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Influence of particle size distribution on minimum fluidization velocity and bed expansion at elevated pressure
Influence of particle size distribution on minimum fluidization velocity and bed expansion at elevated pressure Rongtao Feng, Junguo Li, Zhonghu Cheng, Xin Yang, Yitian Fang PII: DOI: Reference:
S0032-5910(17)30561-2 doi:10.1016/j.powtec.2017.07.024 PTEC 12666
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
21 March 2017 21 June 2017 6 July 2017
Please cite this article as: Rongtao Feng, Junguo Li, Zhonghu Cheng, Xin Yang, Yitian Fang, Influence of particle size distribution on minimum fluidization velocity and bed expansion at elevated pressure, Powder Technology (2017), doi:10.1016/j.powtec.2017.07.024
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ACCEPTED MANUSCRIPT Influence
of
particle size distribution
on
minimum
fluidization velocity and bed expansion at elevated pressure
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Rongtao Fenga,b, Junguo Lia,*, Zhonghu Chenga, Xin Yangc, Yitian Fanga,** a
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State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan 030001, PR China b
University of Chinese Academy of Sciences, Beijing 100039, PR China
c
Department of Mechanical Engineering, University of Sheffield, Sheffield S10 2TN,
NU
UK
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* Corresponding author. Tel.: +86-0351-4048313 ** Corresponding author. Tel.: +86-0351-2021137
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E-mail addresses: [email protected] (J. Li); [email protected] (Y. Fang)
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ACCEPTED MANUSCRIPT 1. Introduction
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Fluidization technology has been widely employed in many industrial processes
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because of the desirable characteristics (e.g. good solids mixing, large contact surface
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area, high heat transfer, slow responses to abrupt changes in operating conditions [1]). There are many fluidized bed applications using particles belong to Geldart B and D
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[2], such as coal gasification, polymers production. Fluid-bed gasification is regarded as a promising technology for the production of syngas because of its advantages in
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fuel flexibility, good scalability of reactors and effectiveness in controlling pollutant emissions and promoting the conversion process through using the in-situ additives
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D
[3]. The fluidization technology is increasingly employed to manufacture polyethylene through the gas-solid phase polymerization process [4]. Compared to
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liquid-phase polymerization, the gas-solid phase process offers a more economical and energy-efficient alternative. This is because there is no need to flash off much
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liquid (a step with high energy consumption) in the gas-phase process. Pressurized operation, which is beneficial to increasing the throughput and reducing the size of reactors, is significant in developing these fluidized bed applications. Therefore, an improved understanding of the hydrodynamic behaviors of fluidized bed for particles belong to Geldart B and D at elevated pressures is imperative for an efficient operation and design of the fluidized bed in the future. Particle size distribution (PSD) (especially uneven particle size distribution resulted from the segregation and mixing) could influence the hydrodynamic behaviors and chemical conversion in the reactor [5]. Fluidized beds of large narrow 2
ACCEPTED MANUSCRIPT PSD particles fluidize poorly with bumping, spouting, and slugging, while the quality of fluidization of these beds can often be improved by adding a small amount of fines
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to act as lubricant [6]. Sun et al. [7] investigated the effect of PSD on the performance
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of a fluidized-bed reactor in different fluidization regimes (bubbling, slugging, turbulent and fast fluidization). It was found that (i) PSD could obviously affect void sizes and regime transitions, (ii) the effect of wide PSD on the chemical conversion
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and reactor efficiency will not be significant until the fluidized gas velocity exceeds
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0.2 m/s, and (iii) however, narrow PSD particles will not show any similar effects in same fluidization regimes except for the fast fluidization regime. Gauthier et al. [8]
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found that Gaussian-type and narrow-cut particle distributions have the same Umf,
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whereas binary PSD and flat PSD exhibit a very different hydrodynamic behavior
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under ambient conditions. Lin et al. [9] concluded that the binary and flat PSDs behave similarly to each other but these two PSDs have higher Umfs than the Gaussian
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and narrow PSD cases at high temperature. Most of the previous studies on the effects of PSD on the hydrodynamic behaviors are mainly undertaken at atmospheric pressure. It is still not clear about the effects of PSD on the hydrodynamic behaviors of fluidized bed at elevated pressures. In order to predict the Umf, many correlations have been proposed to estimate the Umf in the fluidized bed, as listed in Table 1. Among these correlations, most of them have been developed for narrow-cut PSD particles at atmospheric pressure. However, when dealing with coal gasification or natural minerals etc., wide PSD particles are usually fluidized as bed materials and processed under pressure. 3
ACCEPTED MANUSCRIPT This work focused on investigating the influence of PSD on the minimum fluidization velocity and the bed expansion of Geldart B and D-type polystyrene
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particles at elevated pressures (up to 2.7 MPa) in a lab-scale cylindrical fluidized bed.
Gaussian-type) were investigated and analyzed. Table 1.
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Five narrow PSDs and four wide PSDs (binary mixture, ternary mixture, flat, and
Correlation
Wen and Yu
Materials
2
0.5
2
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Researchers
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List of typical correlations to predict minimum fluidization velocity.
2
0.5
Remf=(33.7 + 0.0408Ar) -33.7
[10]
Various
PSD
Presure
Other conditions
Narrow
Ambient
10-3
Narrow
Elevated
102
particles
Chitester et
0.5
Remf=(28.7 + 0.0494Ar) -28.7
al. [11]
Ballotini
Remf=(25.3 + 0.0571Ar) -25.3
D
Saxena et
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al.[12] al.[13]
Umf=(μg/ρgdg)(1.08×10 Ar
Elevated
Glass beads
Narrow
Elevated
0.08
pressure 76
Remf=1.9×10-3Ar0.87
Sand
Narrow
Ambient
None
Remf=(22.1+0.0354Ar)0.5-22.1
Sand
Narrow
Elevated
40
0.947
)
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Ma et al.[17]
6
Ambient
al.[15] Zhu et
Narrow
Wide
al.[14] Barbosa et
Dolomite
Glass beads
-3
CE P
Doichev et
pressure pressure
Remf=(33.92 + 0.0465Ar)0.5-33.9
Nakamura et
al.[16]
Coal Char
Bead
Remf=0.28∑xidi0.599(ρp/ρg)/ν0.066
Sand
pressure Wide
Ambient
Temperature(30-600℃)
Ash
2. Material and methods 2.1 Apparatus
The reactor used in these experiments was a cold model pressurized fluidization facility. The facility consisted of a pressure vessel, a nitrogen supply system, a high speed camera (Photron SA-Z), a computer system, and the peripheral equipment, as
4
ACCEPTED MANUSCRIPT shown in Fig. 1. Height of the pressure vessel was 1600 mm, and with an inside diameter (ID) of 1200 mm. A perspex columnar bed of 60 mm (ID) was inserted into
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the pressure vessel. Pressure drop was measured by the U-type differential pressure
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meter, and the differential pressures were recorded through the camera by the computer. The nitrogen supply system was applied through a high-pressure reciprocating pump, and no nitrogen recirculation system was used. Supply pressure
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in the reciprocating pump was maintained using a central liquid nitrogen system.
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Flow control was accomplished by parallel mass flow meters. The control valve (FCV-1 in Fig.1) was used for large flow rates and the mass flow controller (FCV-2)
D
was used for small flow rates. An upstream pressure control valve (PCV-1) and a back
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pressure control valve (PCV-2) were used to maintain the system pressure. The cable,
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sealed in the flange, was capable of transmitting imaging signal to the external computer system.
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2.2 Materials and preparation
The experimental materials originally included five mean diameters particles (the narrow PSDs). The samples were carefully sieved by the standard test sieve shaker. Density of the polystyrene particles was 1020 kg/m3. Particles of polystyrene of five mean diameters were studied: 0.55 mm (d1), 0.70 mm (d2), 0.90 mm (d3), 1.13 mm (d4), and 1.34 mm (d5), respectively. Particles with diameters of d1, d2, and d3 belonged to Geldart B; the others belonged to Geldart D. Four wide PSDs were derived by mixing these original particles with narrow PSD: a flat distribution powder
5
ACCEPTED MANUSCRIPT (F), a Gaussian-type powder (G), a binary mixture (B), and a ternary mixture (T). The narrow PSD (d3=0.90 mm) was defined as the reference-type powder (R). These
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T
particles were prepared according to the method suggested by Gauthier et al [8], and
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the four wide PSDs were controlled to have the same mean diameters as the reference-type powder (R) with dp = 0.90 mm as follows:
dp
1 xi / di
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i
(1)
with xi the mass fraction of particles having d i as average diameter. The
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characteristics of the bed materials used in the experiment are listed in Table 2, and
D
Fig. 2 describes the four wide PSDs mixtures.
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Table 2
Description of the characteristics and their PSDs Weight
Sieves
Sieves
Average diameter
(%), xi
no.
(mm)
(mm)
100
18-24
0.80-1.00
0.90
14
14-16
1.25-1.43
1.34
23
16-18
1.00-1.25
1.13
36
18-24
0.80-1.00
0.90
17
24-30
0.60-0.80
0.70
10
30-40
0.45-0.60
0.55
25
14-16
1.25-1.43
1.34
23
16-18
1.00-1.25
1.13
19
18-24
0.80-1.00
0.90
17
24-30
0.60-0.80
0.70
16
30-40
0.45-0.60
0.55
35
16-18
1.00-1.25
1.13
35
18-24
0.80-1.00
0.90
30
24-30
0.60-0.80
0.70
55
16-18
1.00-1.25
1.13
45
24-30
0.60-0.80
0.70
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Type of powder
Composition for mean diameter dp=0.90mm Reference
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Gaussian
Flat
Ternary
Binary
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ACCEPTED MANUSCRIPT 2.3. Experimental procedures
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In order to maintain a steady-state operation of the reactor under a desired
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pressure, a pre-pressurizing pressure vessel was equipped in the fluidized bed system.
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Fluidized velocity was gradually reduced from a well-fluidized state to a packed (static) bed, and the pressure drop △P was measured. The point of intersection of the
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pressure drop line for the fixed bed and the horizontal line for the fully fluidized bed is typically defined as the minimum fluidization velocity. In addition, since the
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Renolds numbers were less than 20 for small particles in low velocities in the reactor, the linear fitting of △P as a function of the gas velocity was employed in the packed
D
bed stage. With regard to the Renolds numbers between 20 and 1000, the parabolic
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fitting of △P was employed in the packed bed stage.
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In order to obtain the fluidized bed expansion, a ruler was fixed on the fluidized bed, and a high speed camera was used to capture the images of the bed expansion.
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The feature of high shutter speed is essential for capturing fast moving images without a blurring effect, especially in measuring of the height of the bed expansion. Then the height of the fluidized bed expansion was obtained by analyzing films a frame by a frame. In addition, the effect of static on polystyrene particles fluidization is usually unneglectable when the particles rubbing against each other for long time. In this experiment, the particles were just used for a short period time, then the old particles were replaced by the new particles, and in this way, the effect of static electricity can be minimized.
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ACCEPTED MANUSCRIPT 3. Results and discussion
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3.1. Umf for the narrow PSD
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3.1.1. The effects of pressure on the Umf
Fig. 3 shows the effects of pressure on the Umf of narrow PSD. The corresponding Umfs determined by experiments with these particles ranged from 0.146
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m/s to 0.489 m/s at 0.1 MPa (absolute pressure) and from 0.067 m/s to 0.140 m/s at
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2.7 MPa pressure. The Umfs decreased with an increase in the pressure among the different mean diameters particles. In addition, the effect of pressure on the Umf of
D
large particles was stronger than that of small particles, as shown in Fig. 3. It should
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be noted that the trends of Umf with the narrow PSD sharply decreased with the
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pressure up to about 0.9 MPa, and slowly decreased thereafter. Literatures [18-20] also found a general decrease with increasing pressure, and that the effects of pressure
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on Umf are strongly dependent upon particle size. The effects of pressure on Umf had been explicitly described on the basis of Ergun’s equation [21], which may be written, at minimum fluidization, as 2 1 mf gU mf (1 mf )2 U mf . (1 mf )( s g ) g 150 1.75 3 mf3 (s d p )2 mf s d p
(2)
With the pressure increase, the viscosity of nitrogen does not change, whereas the density can be evaluated by： ρ=1.251P/PΘ. For the large particles, the Eq. (2) 3 ] / (1.75 g ) , which strongly depends on the gas simplifies to U mf [d p ( s g ) g mf
density (namely the pressure). It can be the reason that why the effects of pressure on the Umf of large particles are strong. 8
ACCEPTED MANUSCRIPT 3.1.2 Prediction of Umf for narrow PSD
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Umf is one of the most important measurements for the reactor design. Many
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correlations have been proposed for the prediction of Umf based on the simplified
K1 Re2mf K2 Remf Ar
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Ergun equation, which is developed by Wen and Yu [10] as follows: ,
(3)
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where K1 and K2 are constant parameters. It is regarded that these two parameters stay nearly constant for different kinds of particles over a wide range of experimental
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conditions (Re=0.001 to 4000) at atmospheric pressure. In addition, many researchers derived different values of the two parameters, as shown in Table 3. In this study, the
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D
experimental data obtained for Umf at different pressures are presented in the plot of Remf vs Ar in Fig. 4, and a modified form of Ergun equation was obtained by the
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regression analysis:
Remf 27.92 0.0554 Ar 27.9 ,
(4)
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where K2 / (2K1) = 27.9, 1/K1=0.0554. Table 3.
The values of the two parameters in the correlations to estimate the Umf. Researchers
K2 / (2K1)
1/K1
Specifications
Wen and Yu[10] Babu et al. [22]
33.7 25.3
0.0408 0.0651
Grace et al. [23] Chitester et al.[11]
27.2 28.7
0.0408 0.0494
Richardson [24]
25.7
0.0365
Fine particles, at atmospheric pressure Fuel particles for the coal conversion systems None Coal, char, and ballotini; at elevated pressures up to 6.4 MPa…. None
Saxena et al. [12]
25.3
0.0571
Dolomite at high temperature and pressure
Fig. 5 shows the comparison of the predicted Umfs using the modified correlation 9
ACCEPTED MANUSCRIPT in this study and other typical correlations. The relative errors of these correlations are also given in Table 4. It can be found that the new correlation well predicted the
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values of Umf for the five narrow PSDs at elevated pressures. The relative errors of the
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predicted results using the new correlation were almost in ±15%. Also, it can be found that: among all the narrow PSDs and pressures, i) Babu’s [22] and Saxena’s [12] correlations nearly overestimated the values of Umf, and Chitester’s [11] correlation
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predicted the Umf of large particles well comparing with the small particles; ii)
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however，Wen and Yu’s [10] , Grace’s [23]and Richardson’s [24] correlations obviously underestimated the values of Umf. Obviously, it is difficult to find a formula
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to predict the value of Umf for any materials and under any pressures very well. Only
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when the correlations are derived from the specified particle properties and operating
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conditions can the reasonable agreement be obtained between the predictions from the correlations and the experimental results. Therefore, it should be careful to choose the
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correlations according to the specified particle properties and operating conditions. In the process of olefin polymerization in fluidized bed, our equation can be better than other equations for predicting the Umf of the polymer particles. Table 4 The relative errors of different researcher’ calculated data Mean diameter (mm) 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55
Pressure (MPa)
Experimental data (m/s)
Eq.(4)
Babu
Saxena
Chitester
Grace
Richardon
Wen &Yu
0.1 0.2 0.3 0.5 0.7 0.9 1.1 1.3
0.146 0.140 0.135 0.124 0.104 0.099 0.095 0.091
4.11 0.51 -2.30 -3.51 6.04 3.37 1.75 1.37
30.32 23.32 18.28 14.80 24.77 20.67 18.08 17.09
15.97 10.57 6.57 4.09 13.58 10.16 8.01 7.28
-8.51 -10.91 -12.87 -13.23 -4.13 -6.17 -7.37 -7.49
-19.79 -21.58 -23.08 -23.09 -14.79 -16.45 -17.38 -17.39
-24.07 -25.77 -27.19 -27.21 -19.36 -20.93 -21.82 -21.83
-33.61 -33.92 -34.30 -33.02 -24.77 -25.48 -25.72 -25.24
10
ACCEPTED MANUSCRIPT
D
11
-17.36 -19.27 -15.19 -17.52 -18.34 -17.16 -12.72 -31.03 -20.13 -22.81 -22.99 -16.98 -12.60 -14.35 -17.87 -15.29 -19.64 -15.08 -13.42 -15.28 -15.69 -15.86 -15.04 -11.12 -11.95 -18.64 -15.10 -17.76 -17.98 -19.56 -18.21 -17.64 -18.64 -19.89 -16.71 -18.59 -19.64 -16.77 -16.02 -11.15 -6.22 -9.14 -9.89 -11.06 -9.44 -12.24 -10.77 -11.37 -11.55 -7.67 -10.00 -9.29 -9.00 -1.86 -9.84 -4.41 -4.09
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T
-7.54 -9.75 -5.27 -7.93 -8.89 -7.62 -2.71 -21.66 -9.75 -13.06 -13.62 -7.10 -2.36 -4.44 -8.46 -5.66 -10.56 -5.53 -3.73 -5.85 -6.33 -6.56 -4.06 -0.17 -1.41 -9.21 -5.45 -8.53 -8.87 -10.68 -9.23 -8.65 -9.80 -11.21 -7.71 -9.82 -11.00 -6.50 -6.14 -0.94 4.27 0.87 -0.06 -1.43 0.31 -2.84 -1.25 -1.94 -2.16 2.10 -0.49 0.28 1.80 9.31 0.21 6.02 6.24
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6.74 3.80 8.62 5.27 3.91 5.14 10.52 -2.88 9.06 3.45 0.92 7.35 11.98 9.00 3.97 6.77 0.93 6.35 8.15 5.58 4.87 4.47 27.76 17.28 14.25 3.64 7.01 2.94 2.14 -0.21 1.15 1.59 0.13 -1.58 2.17 -0.28 -1.69 9.93 7.88 12.59 17.12 12.57 11.06 9.20 10.87 7.20 8.79 7.89 7.52 12.11 9.17 9.94 17.48 23.77 12.45 17.87 17.52
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16.34 13.01 18.14 14.42 12.86 14.12 19.89 8.28 20.56 13.80 10.39 17.04 21.82 18.38 12.77 15.70 9.28 15.06 16.94 14.10 13.28 12.80 27.76 28.50 24.67 12.58 15.95 11.36 10.36 7.72 9.12 9.52 7.90 6.01 10.00 7.34 5.79 20.48 17.43 22.15 26.63 21.49 19.71 17.61 19.32 15.31 16.97 15.96 15.53 20.42 17.24 18.04 28.03 34.13 21.55 27.06 26.51
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1.11 -1.47 3.28 0.25 -0.91 0.38 5.63 -11.66 0.68 -3.65 -5.04 1.63 6.46 3.94 -0.62 2.25 -3.19 2.15 3.99 1.63 1.03 0.72 6.92 10.01 7.99 -1.21 2.48 -1.11 -1.66 -3.75 -2.30 -1.77 -3.08 -4.67 -0.96 -3.27 -4.59 3.07 2.44 7.57 12.63 8.64 7.43 5.81 7.57 4.11 5.74 4.94 4.65 9.16 6.35 7.14 11.30 18.51 8.20 13.99 13.97
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0.087 0.085 0.078 0.078 0.076 0.073 0.067 0.257 0.200 0.191 0.169 0.142 0.125 0.119 0.117 0.108 0.109 0.099 0.093 0.092 0.089 0.087 0.308 0.253 0.229 0.211 0.180 0.169 0.157 0.150 0.139 0.131 0.127 0.124 0.114 0.113 0.111 0.425 0.346 0.286 0.226 0.204 0.186 0.173 0.159 0.154 0.143 0.137 0.132 0.121 0.119 0.114 0.489 0.361 0.339 0.261 0.227
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1.5 1.7 1.9 2.1 2.3 2.5 2.7 0.1 0.2 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 0.1 0.2 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 0.1 0.2 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 0.1 0.2 0.3 0.5 0.7
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0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.34 1.34 1.34 1.34 1.34
-21.80 -23.61 -19.75 -21.96 -22.74 -21.62 -17.42 -12.04 -0.35 -4.97 -6.73 -0.42 4.13 1.54 -3.01 -0.29 -5.65 -0.51 1.24 -1.10 -1.72 -2.05 -19.59 -15.89 -16.68 -23.02 -19.67 -22.19 -22.41 -23.90 -22.62 -22.08 -23.04 -24.22 -21.21 -22.98 -23.98 -21.23 -20.54 -15.93 -11.27 -14.04 -14.75 -15.86 -14.33 -16.98 -15.59 -16.16 -16.33 -12.66 -14.86 -13.89 -7.14 -14.70 -9.57 -9.27 -12.60
-24.80 -26.20 -22.17 -24.04 -24.57 -23.26 -18.95 -41.83 -30.96 -32.18 -30.92 -24.54 -19.82 -20.88 -23.71 -20.97 -24.74 -20.22 -18.43 -20.00 -20.21 -20.23 -26.39 -20.78 -20.25 -24.91 -20.78 -22.70 -22.49 -23.66 -22.11 -21.36 -22.13 -23.17 -19.98 -21.66 -22.57 -25.89 -23.16 -17.55 -11.63 -13.65 -13.87 -14.64 -12.81 -15.30 -13.70 -14.13 -14.18 -10.31 -12.46 -11.68 -17.15 -8.48 -14.93 -8.68 -7.76
ACCEPTED MANUSCRIPT 9.55 10.18 3.45 5.75 0.86 0.93 0.23 0.63 2.98 -0.10
21.26 21.73 14.12 16.53 11.02 11.01 10.16 10.54 13.06 9.63
12.75 13.27 6.24 8.52 3.43 3.45 2.68 3.06 5.43 2.24
2.27 2.97 -3.25 -1.02 -5.55 -5.45 -6.07 -5.66 -3.43 -6.30
-7.61 -6.92 -12.51 -10.47 -14.54 -14.43 -14.97 -14.59 -12.56 -15.14
T
0.211 0.192 0.190 0.174 0.172 0.163 0.157 0.150 0.141 0.140
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0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7
-11.95 -17.24 -15.31 -19.16 -19.05 -19.57 -19.21 -17.28 -19.73 -13.89
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1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34
Relative error = [(Calculated data-Experimental data)/Experimental data] ×100
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3.2. Experimental results concerning the wide PSDs
Fig. 6 presents a typical curve to obtain the characteristic velocities through
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determining the transition points when dealing with wide PSD. It can be found that
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the transition from fixed bed state to the fluidized bed state can be defined by more
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than one single points for the wide PSD, which is different from the observations for the narrow PSD. Interestingly, two important additional velocities can be obtained: i),
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the incipient fluidization (Ufi), which corresponds to the breakpoint in theΔP versus Uf curve when the first particles begin to fluidize, and ii), the complete fluidization
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(Ufc) when all particles are fluidized. In our paper, the Umf of the mixed particle system is defined by convention as the intersection of the fixed bedΔP-versus-Uf line with the complete fluidized line. Fig. 7 shows comparison of Umf of the reference type and the wide PSDs at elevated pressures. It can be found that the values of Umf of wide PSDs were larger than the reference type at atmospheric pressure. However, when pressure exceeded 0.3 MPa, the values of Umf of wide PSD exhibited obviously smaller than that of the reference type with the nearly same average diameter. Eq. (2) describes the forces acting on the particles in fluidized beds. On the 12
-10.75 -9.80 -15.00 -12.85 -16.69 -16.46 -16.90 -16.44 -14.38 -16.85
ACCEPTED MANUSCRIPT right-hand side of the Eq. (2), the first term, which represents the pressure loss through viscous effects, is the dominant term in laminar flow region (Re<20). The
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second term, which is the pressure loss due to inertial forces, can be the dominant
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term at high Reynolds numbers (Re>1000).
In this study, since the Reynolds numbers of different particles have values ranged from 7 to 387, the total pressure drop is determined by the inertial force and
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the viscous force. Because gas viscosity does not vary significantly with pressure, the
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only parameter in Eq. (2) which changes with pressure is the gas density. At low pressure (about P ≤ 0.3 MPa), the mixtures of wide PSD tend to segregate. Large
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particles in the wide PSD exhibited a stronger impact on the inertial force than the
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impact of the gas density. Therefore, the large particles exhibited dominant effects on
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the Umf of mixture. Thus, the wide PSDs have higher Umfs than those of the reference type with the same mean diameter at low pressure, as shown in Fig. 7. However, the
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segregation tendency of wide PSD decreases with the increase in the operating pressure, and a well- mixed bed can be obtained [25]. In addition, fine particles can easier slip in the voids among the coarse particles at high pressure and this can reduce the friction forces, which results in the decrease of Umf [26]. Therefore, fine particles could act as the lubricant in wide PSD. These are reasons that the wide PSD exhibit less value of Umf than that of the reference type with increasing of pressure. Fig. 8 illustrates the effects of pressure on the Umf among different types of the wide PSDs. With the increase in the pressure, the values of Umf decreased for the four types of the wide PSDs. In addition, the Umfs had similar values among the four types 13
ACCEPTED MANUSCRIPT of the wide PSDs at the high pressure region. Umfs of the flat and binary distributions were higher than those of the Gaussian and ternary distributions when pressure is
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smaller than 0.5 MPa. Chiba et al. [27] found that there are three types of the mixing
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during the defluidization at atmospheric pressure: completely mixed, completely segregated, and partially mixed. During the defluidization, the Umf of coarse particles in wide PSD is the largest one, and the Umf of fine particles is the smallest one. The
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pattern of completely segregated is the light components and heavy components
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complete separation. The pattern of partial mixing is the light components and heavy components partially mixed. The pattern of completely mixing is the light
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components and heavy components perfectly mixed. The three operating modes can
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be transformation with the change of the operating gas velocity. Due to the different
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mixing modes, during the defluidization, the wide PSD particles might have multiple Umfs at atmospheric pressure. Therefore, we might observe the multiple Umfs at
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atmospheric pressure, typically in the following sequence: coarse particles > completely segregated > partial mixing > completely mixed > fine particles. Gauthier et al. [8] and Lin et al. [9] indicated that the particles of flat and binary distributions tend to move segregation, but the particles of Gaussian-type PSD which is similar to the narrow PSD tend to be good mixing. Therefore, at pressure below 0.5 MPa, flat and binary PSDs tended to move segregation and exhibited higher minimum fluidization velocities. However, high pressure enhances the particles mixing, which can decrease the differences of Umfs among the different wide PSDs. Some correlations for predicting the Umf of the multicomponent mixtures (wide 14
ACCEPTED MANUSCRIPT PSD) have been proposed from previous publication [27-29]. Otero and Corella [30] proposed a correlation using the arithmetic averaging of the minimum fluidization
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velocity as shown in Eq. (5):
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U mf ,mix xU i mf ,i .
(5)
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i
Obata et al. [31] and Rincon et al. [32] recommended using the harmonic averaging of the minimum fluidization velocity of wide PSD as follows:
U mf ,mix
xi / U mf ,i
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1
i
(6)
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Rowe et al. [33] proposed a semi-theoretical equation by extending Hatch’s
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pressure-drop relationship for predicting the minimum fluidization velocity of
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mixtures. The particles with various sizes should have same shape, density, and the correlation is as follows:
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U mf ,mix
U mf ,1 U mf ,1 f ( ) x1 U mf ,2
n /(3n )
x2
(13/ n )
,
(7)
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where n can be taken to be 1.053, an empirical value. The f (ε) is function of the bed voidage and the result of f (ε) is 0.92 in our experiment. Experimental data of Umf of each narrow PSD were taken into Eq. (5，6， 7) and the results were described in Fig. 9. Fig. 9 shows the comparison of predicted results of Umfs through using the Eq. (5), the Eq. (6), and the Eq. (7), respectively. It can be found that the predicted results by using the Eq. (7), which has an average relative error of 5.41%, is closer to the experimental data than those predicted by using the Eq. (5)and the Eq. (6), which have average relative errors of 13.71% and 10.02%, respectively. It should be noted 15
ACCEPTED MANUSCRIPT that, in addition to the requirement that the particles should have same densities and shapes, the information of the bed void fraction is required as the input for the Eq. (7)
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developed by Rowe et al. For the wide PSD, if the bed void fraction can be obtained,
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Rowe equation is recommended. From the results of these three predicting equations in Fig. 9, when the bed void fraction at the incipient fluidization cannot be obtained or the particles with different shapes and densities, the harmonic averaging of Umf of
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mixtures would be better than the arithmetic average.
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3.3 Bed expansion
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The height of the bed expansion in a fluidized bed varies in a complex manner
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depending on the hydrodynamic properties of the bed, such as the initial bed height,
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the particle density, the gas velocity, the gas viscosity, and the pressure. Several correlations have been proposed to predict the bed expansion. Some of them are based
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on the two-phase theory [34, 35], which is not suitable to predict the bed expansion at high pressures [11] and others add to this the growth of bubbles [36, 37]. Fig. 10 illustrates the variation of the expansion ratio (δ =H/Hmf) with increasing the excess gas velocity (U-Umf) for the four narrow PSDs particles. It can be observed that the increase in the bed expansion with the excess fluidized velocity was nearly linear for the four type’s particles at elevated pressures. A less excess fluidized velocity U-Umf, for the initial bed expansion was required at higher pressure. With increasing the pressure, at the same excess fluidized velocity, the buoyancy force and the drag force acting on the fluidized particles would increase and the interparticle
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ACCEPTED MANUSCRIPT distance would increase. Therefore, the higher pressure primarily caused the increase in the bed expansion. In this study, at the same excess fluidized velocity, the bed
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expanded to a higher level at high pressure than that at low pressure, and the bed
particles (Geldart group D), as shown in Fig. 10.
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expansion of small particles (Geldart group B) was slightly less than that of large
Based on the experimental data in this study, a correlation, which based on the
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excess gas velocity, the minimum fluidization velocity, the particle diameter, and the
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density of fluidizing gas has been developed in order to estimate the bad expansion using the regression analysis. The standard deviation and correlation coefficient were
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0.0981 and 0.9345, respectively. The obtained equation is as follows.
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0.154 0.0846 2.58(U U mf )0.2014U mf g H 0.1004 H mf dp
(8)
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Fig. 11 shows the comparison between the experimental data and the predicted values using Eq. (8). The correlation developed for the bed expansion agreed well
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with the experimental data.
4. Conclusion
This work presents an experimental study on the effects of the PSDs and the pressure on the minimum fluidization velocity. The values of Umf of the wide PSDs were different at pressures below 0.9 MPa, whereas these differences tended to disappear with a further increase in the pressure. The minimum fluidization velocity of the Gaussian-type PSD has almost at the same velocity as the reference-type PSD at atmospheric pressure. Interestingly, all mixtures of wide PSDs had very different 17
ACCEPTED MANUSCRIPT hydrodynamic behaviors compared to the reference-type narrow PSD at elevated pressures, and their hydrodynamic behaviors tended to be similar at high pressures. A
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new correlation for predicting Umf of the narrow PSD was developed by modifying
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the Ergun equation. In the narrow PSDs, the proposed equation properly predicted the minimum fluidization velocity of spherical polystyrene particles in a 3D bed at a wide range of pressures. In order to predict the minimum fluidization velocity of powders
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of the wide PSDs, three existing correlations were tested for fitting the experimental
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results, and it was found that Rowe’s equation was better than the other two equations for predicting the Umf of wide PSD under the operation conditions in this study.
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Fluidized-bed expansion almost increased under the same excess fluidized
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velocity with increasing the pressures. The correlation used for predicting the bed
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expansion showed reasonable agreement with the experimental data.
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ACCEPTED MANUSCRIPT Nomenclature
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Binary PSD considered narrow cut diameter (mm) powder harmonic average diameter (mm) Flat PSD Gaussian PSD =9.8m/s2, acceleration of gravity Height of expanded bed (cm) Bed height at incipient fluidization (cm) Pressure (MPa) standard atmospheric pressure (MPa) pressure drop（Pa） Reference PSD Ternary PSD Minimum fluidization velocity (m/s) Minimum fluidization velocity of particles of dia. d1, d2,… (m/s) Superficial gas velocity (m/s) initial fluidization, complete fluidization velocity (m/s), respectively mass fraction of particles with mean diameter di bed expansion ratio, dimensionless void fraction; voidage of a bed of mixture, respectively, dimensionless void fraction in a bed at minimum fluidizing conditions, dimensionless voidage of bed consists of component 1, dimensionless gas viscosity (kg/m·s) solid density (kg/m3) fluidized gas density (kg/m3) sphericity of a particle, dimensionless
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B d1, d2, d3, d4, d5, di dp F G g H Hmf P PΘ ΔP R T Umf Umf,1, Umf,2… Uf，U Ufi, Ufc xi Greek letters Δ ε, εmix εmf ε1 μ ρp ρg φs Dimensionless numbers Ar Re
Archimedes number =dp3ρg(ρp-ρg)g/μ2 Reynolds number = dpUρg/μ
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ACCEPTED MANUSCRIPT Acknowledgement
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This work has been funded by the National Natural Science Foundation (NO.
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21506242) and Strategic Priority Research Program of the Chinese Academy of
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Sciences (NO. XDA07050100). Their supports are greatly appreciated.
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ACCEPTED MANUSCRIPT Appendix A. Details for calculating the Rowe’s equation
The equation for pressure drop through a porous body is
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2n U mf n S (1 ) 3n ) ( ) ( ) , g
(A.1)
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P / L k g (
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where S is the specific surface (i.e. 6/d for spheres). The value of n is among 1 to 2, which depends on the flow regime.
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The onset of fluidization occurs when the drag force is equal to weight of
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particles. P / L ( s g )(1 ) g
(A.2)
s g 1/ n (12/ n ) 1/ n mf3 ) ( ) g ( )1/ n S (13/ n ) 2n g g (1 mf )
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U mf k 1/ n (
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The Umf is found by combining Eq. (A.1) and Eq. (A.2).
(A.3)
d 6 ( x1 1 x2 ) , d1 d2
(A.4)
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S
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mf3 f ( s , g , )( )1/ n S (13/ n ) 2 n (1 mf )
where xi is the mass fraction of particles having d i as diameter. U mf
mf3 d1 1/ n 6 (13/ n ) f ( s , g , )( ) ( ) x x 1 2 (1 mf )2n d1 d2
mf3 ,1 6 U mf ,1 f ( s , g , )( )1/ n ( )(13/ n ) 2 n (1 mf ,1 ) d1 1/ n
U mf ,mix
1 1 2 n U mf ,1 ( mix )( ) 1 mix
d1 x1 x2 d2
(13/ n )
(A.5)
(A.6) (13/ n )
(A.7)
1/ n
1 1 2 n f ( ) ( mix )( ) 1 1 mix
(A.8)
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U mf ,mix
d U mf ,1 f ( ) x1 1 x2 d2
(13/ n )
(A.9)
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(13/ n )
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x2
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n /(3n )
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U mf ,mix
U mf ,1 U mf ,1 f ( ) x1 U mf ,2
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From Eq. (A.5), (d1/d2) can be written in place of (U1/U2)n/(3-n). Eq. (A.9) then becomes
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(A.10)
ACCEPTED MANUSCRIPT Reference
D.
Kunii,
O.
Levenspiel,
H.
Brenner,
Fluidization
Engineering,
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[1]
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Butterworth—Heinemann, New York, 1991.
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[2] D. Geldart, Types of gas fluidization, Powder Technol., 7 (1973) 285-292. [3] M. Siedlecki, W. de Jong, A.H.M. Verkooijen, Fluidized bed gasification as a
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mature and reliable technology for the production of bio-syngas and applied in the production of liquid transportation fuels-A Review, Energies, 4 (2011)
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389-434.
[4] T.F. McKenna, Polyolefin reaction engineering - An overview of recent
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Eng. Chem., 41 (1949) 1099-1104. [7] G.L. Sun, J.R. Grace, Effect of particle-size distribution in different fluidization regimes, AIChE J., 38 (1992) 716-722. [8] D. Gauthier, S. Zerguerras, G. Flamant, Influence of the particle size distribution of powders on the velocities of minimum and complete fluidization, Chem. Eng. J., 74 (1999) 181-196. [9] C.L. Lin, M.Y. Wey, S.D. You, The effect of particle size distribution on minimum fluidization velocity at high temperature, Powder Technol., 126 (2002) 297-301. [10] C.Y. Wen, Y.H. Yu, A generalized method for predicting minimum fluidization 23
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fluidization at high-pressure, Chem. Eng. Sci., 39 (1984) 253-261.
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[12] S.C. Saxena, G.J. Vogel, Measurement of incipient fluidization velocities in a bed of coarse dolomite at temperature and pressure, Trans. Inst. Chem. Eng., 55 (1977) 184-189.
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[13] M. Nakamura, Y. Hamada, S. Toyama, A.E. Fouda, C.E. Capes, An experimental
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investigation of minimum fluidization velocity at elevated temperatures and pressures, Can. J. Chem. Eng., 63 (1985) 8-13.
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[14] K. Doichev, N.S. Akhmakov, Fluidization of polydisperse systems, Chem. Eng.
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Sci., 34 (1979) 1357-1359.
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[15] A. Barbosa, D. Steinmetz, H. Angelino, Fluidization VIII, Laguerie and Large, Tour France, 1995.
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[16] Z.P. Zhu, Y.J. Na, Q.G. Lu, Effect of pressure on minimum fluidization velocity, J. Therm. Sci., 16 (2007) 264-269. [17] J.L. Ma, X.P. Chen, D.Y. Liu, Minimum fluidization velocity of particles with wide size distribution at high temperatures, Powder Technol., 235 (2013) 271-278. [18] D.F. King, D. Harrison, The dense phase of a fluidized-bed at elevated pressures, Trans. Inst. Chem. Eng., 60 (1982) 26-30. [19] P.A. Olowson, A.E. Almstedt, Influence of pressure on the minimum fluidization velocity, Chem. Eng. Sci., 46 (1991) 637-640. 24
ACCEPTED MANUSCRIPT [20] P.N. Rowe, The effect of pressure on minimum fluidization velocity, Chem. Eng. Sci., 39 (1984) 173-174.
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[21] S. Ergun, Fluid flow through packed columns, Chem. Eng. Prog., 48 (1952)
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89-94.
[22] S.P. Babu, B. Shah, A. Talwaldar, Fluidization correlations for coal gasification materials-minimum fluidization velocity and fluidized bed expansion ratio,
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AIChE Symp Ser, 74 (1978) 176-186.
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[23] J.R. Grace, Handbook of Mutiphase Systems, Hetsroni,G. ed., Hemisphere, Washington D.C., 1982.
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New York, 1971.
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[24] J.F. Richardson, Incipient fluidization and particulate systems, Academic Press,
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[25] J.L.P. Chen, D.L. Keairns, Particle segregation in a fluidized-bed, Can. J. Chem. Eng., 53 (1975) 395-402.
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[26] L. Cheung, A.W. Nienow, P.N. Rowe, Minimum fluidization velocity of a binary mixture of different sized particles, Chem. Eng. Sci., 29 (1974) 1301-1303. [27] S. Chiba, T. Chiba, A.W. Nienow, H. Kobayashi, Minimum fluidization velocity, bed expansion and pressure-drop profile of binary particle mixtures, Powder Technol., 22 (1979) 255-269. [28] A. Kumar, P. Sengupta, Prediction of minimum fluidization velocity for multicomponent mixtures, Indian J. Technol., 12 (1974) 225-227. [29] K. Noda, S. Uchida, T. Makino, H. Kamo, Minimum fluidization velocity of binary mixture of particles with large size ratio, Powder Technol., 46 (1986) 25
ACCEPTED MANUSCRIPT 149-154. [30] A.R. Otero, J. Corella, Fluidization of mixtures of solids of distinct
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characteristics. 1. Fluidization velocities, Anales De Quimica-International
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Edition, 67 (1971) 1207-&.
[31] E. Obata, H. Watanabe, N. Endo, Measurement of size and size distribution of particles by fluidization, J. Chem. Eng. Jpn., 15 (1982) 23-28.
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[32] J. Rincon, J. Guardiola, A. Romero, G. Ramos, Predicting the minimum
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fluidization velocity of multicomponent systems, J. Chem. Eng. Jpn., 27 (1994) 177-181.
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[33] P.N. Rowe, A.W. Nienow, Minimum fluidization velocity of multicomponent
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particle mixtures, Chem. Eng. Sci., 30 (1975) 1365-1369.
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[34] M.H. Peters, L.S. Fan, T.L. Sweeney, Reactant dynamics in catalytic fluidized-bed reactors with flow reversal of gas in the emusion phase, Chem. Eng.
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Sci., 37 (1982) 553-565. [35] C.Y. Shen, H.F. Johnstone, Gas-solid contact in fluidized beds, AIChE J., 1 (1955) 349-354.
[36] A.M. Xavier, D.A. Lewis, J.F. Davidson, The expansion of bubbling fluidized bed, Trans. Inst. Chem. Eng.,56 (1978) 274-280. [37] K. Hilligardt, J. Werther, Local bubble-gas hold-up and expansion behavior of gas solid fluidized-beds, Chem. Ing. Tech., 57 (1985) 622-623.
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Fig. 1. Scheme of the experimental set-up 1─fluidized bed column; 2─U-type
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differential pressure meter;3─pressure vessel;4─high speed camera; 5─computer system; 6─mass flow meter/controller; 7─cylinder; 8─tank; 9─heat exchanger; 10─ reciprocating
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pump; 11─Liquid nitrogen storage tank
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Fig. 2. PSD of the considered mixtures: (a) flat distribution powder; (b) Gaussian-type
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powder; (c) binary mixture; and (d) ternary mixture.
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Fig. 3. Relationship between minimum fluidization velocity and pressure for different mean
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diameter particles.
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Fig. 4. Correlations for the prediction of Umf plotted with experimental data
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Fig. 5. Comparison between experimental data and the predicted results: (A) d1=0.55 mm; (B) d2=0.70 mm; (C) d3= 0.90 mm; (D) d4=1.13 mm; (E) d5=1.34 mm.
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Fig. 6. Total pressure drop versus velocity profile for Gaussian-type powders
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Fig. 7. Comparison between the Umf, reference and Umf, mixtures at pressure
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Fig. 8. Effect of pressure on the Umf of different wide PSDs
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Fig. 9. Comparison of experimental data with the results of correlated equations: (A) flat
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PSD; (B) Gaussian-type PSD; (C) binary mixture; and (d) ternary mixture.
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1.125 mm; (D) 1.34 mm
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Fig. 10. Bed expansion vs. U-Umf at different pressures: (A) 0.55 mm; (B) 0.90 mm; (C)
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Fig. 11. Comparison of calculated bed expansion values with experimental data
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Graphical Abstract
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ACCEPTED MANUSCRIPT AB STRACT This paper presents an experimental study on the effects of elevated pressure and
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particle size distribution (PSD) on the minimum fluidization velocity (Umf) and the
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bed expansion. It was developed with Geldart B and D-type polystyrene particles.
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Four wide PSDs and five narrow PSDs were investigated. The four wide PSDs studied included a Gaussian distribution, a flat distribution, a ternary mixture, and a
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binary mixture, all with the same mean diameters. Operation pressure ranged from 0.1 MPa (absolute pressure) to 2.7 MPa. The results revealed that the Umfs of the wide
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PSDs were lower than that of the reference narrow PSD with the same diameter at
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pressures exceeding 0.3 MPa. The segregation tendency of wide PSDs decreases with
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the increase in the operating pressure. The four wide PSDs had obviously different Umfs at pressures below 0.9 MPa; however, this difference in the Umfs was gradually
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reducing with a further increase in the pressure (>0.9 MPa). The bed expansion increased with increasing the pressure at same excess fluidized gas velocity.
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Correlations basing on experimental data were proposed in order to predict the Umf and bed expansion for the narrow PSD at elevated pressures, and three correlations were investigated for predicting the Umf of wide PSD. Keywords: Gas-solid fluidization, Particle size distribution, Minimum fluidization velocity, Bed expansion, Pressure
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ACCEPTED MANUSCRIPT Highlights Different particle size distributions (PSDs) were studied at elevated pressure.
Wide PSDs have smaller Umf than the narrow PSD at the pressures above 0.3
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MPa.
The types of wide PSDs have little effect on the Umf at pressures above 0.9 MPa.
Correlations to predict Umf and bed expansion at elevated pressures were
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proposed.
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S0032-5910(17)30561-2 doi:10.1016/j.powtec.2017.07.024 PTEC 12666
To appear in:
Powder Technology
Received date: Revised date: Accepted date:
21 March 2017 21 June 2017 6 July 2017
Please cite this article as: Rongtao Feng, Junguo Li, Zhonghu Cheng, Xin Yang, Yitian Fang, Influence of particle size distribution on minimum fluidization velocity and bed expansion at elevated pressure, Powder Technology (2017), doi:10.1016/j.powtec.2017.07.024
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ACCEPTED MANUSCRIPT Influence
of
particle size distribution
on
minimum
fluidization velocity and bed expansion at elevated pressure
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Rongtao Fenga,b, Junguo Lia,*, Zhonghu Chenga, Xin Yangc, Yitian Fanga,** a
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State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan 030001, PR China b
University of Chinese Academy of Sciences, Beijing 100039, PR China
c
Department of Mechanical Engineering, University of Sheffield, Sheffield S10 2TN,
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UK
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* Corresponding author. Tel.: +86-0351-4048313 ** Corresponding author. Tel.: +86-0351-2021137
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E-mail addresses: [email protected] (J. Li); [email protected] (Y. Fang)
1
ACCEPTED MANUSCRIPT 1. Introduction
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Fluidization technology has been widely employed in many industrial processes
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because of the desirable characteristics (e.g. good solids mixing, large contact surface
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area, high heat transfer, slow responses to abrupt changes in operating conditions [1]). There are many fluidized bed applications using particles belong to Geldart B and D
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[2], such as coal gasification, polymers production. Fluid-bed gasification is regarded as a promising technology for the production of syngas because of its advantages in
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fuel flexibility, good scalability of reactors and effectiveness in controlling pollutant emissions and promoting the conversion process through using the in-situ additives
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D
[3]. The fluidization technology is increasingly employed to manufacture polyethylene through the gas-solid phase polymerization process [4]. Compared to
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liquid-phase polymerization, the gas-solid phase process offers a more economical and energy-efficient alternative. This is because there is no need to flash off much
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liquid (a step with high energy consumption) in the gas-phase process. Pressurized operation, which is beneficial to increasing the throughput and reducing the size of reactors, is significant in developing these fluidized bed applications. Therefore, an improved understanding of the hydrodynamic behaviors of fluidized bed for particles belong to Geldart B and D at elevated pressures is imperative for an efficient operation and design of the fluidized bed in the future. Particle size distribution (PSD) (especially uneven particle size distribution resulted from the segregation and mixing) could influence the hydrodynamic behaviors and chemical conversion in the reactor [5]. Fluidized beds of large narrow 2
ACCEPTED MANUSCRIPT PSD particles fluidize poorly with bumping, spouting, and slugging, while the quality of fluidization of these beds can often be improved by adding a small amount of fines
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to act as lubricant [6]. Sun et al. [7] investigated the effect of PSD on the performance
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of a fluidized-bed reactor in different fluidization regimes (bubbling, slugging, turbulent and fast fluidization). It was found that (i) PSD could obviously affect void sizes and regime transitions, (ii) the effect of wide PSD on the chemical conversion
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and reactor efficiency will not be significant until the fluidized gas velocity exceeds
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0.2 m/s, and (iii) however, narrow PSD particles will not show any similar effects in same fluidization regimes except for the fast fluidization regime. Gauthier et al. [8]
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found that Gaussian-type and narrow-cut particle distributions have the same Umf,
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whereas binary PSD and flat PSD exhibit a very different hydrodynamic behavior
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under ambient conditions. Lin et al. [9] concluded that the binary and flat PSDs behave similarly to each other but these two PSDs have higher Umfs than the Gaussian
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and narrow PSD cases at high temperature. Most of the previous studies on the effects of PSD on the hydrodynamic behaviors are mainly undertaken at atmospheric pressure. It is still not clear about the effects of PSD on the hydrodynamic behaviors of fluidized bed at elevated pressures. In order to predict the Umf, many correlations have been proposed to estimate the Umf in the fluidized bed, as listed in Table 1. Among these correlations, most of them have been developed for narrow-cut PSD particles at atmospheric pressure. However, when dealing with coal gasification or natural minerals etc., wide PSD particles are usually fluidized as bed materials and processed under pressure. 3
ACCEPTED MANUSCRIPT This work focused on investigating the influence of PSD on the minimum fluidization velocity and the bed expansion of Geldart B and D-type polystyrene
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particles at elevated pressures (up to 2.7 MPa) in a lab-scale cylindrical fluidized bed.
Gaussian-type) were investigated and analyzed. Table 1.
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Five narrow PSDs and four wide PSDs (binary mixture, ternary mixture, flat, and
Correlation
Wen and Yu
Materials
2
0.5
2
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Researchers
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List of typical correlations to predict minimum fluidization velocity.
2
0.5
Remf=(33.7 + 0.0408Ar) -33.7
[10]
Various
PSD
Presure
Other conditions
Narrow
Ambient
10-3
Narrow
Elevated
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particles
Chitester et
0.5
Remf=(28.7 + 0.0494Ar) -28.7
al. [11]
Ballotini
Remf=(25.3 + 0.0571Ar) -25.3
D
Saxena et
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al.[12] al.[13]
Umf=(μg/ρgdg)(1.08×10 Ar
Elevated
Glass beads
Narrow
Elevated
0.08
pressure 76
Remf=1.9×10-3Ar0.87
Sand
Narrow
Ambient
None
Remf=(22.1+0.0354Ar)0.5-22.1
Sand
Narrow
Elevated
40
0.947
)
AC
Ma et al.[17]
6
Ambient
al.[15] Zhu et
Narrow
Wide
al.[14] Barbosa et
Dolomite
Glass beads
-3
CE P
Doichev et
pressure pressure
Remf=(33.92 + 0.0465Ar)0.5-33.9
Nakamura et
al.[16]
Coal Char
Bead
Remf=0.28∑xidi0.599(ρp/ρg)/ν0.066
Sand
pressure Wide
Ambient
Temperature(30-600℃)
Ash
2. Material and methods 2.1 Apparatus
The reactor used in these experiments was a cold model pressurized fluidization facility. The facility consisted of a pressure vessel, a nitrogen supply system, a high speed camera (Photron SA-Z), a computer system, and the peripheral equipment, as
4
ACCEPTED MANUSCRIPT shown in Fig. 1. Height of the pressure vessel was 1600 mm, and with an inside diameter (ID) of 1200 mm. A perspex columnar bed of 60 mm (ID) was inserted into
IP
T
the pressure vessel. Pressure drop was measured by the U-type differential pressure
SC R
meter, and the differential pressures were recorded through the camera by the computer. The nitrogen supply system was applied through a high-pressure reciprocating pump, and no nitrogen recirculation system was used. Supply pressure
NU
in the reciprocating pump was maintained using a central liquid nitrogen system.
MA
Flow control was accomplished by parallel mass flow meters. The control valve (FCV-1 in Fig.1) was used for large flow rates and the mass flow controller (FCV-2)
D
was used for small flow rates. An upstream pressure control valve (PCV-1) and a back
TE
pressure control valve (PCV-2) were used to maintain the system pressure. The cable,
CE P
sealed in the flange, was capable of transmitting imaging signal to the external computer system.
AC
2.2 Materials and preparation
The experimental materials originally included five mean diameters particles (the narrow PSDs). The samples were carefully sieved by the standard test sieve shaker. Density of the polystyrene particles was 1020 kg/m3. Particles of polystyrene of five mean diameters were studied: 0.55 mm (d1), 0.70 mm (d2), 0.90 mm (d3), 1.13 mm (d4), and 1.34 mm (d5), respectively. Particles with diameters of d1, d2, and d3 belonged to Geldart B; the others belonged to Geldart D. Four wide PSDs were derived by mixing these original particles with narrow PSD: a flat distribution powder
5
ACCEPTED MANUSCRIPT (F), a Gaussian-type powder (G), a binary mixture (B), and a ternary mixture (T). The narrow PSD (d3=0.90 mm) was defined as the reference-type powder (R). These
IP
T
particles were prepared according to the method suggested by Gauthier et al [8], and
SC R
the four wide PSDs were controlled to have the same mean diameters as the reference-type powder (R) with dp = 0.90 mm as follows:
dp
1 xi / di
NU
i
(1)
with xi the mass fraction of particles having d i as average diameter. The
MA
characteristics of the bed materials used in the experiment are listed in Table 2, and
D
Fig. 2 describes the four wide PSDs mixtures.
TE
Table 2
Description of the characteristics and their PSDs Weight
Sieves
Sieves
Average diameter
(%), xi
no.
(mm)
(mm)
100
18-24
0.80-1.00
0.90
14
14-16
1.25-1.43
1.34
23
16-18
1.00-1.25
1.13
36
18-24
0.80-1.00
0.90
17
24-30
0.60-0.80
0.70
10
30-40
0.45-0.60
0.55
25
14-16
1.25-1.43
1.34
23
16-18
1.00-1.25
1.13
19
18-24
0.80-1.00
0.90
17
24-30
0.60-0.80
0.70
16
30-40
0.45-0.60
0.55
35
16-18
1.00-1.25
1.13
35
18-24
0.80-1.00
0.90
30
24-30
0.60-0.80
0.70
55
16-18
1.00-1.25
1.13
45
24-30
0.60-0.80
0.70
CE P
Type of powder
Composition for mean diameter dp=0.90mm Reference
AC
Gaussian
Flat
Ternary
Binary
6
ACCEPTED MANUSCRIPT 2.3. Experimental procedures
T
In order to maintain a steady-state operation of the reactor under a desired
IP
pressure, a pre-pressurizing pressure vessel was equipped in the fluidized bed system.
SC R
Fluidized velocity was gradually reduced from a well-fluidized state to a packed (static) bed, and the pressure drop △P was measured. The point of intersection of the
NU
pressure drop line for the fixed bed and the horizontal line for the fully fluidized bed is typically defined as the minimum fluidization velocity. In addition, since the
MA
Renolds numbers were less than 20 for small particles in low velocities in the reactor, the linear fitting of △P as a function of the gas velocity was employed in the packed
D
bed stage. With regard to the Renolds numbers between 20 and 1000, the parabolic
TE
fitting of △P was employed in the packed bed stage.
CE P
In order to obtain the fluidized bed expansion, a ruler was fixed on the fluidized bed, and a high speed camera was used to capture the images of the bed expansion.
AC
The feature of high shutter speed is essential for capturing fast moving images without a blurring effect, especially in measuring of the height of the bed expansion. Then the height of the fluidized bed expansion was obtained by analyzing films a frame by a frame. In addition, the effect of static on polystyrene particles fluidization is usually unneglectable when the particles rubbing against each other for long time. In this experiment, the particles were just used for a short period time, then the old particles were replaced by the new particles, and in this way, the effect of static electricity can be minimized.
7
ACCEPTED MANUSCRIPT 3. Results and discussion
T
3.1. Umf for the narrow PSD
SC R
IP
3.1.1. The effects of pressure on the Umf
Fig. 3 shows the effects of pressure on the Umf of narrow PSD. The corresponding Umfs determined by experiments with these particles ranged from 0.146
NU
m/s to 0.489 m/s at 0.1 MPa (absolute pressure) and from 0.067 m/s to 0.140 m/s at
MA
2.7 MPa pressure. The Umfs decreased with an increase in the pressure among the different mean diameters particles. In addition, the effect of pressure on the Umf of
D
large particles was stronger than that of small particles, as shown in Fig. 3. It should
TE
be noted that the trends of Umf with the narrow PSD sharply decreased with the
CE P
pressure up to about 0.9 MPa, and slowly decreased thereafter. Literatures [18-20] also found a general decrease with increasing pressure, and that the effects of pressure
AC
on Umf are strongly dependent upon particle size. The effects of pressure on Umf had been explicitly described on the basis of Ergun’s equation [21], which may be written, at minimum fluidization, as 2 1 mf gU mf (1 mf )2 U mf . (1 mf )( s g ) g 150 1.75 3 mf3 (s d p )2 mf s d p
(2)
With the pressure increase, the viscosity of nitrogen does not change, whereas the density can be evaluated by： ρ=1.251P/PΘ. For the large particles, the Eq. (2) 3 ] / (1.75 g ) , which strongly depends on the gas simplifies to U mf [d p ( s g ) g mf
density (namely the pressure). It can be the reason that why the effects of pressure on the Umf of large particles are strong. 8
ACCEPTED MANUSCRIPT 3.1.2 Prediction of Umf for narrow PSD
T
Umf is one of the most important measurements for the reactor design. Many
IP
correlations have been proposed for the prediction of Umf based on the simplified
K1 Re2mf K2 Remf Ar
SC R
Ergun equation, which is developed by Wen and Yu [10] as follows: ,
(3)
NU
where K1 and K2 are constant parameters. It is regarded that these two parameters stay nearly constant for different kinds of particles over a wide range of experimental
MA
conditions (Re=0.001 to 4000) at atmospheric pressure. In addition, many researchers derived different values of the two parameters, as shown in Table 3. In this study, the
TE
D
experimental data obtained for Umf at different pressures are presented in the plot of Remf vs Ar in Fig. 4, and a modified form of Ergun equation was obtained by the
CE P
regression analysis:
Remf 27.92 0.0554 Ar 27.9 ,
(4)
AC
where K2 / (2K1) = 27.9, 1/K1=0.0554. Table 3.
The values of the two parameters in the correlations to estimate the Umf. Researchers
K2 / (2K1)
1/K1
Specifications
Wen and Yu[10] Babu et al. [22]
33.7 25.3
0.0408 0.0651
Grace et al. [23] Chitester et al.[11]
27.2 28.7
0.0408 0.0494
Richardson [24]
25.7
0.0365
Fine particles, at atmospheric pressure Fuel particles for the coal conversion systems None Coal, char, and ballotini; at elevated pressures up to 6.4 MPa…. None
Saxena et al. [12]
25.3
0.0571
Dolomite at high temperature and pressure
Fig. 5 shows the comparison of the predicted Umfs using the modified correlation 9
ACCEPTED MANUSCRIPT in this study and other typical correlations. The relative errors of these correlations are also given in Table 4. It can be found that the new correlation well predicted the
IP
T
values of Umf for the five narrow PSDs at elevated pressures. The relative errors of the
SC R
predicted results using the new correlation were almost in ±15%. Also, it can be found that: among all the narrow PSDs and pressures, i) Babu’s [22] and Saxena’s [12] correlations nearly overestimated the values of Umf, and Chitester’s [11] correlation
NU
predicted the Umf of large particles well comparing with the small particles; ii)
MA
however，Wen and Yu’s [10] , Grace’s [23]and Richardson’s [24] correlations obviously underestimated the values of Umf. Obviously, it is difficult to find a formula
D
to predict the value of Umf for any materials and under any pressures very well. Only
TE
when the correlations are derived from the specified particle properties and operating
CE P
conditions can the reasonable agreement be obtained between the predictions from the correlations and the experimental results. Therefore, it should be careful to choose the
AC
correlations according to the specified particle properties and operating conditions. In the process of olefin polymerization in fluidized bed, our equation can be better than other equations for predicting the Umf of the polymer particles. Table 4 The relative errors of different researcher’ calculated data Mean diameter (mm) 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55
Pressure (MPa)
Experimental data (m/s)
Eq.(4)
Babu
Saxena
Chitester
Grace
Richardon
Wen &Yu
0.1 0.2 0.3 0.5 0.7 0.9 1.1 1.3
0.146 0.140 0.135 0.124 0.104 0.099 0.095 0.091
4.11 0.51 -2.30 -3.51 6.04 3.37 1.75 1.37
30.32 23.32 18.28 14.80 24.77 20.67 18.08 17.09
15.97 10.57 6.57 4.09 13.58 10.16 8.01 7.28
-8.51 -10.91 -12.87 -13.23 -4.13 -6.17 -7.37 -7.49
-19.79 -21.58 -23.08 -23.09 -14.79 -16.45 -17.38 -17.39
-24.07 -25.77 -27.19 -27.21 -19.36 -20.93 -21.82 -21.83
-33.61 -33.92 -34.30 -33.02 -24.77 -25.48 -25.72 -25.24
10
ACCEPTED MANUSCRIPT
D
11
-17.36 -19.27 -15.19 -17.52 -18.34 -17.16 -12.72 -31.03 -20.13 -22.81 -22.99 -16.98 -12.60 -14.35 -17.87 -15.29 -19.64 -15.08 -13.42 -15.28 -15.69 -15.86 -15.04 -11.12 -11.95 -18.64 -15.10 -17.76 -17.98 -19.56 -18.21 -17.64 -18.64 -19.89 -16.71 -18.59 -19.64 -16.77 -16.02 -11.15 -6.22 -9.14 -9.89 -11.06 -9.44 -12.24 -10.77 -11.37 -11.55 -7.67 -10.00 -9.29 -9.00 -1.86 -9.84 -4.41 -4.09
IP
T
-7.54 -9.75 -5.27 -7.93 -8.89 -7.62 -2.71 -21.66 -9.75 -13.06 -13.62 -7.10 -2.36 -4.44 -8.46 -5.66 -10.56 -5.53 -3.73 -5.85 -6.33 -6.56 -4.06 -0.17 -1.41 -9.21 -5.45 -8.53 -8.87 -10.68 -9.23 -8.65 -9.80 -11.21 -7.71 -9.82 -11.00 -6.50 -6.14 -0.94 4.27 0.87 -0.06 -1.43 0.31 -2.84 -1.25 -1.94 -2.16 2.10 -0.49 0.28 1.80 9.31 0.21 6.02 6.24
SC R
6.74 3.80 8.62 5.27 3.91 5.14 10.52 -2.88 9.06 3.45 0.92 7.35 11.98 9.00 3.97 6.77 0.93 6.35 8.15 5.58 4.87 4.47 27.76 17.28 14.25 3.64 7.01 2.94 2.14 -0.21 1.15 1.59 0.13 -1.58 2.17 -0.28 -1.69 9.93 7.88 12.59 17.12 12.57 11.06 9.20 10.87 7.20 8.79 7.89 7.52 12.11 9.17 9.94 17.48 23.77 12.45 17.87 17.52
NU
16.34 13.01 18.14 14.42 12.86 14.12 19.89 8.28 20.56 13.80 10.39 17.04 21.82 18.38 12.77 15.70 9.28 15.06 16.94 14.10 13.28 12.80 27.76 28.50 24.67 12.58 15.95 11.36 10.36 7.72 9.12 9.52 7.90 6.01 10.00 7.34 5.79 20.48 17.43 22.15 26.63 21.49 19.71 17.61 19.32 15.31 16.97 15.96 15.53 20.42 17.24 18.04 28.03 34.13 21.55 27.06 26.51
MA
1.11 -1.47 3.28 0.25 -0.91 0.38 5.63 -11.66 0.68 -3.65 -5.04 1.63 6.46 3.94 -0.62 2.25 -3.19 2.15 3.99 1.63 1.03 0.72 6.92 10.01 7.99 -1.21 2.48 -1.11 -1.66 -3.75 -2.30 -1.77 -3.08 -4.67 -0.96 -3.27 -4.59 3.07 2.44 7.57 12.63 8.64 7.43 5.81 7.57 4.11 5.74 4.94 4.65 9.16 6.35 7.14 11.30 18.51 8.20 13.99 13.97
TE
0.087 0.085 0.078 0.078 0.076 0.073 0.067 0.257 0.200 0.191 0.169 0.142 0.125 0.119 0.117 0.108 0.109 0.099 0.093 0.092 0.089 0.087 0.308 0.253 0.229 0.211 0.180 0.169 0.157 0.150 0.139 0.131 0.127 0.124 0.114 0.113 0.111 0.425 0.346 0.286 0.226 0.204 0.186 0.173 0.159 0.154 0.143 0.137 0.132 0.121 0.119 0.114 0.489 0.361 0.339 0.261 0.227
CE P
1.5 1.7 1.9 2.1 2.3 2.5 2.7 0.1 0.2 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 0.1 0.2 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 0.1 0.2 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 0.1 0.2 0.3 0.5 0.7
AC
0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.13 1.34 1.34 1.34 1.34 1.34
-21.80 -23.61 -19.75 -21.96 -22.74 -21.62 -17.42 -12.04 -0.35 -4.97 -6.73 -0.42 4.13 1.54 -3.01 -0.29 -5.65 -0.51 1.24 -1.10 -1.72 -2.05 -19.59 -15.89 -16.68 -23.02 -19.67 -22.19 -22.41 -23.90 -22.62 -22.08 -23.04 -24.22 -21.21 -22.98 -23.98 -21.23 -20.54 -15.93 -11.27 -14.04 -14.75 -15.86 -14.33 -16.98 -15.59 -16.16 -16.33 -12.66 -14.86 -13.89 -7.14 -14.70 -9.57 -9.27 -12.60
-24.80 -26.20 -22.17 -24.04 -24.57 -23.26 -18.95 -41.83 -30.96 -32.18 -30.92 -24.54 -19.82 -20.88 -23.71 -20.97 -24.74 -20.22 -18.43 -20.00 -20.21 -20.23 -26.39 -20.78 -20.25 -24.91 -20.78 -22.70 -22.49 -23.66 -22.11 -21.36 -22.13 -23.17 -19.98 -21.66 -22.57 -25.89 -23.16 -17.55 -11.63 -13.65 -13.87 -14.64 -12.81 -15.30 -13.70 -14.13 -14.18 -10.31 -12.46 -11.68 -17.15 -8.48 -14.93 -8.68 -7.76
ACCEPTED MANUSCRIPT 9.55 10.18 3.45 5.75 0.86 0.93 0.23 0.63 2.98 -0.10
21.26 21.73 14.12 16.53 11.02 11.01 10.16 10.54 13.06 9.63
12.75 13.27 6.24 8.52 3.43 3.45 2.68 3.06 5.43 2.24
2.27 2.97 -3.25 -1.02 -5.55 -5.45 -6.07 -5.66 -3.43 -6.30
-7.61 -6.92 -12.51 -10.47 -14.54 -14.43 -14.97 -14.59 -12.56 -15.14
T
0.211 0.192 0.190 0.174 0.172 0.163 0.157 0.150 0.141 0.140
IP
0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7
-11.95 -17.24 -15.31 -19.16 -19.05 -19.57 -19.21 -17.28 -19.73 -13.89
SC R
1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34 1.34
Relative error = [(Calculated data-Experimental data)/Experimental data] ×100
NU
3.2. Experimental results concerning the wide PSDs
Fig. 6 presents a typical curve to obtain the characteristic velocities through
MA
determining the transition points when dealing with wide PSD. It can be found that
D
the transition from fixed bed state to the fluidized bed state can be defined by more
TE
than one single points for the wide PSD, which is different from the observations for the narrow PSD. Interestingly, two important additional velocities can be obtained: i),
CE P
the incipient fluidization (Ufi), which corresponds to the breakpoint in theΔP versus Uf curve when the first particles begin to fluidize, and ii), the complete fluidization
AC
(Ufc) when all particles are fluidized. In our paper, the Umf of the mixed particle system is defined by convention as the intersection of the fixed bedΔP-versus-Uf line with the complete fluidized line. Fig. 7 shows comparison of Umf of the reference type and the wide PSDs at elevated pressures. It can be found that the values of Umf of wide PSDs were larger than the reference type at atmospheric pressure. However, when pressure exceeded 0.3 MPa, the values of Umf of wide PSD exhibited obviously smaller than that of the reference type with the nearly same average diameter. Eq. (2) describes the forces acting on the particles in fluidized beds. On the 12
-10.75 -9.80 -15.00 -12.85 -16.69 -16.46 -16.90 -16.44 -14.38 -16.85
ACCEPTED MANUSCRIPT right-hand side of the Eq. (2), the first term, which represents the pressure loss through viscous effects, is the dominant term in laminar flow region (Re<20). The
IP
T
second term, which is the pressure loss due to inertial forces, can be the dominant
SC R
term at high Reynolds numbers (Re>1000).
In this study, since the Reynolds numbers of different particles have values ranged from 7 to 387, the total pressure drop is determined by the inertial force and
NU
the viscous force. Because gas viscosity does not vary significantly with pressure, the
MA
only parameter in Eq. (2) which changes with pressure is the gas density. At low pressure (about P ≤ 0.3 MPa), the mixtures of wide PSD tend to segregate. Large
D
particles in the wide PSD exhibited a stronger impact on the inertial force than the
TE
impact of the gas density. Therefore, the large particles exhibited dominant effects on
CE P
the Umf of mixture. Thus, the wide PSDs have higher Umfs than those of the reference type with the same mean diameter at low pressure, as shown in Fig. 7. However, the
AC
segregation tendency of wide PSD decreases with the increase in the operating pressure, and a well- mixed bed can be obtained [25]. In addition, fine particles can easier slip in the voids among the coarse particles at high pressure and this can reduce the friction forces, which results in the decrease of Umf [26]. Therefore, fine particles could act as the lubricant in wide PSD. These are reasons that the wide PSD exhibit less value of Umf than that of the reference type with increasing of pressure. Fig. 8 illustrates the effects of pressure on the Umf among different types of the wide PSDs. With the increase in the pressure, the values of Umf decreased for the four types of the wide PSDs. In addition, the Umfs had similar values among the four types 13
ACCEPTED MANUSCRIPT of the wide PSDs at the high pressure region. Umfs of the flat and binary distributions were higher than those of the Gaussian and ternary distributions when pressure is
IP
T
smaller than 0.5 MPa. Chiba et al. [27] found that there are three types of the mixing
SC R
during the defluidization at atmospheric pressure: completely mixed, completely segregated, and partially mixed. During the defluidization, the Umf of coarse particles in wide PSD is the largest one, and the Umf of fine particles is the smallest one. The
NU
pattern of completely segregated is the light components and heavy components
MA
complete separation. The pattern of partial mixing is the light components and heavy components partially mixed. The pattern of completely mixing is the light
D
components and heavy components perfectly mixed. The three operating modes can
TE
be transformation with the change of the operating gas velocity. Due to the different
CE P
mixing modes, during the defluidization, the wide PSD particles might have multiple Umfs at atmospheric pressure. Therefore, we might observe the multiple Umfs at
AC
atmospheric pressure, typically in the following sequence: coarse particles > completely segregated > partial mixing > completely mixed > fine particles. Gauthier et al. [8] and Lin et al. [9] indicated that the particles of flat and binary distributions tend to move segregation, but the particles of Gaussian-type PSD which is similar to the narrow PSD tend to be good mixing. Therefore, at pressure below 0.5 MPa, flat and binary PSDs tended to move segregation and exhibited higher minimum fluidization velocities. However, high pressure enhances the particles mixing, which can decrease the differences of Umfs among the different wide PSDs. Some correlations for predicting the Umf of the multicomponent mixtures (wide 14
ACCEPTED MANUSCRIPT PSD) have been proposed from previous publication [27-29]. Otero and Corella [30] proposed a correlation using the arithmetic averaging of the minimum fluidization
T
velocity as shown in Eq. (5):
IP
U mf ,mix xU i mf ,i .
(5)
SC R
i
Obata et al. [31] and Rincon et al. [32] recommended using the harmonic averaging of the minimum fluidization velocity of wide PSD as follows:
U mf ,mix
xi / U mf ,i
NU
1
i
(6)
MA
Rowe et al. [33] proposed a semi-theoretical equation by extending Hatch’s
D
pressure-drop relationship for predicting the minimum fluidization velocity of
TE
mixtures. The particles with various sizes should have same shape, density, and the correlation is as follows:
CE P
U mf ,mix
U mf ,1 U mf ,1 f ( ) x1 U mf ,2
n /(3n )
x2
(13/ n )
,
(7)
AC
where n can be taken to be 1.053, an empirical value. The f (ε) is function of the bed voidage and the result of f (ε) is 0.92 in our experiment. Experimental data of Umf of each narrow PSD were taken into Eq. (5，6， 7) and the results were described in Fig. 9. Fig. 9 shows the comparison of predicted results of Umfs through using the Eq. (5), the Eq. (6), and the Eq. (7), respectively. It can be found that the predicted results by using the Eq. (7), which has an average relative error of 5.41%, is closer to the experimental data than those predicted by using the Eq. (5)and the Eq. (6), which have average relative errors of 13.71% and 10.02%, respectively. It should be noted 15
ACCEPTED MANUSCRIPT that, in addition to the requirement that the particles should have same densities and shapes, the information of the bed void fraction is required as the input for the Eq. (7)
IP
T
developed by Rowe et al. For the wide PSD, if the bed void fraction can be obtained,
SC R
Rowe equation is recommended. From the results of these three predicting equations in Fig. 9, when the bed void fraction at the incipient fluidization cannot be obtained or the particles with different shapes and densities, the harmonic averaging of Umf of
NU
mixtures would be better than the arithmetic average.
MA
3.3 Bed expansion
D
The height of the bed expansion in a fluidized bed varies in a complex manner
TE
depending on the hydrodynamic properties of the bed, such as the initial bed height,
CE P
the particle density, the gas velocity, the gas viscosity, and the pressure. Several correlations have been proposed to predict the bed expansion. Some of them are based
AC
on the two-phase theory [34, 35], which is not suitable to predict the bed expansion at high pressures [11] and others add to this the growth of bubbles [36, 37]. Fig. 10 illustrates the variation of the expansion ratio (δ =H/Hmf) with increasing the excess gas velocity (U-Umf) for the four narrow PSDs particles. It can be observed that the increase in the bed expansion with the excess fluidized velocity was nearly linear for the four type’s particles at elevated pressures. A less excess fluidized velocity U-Umf, for the initial bed expansion was required at higher pressure. With increasing the pressure, at the same excess fluidized velocity, the buoyancy force and the drag force acting on the fluidized particles would increase and the interparticle
16
ACCEPTED MANUSCRIPT distance would increase. Therefore, the higher pressure primarily caused the increase in the bed expansion. In this study, at the same excess fluidized velocity, the bed
IP
T
expanded to a higher level at high pressure than that at low pressure, and the bed
particles (Geldart group D), as shown in Fig. 10.
SC R
expansion of small particles (Geldart group B) was slightly less than that of large
Based on the experimental data in this study, a correlation, which based on the
NU
excess gas velocity, the minimum fluidization velocity, the particle diameter, and the
MA
density of fluidizing gas has been developed in order to estimate the bad expansion using the regression analysis. The standard deviation and correlation coefficient were
D
0.0981 and 0.9345, respectively. The obtained equation is as follows.
TE
0.154 0.0846 2.58(U U mf )0.2014U mf g H 0.1004 H mf dp
(8)
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Fig. 11 shows the comparison between the experimental data and the predicted values using Eq. (8). The correlation developed for the bed expansion agreed well
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4. Conclusion
This work presents an experimental study on the effects of the PSDs and the pressure on the minimum fluidization velocity. The values of Umf of the wide PSDs were different at pressures below 0.9 MPa, whereas these differences tended to disappear with a further increase in the pressure. The minimum fluidization velocity of the Gaussian-type PSD has almost at the same velocity as the reference-type PSD at atmospheric pressure. Interestingly, all mixtures of wide PSDs had very different 17
ACCEPTED MANUSCRIPT hydrodynamic behaviors compared to the reference-type narrow PSD at elevated pressures, and their hydrodynamic behaviors tended to be similar at high pressures. A
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new correlation for predicting Umf of the narrow PSD was developed by modifying
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the Ergun equation. In the narrow PSDs, the proposed equation properly predicted the minimum fluidization velocity of spherical polystyrene particles in a 3D bed at a wide range of pressures. In order to predict the minimum fluidization velocity of powders
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of the wide PSDs, three existing correlations were tested for fitting the experimental
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results, and it was found that Rowe’s equation was better than the other two equations for predicting the Umf of wide PSD under the operation conditions in this study.
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Fluidized-bed expansion almost increased under the same excess fluidized
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velocity with increasing the pressures. The correlation used for predicting the bed
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expansion showed reasonable agreement with the experimental data.
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ACCEPTED MANUSCRIPT Nomenclature
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Binary PSD considered narrow cut diameter (mm) powder harmonic average diameter (mm) Flat PSD Gaussian PSD =9.8m/s2, acceleration of gravity Height of expanded bed (cm) Bed height at incipient fluidization (cm) Pressure (MPa) standard atmospheric pressure (MPa) pressure drop（Pa） Reference PSD Ternary PSD Minimum fluidization velocity (m/s) Minimum fluidization velocity of particles of dia. d1, d2,… (m/s) Superficial gas velocity (m/s) initial fluidization, complete fluidization velocity (m/s), respectively mass fraction of particles with mean diameter di bed expansion ratio, dimensionless void fraction; voidage of a bed of mixture, respectively, dimensionless void fraction in a bed at minimum fluidizing conditions, dimensionless voidage of bed consists of component 1, dimensionless gas viscosity (kg/m·s) solid density (kg/m3) fluidized gas density (kg/m3) sphericity of a particle, dimensionless
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B d1, d2, d3, d4, d5, di dp F G g H Hmf P PΘ ΔP R T Umf Umf,1, Umf,2… Uf，U Ufi, Ufc xi Greek letters Δ ε, εmix εmf ε1 μ ρp ρg φs Dimensionless numbers Ar Re
Archimedes number =dp3ρg(ρp-ρg)g/μ2 Reynolds number = dpUρg/μ
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ACCEPTED MANUSCRIPT Acknowledgement
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This work has been funded by the National Natural Science Foundation (NO.
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21506242) and Strategic Priority Research Program of the Chinese Academy of
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Sciences (NO. XDA07050100). Their supports are greatly appreciated.
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ACCEPTED MANUSCRIPT Appendix A. Details for calculating the Rowe’s equation
The equation for pressure drop through a porous body is
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2n U mf n S (1 ) 3n ) ( ) ( ) , g
(A.1)
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P / L k g (
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where S is the specific surface (i.e. 6/d for spheres). The value of n is among 1 to 2, which depends on the flow regime.
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The onset of fluidization occurs when the drag force is equal to weight of
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particles. P / L ( s g )(1 ) g
(A.2)
s g 1/ n (12/ n ) 1/ n mf3 ) ( ) g ( )1/ n S (13/ n ) 2n g g (1 mf )
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U mf k 1/ n (
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The Umf is found by combining Eq. (A.1) and Eq. (A.2).
(A.3)
d 6 ( x1 1 x2 ) , d1 d2
(A.4)
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S
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mf3 f ( s , g , )( )1/ n S (13/ n ) 2 n (1 mf )
where xi is the mass fraction of particles having d i as diameter. U mf
mf3 d1 1/ n 6 (13/ n ) f ( s , g , )( ) ( ) x x 1 2 (1 mf )2n d1 d2
mf3 ,1 6 U mf ,1 f ( s , g , )( )1/ n ( )(13/ n ) 2 n (1 mf ,1 ) d1 1/ n
U mf ,mix
1 1 2 n U mf ,1 ( mix )( ) 1 mix
d1 x1 x2 d2
(13/ n )
(A.5)
(A.6) (13/ n )
(A.7)
1/ n
1 1 2 n f ( ) ( mix )( ) 1 1 mix
(A.8)
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U mf ,mix
d U mf ,1 f ( ) x1 1 x2 d2
(13/ n )
(A.9)
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(13/ n )
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x2
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n /(3n )
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U mf ,mix
U mf ,1 U mf ,1 f ( ) x1 U mf ,2
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From Eq. (A.5), (d1/d2) can be written in place of (U1/U2)n/(3-n). Eq. (A.9) then becomes
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(A.10)
ACCEPTED MANUSCRIPT Reference
D.
Kunii,
O.
Levenspiel,
H.
Brenner,
Fluidization
Engineering,
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[1]
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Butterworth—Heinemann, New York, 1991.
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[2] D. Geldart, Types of gas fluidization, Powder Technol., 7 (1973) 285-292. [3] M. Siedlecki, W. de Jong, A.H.M. Verkooijen, Fluidized bed gasification as a
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mature and reliable technology for the production of bio-syngas and applied in the production of liquid transportation fuels-A Review, Energies, 4 (2011)
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389-434.
[4] T.F. McKenna, Polyolefin reaction engineering - An overview of recent
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developments, Macromol. Mater. Eng., 290 (2005) 507-510. [5] J.R. Grace, G. Sun, Influence of particle-size distribution on the performance of
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Eng. Chem., 41 (1949) 1099-1104. [7] G.L. Sun, J.R. Grace, Effect of particle-size distribution in different fluidization regimes, AIChE J., 38 (1992) 716-722. [8] D. Gauthier, S. Zerguerras, G. Flamant, Influence of the particle size distribution of powders on the velocities of minimum and complete fluidization, Chem. Eng. J., 74 (1999) 181-196. [9] C.L. Lin, M.Y. Wey, S.D. You, The effect of particle size distribution on minimum fluidization velocity at high temperature, Powder Technol., 126 (2002) 297-301. [10] C.Y. Wen, Y.H. Yu, A generalized method for predicting minimum fluidization 23
ACCEPTED MANUSCRIPT velocity, AIChE J., 12 (1966) 610-&. [11] D.C. Chitester, R.M. Kornosky, L.S. Fan, J.P. Danko, Characteristic of
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fluidization at high-pressure, Chem. Eng. Sci., 39 (1984) 253-261.
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[12] S.C. Saxena, G.J. Vogel, Measurement of incipient fluidization velocities in a bed of coarse dolomite at temperature and pressure, Trans. Inst. Chem. Eng., 55 (1977) 184-189.
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[13] M. Nakamura, Y. Hamada, S. Toyama, A.E. Fouda, C.E. Capes, An experimental
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investigation of minimum fluidization velocity at elevated temperatures and pressures, Can. J. Chem. Eng., 63 (1985) 8-13.
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[14] K. Doichev, N.S. Akhmakov, Fluidization of polydisperse systems, Chem. Eng.
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Sci., 34 (1979) 1357-1359.
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[15] A. Barbosa, D. Steinmetz, H. Angelino, Fluidization VIII, Laguerie and Large, Tour France, 1995.
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[16] Z.P. Zhu, Y.J. Na, Q.G. Lu, Effect of pressure on minimum fluidization velocity, J. Therm. Sci., 16 (2007) 264-269. [17] J.L. Ma, X.P. Chen, D.Y. Liu, Minimum fluidization velocity of particles with wide size distribution at high temperatures, Powder Technol., 235 (2013) 271-278. [18] D.F. King, D. Harrison, The dense phase of a fluidized-bed at elevated pressures, Trans. Inst. Chem. Eng., 60 (1982) 26-30. [19] P.A. Olowson, A.E. Almstedt, Influence of pressure on the minimum fluidization velocity, Chem. Eng. Sci., 46 (1991) 637-640. 24
ACCEPTED MANUSCRIPT [20] P.N. Rowe, The effect of pressure on minimum fluidization velocity, Chem. Eng. Sci., 39 (1984) 173-174.
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[21] S. Ergun, Fluid flow through packed columns, Chem. Eng. Prog., 48 (1952)
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89-94.
[22] S.P. Babu, B. Shah, A. Talwaldar, Fluidization correlations for coal gasification materials-minimum fluidization velocity and fluidized bed expansion ratio,
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AIChE Symp Ser, 74 (1978) 176-186.
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[23] J.R. Grace, Handbook of Mutiphase Systems, Hetsroni,G. ed., Hemisphere, Washington D.C., 1982.
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New York, 1971.
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[24] J.F. Richardson, Incipient fluidization and particulate systems, Academic Press,
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[25] J.L.P. Chen, D.L. Keairns, Particle segregation in a fluidized-bed, Can. J. Chem. Eng., 53 (1975) 395-402.
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[26] L. Cheung, A.W. Nienow, P.N. Rowe, Minimum fluidization velocity of a binary mixture of different sized particles, Chem. Eng. Sci., 29 (1974) 1301-1303. [27] S. Chiba, T. Chiba, A.W. Nienow, H. Kobayashi, Minimum fluidization velocity, bed expansion and pressure-drop profile of binary particle mixtures, Powder Technol., 22 (1979) 255-269. [28] A. Kumar, P. Sengupta, Prediction of minimum fluidization velocity for multicomponent mixtures, Indian J. Technol., 12 (1974) 225-227. [29] K. Noda, S. Uchida, T. Makino, H. Kamo, Minimum fluidization velocity of binary mixture of particles with large size ratio, Powder Technol., 46 (1986) 25
ACCEPTED MANUSCRIPT 149-154. [30] A.R. Otero, J. Corella, Fluidization of mixtures of solids of distinct
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characteristics. 1. Fluidization velocities, Anales De Quimica-International
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Edition, 67 (1971) 1207-&.
[31] E. Obata, H. Watanabe, N. Endo, Measurement of size and size distribution of particles by fluidization, J. Chem. Eng. Jpn., 15 (1982) 23-28.
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[32] J. Rincon, J. Guardiola, A. Romero, G. Ramos, Predicting the minimum
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fluidization velocity of multicomponent systems, J. Chem. Eng. Jpn., 27 (1994) 177-181.
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[33] P.N. Rowe, A.W. Nienow, Minimum fluidization velocity of multicomponent
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particle mixtures, Chem. Eng. Sci., 30 (1975) 1365-1369.
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[34] M.H. Peters, L.S. Fan, T.L. Sweeney, Reactant dynamics in catalytic fluidized-bed reactors with flow reversal of gas in the emusion phase, Chem. Eng.
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Sci., 37 (1982) 553-565. [35] C.Y. Shen, H.F. Johnstone, Gas-solid contact in fluidized beds, AIChE J., 1 (1955) 349-354.
[36] A.M. Xavier, D.A. Lewis, J.F. Davidson, The expansion of bubbling fluidized bed, Trans. Inst. Chem. Eng.,56 (1978) 274-280. [37] K. Hilligardt, J. Werther, Local bubble-gas hold-up and expansion behavior of gas solid fluidized-beds, Chem. Ing. Tech., 57 (1985) 622-623.
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Fig. 1. Scheme of the experimental set-up 1─fluidized bed column; 2─U-type
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differential pressure meter;3─pressure vessel;4─high speed camera; 5─computer system; 6─mass flow meter/controller; 7─cylinder; 8─tank; 9─heat exchanger; 10─ reciprocating
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pump; 11─Liquid nitrogen storage tank
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Fig. 2. PSD of the considered mixtures: (a) flat distribution powder; (b) Gaussian-type
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powder; (c) binary mixture; and (d) ternary mixture.
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Fig. 3. Relationship between minimum fluidization velocity and pressure for different mean
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diameter particles.
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Fig. 4. Correlations for the prediction of Umf plotted with experimental data
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Fig. 5. Comparison between experimental data and the predicted results: (A) d1=0.55 mm; (B) d2=0.70 mm; (C) d3= 0.90 mm; (D) d4=1.13 mm; (E) d5=1.34 mm.
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Fig. 6. Total pressure drop versus velocity profile for Gaussian-type powders
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Fig. 7. Comparison between the Umf, reference and Umf, mixtures at pressure
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Fig. 8. Effect of pressure on the Umf of different wide PSDs
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Fig. 9. Comparison of experimental data with the results of correlated equations: (A) flat
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PSD; (B) Gaussian-type PSD; (C) binary mixture; and (d) ternary mixture.
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1.125 mm; (D) 1.34 mm
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Fig. 10. Bed expansion vs. U-Umf at different pressures: (A) 0.55 mm; (B) 0.90 mm; (C)
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Fig. 11. Comparison of calculated bed expansion values with experimental data
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Graphical Abstract
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ACCEPTED MANUSCRIPT AB STRACT This paper presents an experimental study on the effects of elevated pressure and
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particle size distribution (PSD) on the minimum fluidization velocity (Umf) and the
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bed expansion. It was developed with Geldart B and D-type polystyrene particles.
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Four wide PSDs and five narrow PSDs were investigated. The four wide PSDs studied included a Gaussian distribution, a flat distribution, a ternary mixture, and a
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binary mixture, all with the same mean diameters. Operation pressure ranged from 0.1 MPa (absolute pressure) to 2.7 MPa. The results revealed that the Umfs of the wide
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PSDs were lower than that of the reference narrow PSD with the same diameter at
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pressures exceeding 0.3 MPa. The segregation tendency of wide PSDs decreases with
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the increase in the operating pressure. The four wide PSDs had obviously different Umfs at pressures below 0.9 MPa; however, this difference in the Umfs was gradually
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reducing with a further increase in the pressure (>0.9 MPa). The bed expansion increased with increasing the pressure at same excess fluidized gas velocity.
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Correlations basing on experimental data were proposed in order to predict the Umf and bed expansion for the narrow PSD at elevated pressures, and three correlations were investigated for predicting the Umf of wide PSD. Keywords: Gas-solid fluidization, Particle size distribution, Minimum fluidization velocity, Bed expansion, Pressure
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ACCEPTED MANUSCRIPT Highlights Different particle size distributions (PSDs) were studied at elevated pressure.
Wide PSDs have smaller Umf than the narrow PSD at the pressures above 0.3
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MPa.
The types of wide PSDs have little effect on the Umf at pressures above 0.9 MPa.
Correlations to predict Umf and bed expansion at elevated pressures were
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proposed.
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