Numerical Simulation of Swelling Behavior of Coal Particles

Abstract

The swelling of a packed bed of coal during carbonization was numerically investigated. The coal particles were assumed to be spheres capable of swelling. When falling particles of the same size, the height of the packed bed was determined by the particle size, and during swelling of particles of the same size, the height of the packed bed was also determined by the particle size. However, the height of the packed bed with different particle sizes was lower than that of the packed bed with particles of the same size. This was owing to the densifying of the smaller particles between the larger particles. When the swelling ratio of the particles in the differently packed beds was 25%, no difference in dilatation was observed. By fitting the numerical solutions and previous experimental data, the difference in the swelling ratio between the smaller and larger particles was 16.8%.

1. Introduction

Coal used for coke production is a useful carbon resource, and the development of carbon utilization technology in low-carbon fields is essential. Coke is a reducing agent that is used as a spacer in blast furnaces. In a blast furnace, the CO produced from coke and pulverized coal reduces the iron ore (sintered ore). To reduce the quantity of CO₂ emissions from blast furnaces and increase the production of pig iron, a low reducing agent rate (RAR) operation of blast furnaces is a key technology.¹⁾ Recently, the use of ferro coke²⁾ and intensified hydrogen reduction of iron ore in the COURSE50 project³⁾ were studied. To build these technologies, the production of high-strength coke is required. Although non- or slightly-caking coal is used because of the depletion of caking coal, the strength of coke produced from non- or slightly-caking coal is low. Coal undergoes softening and re-solidification during carbonization, and because coal swells during softening, the dilatation of coal is one of the most important factors affecting the quality of metallurgical coke. Nomura et al.⁴⁾ calculated a parameter indicating the degree of void filling due to swelling of coal particles from the product of bulk density and specific dilatation volume using the measurement results of the dilatometer test, and reported that this parameter must be above a certain value to produce high-strength coke. To produce high-strength coke from low-quality coal, the mechanism of coal swelling needs to be clarified.

In a previous study, a single particle of caking coal softened with the release of volatile matter and swelled during carbonization,⁵⁾ and the swelling behavior differed depending on the coal type. In addition, the swelling ratio of a single coal particle varies depending on the coal kind.^6,7) However, coal particles do not swell freely because they are compressed and compacted in dilatometry tests.

Regarding the swelling of the packed bed of coal, Nomura et al. explained that the swelling of coal particles filled the voids between particles.⁴⁾ Hayashi et al. suggested that low-rank coals solidified first, and that gas (i.e., volatile matter) escaped from neighboring high-rank coal particles.⁸⁾ In addition, Fujii et al. showed that the dilatation of coal differed depending on particle size, even when the same coal was used.⁹⁾ The dilatation of coal differed depending on the coal type and particle size.

Focusing on coal particle size, previous studies revealed that smaller coal particles improved the homogeneity of coal and coke strength.^10,11,12,13) Coke strength changed with the size of the inert material,¹⁴⁾ and coal linear shrinkage decreased with an increase in the size of the inert material during carbonization.¹⁵⁾ Dohi et al. reported that the pulverization of blended coals with long penetration distances can mitigate reduction in coke strength.¹⁶⁾ Therefore, the coal’s particle size affects coke strength. However, the effect of coal particle size on dilatation of a packed bed of coal is unknown.

In a numerical analysis for a packed bed of coal, Ono et al.¹⁷⁾ simulated the loading and unloading tests of a packed bed of coal particles in the briquetting process of coal and evaluated the changes in the structure inside the packed bed and the stress during compression. They showed that the friction force between the particles and container wall affected the distributions of the contact force and filling ratio. They evaluated the behavior of coal particle compression at ambient temperatures and did not consider the swelling of coal particles, which occurs during the briquetting process at higher temperatures.

When coal swelled, volatile matter was released,⁷⁾ and the size of the pores changed.⁶⁾ Therefore, to model the swelling of coal particles, the release of volatile matter and swelling of individual particles may need to be considered. The release of volatile matter is a chemical effect, and its release behavior differs depending on the type of coal.⁷⁾ Conversely, the swelling of coal particles is a physical effect, and the height of the packed bed changes as particles push against each other. In other words, the swelling behavior of a packed bed of coal can be divided into chemical and physical effects. However, it is difficult to numerically evaluate the contribution of chemical effects to the swelling of coal because not all volatile matter contribute to coal swelling.⁹⁾ Although the chemical effects are important in coal swelling, the physical effects have not been evaluated. Particularly, the swelling ratio of individual particles in a packed bed is unknown, even though the swelling ratio of a single particle is known.

In this study, the swelling behavior of coal particles was reproduced in a numerical analysis using the discrete element method, and the effects of particle size and composition on the height or dilatation of packed beds were evaluated. The particle composition was assumed to be the experimental results of a previous study, and the effect of particle composition on dilatation of the packed bed was evaluated.

2. Numerical Simulation

2.1. Numerical Method

The discrete element method (DEM) proposed by Cundall and Strack¹⁸⁾ solves the equations of motion of particles, considers the contact forces between neighboring particles, and tracks the behavior of individual particles. This study uses the Voigt model, which comprises springs, dash pods, and friction sliders. Elastic and viscous forces act in the tangential direction, and shear forces act in the normal direction. For the numerical simulation, LIGGGHT-Public 3.8.0¹⁹⁾ was used.

2.2. Numerical Object

In dilatometry tests, pulverized coal particles are pressed to form a pencil-type specimen with a height of 60 mm, and the specimen is placed and heated in a furnace. The specimen is regarded as a packed bed of coal particles of various sizes. A piston is placed on the packed bed in the furnace to measure the displacement of the specimen.

In this numerical study, the swelling behavior of a packed bed of coal particles in the dilatometry tests was reconstructed and analyzed under three different conditions of particle composition and operation: Cases FL, SW, and CL. Case CL (an abbreviation for coal) is a complex system involving different particle sizes, arrangements of particles, and swelling of each particle because an actual TD test was simulated. For simplicity, the effects of particle size were evaluated in Case FL (an abbreviation for falling of particles), and the effects of particle swelling were evaluated in Case SW (an abbreviation for swelling of particles).

The conceptual diagram of these three conditions is shown in Fig. 1. The computational domain of all cases was 8 mm in diameter, which was the same as that of the dilatometry test furnace. The height of the computational domain is sufficiently high. In Cases FL, SW, and CL, coal particles were randomly placed in the computational domain and then fell with an initial velocity in the direction of gravity. The gravitational acceleration was 9.81 m/s². In Cases SW and CL, the fallen particles were pressed by a punch for 0.1 s so that the height of the packed bed was 60 mm. When the height of the packed bed was less than 60 mm, the punch did not affect the packed bed. A group of particles mimicking a piston was placed on the punch, but were removed after adjusting the height of the punch, and the piston was placed on top of the packed bed. Although the weight of the piston was 20 times that of the inserted particles in the actual test, to reduce computational load, the weights of the piston and inserted particles were the same in the present study. To investigate the effect of particle swelling on the height of the packed bed, the diameter of the particles was increased by 25% in this study. In a previous study,^6,7) coal particles swelled freely by 10–120% depending on the coal type. The swelling ratio of each particle was set to 25% because the packed bed of the particles swelled without divergence in any of the cases, and the numerical solution for dilatation was close to the experimental value.

Fig. 1.

Conceptual diagram of numerical simulations. (Online version in color.)

2.2.1. Case FL

In the dilatometry test, JIS M8801 specified that the particles should be crushed to 150 μm or less. One of the key particle sizes was 150 μm. However, because the computational load with 150-μm particles was high, the particle size was set to ten times the actual size (i.e., 1.5 mm). Furthermore, half the size of 1.5 mm (i.e., 0.75 mm) is also important. Therefore, particles of the same size (0.75 and 1.5 mm) fell. These conditions are referred to as FL0.75 and FL1.5, respectively. Moreover, when particles swelled by 25%, the number of particles was the same, but their size increased, which is called FL0.75α and FL1.5α. These correspond to the particle size when they swelled in Case SW, as described below. The total analytical time for Case FL was 0.2 s. The total weight of the particles was 2.2 g. The time step was 1 × 10⁻⁷ s.

2.2.2. Case SW

The particles were felled, pressed by the punch, and swelled under the piston. The particle sizes were 0.75 mm (100 wt%), 1.5 mm (100 wt%), and a combination of 0.75 (50 wt%) and 1.5 mm (50 wt%); the conditions were SW0.75, SW1.5, and SWmid, respectively. In Case SW, the particles were placed for 0.2 s, and their diameters were increased by 25% every 0.001 s for 1 s. After the swelling, the particles stood for 0.2 s, and the initial weight of the particles was set to 2.2 g. Particle splash occurred after the punch was removed because the particles in the packed bed were dense and rigid. When the weight of the particles was small, the height of the initial packed bed did not reach 60 mm, and when it was large, the particle arrangement was greatly changed because the splash after the punch was removed. In the preliminary analysis, the weight of the particles was changed in increments of 0.05 g, and the weight at which the splash was less than 5 mm in SW1.5 was adopted.

2.2.3. Case CL

Fujii et al.⁹⁾ conducted TD tests using two different particle configurations. In Case CL, the particle composition of the coal particles shown in Fig. 2 was reconstructed from the particle composition in the actual TD test. Although Fujii et al. measured the weight of particles within a certain range by sieving, because the numerical analysis needs to determine the particle size, the particle size was represented by a median value of each range. These conditions are referred to as CLsmaller and CLlarger. The average particle size based on weight standards is 0.604 mm and 0.671 mm for CLsmaller and CLlarger, respectively, and based on number standards is 0.393 mm and 0.310 mm for CLsmaller and CLlarger, respectively. The relationship between the average particle sizes may be reversed, depending on the standard. Fujii et al. determined the size of particles using a weight standard. The filling and swelling conditions were the same as those in Case SW, except for the particle composition. The weight of the particles was 2.5 g, which was the average weight before and after the dilatometry test.

Fig. 2.

Initial particle size distribution in Case CL; (a) weight standard; (b) number standard. (Online version in color.)

2.3. Numerical Conditions

From the previous experimental data,⁹⁾ the density of the coal particles was 1349 kg/m³, and the Young’s modulus of the particles was set to 1 GPa based in the study by Yashima and Hashimoto.²⁰⁾ According to Ono et al.,¹⁷⁾ the Poisson’s ratio, restitution coefficient, and friction coefficient of the coal particles were set to 0.3, 0.3, and 0.3, respectively. The Young’s modulus of the piston, which was assumed to be made of stainless steel, was set to 197 GPa, and other parameters of the piston were the same as those of the coal particles. Generally, the density of the coal particles decreased with the swelling of the particles during carbonization. However, the density change of the individual particles in the packed bed during carbonization was not measured, and was therefore unknown. To simplify the numerical simulation, the density of coal swelling was assumed to be constant.

To determine the height of the packed bed, void fractions were calculated for each region at a height 2 mm from the bottom of the computational domain. The highest position in the region with a void fraction less than 0.7 was selected, and the height of the packed bed was determined to reflect the void fraction in that region. When the particles push each other and the region becomes very dense, the void fraction becomes less than zero; in this case, the void fraction was set to zero. The dilatation was calculated as follows:   

$$Dilatation=\frac{H-H_0}{H_0}\times 100[\%],$$

where H is the height of the packed bed, and H₀ is the initial height of the packed bed.

3. Results and Discussion

3.1. Effect of Particle Size on Height and Dilatation of Packed Bed

Figure 3(a) shows the height of the packed bed for different particle sizes. Compared to FL0.75 and FL0.75α, the height of FL0.75α is higher because the particle size of FL0.75α is larger than that of FL0.75. A similar trend was observed for FL1.5 and FL1.5α. When FL0.75 and FL1.5 are compared, the height of FL1.5 is higher, and in FL0.75α and FL1.5α, the height of FL1.5α was higher. Hence, the height of the packed bed was determined by the particle size when the particle number and size were the same.

Fig. 3.

(a) Height of a packed bed and (b) void fraction with height of 0–20 mm in Case SW and Case FL. (Online version in color.)

Subsequently, Cases FL and SW were compared. The height increased in the following order: FL0.75, SW0.75, and FL0.75 α. This tendency was also observed for larger particles. Owing to swelling, the height of SW0.75 was higher than that of FL0.75, and the height of SW0.75 was lower than that of FL0.75α. This was because the upper particles and piston compressed the particles, and clogging occurred at the bottom of the packed bed during swelling. Figure 3(b) shows the void fractions in the region 0–20 mm in height. The void fractions of FL0.75 and FL0.75α were almost the same, and the void fraction of SW0.75 was the lowest. Because the particles in FL0.75 and FL0.75α only fell, they did not clog; but even if they did, the rearrangement of particles occurred because the upper region was free. However, in the case of SW0.75, the particles swell, and pressure is added from the upper particles and piston. The results for FL1.5, SW1.5, and FL1.5α were the same as those for smaller particles. Comparing SW0.75 and SW1.5, the height of the packing bed in SW1.5 is higher. This is because the initial size of the particles in SW1.5 is larger than that in SW0.75.

In the above description, the case where all the particles were of the same size was discussed, and the case of different particle sizes was also discussed. Figure 4(a) shows the height of the packed bed before and after swelling. Under both conditions, the height increased as the particles swelled. The height of SWmid before swelling was the lowest, followed by SW0.75, and then SW1.5. When the particle sizes were equal, the height of the packed bed was determined based on the particle size. However, when the particle sizes are different, the height is not determined by size. This is because the void fraction is the lowest in the 0–20 and 20–40-mm regions of SWmid shown in Fig. 5(a), which allows smaller particles to enter the space between the larger ones. After swelling, the height of SWmid was the lowest, followed by SW0.75, and then SW1.5. As shown in Fig. 5(b), the void fraction of SWmid was the lowest in the 0–20-mm region, and was denser than SW0.75 and SW1.5. This is because the smaller particles entered the space between the large particles, the particles swelled and filled the void, and the upper constraint prevented the movement of particles. However, the void fraction in the 60–80-mm region was higher than that in the 0–20-mm region for all conditions. Therefore, most of the load is applied in the 0–20-mm region.

Fig. 4.

(a) Height before and after swell and (b) dilatation in Case SW. (Online version in color.)

Fig. 5.

Void fractions of a packed bed in Case SW: (a) before swell; (b) after swell. (Online version in color.)

As shown in Fig. 4(b), the dilatation of SW0.75 is larger than that of SW1.5. This is because the height of the initial packed bed was low and particle size was small. When the particle size was small, the particle number was large; the particle number of SW0.75 was 7383, and that of SW1.5 was 923. Consequently, each particle mitigates the effects of the piston and surrounding particles, and the effect increases as the number of particles increases. However, the number of particles in SWmid was 4153, and the dilatation was higher than that in SW0.75 and SW1.5. Hence, the dilatation of a packed bed composed of particles of different sizes does not depend on the number of particles, but is affected by the filling of voids and swelling of particles.

Thus, the height of the packed bed under the piston was lower than that of the packed bed where the particles were felled. When the particles fall, they are rearranged even if the upper particles hold down the lower particles, and the void fraction is constant regardless of the position of the packed bed. However, if there is a piston at the top of the packed bed when the particles swell, clogging occurs because of the constraint from the top and the increase in particle size. When the particles were of equal size, the dilatation of the packed bed was determined based on the initial particle size. However, when the particle size was different, the dilatation of the packed bed comprising non-uniform particles was higher than that of the packed bed containing uniform particles. This is because small particles move in between the larger particles. Therefore, dilatation of the packed bed with different sizes is not additive to the particle size.

3.2. Swelling of Coal Particles

Figure 6 shows the swelling behavior of the packed bed, which reflects the composition of the previous dilatation test and the increase in dilatation with time. When the particle size increased monotonically, dilatation increased in steps. This is because, although the increase in particle size is mitigated by constraints from the surrounding particles and piston, at a certain size, the particles are restituted by compressed particles, thereby causing rearrangement. The timing of the step increments during dilatation for CLsmaller and CLlarger is different, which indicates that the timing of particle rearrangement is independent of the particle composition. There was little difference in the final dilatations of CLsmaller and CLlarger, despite the different particle compositions. There were no significant differences in void fractions, as shown in Fig. 7. The difference in the average particle size between CLsmaller and CLlarger was only 0.067 mm, and the swelling ratio of each particle was the same. Therefore, when the swelling ratios of the particles are the same, regardless of the particle size, the dilatation does not change depending on the particle composition.

Fig. 6.

Transient dilatation in Case CL. (Online version in color.)

Fig. 7.

Void fractions of a packed bed in Case CL: (a) before swell; (b) after swell. (Online version in color.)

The numerical results were compared with previous experimental results. Fujii et al.⁹⁾ showed that dilatation varies greatly depending on particle composition. In this study, the swelling ratio of the particles was set to 25% regardless of the particle composition. In the actual swelling of coal particles, the swelling ratio of the particles differed depending on the particle composition. As shown in Fig. 6, dilatation increased almost linearly with the swelling of the particles, indicating that fitting the dilatation-to-swelling ratio of the particles is possible. From the intersection of the fitted equation and experimental results, as shown in Fig. 8, the swelling ratio of the particles in CLsmaller was expected to be 28.0%, and that in CLlarger was 44.8%. The simulated values are lower than those of the free swelling of caking-coal particles in previous experiments.^6,7) During coke production, the swelling ratio in the packed bed is low because coal cannot swell freely, indicating that the results are valid. In actual dilatation tests, physical and chemical effects occur, but when the physical effects are limited, the swelling ratio of the particles differs by 16.8% depending on the particle composition.

Fig. 8.

Relationship between swelling ratio of particles and dilatation with experimental data. (Online version in color.)

4. Conclusion

Numerical simulations were performed using the discrete element method to evaluate the swelling behavior of coal particles. When the particles fell, they relocated freely, and the height of the packed bed was high. However, when a piston was placed at the top of a packed bed when the particles swelled, the height of the packed bed decreased. Clogging occurred in the lower part of the packed bed owing to the constraint from upper particles, the piston, and its own swelling. Furthermore, dilation of the packed bed with different particle sizes was higher than that with the same particle size because smaller particles entered the void between the larger particles. Dilatation of the packed bed with different sizes would not be additive to the particle size. No difference in dilatation was observed when the particle compositions simulating the previous dilatation test were provided, and the swelling ratios of the particles were equal. Therefore, when the cause of the difference in the dilatation test is the swelling ratio of the particles, the swelling ratio of the particles varies with particle size.

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