected to improve permeability,¹⁸⁾ reverse tilting charging is considered to be effective for more efficient expression of the effect by coke mixed charging.

Fig. 12.

Experimental and calculation results of mixed coke ratio. (Online version in color.)

4. Conclusion

In order to establish the low RAR operation by coke mixed charging, a model which can estimate the distribution of the mixed coke ratio in the ore layer with high accuracy was developed. The findings are summarized below.

(1) The parameters required for the screening layer model to estimate the segregation behavior of granular materials were determined by model experiments and fitting using PIV.

(2) The results of a simulation using the screening layer model confirmed that the distribution of the mixed coke ratio in the ore layer could be estimated with high accuracy under the charging conditions of actual furnaces by introducing a screening layer model including parameters obtained by experiments and fitting into the burden distribution simulator.

(3) The effect of the difference of the tilting direction of the rotating chute (conventional or reverse tilting charging) on the distribution of the mixed coke ratio was evaluated. Compared with conventional tilting charging, in reverse tilting charging, the radial distribution of the mixed coke ratio was more uniform and decreased in the center. Therefore, it was estimated that reverse tilting charging is more effective in coke mixed charging.

References

• 1)   Y.  Shimomura,  K.  Kushima,  F.  Sato and  S.  Arino: Tetsu-to-Hagané, 62 (1976), S404 (in Japanese).
• 2)   K.  Okuda,  K.  Yamaguchi,  N.  Ishioka,  K.  Furukawa and  H.  Endo: Tetsu-to-Hagané, 70 (1984), S102 (in Japanese).
• 3)   K.  Anan,  T.  Nagane,  K.  Nagata,  N.  Ogata,  M.  Honda and  M.  Isobe: CAMP-ISIJ, 12 (1999), 234.
• 4)   S.  Watakabe,  K.  Takeda,  H.  Nishimura,  S.  Goto,  N.  Nishimura,  T.  Uchida and  M.  Kiguchi: ISIJ Int., 46 (2006), 513.
• 5)   S.  Watakabe,  T.  Nouchi,  T.  Hirosawa and  M.  Sato: CAMP-ISIJ, 26 (2013), 21, CD-ROM, (in Japanese).
• 6)   Y.  Kashihara,  Y.  Iwai,  T.  Sato,  N.  Ishiwata and  M.  Sato: Tetsu-to-Hagané, 102 (2016), 661 (in Japanese).
• 7)   Y.  Okuno,  S.  Matsuzaki,  K.  Kunitomo,  M.  Isoyama and  Y.  Kusano: Tetsu-to-Hagané, 73 (1987), 91 (in Japanese).
• 8)   S.  Matsuzaki and  Y.  Taguchi: Tetsu-to-Hagané, 88 (2002), 823 (in Japanese).
• 9)   H.  Mio,  S.  Komatsuki,  M.  Akashi,  A.  Shimosaka,  Y.  Shirakawa,  J.  Hidaka,  M.  Kadowaki,  H.  Yokoyama,  S.  Matsuzaki and  K.  Kunitomo: ISIJ Int., 50 (2010), 1000.
• 10)   K.  Terui,  Y.  Kashihara,  T.  Hirosawa and  T.  Nouchi: ISIJ Int., 57 (2017), 1804.
• 11)   K.  Shinohara: J. Soc. Powder Technol. Jpn., 19 (1982), 462 (in Japanese).
• 12)   K.  Shinohara and  B.  Golman: Chem. Eng. Sci., 57 (2002), 277.
• 13)   K.  Shinohara and  S.  Takamatsu: J. Soc. Powder Technol. Jpn., 17 (1980), 630 (in Japanese).
• 14)   M.  Rahman,  K.  Shinohara,  H. P.  Zhu,  A. B.  Yu and  P.  Zulli: Chem. Eng. Sci., 66 (2011), 6089.
• 15)   S.  Miwa: Funryutai Kogaku, Asakura Shoten, Tokyo, (1972), 221 (in Japanese).
• 16)   S.  Miyagawa,  K.  Takeda,  S.  Taguchi,  T.  Morimoto,  M.  Fujita and  H.  Fujimori: Kawasaki Steel Giho, 23 (1991), 130 (in Japanese).
• 17)   T.  Sato,  T.  Nouchi and  M.  Kiguchi: Kawasaki Steel Tech. Rep., 29 (1997), 30 (in Japanese).
• 18)   A.  Murao,  Y.  Kashihara,  N.  Oyama,  M.  Sato,  S.  Watakabe,  K.  Yamamoto and  Y.  Fukumoto: ISIJ Int., 55 (2015), 1172.