Spouting Characteristics of Wet Particles in a Conical-Cylindrical

Sep 28, 2015 - Moreover, it is found that the maximum spoutable bed height Hmax decreases as particle size or spout nozzle diameter ... C.M. Boyce. Po...
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Spouting Characteristics of Wet Particles in a Conical-Cylindrical Spouted Bed Huibin Xu,†,‡ Wenqi Zhong,*,† Aibing Yu,‡,§ and Zhulin Yuan†,‡ †

Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing 210096, P.R. China ‡ Centre for Simulation and Modelling of Particulate Systems, Southeast University−Monash University Joint Research Institute, Suzhou 215123, P.R. China § Department of Chemical Engineering, Monash University, Clayton, Vic 3800, Australia ABSTRACT: Spout characteristics, such as flow pattern, minimum spouting velocity, and maximum spoutable bed height, are investigated in a wet conical-cylindrical spouted bed. Water and glass beads (Geldart D type) are adopted as the liquid and solid phases, respectively. The evolution of flow pattern of a wet spouted bed is captured by a CCD camera. The experimental results indicate that the minimum spouting velocity decreases when increasing the liquid saturation. The increase of initial bed height, particle size, or spout nozzle size leads to increased minimum spouting velocities. A correlation is formulated based on the experiments results for the prediction of minimum spouting velocities of wet spouted beds. Moreover, it is found that the maximum spoutable bed height Hmax decreases as particle size or spout nozzle diameter increases. However, Hmax is almost constant, approximately 1.5 times higher than that of its corresponding dry spouted bed, when increasing the liquid saturation.

1. INTRODUCTION Wet spouted beds are widely used for different applications, such as petro-chemical,1 granulation,2 particle coating,3 bio-oil refining,4,5 solutions drying,6 and environmental protecting7,8 processes. They have excellent fluid−solid contact characteristics, similar to wet fluidized beds. Besides, wet spouted bed reactors can handle large particles and provide regular particle circulation. Because of these features, wet spouted beds are found to be useful and effective. However, it is difficult to use the wet spouted bed technology in large scale industrial processes because the knowledge about its hydrodynamic characteristics is limited. The spouting characteristics of wet spouted beds are different from those of dry spouted beds. The wet spouting process is more complicated than the dry spouting process because of various effects from liquid phase. Several investigations have been made on wet spouted beds in the past. For example, Vukov et al.9 experimentally investigated the bed pressure drop and bed expansion of a wet spouted bed contactor. Nagahashi et al.10 claimed that introducing a little liquid into a spouted bed can enhance the spouting process. Oliveira et al.11 researched the instability of wet spouted bed and investigated the feasibility of detecting instability via pressure fluctuation time-series analyses. Passos et al.12 analyzed the effect of capillary force on the agglomeration in wet spouted bed and fluidized bed. On the basis of antiparticle force analysis, Bacelos et al.13 argued that the interparticle forces can evidently affect the gas−solid flow behavior. Schneider et al.14 investigated the effect of liquid addition on spouting characteristics including stability of spouting, spouting velocity, bed pressure drop, and fountain height. They claimed that the liquid content and the cohesive forces were the key factors affecting the spouting behavior. Neto et al.15 investigated the effect of paste adding on the © 2015 American Chemical Society

hydrodynamic characteristics of a spouted bed, focusing on the bed pressure drop and the minimum spouting velocity. Understanding the hydrodynamic characteristics is important to the successful scale up of a wet spouted bed reactor from lab to industrial scale. However, to date, many important and essential hydrodynamic characteristics are unknown. For instance, it is well-known that some factors, such as the initial bed height, gas inlet nozzle diameter and particle size, can significantly affect the spouting process of a dry spouted bed.16 But for a wet spouted bed, all these issues are still unknown. Are they similar to the dry spouted bed? How to estimate the minimum spouting velocity Ums in a wet spouted bed? Will the maximum spoutable bed height Hmax be changed when adding some water into a spouted bed? These questions have not been properly answered yet. Actually, Ums and Hmax are two basic parameters when designing and operating a spouted bed, because they can determine the amounts of gas and solids for stable operation. However, there seem to be few previous investigations in the literature aiming to answer the above important questions. To answer these questions, spouting characteristics of wet conical-cylindrical spouted beds are experimentally investigated in the present work. The main target is to examine the changes of wet spouting characteristics for different liquid saturation S, initial bed heights H0, spout nozzle diameters Di, and particle diameters dp. The hydrodynamic characteristics of a wet spouted bed, such as the minimum spouting velocity, flow pattern, and maximum spoutable bed height, are examined in Received: Revised: Accepted: Published: 9894

July 25, 2015 September 22, 2015 September 28, 2015 September 28, 2015 DOI: 10.1021/acs.iecr.5b02742 Ind. Eng. Chem. Res. 2015, 54, 9894−9902

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Industrial & Engineering Chemistry Research

conclusions drawn in the present work correspond to nonhygroscopic particles.

this work. The influence of the liquid bridge force on the spouting process is qualitatively explored.

2. EXPERIMENTAL METHOD 2.1. Experimental Setup. The experimental spouted bed which has been well shown in our previous work17 contains a gas supply system, a conical-cylindrical Plexiglas column, a pressure signal sampling system, an image recording system, and a water adding system. It is schematically plotted in Figure 1. The inside diameter of the cylindrical column is 140 mm and

Table 1. Particle Properties glass beads

dp (mm)

δ(%)

ρp (kg/m3)

ε

particle A particle B particle C

1.9 2.6 3.3

6.5 5.4 4.1

2600 2600 2600

0.39 0.37 0.37

Water is used as the liquid phase in our experiments. Meanwhile, the liquid content in the bed is illustrated by the average liquid saturation S.13 The S is defined as the ratio of liquid volume to the void volume of initial particle packed bed.19 S=

Vl 1 − ε Vl = ε Vp Vvoid

(1)

where Vl is the volume of liquid, Vvoid is the void volume of the initial packed bed, ε is the particle packing voidage fraction, and Vp is the true volume of particles. When the wet spouted bed is operated, water will be lost because spouting air can carry water vapor off the bed. Accordingly, the loss of water in the bed is supplied by a graduated buret in our experiments. To calculate the amount of loss water, the humidity of inlet and outlet air is obtained via the thermo hygrometer. The volume of loss water can be computed based on the difference between them.17 During our experiments, the initial bed height H0 and liquid saturation S are increased gradually by adding the volume of particles and water stepwise. Two metering tanks are used to measure the volumes of particles and water, respectively. The different volumes of particles are added into the bed for setting up different experimental conditions of initial bed height until reaching the maximum spoutable height. The liquid saturations are controlled in the range of S ≤ 0.2 for stable spouting.17 To ensure a relative uniform concentration of water in the bed, spouting the mixture is conducted for 5 min before our measurement. Each test is done three times for the sake of accurate experimental data. The main experimental conditions are shown in Table 2.

Figure 1. Experimental setup of wet conical-cylindrical spouted bed: (1) roots-type blower; (2) control valve; (3) rotor flow meter; (4) spouted bed; (5) glass beads; (6) computer; (7) pressure signal sampling setup; (8) digital camera; (9) digital thermo hygrometer; (10) buret.

the height is 1000 mm. An 85 mm height and 60° cone angle conical base is located at its bottom. Different diameters of spout nozzles (16/20/25 mm) are used in our experiments. The spouting air supplied by a Roots-type blower is jetted into the bed through the spout nozzle. The air flow rates can be adjusted by a valve and measured by rotor flow meter for the range 10−100 m3/h. The bed pressure data are obtained by the pressure signal sampling system with a scale of 0−50 kPa and then recorded by computer. Two pressure taps are fixed on the spouted bed for measuring the bed pressure drop. One of taps is located on the spout nozzle. Meanwhile, another tap is located on the column at the height of 800 mm. The flow patterns of the wet spouting are investigated by a half conical-cylindrical spouted bed during our experiments.18 The size of this half bed is the same as the entire bed described above except it is only half. A digital camera (Nikon Coolpix L200) is used to record the internal structural of spouting. 2.2. Experimental Procedure. Three kinds of nearly spherical glass beads (Geldart D type) are used in our experiments. The particle properties are presented in Table 1. The particles used are glass beads which means that all the

Table 2. Experimental Conditions H0 (mm)

dp (mm)

Di (mm)

S

Q (m3/h)

120−700

1.9/2.6/3.3

16/20/25

0−0.2

10−100

3. RESULTS AND DISCUSSION 3.1. Flow Pattern of Wet Spouting. The spouting process of wet particles is illustrated in Figure 2. It is very similar to the dry spouting process. The upward-flowing air stream which is jetted from the spout nozzle into the column creates drag and buoyancy forces on the particles.20 When the gas velocity is high enough (Q = 20 m3/h for this experiment) to push particles aside from the spout, a small but stable vertical jet is established. Further increase of the fluid flow rate (Q = 30 m3/ h) expands the jet, and an obvious internal spout is established. Finally, the upper bed surface is broken by the internal spout after further increase of the spout gas velocity, which leads to the formation of an external spout. A beautiful fountain forms at this moment (Q = 35 m3/h). Then, the height of this 9895

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Figure 2. Evolution of flow pattern in wet semiconical-cylindrical spouted bed (S = 0.1, dp = 2.6 mm, H0/D = 1.43).

fountain increases with the increase of the spouting gas flow rate (Q = 45 m3/h). A very important difference between wet and dry particle spouting processes is the stability of spouting. Some researchers have found that the stability of the wet spouting is lower than that of the dry spouting.14 One of the typical phenomena is that the fountain of wet spouting sometimes turns to be oblique as illustrated in Figure 2. This phenomenon has been observed not only in our experiment but also in Oliveira’s experiment.11 It may be caused by the unequal liquid content distribution.21,22 To get a stable spouting process, it looks like that the spouted bed with a draft tunnel will be more suitable for the wet spouting process than the conventional spouted bed without a draft tunnel. Another new unstable spouting phenomenon observed in our present experiments is the defluidization as illustrated in Figure 3. The defluidization is more likely to be observed when the flow rate of spouting gas is low or the liquid saturation (S) is high under the low initial bed height condition. The defluidization phenomenon observed in our current experiment is very similar to those in sticky solids spouted reactors.23 It could be easy to understand this similarity between wet particle and sticky particle because both of them are affected by the bond force between particles. To some degree, the wet particle system can be regarded as one kind of the sticky particle systems. 3.2. Minimum Spouting Velocity Ums. In our experiments, to obtain the minimum spouting velocity Ums, the gas flow rate is increased first for the spouting process happening, and then is decreased gradually.20 Usually, two different Ums values can be obtained during this process. One of them is the ascending Ums, the other is the descending Ums. Figure 4 shows the effect of spouting air velocity Ui (inlet based) on the bed pressure drop ΔP under the condition of gas inlet diameter Di = 16 mm, particle diameter dp = 1.9 mm, initial bed height H0 = 195 mm and liquid saturation S = 0.1. The gas flow rate was changed gradually with a step of 5 m3/h. The spouting gas velocity Ui accompanied by a sharp reduction/rise in the bed pressure drop ΔP was taken as Ums. As shown in Figure 4, the ascending Ums (inlet based) for the wet glass beads is about 65 m/s, and the descending Ums (inlet based) is about 55 m/s.

Figure 3. Top view of the defluidized bed at completion of the experiment.

The evolution of the pressures-drop-versus-gas-velocity curve obtained from the wet particles spouting process is similar to that obtained from the dry particles spouting process. The changes of bed pressure drops with gas flow rate ascending and descending are very different. It is because the particle compaction and the longer packed section above the internal spout in the flow ascending process create the extra resistance.20 In all our next experiments, the gas flow decrease process was selected to measure the Ums, following conventional practice. For determining the accurate value of Ums, the gas flow rate was decreased with a small step of 2m3/h until the external spout collapsed. Figure 5 presents the effect of liquid saturation S on the minimum spouting velocity Ums, at the spout nozzle diameter Di = 25 mm. As shown in this figure, the main trend is that the Ums decreases when S for wet particles increases. Generally speaking, the liquid could affect the spouting process in many ways,12 such as adding liquid bonds force 9896

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between particles, changing annular voidage, improving the particle slip ability and so on. Actually, the former two effects are likely to be the most important factors. In the wet spouted bed, the liquid bond effect can show its influence in all regions, that is, spout region, annulus region, and fountain region as illustrated in Figure 6. The liquid bond affecting in these different regions will lead to some special phenomena which are very different from the dry particle spouting. To put it simply, effect ① may lead to the agglomeration in spout and fountain region. Effect ② may lead to the particle near the column cling on the internal surface. Effect ③ may decrease the particle flow velocity from the annulus region to spout region. Effect ④ may impede the particle initial accelerating process in the spout region. At the initiation state of spouting, effects ③ and ④ may be the most important factors. Because of effect ③, the solid circulation rate of the wet spouted bed decreases apparently. This means that the voidage of spout region in the wet spouted bed is higher than that in the dry spouted bed. The resistance in spout region of the wet spouted bed decreases correspondingly. More proportion of the spouting gas flows through the spout region. Finally, it is easy to spout for the wet spouted bed. The influence of effect ④ will be further discussed. At the mean time, the voidage of the spouted bed is changed due to liquid added into the bed. It is well-known that the void state of annular region will affect the spouting. The annular region would be more consolidated because liquid occupies the void volume of the bed. Consequently, the resistance in the annulus would be increased. Under these circumstances, the spouting gas is difficult to diffuse into the annular region which increases the rigidity of the spout jet. Accordingly, Ums decreases with the increase of liquid saturation. In summary, after adding liquid into the spouted bed, the minimum spout velocity will reduce due to the decrease of the annulus solids circulation rate and the voidage of annular region. Figure 7 shows the effect of initial bed height (H0/D) on the Ums, at the gas inlet diameter Di = 25 mm. The results show that Ums increases with the increases of the initial bed height for both dry and wet particles. In a dry spouted bed, the changes of Ums with initial bed height have been widely studied by many

Figure 4. Effect of the inlet-based spouting gas velocity on bed pressure drop (dp = 1.9 mm, Di = 16 mm, H0/D = 1.4, S = 0.1).

Figure 5. Effect of liquid saturation on the Ums (H0/D = 1.89, Di = 25 mm).

Figure 6. Schematic representation of liquid bond effect in wet spouted bed. 9897

DOI: 10.1021/acs.iecr.5b02742 Ind. Eng. Chem. Res. 2015, 54, 9894−9902

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Industrial & Engineering Chemistry Research ReP =

εgρg |ug − vp|d p μ

(4)

where dp is the particle diameter. But in a multi-particle system, the effect of surrounding particles must be considered and the drag coefficient can be revised by the Wen−Yu equation:29 C D = C D0εg−4.7

(5)

2. Liquid Bridge Force FLB. The liquid bridge force FLB is the sum of the static capillary force Fcap and the dynamic viscous force Fvis. a. Static Capillary Force Fcap. The capillary force Fcap caused by the liquid bridge between two adjacent particles consists of two components: a surface tension and a reduced static pressure.14,15,30 It can be calculated from eqs 6−8. Figure 7. Effect of initial bed height on the Ums (dp = 2.6 mm, Di = 25 mm).

Fcap = πd pσ sin 2 β +

researchers. The particles are rapidly accelerated by high velocity gas jet at the inlet zone during the spouting process.24−26 Assuming that a particle from the annulus entering the bottom of the spout is instantly accelerated to an upward velocity Vp due to drag force, and then Vp decelerates to zero because of gravity at the height (H) of the bed surface (loose packed bed) under the minimum spouting condition, by using simple Newtonian dynamics, an equation can be obtained: Vp = (2gH)1/2.27 Then, considering the relationship between Vp and Ums we can have Ums ∝ (2gH)1/2. This relationship has been widely approved by many previous experimental results. According to Figure 7, the minimum-velocity-versus-bedheight curve for wet particles is almost the same as that for dry particles which indicates that the assumption from Ghosh et al.27 is also reasonable for wet spouting. To some extent, it means that the liquid bond almost does not affect the initial particle acceleration process. Accordingly, the effect ④ in Figure 6 even could be neglected for initial spouting. This point can be proven by the analysis of force acting on the particle in the spout region. To explain and understand the mechanism of presenting different hydrodynamic behaviors between wet and dry spouted bed, the key is the analysis of the force that acted on the particle. In the spout region, for a single particle, the particle was mainly accelerated by drag force. Therefore, the liquid bond force FLB has been compared with the drag force FD in the present work. 1. Drag force FD. It is well-known that the drag force on a single particle can be calculated by FD =

1 2 ρv C DA 2

C D0

(6)

1 1 2 cos(β) + = R1 R2 dp 1 − cos(β)

(7)

0.26 ⎡ V⎤ β ≈ ⎢(1 − ε) l ⎥ Vp ⎥⎦ ⎢⎣

(8)

b. Viscous Force Fvis. Besides the static capillary force, the viscous resistance arises during the movement of particles in the liquid due to the liquid shear flow between particles. For a Newtonian fluid, the viscous force in the normal direction Fv,n can be calculated from31 1 Fv,n = 6πμR *2 Vr,n (9) D R (10) 2 where Vr,n is the relative velocity in the normal direction and D is the minimum separation distance between two surfaces. The viscous force in the tangential direction Fv,t can be calculated using the equation given by Goldman:32 R* =

⎛8 ⎞ R* Fv,t = 6πμR *Vr,t⎜ ln + 0.9588⎟ ⎝ 15 ⎠ H

(11)

where Vv,t is the relative velocity in the tangential direction. An optional experimental case is chosen. For example, when particle diameter dp = 2.6 mm, initial bed height H0 = 265 mm, liquid saturation S = 0.1, inlet diameter Di = 20 mm, the minimum spouting velocity Ums is about 56.6 m/s. On the basis of this experimental case, the force balance analysis on the initial spouting particle is done. Assuming the voidage of the bottom zone in spout region ε = 0.86, when air density ρ = 1.2 kg/m3 and gas velocity Ums = 56.6 m/s (inlet based), using eq 2, the calculations indicate that FD acting on the glass beads is 9.1 × 10−3 N. The rupture distance at which the bridge is broken is usually given33 by Hrub = (1 + 0.5θc)V*1/3, but the volume of liquid bridge in this equation is very hard to determine. So another equation Hrup ≈ (0.8−1.4)dp which is obtained from experimental measurement34 is used in our research. Accordingly, the rupture distance Hrup in this case is 3.6 mm. Neglecting other resistance force, under the effect of drag force,

(2)

In a single-particle system, the drag coefficient CD equals the standard drag coefficient CD0 which can be calculated from the correlations based on the particle Reynolds number:28 ⎧ 24 0.687 ) (Rep < 1000) ⎪ (1 + 0.15Re Re ⎨ = ⎪ 0.44 (Rep ≥ 1000) ⎩

⎛1 π 2 1 ⎞ + d p σ sin 2 β ⎜ ⎟ 4 R2 ⎠ ⎝ R1

(3) 9898

DOI: 10.1021/acs.iecr.5b02742 Ind. Eng. Chem. Res. 2015, 54, 9894−9902

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Industrial & Engineering Chemistry Research the maximum velocity that the particle can achieve is 1.65 m/s before the liquid bridge breaks (Hrup = 3.6 mm). Then this value of the maximum departure velocity (i.e., Vr,n = 1.65 m/s) can be used in eq 9 to calculate the viscous force. For calculating the liquid bridge forces, a few assumptions are made in our analysis: (i) The viscous force in the tangential direction Fv,t is neglected. (ii) The minimum separation distance is treated as a fitting parameter, D = 5 μm, as done in the work of Liu et al.35,36 When water surface tension σ = 0.071 N/m and viscosity μ = 0.001 Pas, the calculations indicate that, at the relative collision velocity of v = 1.65 m/s, Fvis for a liquid bond acting on the glass beads is 2.63 × 10−3 N and Fcap is 6.03 × 10−4 N. Thus, the liquid bridge force FLB is about 3.2 × 10−3 N. From the analysis above, it can be found that the viscous force is important in spouted beds. The energy loss due to liquid viscosity is larger than that caused by capillary force. But in the spout region, the force induced by liquid bone is much lower than the drag force. Meanwhile, the action time of the liquid bond force is very short. In this aspect, the effect of the liquid bridge on the initial spouting process can be neglected. Finally, the changes of Ums for wet particles with the initial bed height H0/D show similar trends to spouting of dry particles; that is, Ums ∝ (2gH)1/2. Figure 8 illustrates the minimum spouting velocity Ums as a function of particle diameter, at the initial bed height H0 = 230

Figure 9. Effect of gas inlet diameter Di/D on the Ums (dp = 2.6 mm, H0/D = 1.89).

in a wet spouted bed. These trends are similar to the trends in the dry particle spouting process. 3.3. Correlation of Minimum Spouting Velocity Ums. Because the wet spouting process is similar to the dry spouting, it is easy to think that the correlation of Ums for wet spouted bed can be revised from the correlation of Ums for dry spouted bed by considering the effect of liquid saturation S. As we know, for dry particle spouted bed, we can assume that20 Ums = f (Di , D , H , dP , ρp − ρ , ρ , g )

(12)

In a wet particle spouted bed, there are two kinds of extra factors that can affect the Ums, such as adding liquid bonds force between particles and changing annular voidage. For a kind of definitive liquid (water, in our experiment), both of these effects can be related to liquid volume: FLB ∝ f (V )

(13)

P ∝ f (V )

(14)

where FLB is the liquid bond force, P is the pressure drop when gas flows through the annular region. Thus, for wet a particle spouted bed, we can revise eq 12 to

Figure 8. Effect of particle diameter on the Ums (Di = 25 mm, H0/D = 1.64).

Ums = f (V , Di , D , H , dP , ρp − ρ , ρ , g )

mm and the inlet diameter Di = 25 mm. It is found that the Ums increases as particle size increases. Figure 9 shows the effect of gas inlet diameter on the minimum spouting velocity Ums, at the initial bed height H0 = 265 mm. As we know, the Ums increases with the increase of inlet diameter in dry spouted bed. It can be seen from Figure 9 that spouting wet particles share the same characteristic when spout nozzle diameter changes. In other words, the increase of inlet diameter also will result in the increases of Ums. When the spout diameter increases, the interface between annulus and spout regions will be larger. Consequently, material exchanges between annulus and spout regions will be increased.37 The degree of air jet dissipation will be increased at this moment. Accordingly, larger spouting gas flow rate is needed for initial spouting. Overall, the minimum spouting velocities increase with the static bed height, particle diameter, and spout nozzle diameter

(15)

Then by dimensional analysis, ⎛ D d ρp − ρ ⎞ Ums = f ⎜S , i , P , ⎟ ρ ⎠ 2gH ⎝ D D

(16)

Ghosh et al. first derived eq 17 for a dry particle spouting process based on momentum balance consideration. A brief summary of the derivation process can be found in the Appendix. 27

1/2 ⎛ 2n ⎞1/2 ⎛ d ⎞⎛ D ⎞2 ⎛ ρ − ρ ⎞ Ums = ⎜ ⎟ ⎜ P ⎟⎜ i ⎟ ⎜ P ⎟ ⎝ 3K ⎠ ⎝ Di ⎠⎝ D ⎠ ⎝ ρ ⎠ 2gH

(17)

Mathur-Gishler eq (eq 18) is widely used for estimating Ums in a dry spouted bed. It has been proven that the predictions by this equation agree well with the experimental data. 9899

DOI: 10.1021/acs.iecr.5b02742 Ind. Eng. Chem. Res. 2015, 54, 9894−9902

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Industrial & Engineering Chemistry Research ⎛ d ⎞⎛ D ⎞1/3 2gH(ρP − ρ) Ums = ⎜ P ⎟⎜ i ⎟ ⎝ D ⎠⎝ D ⎠ ρ

3.4. Maximum Spoutable Bed Height Hmax. Usually, Hmax can be measured by adding particles into the bed gradually until the spout terminates in a dry spouting process.38 In a wet spouted bed, when the initial bed height is high enough, stable spouting is difficult to achieve because the fountain easily becomes oblique. In our present experiments, oblique spouting is also considered as a kind of spouting mode. Accordingly, Hmax is measured by adding wet particles gradually into the bed until spouting cannot happen. Figure 11 shows the changes of the maximum spoutable bed height with liquid saturations. It can be seen that Hmax of wet

(18) 1/2

Aside from the numerical coefficient (2n/3K) , the only difference between eq 17 and eq 18 is the exponent on (Di/D). This difference could be due to the likelihood that both n and K are functions of Di/D.20 As discussed above, in the spout region, the liquid bond effect can be neglected at the moment of particle initial acceleration. Consequently, eq 17 is still valid for the wet spouting process. On the basis of eq 17, we can derive the correlation of Ums for the wet spouted bed. In the wet particle spouted bed, because the particle circulation ability decreases due to the liquid bond in the annulus region, the numerical coefficient (2n/3K)1/2 for wet particles will be different from that for dry particles. The Mathur−Gishler equation is chosen to be revised to predict the Ums of the wet spouted bed in the present work. That means the exponent on (Di/D) in this equation should be changed to fit the wet spouting process. If the effect of liquid saturation is considered, combined with eq 16, a relationship for wet particle spouting is given: ⎛ d ⎞⎛ D ⎞ f (S) 2gH(ρP − ρ) Ums = ⎜ P ⎟⎜ i ⎟ ⎝ D ⎠⎝ D ⎠ ρ

(19)

If data analysis is combine with eq 19, it could be rewritten as ⎛ d ⎞⎛ D ⎞3.7S Ums = ⎜ P ⎟⎜ i ⎟ ⎝ D ⎠⎝ D ⎠

2

− 0.37S + 0.3

2gH(ρP − ρ) ρ

Figure 11. Effect of liquid saturation on the maximum spoutable bed height Hmax.

(20)

Figure 10 illustrates the comparison of experimental minimum spouting velocity with Ums predicted by eq 20. It can be seen

spouted beds is higher than that of dry spouted ones. A very interesting phenomenon observed in the present experiment is that Hmax is almost a constant when the liquid saturation increases. The possible reason is that the liquid bond force in the annulus almost does not change when the liquid saturation increases. As we know, there are three distinct mechanisms which could cause spouting to become unstable beyond Hmax (i.e., fluidization of annular solids, choking of spout, instability growth of spout-annulus interface). No matter which kind of mechanism exists in the wet spouted bed, the particle movement state in the annulus region is the most important factor. It can be easily understood that the relative velocity between adjacent particles in the annulus region is almost zero. At this moment, the liquid bridge force in the annulus region mainly is the capillary force. Our previous work17 found that the capillary force almost does not increase as the liquid saturation increases. Consequently, the particle movement state in the annulus region is almost the same although the bed is in different liquid saturations state. Hmax of a wet spouted bed almost does not change with liquid saturation. This is a very important characteristic for the wet spouted bed. Accordingly, it means the wet spouted bed can work stably in a wide range of liquid saturation. The relationship between Hmax,wet and Hmax,dry can be obtained from the experimental data analysis: Hmax,wet ≈ 1.5Hmax,dry (21)

Figure 10. Comparison of experimental minimum spouting velocity with Ums predicted by eq 20.

that the predictions calculated by this correlation agree well with our experimental Ums. Most of the relative errors of the predictions to the experimental data are within 15%. There are only a few predictions that overestimate the Ums with a deviation over 30%. The deviation may attribute to the defluidization. A hollow gas tunnel was formed during the wet spouting process when the initial bed height was low. Thus, the minimum spouting velocity which was measured from experiment was lower than the calculated value of Ums.

Figure 11 also shows the effect of spout nozzle size and particle size on Hmax of a wet spouted bed. It can be seen that Hmax of wet spouted beds decreases with the increase of particle 9900

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ACKNOWLEDGMENTS The financial supports from the Major Program of National Natural Science Foundation of China (No. 51390492), the National Natural Science Funds for Distinguished Young Scholar (No. 51325601) and the National Natural Science Foundation of China (No. 51576046) are gratefully acknowledged.

diameter for coarse particles and inlet diameter, which is similar to that of dry spouted beds.

4. CONCLUSIONS Spout characteristics such as flow pattern, minimum spouting velocity, and maximum spoutable bed height have been experimentally investigated in a wet conical-cylindrical spouted bed. Water and glass beads (Geldart D type of powders) are adopted as the liquid and solid phases, respectively. The effects of liquid saturation, initial bed height, particle size, and spout nozzle size on Ums and Hmax are systematically studied. The main findings can be summarized as follows: 1. Ums of a wet spouted bed decreases with the increase of liquid saturation in general. The increase of initial bed height, particle size, and spout nozzle size leads to the increase of Ums, similar to that for dry spouted beds. 2. A correlation has been formulated, given by eq 20, to predict Ums of a wet spouted bed as a function of all the variables considered in this work. The calculated results agree well with the present experimental results. 3. Hmax of a wet spouted bed decreases as particle size and inlet size increases, which is similar to that of dry spouted beds. But it is almost constant, approximately 1.5 times higher than that of a dry spouted bed, when the liquid saturation increases.

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APPENDIX Ghosh et al.20,27 first derived eq (A.4) based on the momentum balance consideration. They obtained that at the minimum spouting condition, Vp = (2gH)1/2. Assume there are n particles entering a spouted bed from its periphery and occupying the bottom layer of the bed at any instant, and the height of the layer is particle diameter dP. The time it takes to displace this layer is dP/Vp. Then, the total number of particles accelerated per unit time is nVp/DP. The momentum per unit time gained by the particles is then MP = (nVp/dP)(πdP3/6)(ρP − ρ)Vp

(A.1)

(A.2)

Assume that MP = KM j

(A.3)

where the proportionality constant K represents the fraction of the inlet jet momentum that is transmitted to the particles. A combination of eqs(A.1) to (A.3) leads to

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1/2 ⎛ 2n ⎞1/2 ⎛ d ⎞⎛ D ⎞2 ⎛ ρ − ρ ⎞ Ums = ⎜ ⎟ ⎜ P ⎟⎜ i ⎟ ⎜ P ⎟ ⎝ 3K ⎠ ⎝ Di ⎠⎝ D ⎠ ⎝ ρ ⎠ 2gH

NOMENCLATURE dp = diameter of particles, mm D = diameter of the cylindrical column H0 = static bed height, mm Δp = total pressure drop, kPa U = gas velocity, m/s R1; R2 = meniscus radii of curvature of the liquid bridge (m) S = liquid saturation Vp = volume of particles, m3 Vl = volume of liquid phase, m3 ε = packing voidage fraction, dimensionless ρ = density of fluid, kg/m3 ρp = density of particles, kg/m3 φ = particle sphericity, dimensionless αp = volume fraction of particles αl = volume fraction of liquid phase αg = volume fraction of gas phase σ = liquid surface tension, N/m β = particle wetting angle REFERENCES

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where (ρP − ρ) is the particle density corrected for buoyancy. The momentum per unit time of the fluid jet at its inlet is M j = (πDi2 /4)u inlet 2ρ

Article

(A.4)

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-25-83794744. Fax: +86-25-83795508. E-mail: [email protected]. Address: Sipailou 2#, Nanjing 210096, Jiangsu, P.R. China. Notes

The authors declare no competing financial interest. 9901

DOI: 10.1021/acs.iecr.5b02742 Ind. Eng. Chem. Res. 2015, 54, 9894−9902

Article

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DOI: 10.1021/acs.iecr.5b02742 Ind. Eng. Chem. Res. 2015, 54, 9894−9902