Effect of the Size of Coal Briquette on Its Internal Structure

Abstract

This study examines the effect of container size on coal briquette’s internal structure using the Discrete Element Method. It found that when the frictional resistance between particle and wall was large and the inner diameter small, the difference in particle filling ratio between the upper and lower parts of the briquette was significant. Conversely, with a larger inner diameter, this difference nearly disappeared. The distribution of contact force indicated that the frictional force’s inhibiting effect on force transmission lessened with a larger container’s inner diameter. The study also revealed that the height of the container affects the briquette’s internal structure, and these results can be summarized by the container’s height to diameter ratio. Essentially, a larger ratio led to a linear increase in the difference in filling ratio between the upper and lower parts of the briquette.

1. Introduction

In a blast furnace, coke serves as a heat source, a reductant for iron ore and a spacer to maintain good ventilation inside the furnace. In particular, since the role of coke as a spacer is difficult to replace by other materials at present, high strength is one of the properties required of coke.¹⁾ For this reason, many studies have been conducted on the strength and fracture phenomena of coke.²⁾ Kubota et al.³⁾ observed coke using an optical microscope and quantitatively evaluated pore circularity by image processing, showing a negative correlation between the percentage of low circularity pores and coke strength. The research group at Newcastle University is evaluating the strength of coke by abrasion^4,5) and compression⁶⁾ tests while observing the coke with X-ray computed tomography (CT) and discussing the results with image processing.^7,8) In recent years, numerical analysis as well as experiments have become useful tools for clarifying coke strength and fracture phenomena. In particular, stress analysis using the Finite Element Method for the coke model in which the structure of the X-ray CT is reflected has produced many results.^9,10,11,12) On the other hand, since it is difficult to directly evaluate the ultimate strength by stress analysis alone, fracture analysis using the Rigid Bodies-Spring Model^13,14) and the Discrete Element Method¹⁵⁾ have also been conducted, as these models can represent crack initiation and propagation relatively easily.

In recent years, the depletion of coking coal has become a concern, and the production of coke that effectively utilizes low-quality coal, which is difficult to soften and swell, has become one of the major research themes in the ironmaking process. Coke from low-quality coal is known to have low strength,¹⁶⁾ and various studies have been conducted to obtain high-strength coke while blending low-quality coal.^17,18) Nomura et al.¹⁹⁾ produced coke using various coals with different expansive properties and varying bulk densities and evaluated its strength. The strength of the coke decreased not only when the coal was less expansive, but also when the bulk density was lower. This result showed that the strength of coke blended with low-quality coal can be expected to be improved by increasing the bulk density of the coal. Therefore, various technologies have been investigated^20,21) to increase the bulk density of coal.

Formed coke is coke produced by compression molding of coal, a step called briquetting, before carbonization. Compression molding enables the blending of large amounts of low-quality coal by increasing the bulk density. The production of formed coke has been studied in the past, and technologies for continuous formed coke production have been investigated.²²⁾ This method is expected to make it possible to use low-quality raw materials such as brown coal for coke production by adding heat during the compression process.²³⁾ In particular, in recent years, the use of biomass in coke production has been demanded against the background of global warming, and briquetting technology has also been used for the research and development of this technology.²⁴⁾ When biomass was blended with coal, it was shown that the strength of the coke produced with the briquetting process is higher than that of coke produced without the briquetting.²⁵⁾ It has been suggested that high-strength coke can be produced from only woody materials such as bamboo by briquetting with heat.²⁶⁾ In addition, ferro coke, a molded coke blended with iron, is also attracting attention. Ferro coke is expected to improve the reactivity in blast furnaces because the iron inside the coke catalyzes the Boudouard reaction, which produces CO gas and reduces iron ore at relatively low temperatures.²⁷⁾

As mentioned above, coal briquetting is a very important technology in the future of the ironmaking process. However, although there have been some studies on the effects of compression pressure and grain size on the strength of briquettes,^28,29) these studies have been limited to trial and error, and theoretical studies on briquetting have been scarce. Numerical modeling is considered to be one effective solution to reduce the reliance of trial and error. In our previous work,³⁰⁾ loading and unloading tests of a packed bed of coal and numerical analyses using the discrete element method simulating the experiments were conducted. A comparison of the stresses during briquetting confirmed that the analysis was a reasonably good representation of the experiment. This analytical method should make it possible to quantitatively evaluate the effects of the briquetting operation conditions in the briquetting process and the structure of the briquette. The influence of the size of the vessel on the structure of the briquette is one of the most useful findings in the design of equipment. In this study, the effect of the size of the container used to produce the briquettes on the internal structure of the briquettes was investigated numerically. Numerical analyses were conducted to simulate loading and unloading tests of a packed bed of coal in vessels of different sizes, varying in both inner diameters and heights, assuming uniaxial compression tests using cylindrical vessels. Considering the respective effects of the inner diameter and height of the container, we attempted to organize the effects of the container size on the internal structure of the briquette using height to diameter ratios (H/D).

2. Numerical Analysis

2.1. Governing Equation

In this study, we numerically investigate the effect of the size of the container used to produce the coal briquette on its internal structure using the numerical analysis method based on the Discrete Element Method,³¹⁾ as in our previous work.³⁰⁾ The Discrete Element Method models the forces acting on individual particles in a system composed of particles and tracks the motion of each particle based on the equations of motion. The motion of each particle consists of translational and rotational motion, and the equations of motion for each are expressed by the following equations.

  

$$m\ddot{\mathit{x}}=\sum \left({\mathit{F}}_{\text{n}}+{\mathit{F}}_{\text{t}}\right)+m\mathit{g},$$(1)

  

$$I\dot{\omega }=\sum \mathit{T}.$$(2)

F_n and F_t are the normal and tangential components of the contact force acting on each particle. Also, m, x, I, and ω are the particle mass, the particle position, the particle moment of inertia, and the particle angular velocity, respectively. T is the torque generated by the contact and is given by the following.

  

$$\mathit{T}=\sum \left(r\mathbf{n}\times {\mathit{F}}_{\text{t}}\right).$$(3)

r is the particle radius, and n is the unit normal vector.

In the Discrete Element Method, when two particles are in contact, the contact force is calculated as the product of the spring constant k and the displacement δ, which is the overlap between the particles. The normal direction component of the contact force, F_n, was calculated using the model proposed by Walton and Braun³²⁾ to express the plastic deformation of the particles due to contact. F_n was calculated by Eq. (4) when the displacement was increasing (loading) and by Eq. (5) when the displacement was decreasing or increasing again (unloading or reloading).

  

$${\mathit{F}}_{\text{n}}=k_{\text{n},1}{\delta }_{\text{n}},$$(4)

  

$${\mathit{F}}_{\text{n}}=k_{\text{n},2}\left({\delta }_{\text{n}}-{\delta }_{\text{n}}^{\text{p}}\right).$$(5)

k_n,1 and k_n,2 are the spring constants under loading and unloading or reloading, respectively. Besides, δ_n^p is the normal component of the plastically deformed displacement and is given by the following equation.

  

$${\delta }_{\text{n}}^{\text{p}}=\frac{{\mathit{F}}_{\text{n}}^{\text{max}}}{k_{\text{n},2}}.$$(6)

F_n^max is the historical maximum of the normal direction component of the contact force. The spring constant at unloading or reloading is larger than the spring constant at loading, and these are related by the restitution coefficient e as follows.

  

$$e=\sqrt{\frac{k_{\text{n},1}}{k_{\text{n},2}}}.$$(7)

The tangential component of the contact force, F_t, is expressed in the following equation when there is no slippage on the particle surface.

  

$${\mathit{F}}_{\text{t}}=k_{\text{t}}{\delta }_{\text{t}}.$$(8)

k_t and δ_t are the tangential direction component of the spring constant and displacement, respectively. On the other hand, when a slip occurs, i.e., when Eq. (9) holds, the tangential direction component of the contact force is given by Eq. (10).

  

$$\left|{\mathit{F}}_{\text{t}}\right|>\mu \left|{\mathit{F}}_{\text{n}}\right|,$$(9)

  

$${\mathit{F}}_{\text{t}}=-\mu \left|{\mathit{F}}_{\text{n}}\right|\frac{{\mathit{v}}_{\text{t}}}{\left|{\mathit{v}}_{\text{t}}\right|}.$$(10)

μ is the friction coefficient and v_t is the tangential direction component of the relative velocity of two particles in contact.

2.2. Numerical Analysis Condition

To evaluate the effect of the size of the container used to produce the coal briquettes on the internal structure of the briquettes, numerical analyses for the loading and unloading tests of a packed bed of coal particles in the container of various inner diameters and heights were conducted. The computational domain was a cylindrical container with an inner diameter of 9, 18, or 27 mm. A cylindrical container with an inner diameter of 9 mm was filled with 1.0 g of particles assuming coal (Case 1). Since cylindrical containers with inner diameters of 18 and 27 mm have 4 and 9 times the cross-sectional area of the computational domain compared to the cylindrical container with an inner diameter of 9 mm, the number of particles was increased by a factor of 4 and 9 to ensure that the packed bed has the same particle density (Case 2 and 3, respectively). As an example, the initial arrangement of the packed bed in Cases 1 and 3 is shown in Fig. 1. It can be seen that the initial height of the packed bed is almost equal due to the appropriate setting of the number of particles. Numerical analysis using a cylindrical container with an inner diameter of 18 mm was also performed under conditions in which the number of particles was further doubled, and the height of the bed was doubled (Case 4). Since our previous study³⁰⁾ has suggested that the friction between the container wall and the particles affects the force transfer in the packed bed and thus the internal structure of the briquette, we performed the numerical analysis using various values for the friction coefficient between particle and wall (μ_pw) in each case. The numerical analysis conditions are shown in Table 1. Particles with a diameter of 1 mm were generated in a cylindrical container using uniform random numbers. The particles were then allowed to free-fall and remain stationary as the initial configuration. The packed bed was loaded and unloaded by moving the wall simulating a piston until the height was 13 mm in Cases 1–3 and 26 mm in Case 4, relative to the bottom of the container. In this study, the local filling ratio was evaluated as the internal structure of the briquette. The packed bed was divided in the direction of height at a given compression stage, and the local filling ratio was calculated by dividing the total volume of particles present in each region by the volume of that region. The number of divisions in height direction was calculated by the Sturges’ formula based on the number of particles. The height distribution of the contact force acting on the particles was also calculated for the same number of divisions.

Fig. 1. Examples of the analytical objects and the initial arrangement of particles.

Table 1. Numerical conditions for the loading and unloading test of the coal in the various size of the analytical objects.

	Case 1	Case 2	Case 3	Case 4
Cylinder diameter (D)	9.0	18.0	27.0	18.0	mm
Number of particles	1365	5460	12285	10920
Particle diameter	1.0				mm
Particle density	1400				kg/m3
Loading and unloading rate	100				mm/min
Spring constant	3.0 × 105				N/m
Restitution coefficient	0.3				[–]
Inter-particle friction coefficient	0.3				[–]
Particle-wall friction coefficient (μPW)	0.1, 0.3, or 0.5				[–]
Time increment	1.0×10−7				s

3. Results and Discussion

3.1. Effect of an Inner Diameter of Container on the Internal Structure of Briquette

The changes in local filling ratio with compression are shown in Fig. 2 for analyses of compression tests of a packed bed of coal in a cylindrical container with inner diameters of 9, 18, and 27 mm (Cases 1, 2, and 3, respectively) with various friction coefficients. It can be seen that the local filling ratio increases with compression in all cases. The filling ratio at the top and bottom of the packed bed was much larger than that of the other area when the compression was sufficiently advanced, such as when the height of the packed bed was 13 mm. This is because the numerical model allows particles to overlap not only with each other but also with the wall in order to express the plastic deformation of particles, and the volume of particles overlapping with the wall is added to the region closest to the wall when calculating the filling ratio. Therefore, the uppermost and lowermost regions, where the number of particles in contact with the wall is large, showed different behavior from the other regions. Focusing on the case with a container diameter of 9 mm (Case 1), the filling ratio was almost equal from the top to the bottom of the packed bed when the value of the friction coefficient between particle and wall was small, while the filling ratio was higher at the top of the packed bed and lower at the bottom when the value of the friction coefficient between particle and wall was large. This is thought to be due to the friction resistance between particle and wall, which inhibits the transmission of force in the compressive direction, as discussed in our previous paper.³⁰⁾ In other words, the force applied to the top of the packed bed was not sufficiently transferred to the bottom, resulting in a relatively sparse structure with insufficient compression at the bottom, while the force was concentrated at the top, resulting in a dense structure. Next, we compare the differences between the large and small inner diameters of the containers. For small values of the friction coefficient between particle and wall, there was little difference in the filling ratio between the top and bottom of the packed bed, while for larger values of the friction coefficient, the difference between the top and bottom of the packed bed was smaller.

Fig. 2. Distribution of the filling ratio in the height direction at a loading stage (Case 1–3). (Online version in color.)

In order to discuss the results presented in Fig. 2, Fig. 3 shows the variation with compression of the height distribution of the normal direction component of the contact force acting on the particles for each of the packed beds in Cases 1–3. In all cases, the contact force increases with compression. Focusing on the case with a container inner diameter of 9 mm (Case 1), the contact force was almost equal from the top to the bottom of the packed bed when the value of the friction coefficient between particle and wall was small, while the contact force was higher at the top of the packed bed and lower at the bottom when the value of the friction coefficient between particle and wall was large. Comparing the case with a larger inner diameter of the container to the one with a smaller inner diameter, there is little difference in the magnitude of the contact force for small values of the friction coefficient between particle and wall, while the difference in the magnitude of the contact force between the top and bottom of the packed bed is smaller for large values of the friction coefficient. These trends are consistent with the local filling ratio, suggesting that contact forces are closely related to the local filling ratio within the briquette. The tangential component of the contact force, which is not shown here, has a similar trend to the normal component, although the magnitude of the tangential component is different from that of the normal component, as shown in our previous studies.³⁰⁾

Fig. 3. Axial distribution of the normal component of the contact force at a loading stage (Case 1–3). Plots show the average value, and the error bars represent standard deviations. (Online version in color.)

For further discussion of the contact force, Fig. 4 shows the contact forces acting on each particle at the corresponding coordinates for Cases 1 and 3 when the packed bed is at its most compacted (height of packed bed = 13 mm). The horizontal axis of the figure is the dimensionless distance in the radial direction, where 0 represents the center and 1 represents the wall of the container. The vertical axis is the dimensionless height, where 0 is the fixed wall and 1 is the moving wall that imitates a piston. Focusing on the small values of the friction coefficient between particle and wall, it can be seen that particles with strong contact forces are present over a wide area from the top to the bottom of the packed bed. Focusing on the case where the inner diameter of the container is small and the friction coefficient between particle and wall is large, it can be seen that particles with strong contact force are concentrated in the upper part of the container and are almost nonexistent in the lower part. On the other hand, even for large values of the friction coefficient between particle and wall, particles with large contact force existed in the lower part of the vessel when the inner diameter of the container was large. However, areas with few particles with strong contact force were observed near the wall of the container. These results suggested that although large values of the friction coefficient between particle and wall affect the force transmission of the particles, the effect is limited to a few particles in the vicinity of the wall, and the effect becomes relatively small as the inner diameter of the container increases.

Fig. 4. Spatial distribution of the normal component of the contact force acting each particle when the packed bed was most compressed. (Online version in color.)

3.2. Effect of the Height of Briquette on Its Internal Structure

Figure 5 shows the change in filling ratio with compression of the packed bed for an analysis in which the height of the briquette is doubled by doubling the number of particles when a container with an inner diameter of 18 mm is used as the analytical domain (Case 4). When the value of the friction coefficient between particle and wall is small, the filling ratio is approximately equal from the top to the bottom of the packed bed, while when the value of the friction coefficient between particle and wall is large, the filling ratio is higher at the top of the packed bed and lower at the bottom. Compared to Fig. 2, the difference in filling ratio between the top and bottom of the packed bed is larger for a large value of friction coefficient compared to Case 2, where the inner diameters are equal. Therefore, it was shown that not only the inner diameter of the container but also its height affects the internal structure of the briquette. Case 4 is a case in which the inner diameter and height of the container are doubled compared to Case 1, and the H/D of the two cases are equal. Comparing the numerical results of Case 4 with those of Case 1 the spread of filling ratio between the top and bottom of the packed bed was generally comparable. Therefore, it is suggested that the filling ratio of the briquettes is similar when their H/D are equal.

Fig. 5. Distribution of the filling ratio in the height direction at a loading stage (Case 4). (Online version in color.)

Figure 6 shows the change with compression of the height distribution of the normal direction component of the contact force for the packed bed in Case 4. The contact force also increases with compression, as in the study of the vessel’s inner diameter, and the difference between the top and bottom of the packed bed is large when the value of the friction coefficient between particle and wall is large. Compared with Fig. 3, the difference in contact force between the top and bottom of the packed bed is larger than in Case 2, where the inner diameters are equal, for larger values of the friction coefficient between particle and wall as well as the filling ratio. Compared to Case 1, where the H/D were equal, the spread of the top and bottom of the packed bed was roughly equivalent.

Fig. 6. Axial distribution of the normal component of the contact force at a loading stage (Case 4). Plots show the average value, and the error bars represent standard deviations. (Online version in color.)

These results indicate that not only the radial size but also the height of the briquette has a significant effect on its internal structure. Furthermore, when the H/D are equal, the internal structures of the briquette are generally the same, suggesting that the internal structure of coal briquettes can be organized according to the H/D.

3.3. Effect of the Height to Diameter Ratio of Briquette on Its Internal Structure

Figure 7 shows the relationship of the slope of the filling ratio with respect to the height direction to the ratio of the height to the inner diameter of the container, i.e., the H/D, when the packed bed is at its most compressed. Note that the slope between the second points from the top and the second points from the bottom of Figs. 2 and 5 were calculated here, since the filling ratio may be overestimated at the top and bottom due to the overlap between particles and wall, as described in Section 3.1. When the values of the friction coefficients were equal, the slopes of the filling ratios were nearly equal for the same H/D (Case 1 and 4), as discussed in Section 3.2. The reason why the plots did not match may be due to the small number of particles used in Case 1, which caused an error. It was observed that for each value of friction coefficient, the relationship between the slope of the filling ratio in Cases 1 and 4 was different. The figure also shows that for each friction coefficient, the larger the H/D, the larger the slope of the filling ratio. The slope of the filling ratio increases linearly with the H/D, especially when the friction coefficient is large, indicating that the internal structure of the briquette is determined by its H/D.

Fig. 7. Effect of the H/D of the packed bed on the slope of filling ratio in height direction when the bed was most compressed. (Online version in color.)

4. Conclusion

In this study, the effect of the size of the container used to produce formed coke on the internal structure of the briquette was investigated numerically. When the friction resistance between the particles and the container wall is large, the difference in filling ratio between the moving wall side and the fixed wall side during briquetting is large when the container inner diameter is small, while the difference is almost nonexistent when the container inner diameter is large. From the distribution of the contact forces acting on the particles, it is inferred that this is because the inhibition of force transmission caused by the friction force with the container wall is relatively small when the container’s inner diameter is large. It was also found that not only the inner diameter but also the height of the container affected the internal structure of the briquette, and these results can be organized by H/D. In other words, the higher the ratio of the height to the inner diameter of the container, the more the difference in filling ratio between the moving wall side and the fixed wall side during briquetting inside the briquette increases in an almost linear fashion. In actual operations, egg- or pillow-shaped cups are expected to be used. The inner diameter and height in this study correspond to the width and depth of the cup, respectively. We believe that the results of this research can provide extremely useful guidelines for designing cup shapes to produce briquettes with the desired structure.

In the case of briquettes produced using a double roll, as used in actual briquette manufacturing, the H/D ratio typically ranges from 0.4 to 0.6. As revealed in this study, this ratio minimizes the occurrence of local filling ratio differences within the briquette. Therefore, it can be concluded that the current process does not present issues concerning local filling ratio differences. However, when handling particles with extremely high friction against the wall or when there is a need to increase the H/D ratio for specific objectives, the influence of local filling ratio differences becomes significant, necessitating caution. Additionally, in experimental investigations, it is often challenging to use a double roll briquette manufacturing machine with a small amount of sample. Instead, a common practice is to compress the material inside a cylindrical container using a plunger. This study reveals that in such cases, careful attention must be paid to the H/D ratio to avoid the impact of local filling ratio differences, which otherwise may result in undesirable experimental outcomes.

Acknowledgement

This study is a part of Technology Development for “Ironmaking Process Utilizing Ferro-coke” launched by NEDO (New Energy and Industrial Technology Development Organization) in 2017. NEDO’s partial financing for the project is gratefully appreciated.

Nomenclature

D Inner diameter of cylindrical container [m]

e Restitution coefficient [–]

F Contact force [N]

g Gravitational acceleration [m/s²]

H Height of briquette [m]

I Moment of inertia [kg/m²]

k Spring coefficient [N/m]

m Particle mass [kg]

n Normal unit vector [–]

r Particle radius [m]

T Torque [N m]

v Velocity [m/s]

x Position [m]

<Greek symbols>

δ Displacement [m]

μ Friction coefficient [–]

ω Angular velocity [rad/s]

<Subscripts>

n Normal direction

PW Particle-Wall

t Tangential direction

1 Loading process

2 Unloading and reloading process

<Superscripts>

max Maximum value

p Plastic deformation

References

• 1)   T.  Ariyama,  M.  Sato,  T.  Sato,  S.  Watakabe and  R.  Murai: Tetsu-to-Hagané, 92 (2006), 114 (in Japanese). https://doi.org/10.2355/tetsutohagane1955.92.3_114
• 2)   T.  Arima: Tetsu-to-Hagané, 92 (2006), 106 (in Japanese). https://doi.org/10.2355/tetsutohagane1955.92.3_106
• 3)   Y.  Kubota,  S.  Nomura,  T.  Arima and  K.  Kato: ISIJ Int., 51 (2011), 1800. https://doi.org/10.2355/isijinternational.51.1800
• 4)   H.  Lomas,  R.  Roest,  T.  Thorley,  A.  Wells,  H.  Wu,  Z.  Jiang,  R.  Sakurovs,  S.  Wotherspoon,  R. A.  Pearson and  M. R.  Mahoney: Energy & Fuels, 32 (2018), 12021. https://doi.org/10.1021/acs.energyfuels.8b01339
• 5)   R.  Roest,  H.  Lomas,  K.  Hockings and  M. R.  Mahoney: Energy & Fuels, 31 (2017), 1422. https://doi.org/10.1021/acs.energyfuels.6b02902
• 6)   D. R.  Jenkins,  H.  Lomas and  M.  Mahoney: Fuel, 226 (2018), 163. https://doi.org/10.1016/j.fuel.2018.03.173
• 7)   K. M.  Steel,  R. E.  Dawson,  D. R.  Jenkins,  R.  Pearce and  M. R.  Mahoney: Fuel Process. Technol., 155 (2017), 106. https://doi.org/10.1016/j.fuproc.2016.04.027
• 8)   K. M.  Steel,  D. R.  Jenkins,  R. D.  Balucan and  M. R.  Mahoney: Fuel, 296 (2021), 120688. https://doi.org/10.1016/j.fuel.2021.120688
• 9)   D.  Anraku,  Y.  Nagashima,  K.  Nango,  H.  Matsumoto,  J.  Shen and  K.  Oda: ISIJ Int., 59 (2019), 1506. https://doi.org/10.2355/isijinternational.ISIJINT-2018-805
• 10)   K.  Hiraki,  Y.  Yamazaki,  T.  Kanai,  A.  Uchida,  Y.  Saito,  Y.  Matsushita,  H.  Aoki,  T.  Miura,  S.  Nomura and  H.  Hayashizaki: ISIJ Int., 52 (2012), 1966. https://doi.org/10.2355/isijinternational.52.1966
• 11)   Y.  Ono,  Y.  Fukuda,  Y.  Sumitani,  Y.  Matsukawa,  Y.  Saito,  Y.  Matsushita,  H.  Aoki,  T.  Shishido and  N.  Okuyama: Fuel, 309 (2022), 122061. https://doi.org/10.1016/j.fuel.2021.122061
• 12)   N.  Tsafnat,  G.  Tsafnat and  A. S.  Jones: Fuel, 87 (2008), 2983. https://doi.org/10.1016/j.fuel.2008.03.027
• 13)   Y.  Saito,  S.  Matsuo,  T.  Kanai,  A.  Toishi,  A.  Uchida,  Y.  Yamazaki,  Y.  Matsushita,  H.  Aoki,  S.  Nomura,  H.  Hayashizaki and  S.  Miyashita: ISIJ Int., 54 (2014), 2519. https://doi.org/10.2355/isijinternational.54.2519
• 14)   Y.  Sumitani,  Y.  Ono,  Y.  Saito,  Y.  Matsushita,  H.  Aoki,  T.  Shishido and  N.  Okuyama: ISIJ Int., 61 (2021), 119. https://doi.org/10.2355/isijinternational.ISIJINT-2020-292
• 15)   S.-Y.  Kim and  Y.  Sasaki: ISIJ Int., 50 (2010), 813. https://doi.org/10.2355/isijinternational.50.813
• 16)   T.  Arima: Tetsu-to-Hagané, 87 (2001), 274 (in Japanese). https://doi.org/10.2355/tetsutohagane1955.87.5_274
• 17)   T.  Kanai,  Y.  Yamazaki,  X.  Zhang,  A.  Uchida,  Y.  Saito,  M.  Shoji,  H.  Aoki,  S.  Nomura,  Y.  Kubota,  H.  Hayashizaki and  S.  Miyashita: Journal of Thermal Science and Technology, 7 (2012), 351. https://doi.org/10.1299/jtst.7.351
• 18)   Y.  Saito,  T.  Kanai,  D.  Igawa,  Y.  Miyamoto,  S.  Matsuo,  Y.  Matsushita,  H.  Aoki,  S.  Nomura,  H.  Hayashizaki and  S.  Miyashita: ISIJ Int., 54 (2014), 2512. https://doi.org/10.2355/isijinternational.54.2512
• 19)   S.  Nomura,  T.  Arima and  K.  Kato: Fuel, 83 (2004), 1771. https://doi.org/10.1016/j.fuel.2004.03.006
• 20)   S.  Nomura: Fuel Process. Technol., 159 (2017), 1. https://doi.org/10.1016/j.fuproc.2017.01.016
• 21)   S.  Nomura: ISIJ Int., 59 (2019), 1512. https://doi.org/10.2355/isijinternational.ISIJINT-2018-704
• 22)   Y.  Miura and  T.  Okuhara: Transactions of the Iron and Steel Institute of Japan, 23 (1983), 700. https://doi.org/10.2355/isijinternational1966.23.700
• 23)   A.  Mori,  S.  Kubo,  S.  Kudo,  K.  Norinaga,  T.  Kanai,  H.  Aoki and  J.-i.  Hayashi: Energy & Fuels, 26 (2012), 296. https://doi.org/10.1021/ef201168g
• 24)   L.  Florentino-Madiedo,  E.  Díaz-Faes and  C.  Barriocanal: Renewable Energy, 146 (2020), 1717. https://doi.org/10.1016/j.renene.2019.07.139
• 25)   M. G.  Montiano,  E.  Díaz-Faes and  C.  Barriocanal: Fuel, 137 (2014), 313. https://doi.org/10.1016/j.fuel.2014.08.012
• 26)   S.  Kudo,  A.  Mori,  R.  Soejima,  F.  Murayama,  Karnowo,  S. Nomura, Y. Dohi, K. Norinaga and J.-i. Hayashi: ISIJ Int., 54 (2014), 2461. https://doi.org/10.2355/isijinternational.54.2461
• 27)   K.  Higuchi,  S.  Nomura,  K.  Kunitomo,  H.  Yokoyama and  M.  Naito: ISIJ Int., 51 (2011), 1308. https://doi.org/10.2355/isijinternational.51.1308
• 28)   F.  Fehse,  K.  Rosin,  H.-W.  Schröder,  R.  Kim,  M.  Spöttle and  J.-U.  Repke: Fuel, 203 (2017), 915. https://doi.org/10.1016/j.fuel.2017.05.002
• 29)   B.  Sun,  J.  Yu,  A.  Tahmasebi and  Y.  Han: Fuel Process. Technol., 124 (2014), 243. https://doi.org/10.1016/j.fuproc.2014.03.013
• 30)   Y.  Ono,  M.  Ramdzuanny,  Y.  Matsushita,  H.  Aoki,  S.  Wada and  T.  Shishido: ISIJ Int., 61 (2021), 2737. https://doi.org/10.2355/isijinternational.ISIJINT-2021-272
• 31)   P. A.  Cundall and  O. D. L.  Strack: Géotechnique, 29 (1979), 47. https://doi.org/10.1680/geot.1979.29.1.47
• 32)   O. R.  Walton and  R. L.  Braun: Journal of Rheology, 30 (1986), 949. https://doi.org/10.1122/1.549893