Fluidization of Cohesive Fluorite Particles at ... - ACS Publications

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Fluidization of cohesive fluorite particles at ambient/ high temperatures and enhancement methods Zhongxuan Liu, Wangmin Lin, Zhengliang Huang, Jingyuan Sun, Yao Yang, Jingdai Wang, and Yongrong Yang Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b05317 • Publication Date (Web): 13 Mar 2018 Downloaded from http://pubs.acs.org on March 13, 2018

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Industrial & Engineering Chemistry Research

Fluidization of cohesive fluorite particles at ambient/high temperatures and enhancement methods Zhongxuan Liu, Wangmin Lin, Zhengliang Huang, Jingyuan Sun, Yao Yang*, Jingdai Wang, Yongrong Yang Zhejiang Provincial Key Laboratory of Advanced Chemical Engineering Manufacture Technology, College of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, P. R. China

ABSTRACT: Fluidization of fine fluorite particles, classified as Geldart A/C particles, were studied at ambient/high temperatures by experiments. Results showed that fine fluorite particles could not be fully fluidized at ambient temperatures, due to the agglomeration phenomenon. What’s worse, due to the great increase of van der Waals forces with the increasing temperature, the fluidization quality was further depressed and they were totally de-fluidized at 723 K unless the loose gases were used during the heating process. In order to improve the fluidization quality, an enhancement method of adding cohesive calcium sulfate particles was established. The best improvements at ambient/high temperatures both appeared when the addition fraction was

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20wt%. Moreover, theoretical analysis showed that the effect mechanism of calcium sulfate particle was the ‘coordination’ theory. According to the ‘coordination’ theory, the optimum addition fraction of calcium sulfate particles was calculated as 16.5wt%-22.4wt%, which agreed well with the experimental results.

1 Introduction Anhydrous hydrogen fluoride (AHF) is an important chemical raw material, and its products such as organic fluoride and inorganic fluoride salts are widely used in the production of fluorine chemicals, petrochemicals and some other related industries1. For a long time, the rotary kiln process which takes fluorite particles as raw materials is the main process for production of AHF. But due to the low heat/mass transfer efficiencies in the rotary kiln reactor, the conversion is relatively low especially when dealing with low-grade fluorite ore. As one of the top reserves of fluorite ore, China has been the largest producer of AHF in the world. However, the reserves of high-grade fluorite in China are low, developing new processes for the utilization of lowgrade fluorite is significant and meaningful confronting the increasing demand of AHF and decrease of high-grade fluorite ore. In terms of these problems, a new process was proposed to produce AHF in the gas-solid fluidized bed2. Specifically, the multi-stage fluidized bed is adopted in this process to provide the reaction space where countercurrent contact happens between gas phase and solid phase and fine fluorite particles (1-100 µm) are fluidized by the gas mixture (mainly steam and sulfur trioxide). Because of the greatly improved mass and heat transfer efficiencies, this process is possible for dealing with low-grade fluorite ore. However, fluorite particles used in this process are fines with a wide particle size distribution and consist of Geldart A particles as well as lots of ultrafine Geldart C particles. As is well known, the ultrafine particles can lead to agglomeration during the


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fluidization3,4 and result in low fluidization quality, which severely hinders the industrialized process. Up to now, there are still no reports related to the successful industrialization of this process. Therefore, it is of great significance to study the fluidization of fine fluorite particles at low/high temperature and develop methods to improve the fluidization quality of fine fluorite particles. As early as 1984, Geldart5 investigated the fluidization of a series of fine particles with size lower than 70 µm. In his work, various experimental methods were adopted to characterize the flow behavior of fine particles, such as the measurements of initial fluidization curves, detecting the bed pressure drops, analyzing the bed expansion/collapse behaviors and measuring the ratio of tap density to bulk density of particles. Hereafter, these methods are widely used in other research. Through above methods, great differences were observed between Geldart C particles and other coarse particles. Firstly, it became virtually impossible for cohesive Geldart C particles to determine the minimum fluidization velocity and minimum bubbling velocity by initial fluidization curves because Geldart C particles always cannot actually achieve the fluidization regime. Meanwhile, it was well-known that the theoretical pressure drop across the fluidized bed of the free-flowing particles was nearly equal to the Ws/AT ((static bed weight)/(the crosssectional area of the bed)) and the ratio between the actual pressure drop and Ws/AT reduced as the Geldart C particles became more cohesive. Secondly, Geldart and Quintanilla et al.6 both observed that the bed expansion of Geldart C particles was higher than that of Geldart A particles. Moreover, as to the collapse behavior of Geldart C particles, an apparent feature was observed that a relative long solids consolidation stage existed after the rapid collapse. Yang et al.7 studied and compared the collapse curve of Geldart A, B and C particles, respectively. He further put forward the dimensionless time Θ to evaluate the fluidization quality of particles and


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a larger Θ implied a better fluidization quality. Finally, by comparing the ratio between the tap density and bulk density of different particles, Geldart proposed a criterion for particles. He concluded that powders having a ratio larger than 1.4 should be considered as group C particles, while powders with a ratio smaller than 1.4 and higher than 1.25 should be group A particles. This density ratio was also known as Hausner Ratio (HR), and it was also conducted to characterize the fluidity of particles in other investigations8. In addition to above methods, other methods including the direct cohesion measurement of fine particles by shear test and microscopic image analysis were also developed. Wang et al.9 investigated the fluidization of various cohesive fine particles based on these two methods in additions to pressure drop measurements and bed expansion behaviors. He concluded that the fluidization of cohesive particles could be divided into four patterns in details, which consisted of the channeling, the fluidization without bubbles just similar to that of Geldart A particles, the bubbling fluidization and the stratified fluidization. But no matter which fluidization pattern was involved, the agglomeration existed all the time during the fluidization of fine particles and led to the poor fluidization quality. The underlying reason for agglomeration of fine particles is the strong interparticle force (IPF) between particles. Wang et al.10 and Rhodes et al.11 studied the influence of IPFs between particles by discrete element method (DEM). They found that for Geldart B and A particles the IPF is relatively small, but when artificially increasing the IPF, the fluidization behavior of Geldart B particles would change to that of Geldart A particles, and even that of cohesive Geldart C particles. Shabanian et al.12 applied the polymer coating to increase the level of IPFs in a gas-solid fluidized bed and observed the same transition by experimental methods. Raganati et al.13 found that the minimum fluidization velocity, size of fluidized particles and bed voidage


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increased with the increment of temperature and the effect of sound field disaggregating cluster decreased with increasing temperature for both of the Geldart A and C particles. In addition, the author also proposed a cluster/subcluster model to account for the temperature effects on both hydrodynamic and cohesive forces, so it is possible to evaluate IPFs between Geldart A and C particles. Chirone et al.14 also applied the cluster/subcluster model to calculate IPFs and compared the IPFs to those obtained from the shear test, the values calculated adopting two methods are of the same order of magnitude. Electrostatic forces and van der Waals forces are the main IPFs for the agglomeration of fine particles in a dry environment15,16, however, the liquid bridge force might be the main cause of agglomerates in a wet environment. Meanwhile, the IPFs can vary with the temperatures. Moughrabiah et al.17 reported that the electrostatic force decreased as the temperature increased, while van der Waals forces would increase with increasing temperature18. Morooka et al.19 observed that when agglomerates of submicron Si3N4 particles were placed in a high-temperature environment, the size of agglomerates decreased by about 10% because of a lower humidity at high temperature. Above all, extensive investigations on fluidization of cohesive particles have been made by former researchers, however, nearly all of the published conclusions related mainly to Geldart C particles and nanoparticles. A special kind of particles called Geldart A/C particles is not adequately researched20. This kind of particles have a wide particle size distribution, some of which are Geldart A particles but the other of which are classified as Geldart C particles. As it is, fluidization of the particles may show the characteristics of both group A and C particles. Furthermore, aforementioned research has shown that the temperature significantly affected the IPFs, however, scarce research was directly conducted in the high temperature system close to industrial conditions (in the real industrial process for production of AHF, the reaction


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temperature is between 443 and 611 K2). Therefore, investigating the fluidization of Geldart A/C particles at room/high temperature will be a good supplement for the current investigation of fluidization of cohesive fines. Moreover, since fine fluorite particles are just the Geldart A/C particles, this investigation will also show a good guidance for the development of new process for the production of AHF. The character that fine particles were extremely difficult to be fluidized or processed has led to a series of enhancement methods, such as external fields assistance (sound field21-24, vibration field25, electromagnetic field26,27) and pulse gas28. However, when taking into account problems of scale production, installation complexity and process safety, these methods couldn’t be applied. Application of new equipment and increase of the system complexity might lead to new problems. Besides, some researchers also suggested that adding particles could also strengthen the fluidization quality of fine cohesive particles29. Considering that there are fluorite particles and calcium sulfate particles involved in the fluidized bed process for production of AHF, adding calcium sulfate particles may be a perfect method to enhance the fluidization of fine fluorite particles which will not increase the difficulty of subsequent separation process. But the commercial calcium sulfate particles are particles with high hydrogen bonds between particles30, which means that although the calcium sulfate particles are not Geldart C particles, they are still cohesive particles the same to fine fluorite particles. Thus, effects and mechanism of calcium sulfate particles may be totally different from current research related to adding particles. Therefore, it is necessary to study the feasibility and mechanism of this method. In summary, the objective of this work was to study the fluidization of Geldart A/C particles (fine fluorite particles) and methods to enhance it. Firstly, this work would investigate the fluidization behavior of fine fluorite particles in room/high temperature, mainly to reveal the


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fluidization characteristics of Geldart A/C particles and understand the effect mechanism of temperature on fluidization. Secondly, a method by adding calcium sulfate particles was developed to enhance the fluidization of fine fluorite particles, and the effect mechanism of calcium sulfate particles was revealed. 2 Experimental apparatus, materials and methods The apparatus used in this work were divided into two types, one was the Plexiglas fluidized bed for experiments at the room temperature, and another one was the stainless steel fluidized bed for high temperature. The Plexiglas fluidized bed is schematically illustrated in Figure 1(a). The fluidization column (240 mm in inner diameter and 1300 mm in height) was made of Plexiglas to provide visual observation of the fluidization, and an assemble air distributor with the combination of a porous stainless steel plate (the pore diameter is 1.0 mm and the open area ratio is 1.6%) and a 100 mesh screen was installed under the column to make sure the uniform distribution of gases. In the outlet of the column, the two-stage cyclone was used to collect the entrained particles. The schematic of the stainless fluidized bed is shown in Figure 1(b). The column of the bed was made of stainless steels to afford the high temperatures and which was 80 mm in inner diameter and 1000 mm in height. The same assemble air distributor was used and installed to make the uniform distribution of gases. In order to acquire and keep the designated temperature, an electric heating jacket was used around the outside wall of the bed and two thermocouples were designed to detect the temperatures in the bed. At the beginning of each experiment, the fluidized bed was pre-heated with gases until the temperature reached 723 K.


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Figure 1. Schematic diagram of (a) the Plexiglas fluidized bed; (b) the stainless steel fluidized bed. Pressure drop measurement was the main method used to characterize the fluidization quality. The differential pressure transducers were used to measure the pressure drop across the whole bed during experiments. The measuring range of the transducer is ±5 kPa and relative accuracy is ±0.25%. The sampling frequency was set to 400 Hz and the sampling time was 120 s. During the experiments at the ambient temperature, three pressure tubes, 80 mm in length and 4 mm in diameter, were installed 5 mm above the distributor in order to collect pressure drop signals on the left, middle and right side of the bed, respectively. But during experiments at high temperature, the pressure probe was located 10 mm below the distributor, therefore, when the pressure drop of the whole bed was needed, the pressure drop of the gas distributor should be excluded. The pressure drop of gas distributor at different gas velocities were pre-detected before the fluidization of particles. In this study, fine fluorite particles and compressed ambient air with a humidity lower than 10% were used as the fluidized particles and fluidizing gas, respectively. Calcium sulfate particles were used as the adding component to improve the fluidization quality of fluorite


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particles. The key physical properties of particles are given in Table 1. The particle size distributions measured by particle size analyzer (Malvern Mastersizer 2000) are shown in Figure 2. Table 1. Particles used for the fluidization experiments Geldart group31

Particles

Density (kg/m3)

dp (µm)

A/C

CaF2

3180

28.4

B

CaSO4

2320

75.8

8

(a)

(b)

Geldart Particle Classification

8

6

Volume fraction (%)

Volume fraction (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


C

4

particles

A particles

2

0

6

4

2

0

0

50

100

150

200

0

200

Particle size (µm)

400

600

800

1000

Particle size (µm)

Figure 2. Particle size distribution of (a) fluorite particles; (b) calcium sulfate particles.


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3 Results and discussion 3.1 Fluidization of fine fluorite particles at ambient temperature 3.1.1 Initial fluidization curve 2000 1600

Pressure drop (Pa)

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The theoretical pressure drop of the bed(Ws⋅g/AT)

1200

800

t=298 K increasing gas velocity decreasing gas velocity 400 0.01

0.1

Gas velocity (m/s)

Figure 3. Variations of pressure drop with gas velocity for fluidization of fine fluorite particles at 298 K. According to previous research, measurement of initial fluidization curve is the most commonly used method to determine and evaluate the fluidization quality of particles32, and it is also applicable for fine particles33. Figure 3 shows the initial fluidization curve of fine fluorite particles at ambient temperature. It was observed that there were several humps in the pressure drop curve while increasing the superficial gas velocity, and the pressure drop always increased with increasing gas velocity in the range of gas velocities used in this work. These results were consistent with previous research related to fluidization of ultrafine particles34. Because of strong IPFs between particles, the cohesive particles adhered to each other and formed agglomerates, resulting in channels and cracks during the initial fluidization. When the formation and collapse of channels and cracks led to bubbles and dense phase alternately passing the pressure tubes, self-oscillation of pressure drop was set up, thereby the vertical interval and humps appeared in the pressure drop curve35. Furthermore, the initial fluidization velocity of fine fluorite particles


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determined by the changing point in the bed pressure drop curve with descending gas velocity was 0.049 m/s, however, the fine fluorite particles can be just partially fluidized probably to channeling phenomena, so initial gas velocities of fine fluorite particles are larger than 0.049m/s, which was more than 59 times of the initial fluidization velocity calculated by the Wen-Yu formula36 (0.00083 m/s). This also illustrated that strong IPFs between particles caused the formation of a variety of agglomerates during the fluidization of fine fluorite particles. What’s worse, some agglomerates whose sizes were large enough might even deposit on the distributor and form the de-fluidized dead zone. This just explained why the bed pressure drop did not reach the theoretical pressure drop of the bed in Figure 3. Therefore, a preliminary conclusion can be drawn that the fluidization of fine fluorite particles was the same to fluidization of Geldart C particles and which was the agglomerate fluidization. 3.1.2 Bed collapse and expansion In addition to the initial fluidization curve, detection of bed collapse is also an important way to characterize the fluidization of cohesive particles. Figure 4 illustrates the bed height as a function of time in the collapse process. The result indicated that the collapse curve could be divided into three stages: bubble escape stage, hindered sedimentation stage and solids consolidation stage, which is similar to the bed collapse curve of Geldart A particles. But the hindered sedimentation stage (about 5 s) was shorter and the solids consolidation stage (about 55 s) was longer compared to Geldart A particles, which was just one of the characteristics of cohesive particles7. The longer solids consolidation stage resulted from the escape of gases among agglomerates. Because the structure of emulsion changed gradually during this process, the gas escape was hindered, thus prolonging the solids consolidation stage. Figure 4 also shows


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that the bed expansion ratio is 1.7, which is larger than the common value of Geldart A particles and caused by the increase in the number and size of the horizontal/sloping cracks37. 18 t=298 K

16

Bed height (cm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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stage1: bubble escape

14

12

stage2: hindered sedimentation stage3: solids consolidation

10 0

10

20

30

40

50

60

70

Time (s)

Figure 4. The three-stage bed collapsing process for fine fluorite particles. Furthermore, Liu38 proposed a method to characterize the fluidization quality of cohesive fine particles by comparing the difference between real expansion and ideal expansion of the bed with the increasing gas velocity and further defined the non-ideal index fh, which was given as: ut

AR = ∫ ε du umf

AP =

(1)

n n +1 ) ut (1 − ε mf n +1

(2)

AR − AP AP

(3)

fh =

where AR is the real expansion, AP is the ideal expansion, umf and ut are the initial fluidization velocity and terminal velocity of particles, ε and εmf are the voidage and critical voidage of the bed, n is the voidage index, which can be determined by the relationship with the terminal Reynolds number39 and is 4.19. Figure 5 shows the deviation between the real bed expansion and the ideal bed expansion. It was observed that the actual bed voidage was always smaller than the ideal bed voidage, and the


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difference between them increased with the increasing gas velocity. The non-ideal index fh of fine fluorite particles was calculated and which was 0.678, which belonged to the agglomeration fluidization based on the criteria of Liu38. This further implied that the fluidization of fine fluorite particles was agglomerate fluidization. ε=1

0.9 0.8

Ideal expansion Ap

0.7

lgε

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0.6 Ap-Ar

0.5

0.4 ε =0.381 mf

Real expansion Ar

0.05

0.06

0.07

0.08

0.09

0.1

lgu

Figure 5. Comparison between the real bed expansion and ideal bed expansion. 3.1.3 Particle size analysis of fine fluorite particles In former parts, the initial fluidization curve, bed collapse/expansion curves and overall nonideal index of the bed all showed that fine fluorite particles were easy to form agglomerates because of strong IPFs between particles, and the corresponding fluidization was agglomeration fluidization. But all of these methods didn’t directly confirm the existence of agglomerates. The photography40 was always adopted in the existing research to characterize agglomerates during the fluidization of cohesive particles. However, in this work, the freeboard of the bed was filled with elutriated fine fluorite particles and the bed level was fuzzy, thus the photography wasn’t available and we had to conduct another indirect method to prove the existence of fluorite agglomerates. Figure 6 showed the particle size distribution of fine fluorite particles sampled at the bottom and top of the fluidized bed. The sampling procedure was as follow. When the fluidized bed reached steady fluidization (after fluidization 5 minutes under a certain gas


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velocity), the gas was shut down and solids were sampled from the top and bottom of the bed from the sampling ports. The particle size analysis indicated that the particle size distributions at the bottom and top of the fluidized bed were almost the same, and their average particle size was 31.01 µm and 30.42 µm, respectively, which indicated that particle segregation phenomenon did not occur. It is well known that particles with the same density and different particle size will be segregated after fluidization, and large particles are prone to distribute at the bottom of the bed, while small particles will distribute in the upper layer of the bed41. Apparently, the result in this work doesn’t comply with this well-known conclusion. This indirectly proved the formation of agglomerates. Because particles were not dispersed well in the fluidized bed, on the contrary, particles with different size were agglomerated and they were fluidized as agglomerates, then the segregation disappeared. 8 upper bed lower bed

6

Volume (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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4

2

0 0

40

80

120

160

200

Particle size (µm)

Figure 6. Particle size distribution of fine fluorite particles sampled from different positions of the fluidized bed. To sum up, although fine fluorite particles consisted of Geldart A particles as well as Geldart C particles, the fluidization behavior of them under ambient temperature looked much more like fluidization of cohesive Geldart C particles, namely the agglomerates fluidization. In the range of gas velocity used in this work, the ratio of real bed pressure drop to the theoretical bed pressure


14

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drop was only 60%, which was far away from the complete fluidization of the whole bed. Besides, the fluidized particles were fluidized as agglomerates, not the dispersed particles. This non-complete fluidization and formation of agglomerates would definitely hinder the performance of the fluidized bed reactor, therefore, developing methods to enhance the fluidization is necessary. 3.2 Fluidization of fine fluorite particles at high temperature It is obvious the IPFs between particles at high temperatures will be different from those at room temperatures, such as van der Waals force. Therefore, the fluidization of particles under high temperatures can be significantly different. The fluidization of fine fluorite particles at 723 K (much higher than the highest temperature in the real process) was investigated in a stainless steel fluidized bed. Figure 7 illustrates the initial fluidization curve of fine fluorite particles at 723 K. It was observed that the pressure drop was only 100 Pa even at the superficial gas velocity as large as 0.3 m/s, which indicated that fine fluorite particles were always unable to be fluidized at 723 K. Because fluidizing gases only flew through the stable cracks among the static bed, the pressure drop kept at a relatively low level. Obviously, this phenomenon was caused by the fact that IPFs between particles were enhanced at high temperature. According to former research, the IPFs in this work might include the van der Waal’s force, liquid/solid bridge forces caused by surface melting, and even chemical bonds resulted by oxidation reactions on particles surface. But to be specific, which kind of IPF dominated the de-fluidization of fine fluorite particles? In order to further determine the dominant force, another experiment was conducted that the pressure drop of the whole bed was measured during the cooling of the bed at the gas velocity of 0.14 m/s, and the result was shown in Figure 8. The theoretical pressure drop of the bed was


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determined corresponding to the static bed weight and was 1518 Pa. During the process of temperature reduction, when the temperature in the bed was higher than 331.5 K, the total pressure drop of the bed was always about 100 Pa, which indicated that the bed remained defluidization. In addition, it could also be observed that apparent channeling occurred near the thermocouple when the bed failed to fluidize, obviously, the thermocouple temperature was the temperature of gases flowing through the channels in this case. However, the bed pressure drop suddenly increased to 900 Pa when the bed temperature reached 331.5 K, then the bed pressure drop was almost constant when the temperature continued to decrease, which meant the bed began to fluidize. Meanwhile, the measured temperature by thermocouples increased slightly, this is due to the fact that the channeling disappeared and the thermocouple directly contacted with the fluidized particles when the bed started to fluidize uniformly, thus the temperature detected by the thermocouple increased slightly considering the fact that the temperature of fluidizing gases was slightly lower than that of particles. This could reflect that in this work IPFs decreased with the decreasing temperature and the de-fluidization at high temperature was reversible. Fine fluorite particles couldn’t be fluidized at high temperature because of stronger IPFs between particles. With the temperature gradually decreased, the IPFs between particles reduced as well and when the temperature was lower than a threshold that the drag force was equal to the IPFs, the bed started fluidizing.


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Pressure drop (Pa)

1000

The theoretical pressure drop of the bed(WSg/AT)

100

10

t=723 K

1 0.1

0.2

0.3

0.4

Gas velocity (m/s)

Figure 7. Variation of pressure drop with gas velocity for fluidization of fine fluorite particles at 723 K. 1600 1400

The theoretical pressure drop of the bed(WSg/AT)

700

600 1000 temperature 1 temperature 2 pressure drop

800 600

500

400

400

Temperature (K)

1200

Pressure drop (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


200 300 0 -5

0

5

10

15

20

25

30

35

40

45

Time (min)

Figure 8. Variations of bed pressure drop and temperatures with time during the cooling of the bed (ug=0.14 m/s). In summary, according to results in Figure 8, the de-fluidization at high temperature was reversible. Therefore, the suspicion of liquid/solid bridge forces resulted from the surface melting was ruled out, since the agglomerates caused by surface melting would be irreversible. Furthermore, Figure 9 showed the scanning electron microscope (SEM) photographs of fine fluorite particles sampled after fluidization at 293 K and 723 K, respectively. This confirmed again that the surface melting didn’t occur. What’s more, the crystal form and chemical elements of fine fluorite particles sampled after fluidization at 293 K and 723 K were analyzed by the X-


17


ray diffraction (shown in Figure 10) and X-ray fluorescence (shown in Supporting Information Table S1). Results showed that the crystal form was unchanged and no new elements (The total percent of F and Ca was always larger than 93%, others were mainly Al, Si, Mg etc.) appeared on the surface of particles after fluidization at 723 K. Thus chemical reactions were excluded as well. Therefore, the forces that affected the fluidization of fine fluorite particles could only be van der Waals force at high temperature. In fact, Pagliai et al.18 have found that the van der Waals force changed with the temperature and a higher temperature would lead to a larger van der Waals force.

(a) at 293 K

(b) at 723 K.

Figure 9. SEM photographs of fine fluorite particles sampled after fluidization.

Experiental fluorite particles at 723 K

Intensity(a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Experiental fluorite particles at 293 K

Standard XRD of fluorite particles

20

30

40

50

60

70

80

2 Theta(degree)


18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 10. Selected X-ray diffraction scans of experimental fine fluorite particles and standard X-ray diffraction of fine fluorite particle. Considering the van der Waals forces between particles are inversely proportional to distances between particles, an assumption was made that an extra gas flow supplied during the heating process would increase distances between particles and decrease the maximum van der Waals at high temperature. Therefore, supplying an extra gas flow (defined as ‘loose gas’ in this work, hereafter) during the heating process might improve the de-fluidization of fine fluorite particles at high temperatures. In order to confirm this assumption, Figure 11 illustrates the total bed pressure drop as a function of gas velocity at 723 K when the loose gases of different gas velocities were supplied. With a loose gas velocity of 0.0027 m/s, the fluorite particles still defluidized and the total bed pressure drop was far less than the theoretical one. While as the loose gas velocity was increased to 0.027 m/s, fine fluorite particles started to be fluidized at 723 K. Therefore, supplying enough loose gas during the heating process could increase distances between particles and reduce the possibilities that particles contacted each other, thus the fluidization quality of the fluorite particles was improved. The theoretical pressure drop of the bed(WSg/AT)

1000

Pressure drop (Pa)

Page 19 of 40

100

10 t=723 K losse gas velocity (0.0027 m/s) losse gas velocity (0.027 m/s)

1 0.1

0.2

0.3

Gas velocity (m/s)

Figure 11. Variations of pressure drop with gas velocity for fine fluorite particles under different loose gas velocities at 723 K.


19


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3.3 Method to enhance the fluidization of fine fluorite particles As shown above, fine fluorite particles cannot be fully fluidized at room temperature and high temperature due to strong van der Waals forces between particles, therefore, it is necessary to develop methods to improve the fluidization quality. Adding calcium sulfate particles is adopted at room/high temperatures and the effect is revealed in the next. 3.3.1 Adding calcium sulfate particles at ambient temperature Figure 12 illustrates effects of calcium sulfate particles on the fluidization of fine fluorite particles at ambient temperature, in which Figure 12(a) shows the pressure drop with the descending velocity for different mixtures. Except for the case with 20wt% calcium sulfate, all cases experienced sharp decreases during the descending velocity. These sharp decreases were caused by the formation of channeling or cracks during the descending velocity. When channeling or cracks were formed by strong IPFs, fluidizing gases would flow through the channels or cracks and then the sharp decrease of bed pressure drop appeared. Thus, Figure 12(a) preliminarily indicates that adding 20% calcium sulfate might enhance the fluidization of fine fluorite particles. Besides, the ratio of the real bed pressure drop to the theoretical pressure drop (defined as fluidized ratio, hereafter) directly reflects the fraction of particles fluidized in the bed, since the bed pressure was proportional to the total weight of the fluidized particles for a certain fluidized bed. Therefore, in order to quantitatively compare the fluidization quality of fine fluorite particles with different addition of calcium sulfate particles, the fluidized ratio for different mixtures were calculated by the ratio of measured pressure drop to theoretical pressure drop, which was shown in Figure 12(b). The measured pressure drops for different cases were the average value of the measured steady pressure drops in Figure 12(a). Figure 12(b) illustrated that compared to the fluidization of pure fine fluorite particles, adding calcium sulfate particles


20

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enhanced the fluidized ratio. Meanwhile, a continuous improvement of the fluidized ratio was obtained when the fraction of calcium sulfate particles increased to 20wt%, but a continuous decrease of fluidized ratio was observed when further increasing the calcium sulfate particles. The largest fluidized ratio (82.4%) appeared for the binary mixture comprising 20wt% calcium sulfate particles, which concluded that adding calcium sulfate particles could indeed enhance the fluidization of fine fluorite particles and the addition fraction of 20wt% was the best. 100 (a)

90

1000

(b)

t=298 K

80

100

t=298 K

CaF2(100wt%) CaF2(90wt%)+CaSO4(10wt%) CaF2(85wt%)+CaSO4(15wt%)

10

CaF2(80wt%)+CaSO4(20wt%)

Fluidized ratio (%)

Pressure drop (Pa)


1 0.01

70 60 50 40 30 20 10


0 50

0.1

10

15

20

25

30

CaSO4 content (wt%)

Gas velocity (m/s)

Figure 12. Effects of calcium sulfate particles on fluidization of fine fluorite particles. (a) Variations of pressure drops with descending gas velocity for different mixtures; (b) the ratio of real bed pressure to the theoretical value for different mixtures.

Standard deviation of bed pressure drop (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


200 t=298 K

150

100

50

0 0

5

10

15

20

25

30

CaSO4 content (wt%)

Figure 13. The standard deviation of bed pressure drops measured at different directions for fluidized bed with different mixtures.


21


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In the meantime, the standard deviation of the bed pressure drops measured in the left, middle and right side of the bed was further conducted to characterize the uniformity of fluidization around the circumferential direction. Figure 13 shows the standard deviation of circumferential bed pressure drops for different mixtures. Results in Figure 13 were the same to those in Figure 12. In the case adding 20wt% calcium sulfate particles, the standard deviation was the smallest and the fluidization was the most uniform around the circumferential direction. 3.3.2 Adding calcium sulfate particles at high temperature The influences of calcium sulfate particles on the fluidization behavior of fine fluorite particles at 723 K are presented in Figure 14. A marked difference of the pressure drop with the descending velocity can be observed in Figure 14(a) after calcium sulfate particle were added. The pressure drop of the fluidized bed with pure fine fluorite particles was apparently lower than the mixtures. By comparing different cases with different adding fraction of calcium sulfate particles, the decrease of pressure drop with the descending velocity was more smooth in the case 20wt% calcium sulfate added. This indicated that fewer channeling appeared in this case. Figure 14(b) shows the fluidized ratio for different mixtures of fine fluorite particles and calcium sulfate particles at 723 K. The data confirmed that the fluidized ratio was greatly improved from 20% to 74% compared with the fluidization of pure fine fluorite particles. Meanwhile, when the fraction of calcium sulfate particles was 20wt%, the largest fluidized ratio was obtained, which indicated that the fluidization quality was the best. However, the variation trend of fluidized ratio with the adding fraction of calcium sulfate particles differed from that at ambient temperature, and there was not a clear variation trend which could be deduced from Figure 14(b).


22

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(a)

The theoretical pressure drop of the bed(W g/A ) S

80

T

1000

(b)

t=723 K

70

100

Fluidized ratio(%)

Pressure drop (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


t=723 K

CaF2(100%) CaF2(90%)+CaSO4(10%) CaF2(85%)+CaSO4(15%)

10

CaF2(80%)+CaSO4(20%) CaF2(75%)+CaSO4(25%)

0.1

50 40 30 20 10

CaF2(70%)+CaSO4(30%)

1

60

0 0.2

50

Gas velocity (m/s)

10

15

20

25

30

CaSO4 content(%)

Figure 14. Effects of calcium sulfate particles on fluidization of fine fluorite particles at 723 K.(a) Variations of pressure drop with superficial gas velocity for different mixtures; (b) the ratio between the real bed pressure and the theoretical value for different mixtures. 3.4 Enhancement mechanism of calcium sulfate particles 3.4.1 Particle size analysis Results in former parts showed that adding calcium sulfate particles could enhance the fluidization of fluorite particles and the effect changed with the adding fraction of calcium sulfate particles. According to published literatures21-29, enhancement methods which could improve the fluidization of cohesive particles all depended on the fact that agglomerates were broken up by external fields or additions of other particles. Therefore, in order to prove the breakup of agglomerates also existed when calcium sulfate particles were added, the particle size distribution in the fluidized beds with different mixtures was analyzed, which was shown in Table 2. It could be found that for the addition fraction of calcium sulfate particles was 20wt% and 25wt%, an apparent difference of the average particle size was observed between the samples taken from the bottom and top of the fluidized bed, and particles sampled from the bottom had a larger size than those sampled from the top, which indicated that particle segregation appeared. As analyzed in former parts, when particles with a wide particle size


23


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distribution are fluidized dispersedly, particles segregation happens. While if particles are fluidized as agglomerates, particles segregation disappears just as the fluidization of pure fluorite particles. Therefore, the appearance of segregation in the cases that 20wt% or 25wt% calcium sulfate particles were added demonstrated that the calcium sulfate particles apparently led to the breakup of fluorite agglomerates. This was just the reason why the fluidization quality of fluorite particles was enhanced when calcium sulfate particles were added and the addition fraction of 20wt% was the best condition. Table 2. The average diameter of particles sampled at the bottom and top of various fluidized beds with different mixtures after fluidization at 298 K. Average particle size/µm Particles Top

Bottom

100wt%CaF2

31.0

30.4

90wt% CaF2 +10wt% CaSO4

37.1

36.3


42.5

41.6


40.3

43.1


43.2

46.3


48.1

48.5

3.4.2 ‘Coordination’ theory As shown above, the calcium sulfate particles are also cohesive and easily bonded to form agglomerates because of hydrogen bonds between particles. Thus how did the original cohesive calcium sulfate particles prevent the agglomeration of fine fluorite particles? This might be caused by the fact that cohesive forces among calcium sulfate particles were different with the cohesive forces among fluorite particles. Therefore, when proper amount of calcium sulfate particles were added and mixed with fluorite particles, the calcium sulfate particles would exist


24

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between fluorite particles and prevent the van der Waals forces between adjacent fluorite particles as well as the fluorite particles agglomeration. Meanwhile, fluorite particles also existed between calcium sulfate particles and prevented the self-agglomeration of calcium sulfate particles resulted from hydrogen bonds. In a word, these two kinds of cohesive particles prevented each other’s self-agglomeration, and because the calcium sulfate particles could not agglomerate with fluorite particles, then the fluidization quality of fine fluorite particles was enhanced by the cohesive calcium sulfate particles. Here this effect preventing each other’s self-agglomeration was defined as ‘coordination’ theory, and Figure 15 shows the ‘coordination’ theory schematically. Figure 15(a) shows the case in which fluorite particles were excessive, thus self-agglomeration of fluorite particles happened. On the contrary, Figure 15(c) shows the case calcium sulfate particles were excessive and self-agglomeration of calcium sulfate particles happened. Figure 15(b) shows the case with the moderate amount of calcium sulfate particles, particles were distributed dispersedly and no agglomerates appeared. Therefore, when calcium sulfate particles were added, both short and overdose of calcium sulfate particles were bad to their effects, which was consistent with experimental results under the ambient temperature in former parts. With the increasing addition fraction of calcium sulfate particles, the fluidization quality increased firstly and then decreased at ambient temperature and the addition fraction of 20wt% was the best.


25


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Figure 15. The schematic diagram of ‘coordination’ theory. (a) Excessive fluorite particles; (b) Moderate calcium sulfate particles; (c) Excessive calcium sulfate particles. In fact, according to the ‘coordination’ theory, the optimal addition fraction of calcium sulfate particles can be estimated by analyzing the mixing and packing of two particles42. Here the optimal addition fractions in two limiting packing situations (the loosest and the closest packing) are discussed and calculated by theoretical analysis to validate the experimental results. (1) The loosest packing. Here the following assumptions were made for simplicity according to the SEM pictures of particles. 1) All fluorite particles were cylindrical with the same size, and the diameter of the bottom was equal to the height. 2) All calcium sulfate particles were cylindrical with the same size. The diameter of the bottom was equal to the height of fluorite particles, and the average height of calcium sulfate particles was about 6 times of its bottom diameter (based on Figure 16).

Figure 16. SEM photographs of the mixture of fine fluorite particles and calcium sulfate particles.


26

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3) Only packing with the square arrangement (Figure 17) was considered.

Figure 17. The loosest packing for mixtures with the moderate fraction of calcium sulfate particles. Figure 17 schematically shows a single packing unit of the loosest packing. The yellow and white cylinders represented the calcium sulfate particles and fluorite particles, respectively. In this case, fine fluorite particles around the calcium sulfate particle could be divided into 5 types according to the relative positions between fluorite particles and calcium sulfate particles, and every type was labelled in Figure 17. Type a - Fine fluorite particles around the side face of the calcium sulfate particle and also contacted with it. The total number was 24 and each one was shared by 2 calcium sulfate particles, so the number of Type a fluorite particles na,loosest assigned to a single calcium sulfate particle was calculated as n a, loosest = 24 ×

1 2

= 12

(4)

Type b - Fine fluorite particles around the side face of the calcium sulfate particle but not contacted with it. The total number was also 24, but each fine fluorite particle was shared by 4 calcium sulfate particles, so the number of Type b fluorite particles nb,loosest assigned to a single calcium sulfate particle was written as


27


n b, loosest = 24 ×

1 4

Page 28 of 40

(5)

=6

Type c - Fine fluorite particles which contacted with the end face of the calcium sulfate particle. The total number was 2 and each one shared by 2 calcium sulfate particles. The number of Type c particles nc,loosest assigned to a single calcium sulfate particle was nc, loosest = 2 ×

1 2

(6)

=1

Type d - Fine fluorite particles adjacent to the end edge of the calcium sulfate particle rather than the end face. The number was 8, and each was shared by 4 calcium sulfate particles. Thus the number of Type d particles nd,loosest assigned to a single calcium sulfate particle was given as n d , loosest = 8 ×

1

(7)

=2

4

Type e - Fine fluorite particles located on the corner of the end side of the calcium sulfate particle. The total number was 8, and every particle was shared by 8 calcium sulfate particles. The number of Type e particles ne,loosest assigned to a single calcium sulfate particle was given as n e, loosest = 8 ×

1 8

(8)

=1

Thus, the total number of fine fluorite particles surrounding a calcium sulfate particle was nCaF −CaSO ,l = ∑ni,loose = 12 + 6 +1+ 2 +1 = 22 2

4

(9)

And the mass fraction of calcium sulfate particles in the loosest packing was given as ρ CaSO VCaSO nCaSO 4

4

4

ρ CaSO VCaSO nCaSO + ρ CaF VCaF nCaF 4

4

4

2

2

= 16.5%

(10)

2

Therefore, in this case, the content of calcium sulfate particles for the moderate addition was calculated as 16.5wt%. (2) The closest packing.


28

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In this case, other assumptions were the same with case (1), but the arrangement was the regular hexagonal (Figure 18). Therefore, all fine fluorite particles around the side face of the calcium sulfate particle contacted with it. Figure 18 shows the closest packing schematically. Identically, the yellow and white cylinders represented the calcium sulfate particles and fluorite particles, respectively. In this case, fine fluorite particles could be similarly divided into 3 types according to the relative positions between fluorite particles and calcium sulfate particles.

Figure 18. The closest packing for mixtures with the moderate fraction of calcium sulfate particles. Type a - Fine fluorite particles adjacent to the side face of calcium sulfate particle and contacted with it. The number was 36, and each one was shared by 3 calcium sulfate particles. So the number of Type a particles na,closest assigned to single calcium sulfate particle was calculated as n a, close s t = 36 ×

1 3

= 12

(11)

Type b - Fine fluorite particles adjacent to the end face of the calcium sulfate particle and contacted with it. The number was 2 and each one was shared by 2 calcium sulfate particles. Thus the number of the Type b particles nb,closest assigned to single calcium sulfate particle was


29


n b, closest = 2 ×

1

(12)

=1

2

Page 30 of 40

Type c - Fine fluorite particles adjacent to the end edge of the calcium sulfate particle rather than the end face. The number was 12, and each one was shared by 6 calcium sulfate particles. The number of Type c particles nc,closest assigned to single calcium sulfate particle was given as 1

n c, closest = 12 ×

6

(13)

=2

Therefore, the number of fine fluorite particles surrounding a calcium sulfate particle was nCaF −CaSO ,c = 2

4

∑n

i , closest

= 12 + 1 + 2 = 15

(14)

And the mass fraction of calcium sulfate particles in this case was given as ρ CaSO VCaSO nCaSO 4

4

4

ρ CaSO VCaSO nCaSO + ρ CaF VCaF nCaF 4

4

4

2

2

= 22.4%

(15)

2

In real process, considering the packing arrangement was between the loosest packing and closest packing, the theoretical mass fraction of calcium sulfate particles for the mixture with moderate addition was 16.5wt%-22.4wt%. It just covered the experimental optimum fraction of calcium sulfate particles (20wt%). Therefore, it was the ‘coordination’ theory that accounted for enhancement of fluidization quality, and theoretical calculation and experimental results all showed that the addition faction near 20wt% of calcium sulfate was the best choice. Less addition led to the self-agglomeration of fluorite particles while excessive addition resulted in the self-agglomeration of calcium sulfate particles, both of which decreased the fluidization quality. However, based on the ‘coordination’ theory, these were still unexplained results in above parts. Although the best fluidization quality was also acquired in the case with 20wt% calcium sulfate particles at high temperature, there was not a clear variation trend of the fluidized ratio with the increasing mass fraction of calcium sulfate particles. This might be caused by the fact that the


30

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water molecules in the calcium sulfate dehydrate escaped at high temperature which made the decrease of calcium sulfate particle size as well as the hydrogen bonds between particles. These changes might affect effects of calcium sulfate dehydrate. Moreover, the flowability of particles can be directly characterized by the cohesion measurements by shear cell. In this work, this method was also used to further prove the best addition fraction of calcium sulfate particles, and the results were shown in Table 3. The cohesion measurement was consistent with former theoretical calculation and experimental results. With the increasing fraction of calcium sulfate particles, the cohesion decreased firstly and then increased. For the mixture with 15wt% and 20wt% calcium sulfate particles, the measured cohesion was the lowest. Therefore, the cohesion measurement further proved that the addition fraction of 20wt% was the best because of the lowest IPFs. Table 3. Cohesion for different mixtures.

a

Particles

Cohesion-averagea (kPa)

100wt%CaF2

2.22


1.79


0.69


0.70


1.20


1.53

100wt% CaSO4

6.04

All results were repeated for three times.


31


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4 Conclusion The fluidization of fine fluorite particles at ambient and high temperature was investigated by experiments, and the enhancement effects and effect mechanism of cohesive calcium sulfate particles on the fluidization of fluorite particles were revealed. The conclusions are as follows. (1) Fine fluorite particles, classified as Geldart A/C particles, could not be completely fluidized under ambient temperature, whose fluidization was similar to the fluidization of Geldart C particles and belonged to the agglomeration fluidization. Therefore, the minimum fluidization velocity was much larger than the theoretical one, a longer solids consolidation stage appeared during the bed collapse process and the particle segregation disappeared. (2) The fluidization quality of Geldart A/C particles was significantly decreased at high temperature because of high van der Waals forces. For fine fluorite particles used in this work, they could not be fluidized at 723 K, but it could be fluidized when the temperature decreased to a certain value. De-fluidization of fluorite particles at high temperature was reversible. Considering the fact that the van der Waals force is inversely proportional to distances between particles, supplying loose gases during the heating process to increase particle-particle distances could improve the fluidization of Geldart A/C particles at high temperature. (3) Adding cohesive calcium sulfate particles could improve the fluidization quality of fine fluorite particles at both room and high temperature, and the best improvements of fluidization quality both appeared in the cases when the addition fraction was 20wt%. Specifically, under room temperature, the fluidized ratio was increased from 60% to 82.4% when the addition fraction of calcium sulfate particles was 20wt%, while for the high temperature, the fluidized ratio was increased from 20% to 74%.


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(4) The ‘coordination’ theory between cohesive calcium sulfate particles and fine fluorite particles was the reason for the improvement of fluidization quality. At a proper addition fraction of calcium sulfate particles, fine fluorite particles and calcium sulfate particles were arranged alternately. Then the fluorite particles agglomeration resulted from van der Waals forces were prevented by calcium sulfate particles between them, meanwhile, the calcium particles agglomeration resulted from hydrogen bonds were prevented by fluorite particles. According to the ‘coordination’ theory, the optimum addition fraction of calcium sulfate particles was calculated as 16.5wt%-22.4wt%, which was consistent with the experimental results. This work will show a significant guidance for the development of new fluidized bed process for the production of AHF. Moreover, this work will also work as a supplement for the fluidization of cohesive particles as well as the fluidization at high temperature. ASSOCIATED CONTENT Supporting Information The detailed chemical elements analysis results of fine fluorite particles sampled after fluidization at 293 K and 723 K, respectively. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *Tel.: +86-571-87951227. Fax: +86-571-87951227. E-mail: [email protected]. ORCID Yao Yang: 0000-0003-3611-2859 Yongrong Yang: 0000-0002-5598-6925


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ACKNOWLEDGMENTS The work was supported by The Project of National Natural Science Foundation of China (91434205), the National Science Fund for Distinguished Young (21525627), and the Science Fund for Creative Research Groups of National Natural Science Foundation of China (61621002). NOMENCLATURE A = expansion curve of the bed AT = the cross-sectional area of the bed, m2 d = Sauter’s diameter of the particles, m fh = the non-ideal index of the bed g = gravitational acceleration, 9.81 N kg-1 n = the voidage index or the number of particles ni, closest = the number of Type i fluorite particles in the closest packing case. (i is a, b and c). nCaF2-CaSO4, c = the number of fine fluorite particles surrounding a calcium sulfate particle in the closest packing case. ni, loosest = the number of Type i fluorite particles in the loosest packing case. (i is a, b, c, d and e). nCaF2-CaSO4, l = the number of fine fluorite particles surrounding a calcium sulfate particle in the loosest packing case. u = velocity, m-1s


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V = the volume of particles, kg-1 m3 Ws = static bed weight, kg Greek Letters ε = voidage of the bed Θ = dimensionless time in bed collapse method ρ = density, kg m-3 Subscripts mf = minimum fluidization conditions p = particle P = perfect R = real t = terminal fluidization conditions

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(30) Pedersen, B. F.; Semmingsen, D. Neutron diffraction refinement of the structure of gypsum, CaSO4. 2H2O. Acta Crystallogr. Sect. B: Struct. Crystallogr. Cryst. Chem. 1982, 38, 1074. (31) Geldart, D. Types of gas fluidization. Powder Technol. 1973, 7, 285. (32) Saleh, K.; Cami, X. B.; Thomas, A.; Guigon, P. An experimental study on the fluidisation behaviour of Geldart C glass powders. KONA Powder Part. J. 2006, 24, 134. (33) Jin, Y.; Zhu, J.; Wang, Z.; Yu, Z. Fluidization engineering principles; Tsinghua University Press: Beijing, 2001. (34) Ajbar, A.; Alhumazi, K.; Asif, M. Improvement of the fluidizability of cohesive powders through mixing with small proportions of group a particles. Can. J. Chem. Eng. 2005, 83, 930. (35) Bi, H.; Grace, J.; Zhu, J. Propagation of pressure waves and forced oscillations in gas-solid fluidized beds and their influence on diagnostics of local hydrodynamics. Powder Technol. 1995, 82, 239. (36) Wen, C.; Yu, Y. A generalized method for predicting the minimum fluidization velocity. AIChE J. 1966, 12, 610. (37) Geldart, D.; Wong, A. Fluidization of powders showing degrees of cohesiveness—I. Bed expansion. Chem. Eng. Sci. 1984, 39, 1481. (38) Liu, D.; Kwauk, M.; Li, H. Aggregative and particulate fluidization—the two extremes of a continuous spectrum. Chem. Eng. Sci. 1996, 51, 4045. (39) Kwauk, M. Generalized Fluidization Ⅰ. Steady-State Motion. Sci. Sin. 1963, 12, 587.


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(40) Valverde, J.; Quintanilla, M.; Espin, M.; Castellanos, A. Nanofluidization electrostatics. Phys. Rev. E 2008, 77, 031301. (41) Hoffmann, A.; Romp, E. Segregation in a fluidised powder of a continuous size distribution. Powder Technol. 1991, 66, 119. (42) Fayed, M. E.; Otten, L. Handbook of powder science & technology; Chapman and Hall, 2004. For Table of Contents Only(TOC) 100 fluidization at 293 K fluidization at 723 K

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The effect of adding sulfate calcium particles on fluidization of fine fluorite particles at 293 K and 723 K


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Fluidization of Cohesive Fluorite Particles at ... - ACS Publications

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