Effect of Coal Particles on Bed Characteristics and Their Motion Behavior in a Gas–Solid Separation Bed

Abstract

Air-dense medium fluidized beds have attracted more attention due to their unique advantage of forming a density bed suitable for coal separation without water participation. However, the detailed effects of coal particles on separation fluidization are not yet fully understood. In this study, the effects of feeding particles on bed fluidization characteristics and bed voidage (including single emulsion phase and bubbling state), as well as their motion behavior, are investigated comprehensively. The results indicate that the initial critical fluidization velocity decreases when a middle- or high-density feeding particle layer is present. Moreover, it is found that the feeding particles exert compression and expansion effects on the emulsion phase or the bubbling fluidized bed with a lower fluidization number when the feeding particle volume is below and above a certain value, respectively, and that the expansion ratio can also be affected by the static bed height. Additionally, the fluidization number corresponding to the optimal settlement performance of high-density feeding particles presents an ascending trend with decreasing medium particle size and static bed height, and the influence of fluidization number on the settlement performance can be weakened and separation time can be shortened with increasing feeding particle size. The backmixing degree of low-density feeding particles is expected to decrease by reducing fluidization number and increasing medium particle size.

1. Introduction

Coal, as one of the primary energy resources, plays an important role in power production and chemical raw materials acquisition. − However, the gangue in raw coal usually leads to low efficiency production and environmental issues. , Heavy medium separation as an effective way to improve the quality of raw coal has been widely applied, while air-dense medium fluidized bed (ADMFB) dry coal separation receives great attention in recent years due to its advantages of not requiring water compared to the traditional wet method, , which helps to develop coal resources in water-deficient areas. The ADMFB is essentially a gas–solid two-phase flow, and the heavy medium particles are lifted up by introducing fluidization gas, thus forming uniform density, which is the theoretical basis for coal particles separation based on density difference. As illustrated in Figure , when the coal particle density, ρ _p , is lower than bed density, ρ_f, i.e., ρ_p<ρ_f, the resultant force on the coal particles is upward, thus causing the corresponding particles to float on the surface of ADMFB. Conversely, heavier particles sink to the bottom of the bed. While the coal particles with a similar density to the separation bed can reach an equilibrium state, they are difficult to accurately separate due to their uncertain behavior within the separation bed. As is known, the gas–solid fluidized bed consists of the emulsion phase and the bubble phase. With regard to the emulsion phase, the gas is uniformly dispersed among medium particles and form relatively stable bed density, but its separation space is limited. While the bubble phase can improve the coal particles’ motion space and simultaneously adjust the bed density, it easily causes uneven bed density distribution and also increases the separation error due to the interference of rising bubbles. Therefore, the regulations on fluidization gas velocity and the characteristics of dense medium particles are crucial.

1.

Theoretical diagram of coal particle stratification based on density difference.

It was reported that coarser particles usually led to larger bubble sizes in the ADMFB compared to Geldart A particles, which was not favorable for the formation of a uniform bed density distribution and also caused lower expansion of the emulsion phase. Duan et al. and Zhou et al. observed that slightly Geldart C ultrafine coal powder added to Geldart A magnetite powder exhibited both good bed expansion and high emulsion phase and also had the potential to separate fine coal. Yang et al. investigated the effects of different particle sizes on bubble dynamic behavior and found that larger particle size increased the bubble equivalent diameter and bed expansion ratio and also helped reduce bed fluctuation. Based on the same average particle diameter, Chalermsinsuwan et al. further investigated the effect of particle size distribution on the minimum fluidization velocity and declared that the minimum fluidization velocity of narrow particle size distribution was greater than that of wide particle size distribution, it is also noted that the proportion of small particles in the particle bed had a significant effect on fluidizability, improving the drag force of large particles. Rasteh et al. proposed that the minimum fluidization velocity increased with increasing average particle diameter and initial bed height. Generally speaking, smaller particles correspond to greater emulsion phase expansion and also specific surface area compared to larger particles. Moreover, finer particles exhibited a smoother flow due to smaller bubbles existing in the bed. Therefore, the separation performance of the ADMFB is closely related to the medium particle size. However, the coupling effect of medium particle size distribution, fluidization gas velocity, and feeding particle properties has not been fully clarified, making it difficult to accurately predict changes in bed stability under complex operating conditions. In practical coal separation processes, the airflow inevitably experiences a redistribution by the separation particle layer before entering the medium-particle bed due to the failure to discharge by the scraper in time. Given this situation, Zhang et al. investigated the effects of a secondary accumulation layer on bed stability, and the results showed that the secondary bed reduced the fluctuation of bed pressure drop and also improved the fluidization quality of the initial bed. Similar results were also presented in related literature. It should be emphasized that prior research has concentrated exclusively on the influence of high-density material layers on the fluidization properties of the bed, while the regulatory mechanism and effect characteristics of the middle-density material layers remain largely unexplored. Additionally, there remains a lack of targeted experimental verification and theoretical analysis of the fundamental question of whether the volume of the separation bed produces an increment equivalent to that of water after raw coal particles are added, a question that has not been effectively resolved in the existing academic work.

It is well known that accurately regulating the separation and fluidization of polydisperse particles in the ADMFB is a difficult task. Zhou et al. studied the influence of bubbles on particle motion and the detailed behavior between particles and the dense medium and concluded that the wake vortex effect caused particles to rise along with the bubble, while the emulsion phase effect caused particles to descend. Moreover, the particle motion path was closely related to the gas velocity and mainly affected by the driving and inhibitory effects of bubbles. Consequently, the behavior of bubbles in the gas–solid bed is an important factor affecting the backmixing/circulation of the dense medium and mixing/segregation of the feeding particles. However, it should be clear that the characteristics of bubbles depend on the medium particle size, fluidization gas velocity, and static bed height.

In this study, the fluidization characteristics of different narrow medium-size distributions are first investigated, and then the critical fluidization velocity of medium particles with different mixing ratios of narrow size is evaluated. Subsequently, the effects of the secondary air distribution layer formed by middle-density or high-density feeding particles on the bed fluidization characteristics are studied. Moreover, the detailed effects of feeding particles on the bed with a single emulsion phase or bubbling state are explored, which helps to understand the variations in bed density and also the separation space. Additionally, to analyze the motion behavior of low-density and high-density particles, different factors such as medium particle size, static bed height, and feeding particle size are considered.

2. Experimental Section

2.1. Materials and Methods

High-density magnetite powder is used as the heavy medium, which can form a gas–solid fluid by introducing air from the bottom of the separation bed. Because of the strong magnetism of medium particles, they can be separated from the pulverized coal, which is produced during the coal beneficiation process, or added to the heavy medium to construct the separation bed with adjustable density. To be noted, the true density of the heavy medium is 4.616 g/cm³, and the bulk densities of different size fractions of 0.3–0.25, 0.25–0.18, 0.18–0.125, and 0.125–0.074 mm are 2.455, 2.527, 2.565, and 2.642 g/cm³, respectively, and their average particle sizes are 0.266, 0.208, 0.147, and 0.093 mm, respectively.

To investigate the effects of the secondary air distribution layer formed by feeding particles on the bed fluidization characteristics, high-density and middle-density balls with a diameter of 13 mm are used, with densities of 2.5 and 2.1 g/cm³, respectively. Moreover, the middle-density balls are used to study the effects of feeding particles on the bed voidage. It is worth noting that these middle-density balls are always immersed in the fluidized bed, as verified by preliminary experiments.

To explore the effects of various factors, such as medium particle size, static bed height, and feeding particle size, on the motion behavior of coal particles with different densities, low- and high-density coal particles in the size range of −6 + 3 mm were used. These particles are obtained from the same raw coal through float-sink tests, and their average densities are 1.35 g/cm³ and 2.30 g/cm³, respectively. Notably, this part employs a single-variable test scheme to focus on the independent influence of each core factor under controlled conditions, and full-factorial cross-condition tests are not conducted at this stage.

2.2. Experimental System

The experimental system, as shown in Figure , consists of four units, i.e., air supply, separation fluidized bed, differential pressure measurement, and dust removal. The fan blower supplies fluidization gas to the separation unit, and the gas pressure is controlled at around 0.02 MPa. The fluidized bed body, made of transparent plexiglass, is cylindrical, and detailed parameters can be found in our previous paper. Compressed air first enters the air predistributor, with the gas flow rate controlled by a rotor flowmeter, and then it is evenly distributed through a distribution plate and filter cloth. Subsequently, the heavy medium particles can be lifted to form a uniform and stable particle bed by adjusting the fluidization gas velocity. The pressure drop between two measurement points is obtained using a U-shaped tube. It should be noted that the sidewall of the cylinder is marked with scales to easily measure the bed surface height under fluidization.

2.

Experimental system of a gas–solid fluidized bed: (1) blower, (2) buffer tank, (3) pressure gauges, (4) flowmeter, (5) blast gate, (6) gas predistribution chamber, (7) air distributor, (8) separation fluidized bed, and (9) pressure measurement device.

2.3. Data Evaluation

The fluidization number, N, is calculated by

$$N=\frac{U}{U_{\mathrm{mf}}}$$ 1

where U and U _mf represent the operation gas velocity and critical fluidization gas velocity, respectively.

The axial distribution coefficient, t, is expressed as

$$t=\sum _{i=1}^m\frac{i-1}{m-1}·t_i$$ 2

where m is the number of bed layer divided after the separation process is completed and t _i is the mass ratio of bed material at layer i to the total. t = 0, 1, and 0.5 represent the feeding particles all floating near the surface of the bed, all sinking at the bottom of the bed, and distributed uniformly in each layer, respectively. Notably, the bed material after separation is evenly divided into five layers under closed airflow conditions, and then the medium particles are removed using a standard sieve to obtain the feeding particles.

3. Results and Discussion

3.1. Fluidization Characteristics of Heavy Medium Particles

Here, the fluidization bed is uniformly divided into four layers under various gas velocity conditions, and the detailed distribution of pressure drop measurement points in each layer is shown in Figure . The distance between two pressure measurement heads is set as 1 cm, and the average of the collected data represents the bed pressure drop per centimeter.

3.

Distribution of pressure measurement points.

3.1.1. Pressure Drop Curves of Heavy Medium Particles with Different Size Distributions

It should be pointed out that the critical fluidization velocity is obtained from the intersection of the pressure drop rising line in the fixed bed period and the horizontal line in the fluidization period. As shown in Figure , when the size range of heavy medium particles is relatively narrow, the critical fluidization velocity of the bed changes little with increasing static bed height H _s, indicating that the static bed height is not the main factor affecting the critical fluidization velocity. In other words, a limited increase in static bed height has no obvious effect on the gas mobility, and the heavy medium particles in the upper part of the bed can also fully contact the rising gas. By analyzing the pressure drop distributions for different medium particle sizes, it is found that finer particles exhibit larger fluctuations in pressure drop once the gas velocity exceeds the critical fluidization velocity, indicating that bed stability deteriorates with decreasing medium particle size.

4.

Pressure drop–gas velocity curves of heavy medium particles with different size distributions.

The maximum change rate of the critical fluidization velocity, X _max, is defined as

$$X_{\max }=\frac{\mathrm{\Delta }{U}_{\mathrm{mf},\max }}{{\mathrm{U̅}}_{\mathrm{mf}}}\times 100\%$$ 3

where ΔU _mf,max represents the difference value between the maximum and minimum critical fluidization velocities of each medium particle under different static bed heights and U̅ _mf is the average value of the critical fluidization velocity of each medium particle under different static bed heights.

In Figure , it can be seen that the X _max values for the two size ranges of 0.3–0.25 mm and 0.25–0.18 mm are smaller, both less than 10%. Therefore, the influence of static bed height on critical fluidization velocity is relatively small. Moreover, the above two sizes are the main medium-particle components in the modularized air-dense medium dry coal separator, which helps evaluate the critical fluidization velocity in the actual separation process. For the two fine medium particle size ranges of 0.18–0.125 and 0.125–0.074 mm, the bed is easy to form channeled flow due to their high viscosity, thus resulting in poor bed stability.

5.

X _max values corresponding to various size distributions of heavy medium particles.

3.1.2. Critical Fluidization Velocity of Mixing Medium Particles with Different Narrow Sizes

The static bed height here is set as 100 mm, and then the critical fluidization velocity of mixing medium particles with different mass percentages is explored using two narrow size ranges of 0.3–0.25 and 0.15–0.125 mm. The results indicate that an increase in the mass percentage of the coarser medium particle, labeled as W, leads to a nearly linear growth in the critical fluidization velocity of the bed, as shown in Figure . This is not difficult to understand, as particle size determines the drag force required to lift them. Generally, smaller particles require less drag force, so their bed fluidization can be achieved under lower fluidization gas velocity.

6.

Critical fluidization velocity at different mass percentages of coarser medium particles.

3.2. Effect of Feeding Particles on Bed Fluidization Characteristics

Medium powder with a size fraction of 0.3–0.25 mm is selected as the bed material, and the static bed height is determined as 100 mm. The initial fluidization characteristics curve is presented in Figure a, and its corresponding critical fluidization velocity is 23.58 cm/s. Notably, the fluidization characteristics curve of the bed with a secondary feeding particle layer is obtained by a gradual decrease in the inlet gas velocity. To eliminate the influence of feeding particles’ shape on bed fluidization characteristics, a secondary feeding particle accumulation layer is constructed using standard density balls. Specifically, at the bottom of the bed, 60 high-density balls are laid flat, and then the medium particles are added. The detailed fluidization characteristics are shown in Figure a; it is found that the critical fluidization velocity has decreased to 22.90 cm/s. Moreover, a suspended feeding particle layer is also constructed using middle-density balls. After placing the density balls flat in the middle of the bed, the same experiment by decreasing the inlet gas velocity is performed, and the fluidization characteristics curve based on the upper bed layer is obtained, as presented in Figure b. It is noted that the critical fluidization velocity has decreased further to 22.75 cm/s.

7.

Fluidization characteristics curves of the bed with a secondary air distribution layer: (a) high-density feeding particle layer and (b) middle-density feeding particle layer.

In summary, the secondary air distribution layers formed by middle- and high-density feeding particles affect the fluidization characteristics of the bed, decreasing the critical fluidization velocity, likely because these secondary air distribution layers lead to a more uniform gas distribution in the upper bed.

3.3. Effect of Feeding Particles on Bed Voidage

As is well known, constructing a stable separation environment is extremely challenging due to the significant density difference between the fluidization gas and heavy medium particles. Specifically, the density regulation of gas–solid two-phase flow is influenced by multiple factors, including the fluidization gas and static bed height. Moreover, external disturbances such as feeding particles can alter the gas pathways from the bottom to the top of the bed, further leading to the concentration change in the gas–solid two-phase flow. In short, whether the increase in bed volume is equal to the immersion volume of feeding particles is still a question that needs to be studied, as it directly affects the bed voidage.

The tests use medium-density balls as the feeding particles, and the total feeding volume can be adjusted by varying the number of balls added. Certainly, to prevent the separation bed from being a defluidized state, the feeding volume is limited.

To minimize measurement errors, the fluidization number is kept low. The fluctuation of the bed surface under different gas velocities is illustrated in Figure , specifically represented by Δh.

$$\mathrm{\Delta }h=h_{\mathrm{f},\max }-h_{\mathrm{f},\min }$$ 4

where h _f,max and h _f,min represent the maximum and minimum heights of the bed surface, respectively.

8.

Bed surface fluctuation under different fluidization numbers.

The change in bed voidage is reflected by comparing the total volume of the feeding balls with the expansion volume of the bed after ball feeding, quantified using the following formulas. The expansion volume of the bed is expressed as

$$\mathrm{\Delta }{V}_1=\pi {r_1}^2\mathrm{\Delta }H$$ 5

where r ₁ is the inner radius of the fluidized bed and ΔH is the expansion height of the bed after feeding.

The total volume of the feeding balls is calculated as

$$\mathrm{\Delta }{V}_2=\frac{4}{3}\pi {r_2}^{3}m$$ 6

where r ₂ is the radius of the ball and m is the number of feeding balls.

The ratio of the expansion volume of the bed to the total volume of the feeding balls, simplified as the expansion ratio, is given as

$$V_{1,2}=\frac{\mathrm{\Delta }{V}_1}{\mathrm{\Delta }{V}_2}$$ 7

The static bed heights here are selected as 40, 80, and 120 mm. The detailed results of V _1,2 are presented in Figure . It can be observed in Figure a that when the number of feeding balls is fewer than 30, the V _1,2 at N = 1.0 (regarded as the emulsified phase) is less than 1, indicating that the feeding balls exert a compressive effect on the emulsion phase. This causes the medium particle concentration in the emulsion phase to increase, which is unfavorable for separation due to the increased voidage, increasing the resistance to the movement of feeding particles. However, V _1,2 will exceed 1, ranging from 1.06 to 1.11, once the number of feeding balls exceeds 30. To compare the expansion characteristics of the emulsified phase and the bubbling state after adding balls, low fluidization numbers of N = 1.05 and 1.1 are adopted to capture small fluctuations on the bed surface. The results indicate the same compression effect at a smaller ball number and similar ranges of V _1,2 at a larger ball number for these two fluidization numbers. Moreover, the effect of the static bed height on V _1,2 is also explored. By comparing Figure a,b, it is found that the V _1,2 at H _s = 80 mm exhibits a larger value than that at H _s = 40 mm, and the average values of V _1,2 are 1.21 vs. 1.03, 1.14 vs. 1.00, and 1.24 vs. 0.93 at N = 1.0, 1.05, and 1.1, respectively. The average values of V _1,2 become 1.11, 1.22, and 1.20 at N = 1.0, 1.05, and 1.1, respectively, when the static bed height increases further to 120 mm, as shown in Figure c, and these values are also greater than those at H _s = 40 mm. Therefore, a greater expansion effect occurs when the static bed height exceeds 40 mm. However, this does not mean that the higher the static bed height, the better the bed expansion, because when N is 1.0 or 1.1, the average value of V _1,2 at H _s = 120 mm is lower than that at H _s = 80 mm. This may be ascribed to the influence of added balls on the gas flow channels inside the medium-particle bed. Additionally, it is observed that a small number of bubbles appear on the bed surface at N = 1.0, which may result from the secondary air distribution layer formed by the feeding balls. This phenomenon once again confirms the results presented in Figure .

9.

Expansion ratios under different static bed heights.

3.4. Motion Behavior of High-Density and Low-Density Coal Particles

For the gas–solid separation fluidized bed, a stable separation environment is the foundation for achieving an effective separation of coal particles. Generally, the fluidization environment is influenced by factors such as the size of the heavy medium particles, the static bed height, and the fluidization gas velocity. Moreover, external factors such as coal particles can also interfere with the fluidization state of the medium particles. Therefore, the effects of various factors on the motion behavior of coal particles is worth investigating. Here, high- and low-density coal particles are selected as the feed.

To ensure equal feeding volumes, the feeding masses of clean coal and gangue are 70 and 120 g, respectively. Unless otherwise specified, the separation time here is set to 5 min.

3.4.1. Settlement of High-Density Coal Particles

3.4.1.1. Effect of Medium Particle Size

Typically, the heavy medium particle size selected for a gas–solid separation fluidized bed is 0.3–0.074 mm. To investigate the effect of different medium particle sizes, four narrow size fractions, i.e., 0.3–0.25, 0.25–0.18, 0.18–0.125, and 0.125–0.074 mm, are chosen at a fixed static bed height of 100 mm.

In Figure , it can be observed that as the fluidization number increases, the axial distribution coefficient for each medium particle size fraction first increases and then decreases. It is also noted that the axial distribution coefficients are all greater than 0.750 in the medium size range of 0.3–0.25 mm and the fluidization number range of 1.0–1.4. Therefore, under the condition of coarser heavy medium particles, high-density feeding particles exhibit a relatively good settlement performance. At fluidization number N = 1.0, due to the relatively low bed expansion, the movement space for high-density feeding particles is small, resulting in poor settlement performance within a limited time. However, as the fluidization number increases, the settlement performance gradually improves, reaching a maximum axial distribution coefficient of 0.929 at N = 1.15. Beyond this point, further increasing the gas velocity will increase the average bubble diameter within the bed, causing the bed stability to deteriorate. Consequently, the axial distribution coefficient sharply drops from 0.929 at N = 1.15 to 0.799 at N = 1.2. When the medium particle size decreases to 0.25–0.18 mm, its corresponding axial distribution coefficient curve presents a relatively smooth trend at N ≤ 1.4 compared to 0.3–0.25 mm, and the optimal value of 0.830 is attained at N = 1.4. According to the Kato and Wen formula, at the same fluidization number, the smaller the heavy medium particle size, the smaller the bubble size. Thus, finer heavy medium particles help expand the adjustable range of gas velocity, which benefits the separation of feeding particles. However, the adverse effects of increased bed viscosity resulting from finer heavy medium particles must also be considered. When the heavy medium particle size further decreases to 0.18–0.125 mm, the best settlement performance is achieved at N = 1.6, with an axial distribution coefficient of 0.792. It is found that when N ≤ 1.4, the axial distribution coefficient curve of 0.18–0.125 mm fluctuates more significantly compared to coarser heavy medium particles, which is attributed to the prominent influence of bed viscosity. When the heavy medium particle size becomes 0.125–0.074 mm, its corresponding axial distribution coefficient reaches a maximum value at N = 2.4. Based on the above analysis, it can be seen that a finer heavy medium-particle bed requires a larger fluidization number to achieve optimal settlement performance compared to coarser ones.

10.

Axial distribution coefficient of high-density coal particles under different medium particle sizes.

3.4.1.2. Effect of Static Bed Height

Here, the heavy medium particle size adopts 0.3–0.25 mm, and four static bed heights of 60, 100, 140, and 180 mm are used. Notably, the mass ratios of feeding particles to medium-particle bed remain unchanged, and the detailed data are listed in Table .

1. Mass Ratios of Feeding Particles to the Medium-Particle Bed under Different Static Bed Heights.

static bed height/mm	medium particles’ mass (m1)/g	feeding particles’ mass (m2)/g	m2/m1
60	1665.92	72	0.043
100	2776.54	120	0.043
140	3887.16	168	0.043
180	4997.77	216	0.043

It can be observed in Figure that when the static bed height is 60 mm, the axial distribution coefficient curve shows slight fluctuations as the fluidization number increases, remaining at ca. 0.85. This is because, under low bed height conditions, the gas velocity adjustment within a certain range has a small impact on the average bubble size in the bed. Therefore, it can be considered that low static bed height is beneficial for expanding the adjustable range of gas velocity and facilitating the separation process. When the static bed height rises to 100 mm, the axial distribution coefficient gradually increases with increasing fluidization number from 1.05 to 1.15 and reaches a better value of 0.929 at N = 1.15. However, when N > 1.15, the axial distribution coefficient decreases significantly and stabilizes at around 0.8. Thus, the influence of gas velocity at H _s = 100 mm becomes more pronounced compared to that at H _s = 60 mm, causing a relatively reduced adjustable range of gas velocity. When the static bed height is further increased to 140 mm, the axial distribution coefficient fluctuates significantly within the fluidization number range of 1.05–1.40 and reaches a maximum value of 0.864 at N = 1.1. This is due to the further enhancement effect of bubbles in the bed. As the static bed height reaches 180 mm, the axial distribution coefficient generally decreases with increasing fluidization number. In summary, the effect of bed height is inconsistent at low gas velocities (N < 1.2). However, when N > 1.2, the influence of bubbles on the movement of high-density coal particles becomes more prominent, and the axial distribution coefficient seems to be better at lower static bed height. This is ascribed to the larger average bubble size in the higher bed, which more severely interferes with the settlement of high-density coal particles. Therefore, for the separation of fine coal particles, a low bed height can achieve relatively good separation performance. However, it should be clear that increasing bed height can increase the stratification space for coal particles, which is conducive to improving the throughput of the separation bed. In practical separation processes, it is necessary to consider both separation accuracy and throughput and strike a balance between them. The optimal fluidization numbers for static bed height of 60 mm, 100 mm, 140 mm, and 180 mm are N = 1.4, 1,15, 1.1, and 1.05, respectively, presenting a decreasing trend with increasing static bed height. Therefore, it can be concluded that the influence of static bed height on high-density coal particle separation ultimately depends on the action of bubbles.

11.

Axial distribution coefficient of high-density coal particles under different static bed heights.

3.4.1.3. Effect of High-Density Coal Particle Size

The heavy medium particles adopted here are 0.3–0.25 mm, and the static bed height is set to 100 mm. High-density coal particles with three different size fractions of −6 + 3 mm, −13 + 6 mm, and −20 + 13 mm, obtained from the same raw coal, are used as feeding particles, and the feeding mass is controlled at 120 g.

As can be seen in Figure a, the axial distribution coefficient of −6 + 3 mm high-density particles increases with the increase in fluidization number when the separation time, τ, is less than 108 s, which means that increasing gas velocity is beneficial for particle settlement. Thereafter, as the separation time further increases, the axial distribution coefficient of N = 1.1 surpasses those of N = 1.2, N = 1.3, and N = 1.4 at 108, 157, and 173 s, respectively, while the corresponding separation time required for N = 1.05 are 250, 275, and 287 s. Noting that when the separation time is less than 250 s, N = 1.05 always maintains the worst separation performance. Thus, increasing the fluidization number by only 0.05 can significantly enhance the separation performance. However, if the separation time is further increased, N = 1.05 exhibits the potential to reach the separation performance of N = 1.1 or even exceed it. Nevertheless, in the practical separation process, processing capacity must be taken into account. It is found that the curves of N = 1.2, N = 1.3, and N = 1.4 present a similar trend before τ = 300 s, and the order of superiority and inferiority of settlement performance for −6 + 3 mm particles is N = 1.4, N = 1.3, and N = 1.2. Therefore, within the fluidization number range of N = 1.2–1.4, increasing the fluidization number is beneficial for particle settlement, but their axial distribution coefficients are close at τ = 300 s, indicating that fluidization number has little impact on the separation results at this point. In summary, the selection of the separation fluidization number should be determined based on the separation time.

12.

Axial distribution coefficient of high-density coal particles under different feeding sizes.

For −13 + 6 mm high-density particles in Figure b, at τ = 30 s, the axial distribution coefficients corresponding to different fluidization numbers are improved compared with −6 + 3 mm particles. It is also observed that the axial distribution coefficient at N = 1.05 surpasses that of fluidization numbers greater than 1.1 at around 120 s, while the separation time required for N = 1.1 can be shortened to about 60 s, which is significantly shorter than that of −6 + 3 mm particles. Therefore, a larger coal particle size is advantageous for reducing the separation time. When the separation time exceeds 120 s, the axial distribution coefficients under different fluidization numbers show a fluctuating state; this is mainly attributed to the relatively larger particle size, which can easily cause uneven particle accumulation and have a significant impact on the stratified sampling.

For −20 + 13 mm particles in Figure c, at τ = 30 s, the axial distribution coefficients corresponding to different fluidization numbers increase significantly compared to the other two smaller coal particle sizes, and the difference between the maximum and minimum values obviously reduces, indicating a diminished influence of the fluidization number. As a result, at τ = 60 s, the axial distribution coefficients under different fluidization numbers become closer. Moreover, it is observed that the axial distribution coefficient exhibit smaller fluctuations across different fluidization numbers once the separation time exceeds 180 s. Therefore, an excessively long separation time is of little practical significance for −20 + 13 mm particles.

In summary, as the high-density coal particle size increases, the influence of the fluidization number on settlement performance decreases, and the separation time required to achieve better settlement performance shortens.

3.4.2. Backmixing of Low-Density Coal Particles

Low-density coal particles usually float on the surface of a fluidized bed, but the particles will move due to the fluctuation of the bed surface in a bubbling bed. From Figure , it is observed that the axial distribution coefficient of the low-density particles generally increasing with increasing fluidization number under different medium particle size conditions, indicating that the backmixing degree of low-density particles gradually intensifies. As can be seen in Figure a that when N ≤ 1.3, the axial distribution coefficient presents small change. However, when the fluidization number exceeds 1.3, the axial distribution coefficient increases significantly. This is mainly due to a larger bubble on the bed surface easily causing stronger fluctuation of the bed surface, making it difficult for some low-density particles to strictly follow the principle of density separation and float on the surface, so the influence of the external interfere becomes more pronounced. Figure b shows that the axial distribution coefficients at N = 1.4 and 1.5 are obviously lower than those in Figure a with the corresponding fluidization number, which is ascribed to the fact that the finer the medium particles, the smaller the bubble size on the bed surfaces. It is found that the axial distribution coefficients in Figure c,d are higher than those in Figure a,b under the same fluidization number, this may result from the combined effect of bubbles and weaker collision from finer medium particles, which makes the low-density particles easier to move. From the above analysis, it can be concluded that an increase in the medium particle size helps reduce the backmixing degree of low-density particles, but gas velocity remains a key factor.

13.

Axial distribution coefficient of low-density coal particles under different medium particle sizes.

From the motion behavior exhibited by high-density and low-density coal particles, it can be concluded that, under appropriate fluidization gas velocity conditions, coarser medium particles are more conducive to the separation of high-density and low-density particles. However, it is necessary to optimize the gas velocity before the separation process begins.

3.5. Discussion

In a separation bed, the stability of the bed layer, bubble behavior, and coal particle movement trajectories are closely related and determined by a dynamic balance among fluidization gas velocity, medium particle size, bed height, and feeding amount. Among them, a single fluidization gas velocity regulation often makes it difficult to achieve a stable and controllable separation state in practical production, requiring multiparameter collaborative optimization. First, the medium particle size exerts a fundamental influence on the bed fluidization and separation window. Its fine particles can reduce the minimum fluidization velocity but are more likely to induce bed pressure fluctuations and channeling, thereby interfering with coal particle separation. In contrast, coarser medium particles generally provide a more stable fluidization environment but require a larger fluidization velocity to lift up the medium particles. In practical operation, a finer medium may require tighter control of airflow to suppress instability, whereas a coarser medium allows broader adjustment of operating gas velocity for better separation performance; however, bubble-induced disturbance should be noted at excessively high gas velocities. Second, static bed height is also found to significantly affect the separation behavior. An increase in bed height expands the available separation space and improves throughput; however, it simultaneously amplifies the bubble effects and increases the risk of coal particle remixing, thereby decreasing the separation accuracy. The observed optimal fluidization number for high-density particle separation decreases with increasing bed height, indicating that a deeper bed requires lower gas velocity to maintain favorable separation conditions. This finding has direct implications for industrial practice: the bed height should be adjusted in coordination with airflow and feed rate rather than treated as an independent setting. When higher separation accuracy is required, a relatively lower bed height may be preferable. Conversely, when throughput is the primary objective, an appropriate increase in bed height may be acceptable, provided that gas velocity is decreased and medium-size distribution is optimized. Moreover, the feeding particles themselves have been shown to alter bed porosity and fluidization state. High-density feeding particles can act as a secondary packing layer within the bed, affecting local porosity and redistributing the gas phase, demonstrating that the feed rate is not merely a capacity parameter; it also directly changes the local flow field and gas path structure of the bed. In industrial operation, an increase in feed rate without a corresponding adjustment in airflow is likely to increase local compaction and degrade separation performance. Conversely, excessive airflow is intended to compensate for higher feeding loads, which may intensify bed perturbation. Therefore, the feed capacity must be matched with airflow and medium through coordinated control rather than through independent adjustment.

The particle motion behavior analysis further indicates that the optimal separation state results from a balance among gravitational settling, drag force, buoyancy, and bubble-induced disturbances. High-density particles require sufficient bed expansion to migrate and stratify effectively, but an excessive gas velocity can disrupt this process by increasing bubble coalescence and bed fluctuation. Low-density particles, by contrast, benefit from a more stable interface that minimizes the remixing. These observations imply that the operating window for industrial systems should be determined according to the desired product quality, feed composition, and throughput targets. It should be noted that this work mainly focuses on the regularities revealed by the experimental results, and future work should extend these findings to industrial conditions by accounting for scale effects, gas distribution uniformity, and continuous feed disturbance.

4. Conclusions

In this study, the fluidization characteristics of different narrow medium particle sizes are first investigated, and the critical fluidization velocity of medium particles with different mixing ratios of narrow size is also evaluated. Meanwhile, the effects of the secondary air distribution layer formed by middle-density or high-density feeding particles are considered. Moreover, the effects of feeding particles on the bed with a single emulsion phase or bubbling state are explored by controlling different bed heights and feeding amounts. Additionally, the motion behavior of high-density and low-density coal particles under different factors, such as medium particle size, static bed height, and coal particle size, is studied. The detailed conclusions are as follows:

• (1)The pressure drop of finer medium particles presents a larger fluctuation once the gas velocity exceeds the critical fluidization velocity, indicating that the bed stability will deteriorate with the decrease of the medium particle size. This is why the static bed height has a relatively significant impact on the critical fluidization velocity of medium particles smaller than 0.18 mm. Moreover, an increase in the mass percentage of the coarser medium particles results in a nearly linear increase in the critical fluidization velocity of the bed. It is worth noting that the bed fluidization characteristics can be affected by the middle-density or high-density feeding particles, which can reduce the critical fluidization velocity.
• (2)The feeding balls generate a compression effect on the emulsion phase when the number of feeding balls is smaller, but an expansion effect occurs once the volume of feeding balls exceeds a certain value. A similar phenomenon is also observed in a bubbling fluidized bed at lower fluidization numbers of N = 1.05 and 1.1. Moreover, the expansion ratio corresponds to a greater value with increasing static bed height from 40 mm to 80 mm, but it does not mean that the higher the static bed height, the better the bed expansion, as the expansion ratio decreases when the static bed height further increases from 80 mm to 120 mm with the fluidization number being 1.0 or 1.1. This may be ascribed to the influence of feeding balls on the gas flow channels inside the medium-particle bed.
• (3)For high-density coal particles, a finer heavy medium-particle bed requires a larger fluidization number to achieve optimal settlement performance compared to coarser ones, and the optimal fluidization number presents a decreasing trend with increasing static bed height; this is ascribed to the larger average bubble size in the higher bed, which more severely interferes with the settlement of high-density coal particles. As the high-density coal particle size increases, the influence of the fluidization number on settlement performance decreases, and the separation time required to achieve better settlement performance shortens.
• (4)For low-density coal particles, their corresponding axial distribution coefficients generally show an upward trend with increasing fluidization number under different medium particle size conditions, indicating that the backmixing degree of low-density particles gradually intensifies. Moreover, an increase in the medium particle size helps reduce the backmixing degree of low-density particles, but gas velocity remains a key factor.

Y.W.: Writingreview and editing, Writingoriginal draft, Validation, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. H.Z.: Writingoriginal draft, Visualization, Data curation. Y.F.: Writingoriginal draft, Data curation. Z.L.: Supervision, Resources, Conceptualization.

This work was financially supported by the Natural Science Foundation of Jiangsu Province (BK20240971), the Fourth Batch of Leading Innovative Talent’s Introduction and Cultivation Projects of Changzhou (CQ20240120), the Scientific Research Foundation for Innovative Talents Introduction of Changzhou University (ZMF23020049), and the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province of China (23KJB480002).

The authors declare no competing financial interest.