Solids mixing in a dual-column slot-rectangular spouted bed

Powder Technology 301 (2016) 1264–1269

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Solids mixing in a dual-column slot-rectangular spouted bed Ziliang Wang, C. Jim Lim, John R. Grace ⁎ Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, Canada

a r t i c l e

i n f o

Article history: Received 9 March 2016 Received in revised form 4 June 2016 Accepted 29 July 2016 Available online 30 July 2016 Keywords: Dual-column slot-rectangular spouted bed Solids mixing Solids exchange coefficient Suspended partition

a b s t r a c t Solids exchange between two adjacent chambers was studied in a dual-column slot-rectangular spouted bed with a suspended partition, a geometry potentially useful for scale-up. Solids transfer between the chambers was quantitatively evaluated by the Lacey mixing index and a solids exchange coefficient. Effects of partition position, superficial gas velocity, static bed height and partition height on solids mixing were demonstrated. The solids exchange between the chambers was strongly influenced by partition position and superficial gas velocity. Static bed height had only a slight effect on solids mixing behavior. A shorter partition helped to promote solids exchange between the chambers. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Since being invented by Mathur and Gishler [1], spouted beds have been utilized in a number of processes, such as drying [2], coating [3], combustion [4], pyrolysis [5], reforming [6] and gasification [7]. The particle movement in such systems is a determining factor, regulating mass and energy transfer, and affecting chemical reactions. In the literature, studies on solids mixing have extensively focused on single-compartment spouted beds, and can be classified into two major categories: quantitative estimation of mixing rate [8–10] and explorations of solids mixing mechanics [11–15]. Solids mixing is often characterized by the residence time distribution [8,9]. Commercial applications of spouted beds have been limited by difficulties in scale-up [16]. Multiple slot-rectangular spouted beds provide a promising geometry to address the scale-up challenge [16–18]. In a continuously operated multiple spouted bed reactor, lateral mixing and exchange of reactant particles fed into the bed affect the residence time distribution of the reacting particles and hence the reactor performance. Since solids mixing is important for design and operation of spouted beds, Saidutta and Murthy [19] conducted stimulus-response experiments in four different rectangular configurations, including those with two and three spouting cells. They revealed the solids mixing behavior in columns operated in stable spouting. Gan et al. [20] studied experimentally the lateral mixing of particles in a quasi-slot-rectangular spouted bed by means of bed collapse experiments with a set of partitions. However, the central region of the bed operated as a fluidized bed in a turbulent state. Beltramo et al. [21] investigated the hydrodynamics of a multiple-compartment square-based reactor for solid state polymerization. They found that levels in the various sectors were ⁎ Corresponding author. E-mail address: [email protected] (J.R. Grace).

http://dx.doi.org/10.1016/j.powtec.2016.07.070 0032-5910/© 2016 Elsevier B.V. All rights reserved.

very hard to control, due to reciprocal interference between spouted bed cells at high solids throughout, related to the solids mixing and circulation in each cell. Akarregi et al. [22] developed a novel twointerconnected-spouted-bed system for improving heat integration efficiency in highly endothermic processes. They revealed that solids circulation between the contactors was a critical parameter for increasing the heat integration efficiency. The above review reveals that there has been little investigation of solids inter-compartment exchange in multiple spouted beds. The rate of mixing is important in determining the achievable homogeneity and the performance of multiple-stage units. Moreover, the mixing process in practical operation depends on the operating conditions. Therefore, it is important to explore solids mixing in multiple-compartment spouted beds. As mentioned above, the slot-rectangular geometry is beneficial in overcoming the scale-up challenge of spouted beds. An internal partition is essential for minimizing interference between compartments and in achieving stability in multiple spouted beds. In the present work, a dual-column slot-rectangular spouted bed reactor (DSRSB) with a suspended partition was investigated to address the scale-up issue, while also providing crucial information needed for the design and operation of dual-column slot-rectangular spouted bed reactors, e.g. for biomass torrefaction. A solids exchange coefficient is determined to characterize the solids exchange rate between adjacent compartments. The solids mixing between adjacent chambers is studied for different operating conditions of superficial gas velocity, static bed height, particle size, partition position and partition height. 2. Experimental set-up and procedure The configuration of the DSRSB column is shown schematically in Fig. 1(a). The column consists of a Plexiglas vessel, 300 × 100 mm in

Z. Wang et al. / Powder Technology 301 (2016) 1264–1269

Nomenclature C1 C2 Ci,t C dp Gair H0 Hd Hsp Ht Κse IL L Lslot Lsp m M n N p t U Ums W Wb Wslot Wsp

Concentration of tracer particles in left chamber at time t (−) Concentration of tracer particles in right chamber at time t (−) Concentration of tracer particles in sample i at time t (−) Average concentration of tracer particles (−) Particle diameter (mm) Mass flow rate of air (g/s) Static bed height (mm) Divergent base height (see Fig. 1) (mm) Suspended partition height (mm) Column height (mm) Solids exchange coefficient (−) Lacey mixing index (−) Column thickness (mm) Gas entry slot length (mm) Suspended partition width (mm) Solids exchange rate between compartments (g/s) Initial mass of particles (g) Number of particles in a sample (−) Number of samples (−) Proportion of one of the binary components in a sample (−) Time (s) Superficial gas velocity (m/s) Minimum spouting velocity (m/s) Column width (mm) Base width (mm) Gas entry slot width (mm) Suspended partition thickness (mm)

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cross-section, 800 mm in height, with a W-type lower divergent section with 60° inclination angles. A thin partition is suspended centrally and rigidly in the upper freeboard section to create two compartments of equal volume. Two horizontal-axis ports (A and B), just above the distributor, are available for insertion of a probe from the wall to measure the bed pressure drop. Two rectangular slots shown in Fig. 1(b) are located symmetrically at the base, and connected to an independent windbox of volume 4.5 L. The key particle properties, fluid properties and column dimensions are listed in Table 1. In order to quantitatively analyze the exchange of particles between the chambers, half of the original glass beads were painted red and half black. The red and black solids have virtually identical density, diameter and sphericity. The red particles were assigned to be tracers. The partition was first inserted into the upper section to separate the DSRSB into two independent compartments. The left compartment was next loaded with red tracer particles, while the right compartment was filled to the same height, H0, with black particles. The air flow rate was then adjusted to the desired value. When both compartments reached the same stable spouting state, the partition was quickly raised to its required position. After each pre-determined time, the air flow was rapidly terminated. Next a 4 mm thick vertical partition was inserted to divide the bed into two identical volumes. The particles from each compartment were then discharged by an electric vacuum, and ten 70 g samples were taken from the discharged particles for each column. The number of particles of each colour in the sampled mixture was then determined by an image analysis method with Adobe Photoshop CS4 software, and represented by the area of each colour in one picture. The tracer mass fraction ci of each sample was then calculated from the ratio of the area of the tracer particles divided by the total area of the particle mixture. Each experiment was repeated, so that each measured concentration is based on 20 determinations.

Fig. 1. (a) Schematic and definition of symbols for two-compartment slot-rectangular spouted bed column, (b) top view.

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Table 1 Key properties of experimental particles, gas and DSRSB column. See Fig. 1 for definition of dimensions.

ln ð2C 1 −1Þ ¼ −

Value Particles Diameter, dp (mm) Density, ρp (kg/m3) Sphericity, Φ (−) Angle of repose (°)

Red 1.16, 1.61, 2.85 2530 1.0 22.0, 20.4, 22.8

Gas (at 20 °C and 1 atm) Density, ρg (kg/m3) Viscosity, μg (kg/m · s) Superficial spouting velocity, U (m/s)

1.2 1.88e-5 0.34–1.4

Column Overall height, Ht (mm) Width, W (mm) Thickness, L (mm) Base width, Wb (mm) Gas entry slot width, Wslot (mm) Gas entry slot length, Lslot (mm) Divergent base height, Hd (mm) Included base angle, θ (°) Suspended partition height, Hsp (mm) Suspended partition width, Lsp (mm) Suspended partition thickness, Wsp (mm) Gap between partition and bed surface, Δh (mm) Static bed height, H0 (mm)

800 300 100 25.4 4.0 30 120 60 100 and 300 100 6.35 20, 40, 60 150–210

After integration

Black 1.16, 1.61, 2.85 2530 1.0 19.9, 21.8, 23.3

2mt M

o 1n 1 þ e2mt=M 2

C1 ¼

ð5Þ

ð6Þ

For our purpose, we want to find m, which is obtained from Eq. (6) as m¼

M ln ð1−2C 1 Þ 2t

ð7Þ

This can be expressed in dimensionless form as Κse ¼

m M ln ð1−2C 1 Þ ¼ Gair 4ρg UAt

ð8Þ

where A is the cross-sectional area of each of the two equal compartments. 3.2. Lacey mixing index In order to quantitatively identify the solids mixing degree, we employ the well-known Lacey mixing index [23] to characterize the degree of mixing. The DSRSB has two sampling cells, the left and right chambers. The variance of the concentration in each sample is expressed as

3. Quantitative study of solids mixing Before initiating the flow, M g of red tracer particles were loaded into the left chamber (compartment 1), whereas M g of black particles were added to the right chamber (compartment 2). Initially, the weight fractions of tracer particles in the left and right chambers are C1 = 1 and C2 = 0, respectively. The variation in C1 and C1 with time t depends on the lateral exchange of solids between the chambers.

N  2 X C i;t −C

σ2 ¼

C¼

i¼1

N−1

N 1X C N i¼1 i;t

ð9Þ

ð10Þ

3.1. Solids exchange between chambers where N is the number of samples, Ci,t is the concentration of tracer parIt is assumed that: (a) each compartment is well mixed; (b) each compartment maintains a total mass of M g particles; (c) there is a constant mass flow of m from compartment 1 to compartment 2 and from compartment 2 to compartment 1. Mass balance for compartment 1: dðMC 1 Þ ¼ mC 2 −mC 1 dt Similarly for compartment 2:

ð1Þ

dðMC 2 Þ ¼ mC 1 −mC 2 dt

ð2Þ

ticles in sample i at time t, and C is the average concentration. The Lacey mixing index (IL) is then defined as IL ¼

σ 20 −σ 2 σ 20 −σ 2R

where σ20 and σ2R represent the variances of a completely segregated mixture and a completely random mixture, respectively. Hence σ 20 ¼ pð1−pÞ

ð12Þ

pð1−pÞ n

ð13Þ

σ 2R ¼

Initial conditions: at t ¼ 0; C 1 ¼ 1; C 2 ¼ 0

ð3Þ

But C 1 þ C 2 ¼ 1; i:e: C 2 ¼ 1−C 1

ð4Þ

ð11Þ

where p and (1− p) are the proportions of the two components determined from sampling, and n is the number of particles in each sample. 4. Results and discussion

Substitute Eq. (4) into Eq. (1), M

dC 1 ¼ mð1−2C 1 Þ dt

ZC 1 C 1 ¼1

dC 1 m ¼ 1−2C 1 M

Zt dt 0

Table 2 presents the minimum spouting velocities and maximum pressure drops for different operating conditions. As expected, these critical parameters are almost identical at the same operating conditions for the red and black particles. In addition, with increasing static bed height, the minimum spouting velocity and maximum pressure drop increase in a similar manner. Also as expected, larger particles give higher minimum spouting velocities and maximum pressure drops for a given static bed height.

Z. Wang et al. / Powder Technology 301 (2016) 1264–1269

1.1

Table 2 Experimental minimum spouting velocities and maximum pressure drops.

GB1.16⁎

150 180 210 150 180 210 150

GB1.61⁎

GB2.85⁎

1.0

ΔPmax (Pa)

Ums (m/s)

0.9

Black

Red

Black

Red

0.34 0.38 0.42 0.54 0.68 0.79 1.0

0.34 0.40 0.44 0.58 0.68 0.78 1.0

911 1230 1477 1243 1424 1625 1480

900 1206 1509 1293 1439 1600 1495

⁎ GB: glass beads; 1.16, 1.61 and 2.85: diameter of glass beads.

0.8 0.7 0.6

IL(-)

H0 (mm)

Particles

1267

0.5 0.4 0.3

4.1. Image analysis method

dp = 2.85 mm

0.2

In order to assess the validity of the image analysis method, samples of known tracer mass fraction were tested by the image analysis method. Each sample contained a 70 g mixture of red and black glass beads. The glass beads were in a single layer, when each sample was photographed. As shown in Fig. 2, measured values are in good agreement with true values based on the image analysis method, with maximum absolute deviations of 1.0%, 2.2%, and 2.0% for the 2.85, 1.61 and 1.16 mm glass beads, respectively. Therefore, the image analysis method is capable of providing accurate results.

dp = 1.61 mm

0.1

t'2

t'1

0.0 0

100

200

300

400

t'3 500

dp = 1.16 mm 600

700

800

Time (s) Fig. 3. Lacey mixing index for glass beads of three sizes with H0 = 150 mm, U = 1.2Ums, and Δh = 20 mm; t' is the time to reach equilibrium.

which promotes particle mixing. Note that 1.2Ums corresponds to 1.2 m/s, 0.67 m/s, and 0.41 m/s for the 2.85, 1.61 and 1.16 mm glass beads, respectively, at a static bed height of 150 mm.

4.2. Evolution of solids exchange with time After a long time, it is expected that each compartment should approach 50% tracer particles, corresponding to a completely random mixture. This was indeed the case for the 2.85 mm and 1.61 mm particles. However, in the case of the 1.16 mm glass beads, the net transferred tracer mass fraction approached a maximum value of 42%, indicating that 16% of the tracer particles were in a dead zone for these smaller glass beads. Fig. 3 plots the Lacey mixing index against time for the three sizes of glass beads tested. The mixing index shows the same trend for all cases. The maximum Lacey mixing indexes for the 2.85 and 1.61 mm glass beads approach unity, whereas for the 1.16 mm glass beads, the maximum is ~0.95. The elapsed times to reach the maximum mixing index were ~180, 420 and 540 s for the 2.85, 1.61 and 1.16 mm glass beads, respectively. The differences are attributed to different superficial velocities. A higher superficial gas velocity results in faster particle motion,

4.3. Effect of suspended partition position In principle, the DSRSB does not require a partition [17], but a partition stabilizes the flows, reduces intermingling of the fountains and prevents side-to-side percolation of gas from a spout into the corresponding annulus [24]. Fig. 4 shows that the partition position had a significant influence on the solids exchange between the chambers. As the gap (Δh) between the bottom of the partition and the top surface of particles increased from 20 mm to 60 mm, the magnitude of the solids exchange coefficient and the concentration of tracer particles increased by a factor of 2.2. The gap is the main area available for solids exchange between the chambers. Fountain spreading provides the principal mechanism for interchange of particles between the chambers [17]. When the partition was raised, the wider gap allowed more particles to pass in both directions, facilitating solids exchange.

100

dp = 2.85 mm

90

dp = 1.61 mm

Measured proportion (%)

80

dp = 1.16 mm

70 60 50 40 30 20 10 0 0

10

20

30

40

50

60

70

80

90

100

True proportion (%) Fig. 2. Comparison of measured and true mass fraction of tracer particles in mixtures.

Fig. 4. Effect of partition position on solids exchange coefficient and tracer concentration for 1.61 and 1.16 mm glass beads with H0 = 150 mm, U = 1.2Ums, t = 30 s.

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4.4. Effect of superficial gas velocity Fig. 5 reveals the effect of superficial gas velocity on the solids exchange between the chambers. The superficial gas velocity is seen to have had a secondary effect on the solids exchange. As the superficial gas velocity increased, the solids exchange coefficient increased and more solids exchanged between the chambers. This occurred because a higher superficial gas velocity resulted in faster particle motion, not only in the axial direction, but also in the lateral direction, which is helpful for particle mixing [25]. Moreover, the spout diameter increased as the gas flow increased [26], strengthening the spout intensity, and promoting solids circulation and flow into the fountain. 4.5. Effect of static bed height Fig. 6 presents the effect of static bed height on the exchange of solids between the chambers. The exchange coefficient increased as the static bed height increased at a given U/Ums. Slower axial mixing is expected in a deeper bed than in a shallower one [10,25]. With increasing static bed height, the gap (Δh') shown in Fig. 1 between the top of the divergent base and the bottom of the partition, available for solids exchange, increases and the fountain surface coverage declines. The enlarged gap is helpful in promoting solids exchange between the chambers. However, the reduction in fountain particles reaching the wall retards particle mixing. For the 1.61 and 1.16 mm glass beads, the gap effect was predominant as shown in Fig. 6. Overall, although there was less fountain coverage, solids exchange in the lateral direction increased slightly as the static bed height increased for the cases considered here. 4.6. Effect of partition height The suspended partition prevents the fountains from merging, and improves the stability of the DSRSB [27]. However, it also impedes solids exchange between the chambers. Fig. 7 shows the effect of the partition height on solids exchange between the chambers. Both chambers of the DSRSB contained stable overdeveloped fountains, i.e. the outermost returning particles bounced off the column wall. Less time was required to reach equilibrium when a shorter partition was used in the experiments. The average fountain height for the 1.61 mm glass beads with H0 = 150 mm, U = 1.2Ums, and Δh = 20 mm was 175–184 mm for partition heights of 100 and 300 mm. Since the fountain height exceeded the sum of the 20 mm gap (Δh) and the 100 mm height of the shorter

Fig. 6. Effect of static bed height on solids exchange coefficient and tracer concentration for 1.61 and 1.16 mm glass beads with U = 1.2Ums, Δh = 20 mm, t = 30 s.

partition, solids exchange occurred not only through the gap (Δh'), but also over the top of partition in the case of the shorter partition. Fig. 8 demonstrates that a higher solids exchange coefficient was obtained with the 100 mm partition height than with the 300 mm partition height. The dependence of the solids exchange coefficient on time was the same for the short and long partitions. The magnitude of the solids exchange coefficient was less than unity, indicating that most of the energy of the air was used to accelerate particles in the vertical direction, rather than to facilitate solids exchange in the lateral direction. In addition, the solids exchange coefficient decreased slightly as time elapsed because the difference between the tracer concentrations in the two chambers was becoming smaller with time, and particles which had traveled from one side to the other were then included in those transferring in the opposite direction. For a DSRSB running a continuous process with feeding from one side and discharge from the opposite side, it is seen to be possible to promote solids mixing between chambers by reducing the height of the suspended partition.

1.0

0.8

IL (-)

0.6

0.4

Hsp = 300 mm

0.2

Hsp = 100 mm 0.0 0

100

200

300

400

500

600

700

800

Time (s) Fig. 5. Effect of superficial gas velocity on solids exchange coefficient and tracer concentration for 1.61 and 1.16 mm glass beads with H0 = 150 mm, Δh = 20 mm, t = 30 s.

Fig. 7. Evolution of Lacey mixing index in the DSRSB with 100 mm and 300 mm partition heights for 1.61 mm glass beads, H0 = 150 mm, Δh = 20 mm, U = 1.2Ums.

Z. Wang et al. / Powder Technology 301 (2016) 1264–1269

1.0

1269

Acknowledgement

0.9

Hsp = 300 mm

0.8

Hsp = 100 mm

Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and a scholarship from the China Scholarship Council (CSC) are acknowledged with gratitude.

0.7

Κse(-)

0.6

References

0.5 0.4 0.3 0.2 0.1 0.0 0

100

200

300

400

500

Time (s) Fig. 8. Solids exchange coefficient for 100 mm and 300 mm partition heights for 1.61 mm glass beads, H0 = 150 mm, Δh = 20 mm, U = 1.2Ums.

5. Conclusions (1) Comparison of glass beads of diameter 2.85, 1.61 and 1.16 mm shows that exchange of larger particles between compartments reached an equilibrium composition in less time in the dualcolumn slot-rectangular spouted bed than for smaller particles, in each case operating with a superficial gas velocity equal to 1.2 times the minimum spouting velocity. (2) The effect of the partition position on solids exchange between the compartments was more important than other factors, with a larger gap leading to faster exchange. (3) A shorter partition accelerated solids exchange between the compartments by allowing some fountain particles to pass over the partition. (4) Increasing the superficial gas velocity caused a significant increase in solids exchange. (5) The static bed height had only a slight influence on solids exchange for the range of conditions investigated.

Greek symbols Δh Gap between bottom of partition and static bed surface (mm) Δh' Distance between top of diverging base to bottom of partition (see Fig. 1) (mm) ΔPmax Maximum pressure drop (Pa) θ Included base angle (°) μg Gas viscosity (kg/m · s) ρg Air density (kg/m3) ρp Particle density (kg/m3) σ2 Variance of concentration of tracer particles in a mixture (−) σ20 Variance of concentration of tracer particles in a completely segregated mixture (−) σ2R Variance of concentration of tracer particles in a completely random mixture (−) Φ Particle sphericity (−)

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