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Ind. Eng. Chem. Res. 2006, 45, 818-829

Dispersion of Floating Solid Particles in Aerated Stirred Tank Reactors: Minimum Impeller Speeds for Off-Surface and Ultimately Homogeneous Solid Suspension and Solids Concentration Profiles Atsushi Tagawa,† Naoki Dohi,‡ and Yoshinori Kawase†,* Research Center for Biochemical and EnVironmental Engineering, Department of Applied Chemistry, Toyo UniVersity, Kawagoe, Saitama 350-8585, Japan, and Mitsubishi Chemical Engineering Co., Towada, Kamisu-machi, Kashima-gun, Ibaraki 314-0102, Japan

Effects of impeller design, baffle, and gas flow rate on distributions of floating solid particles were examined in a stirred tank of 0.2 m i.d. for solid concentrations up to 50 vol %. Dual small cross-section impeller systems, i.e., dual four-flat blade disk turbines and dual four-pitched blade downflow disk turbines, and large cross-section impellers, i.e., Maxblend impeller and Fullzone impeller, were used. The minimum impeller speeds for off-surface floating-particle suspension decreased with aeration because bubbles rising near the tank wall enhanced the breakup of the floating-particle stagnant layer formed on the liquid surface and then the dispersion of floating particles into the liquid. The minimum impeller speeds for ultimately homogeneous floating-particle suspension also decreased with aeration. These results are contrary to those for the settling particles. The local solid particle concentrations at different heights in the stirred tank were measured. The axial solid particles concentration profiles were examined using the proposed one-dimensional floating-particle dispersion model. The Peclet numbers for floating-particle dispersion in the model were reasonably correlated in terms of impeller speed, power consumption, and forces exerted on floating particles. It was found that the large cross-section impellers could disperse completely floating particles into the liquid with less agitated speed and power consumption as compared with the dual small cross-section impeller systems used in this work. 1. Introduction Mechanically agitated solid-liquid or solid-liquid-gas contactors are widely used in industry, and it is essential to know the solid particle distributions for efficient design of the slurry stirred tank reactors. The solid particles usually need to be completely suspended to attain the maximum interfacial area between the solid and liquid phase and to avoid the accumulation of solids at any position of the reactor. Therefore, suspension of solids heavier than the liquid has received extensive attention.1,2 However, the published literature does not give sufficient understanding of solid-liquid two-phase flows in stirred tanks involving a higher degree of complexity and uncertainty. Although there are several applications where solids are lighter than the liquid in fermentation, mineral processing, sewage treatment, and polymerization reactions, relatively few studies have been published on the suspension or drawdown of floating solids in liquids by agitation.3-11 In particular, suspension of floating solids in aerated stirred tanks which is a problem of considerable industrial importance has rarely been studied. Xu et al.9 experimentally discussed floating-particle mixing in a stirred tank under aerated conditions, but effects of aeration on distributions of solids concentration were examined only at the tank bottom rather than throughout the tank. Recently Bao et al.11 reported the data for the suspension of buoyant particles which were polypropylene beads of equivalent diameter ranging from 3 to 4 mm and density of 900 kg/m3. In their study, two types of impeller, a hydrofoil impeller with four wide blades and a disk turbine with half elliptical blades were used. The * To whom correspondence should be addressed. Tel.:+81-49-2391377. Fax:+81-49-231-1031. E-mail: [email protected]. † Toyo University. ‡ Mitsubishi Chemical Engineering Co.

solid volume fraction and the gas velocity were varied from 0.015 to 0.15 and from 0.00234 to 0.0547 m/s, respectively. They found that the just drawdown agitation speed increased with increasing solid concentration. It was also observed that with increasing gas flow rates the just drawdown agitation speed first increased, passed through a maximum, and then decreased. However, no generalized correlation for the just drawdown agitation speed was proposed. The behavior of highly concentrated suspensions of floating solids is not published in the open literature and very indistinct. In this study, dispersion of floating solid particles in aerated stirred tank reactors has been examined. It is of great importance to be able to predict the minimum impeller speed at which the complete dispersion of floating particles is achieved. Therefore, we have measured the minimum impeller speeds for off-surface floating-particle suspension and the minimum impeller speeds for ultimately homogeneous floating-particle suspension in solid-liquid two-phase and solid-gas-liquid three-phase systems. The local solids concentrations at different heights have been also measured to provide more detailed pictures for solid particles dispersion in the stirred tank. The axial solids concentration profiles have been modeled using a onedimensional floating-particle dispersion model. Beside the traditional dual small cross-section impeller systems, four-flat blade disk turbines and four-pitched blade downflow disk turbines, two large cross-section (wide side area) impellers developed to be applicable over a wide range of hydrodynamic conditions,12 Maxblend and Fullzone impellers, have also been used. 2. Experimental Section A schematic of the experimental apparatus used in this work is shown in Figure 1. Experiments were carried out in a 0.2 m

10.1021/ie050634k CCC: $33.50 © 2006 American Chemical Society Published on Web 12/21/2005

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Figure 1. Stirred tank with dual four-pitched blade downflow disk turbines (Three distinct regions in the stirred tank: an upper stagnant layer of particles, a middle mixed slurry region, and a lower clear liquid layer). Maxblend impeller. Fullzone impeller.

i.d. stirred tank. The tank is cylindrical and has an oval bottom with or without four equally spaced vertical baffles having width equal to 1/10th of the tank diameter. The distance between the tangent limit (TL: the transition point from the curved bottom to the vertical wall) and the stirred tank bottom is 0.25DT. This rather large curvature of the tank bottom is common in the process industry. The height between the liquid free surface and the TL, H, was maintained as H ) DT. Dual four-flat blade disk turbines (DT), dual four-pitched blade downflow disk turbines (PDT), Maxblend impeller (MB) and Fullzone impeller (FZ), were used as impellers in this work. The impeller clearance from tank bottom was maintained 0.25DT for all impellers. It should be noted here that usually impellers are placed with a small clearance from the tank bottom to improve the off-bottom suspension of settling particles. The flat disk turbines (DI ) 0.4DT) having four blades with width equal to 1/4 of the impeller diameter discharge radially, deriving suction from both top and bottom. The pitched blade turbines (DI ) 0.4DT) having four blades at 45° from the vertical produce downward-thrusting besides radial flow. The spacing between impellers for the dual impeller systems was 0.15 m. The characteristic feature of the large cross-section impellers, Maxblend and Fullzone impellers, is that they create strong axial liquid recirculation flowing downward near the impeller shaft and upward near the wall.12 The large cross-section impellers have been increasingly becoming popular in chemical process industries. The Maxblend impeller is a single paddle impeller having four vertical slits on their upper parts (Figure 2). The diameter and height of the Maxblend impeller are 0.53DT and 0.93DT, respectively. The lower part is a large paddle impeller and creates strong radial liquid flows converted to strong axial upward-flows near the tank wall by the configurations of oval bottom and tank wall.

Figure 2. Maxblend impeller.

The large cross-section impellers are placed with a small clearance from the bottom. At the free-surface, the liquid flow changes direction and goes toward the shaft. Again it changes direction and spirally flows downward along the shaft to the bottom. The slits on the upper part draw in liquid flows and create rather defined downflow along the impeller shaft. The Fullzone impeller consists of two large paddle impellers, and the upper paddle is shifted at 45° in the rotating direction (Figure 3). The diameter and height of the Fullzone impeller are 0.55DT and 0.82DT, respectively. The liquid flow pattern with the Fullzone is also characterized by a global axial recirculation. This axial circulation loop prevents the bulk rotation of the liquid formed generally in a tank without baffles. The lower paddle with bent tips drives significant radial flows converted to strong axial upflow along the tank wall as well as the Maxblend impeller. The liquid flow traveling up away from the tank base changes direction at the free-surface and flows downward to the bottom. There is a rapid downflow near the shaft axis. The shift of two-paddles, upper and lower paddles, enhances downflow spiraled along the shaft. Although the distance of the impeller from the liquid free surface was not changed in this study, it is very important for floating-particle suspension. The impeller clearance from liquid surface is 0.185DT, 0.20DT, 0.07DT, and 0.185DT for DT, PDT, MB, and FZ, respectively. For φs g 0.2, therefore, a part of the impellers was immersed in the floating-solid layer formed on the liquid surface as described below. For φs ) 0.1, only MB was partially immersed in the particle layer. Air was used as gas phase and introduced through a ring sparger (Dring ) 0.65DT) having eight holes 1 mm in diameter which was installed between the TL and the bottom of the tank. Note that this rather large ring diameter was selected for the large cross-section impellers.12 Rewatkar et al.13 found a decrease in the critical impeller speed for gas dispersion for Dring > DI by depressing the formation of the gas cavities behind

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Figure 3. Fullzone impeller.

the impeller blades. It was also found that the larger sparger ring diameter gives the lower critical impeller speed for solid suspension since the gas is sparged along the periphery and generates a flow pattern in the same direction as that generated by the impeller action.13 The gas flow rate was measured with a rotameter. The rotational speed of the impellers was varied by means of a variable-frequency drive. The impeller speed and gas velocity were varied from 0.5 to 7.33 s-1 and from 0 to 0.0025 m/s, respectively. Since rather large power inputs or impeller speeds were required to move and suspend floating solid particles, flow conditions in the stirred tanks were turbulent. As floating solid particles, particles of two different densities, synthetic adsorbent particles (SA: average particle size of 375 µm and wet density of 793 kg/m3) and polypropylene particles (PP: average particle size of 480 µm and wet density of 854 kg/m3), were used. The solids loading was varied in the range 0 to 50 volume %. Tap water was used as liquid phase. Experiments were performed in a semi-batch manner. Power consumption was measured using a torque meters (Three-One Motor 1200RX, Shinnto Sci. Co., Japan). According to the manufacturer, the minimum readability of the torque meter is 0.01 W and its accuracy is 0.5%. The minimum impeller speeds for off-surface floating-particle suspension for solid-liquid two-phase and solid-gas-liquid three-phase systems were determined by visual observation of the full liquid surface as well as the previous studies.3,4,11 The minimum impeller speed for off-surface floating particle suspension is defined as the impeller speed when stagnant particles at the free surface have just disappeared or no particle is visually observed to remain at rest at the liquid surface for more than one or two seconds.3,4

The minimum impeller speed for ultimately homogeneous floating-particle suspension for solid-liquid two-phase and solid-gas-liquid three-phase systems is defined as the impeller speed beyond which more uniform or homogeneous solids suspension cannot be obtained.14 It should be emphasized here that the minimum impeller speed for ultimately homogeneous floating-particle suspension is not always the impeller speed at which completely homogeneous or uniform suspension is achieved. Under some conditions, a more homogeneous dispersion state cannot be accomplished with increasing impeller speed. It is systematically determined using the plots of the volume fraction of solid particles in the sample taken from the bulk of the mixture against the corresponding impeller speed.14 The sampling tube was hooked to a vacuum system to take the sample from the reactor to the graduated cylinder almost instantaneously. Of course, we paid attention to ensure that the solids particles and water initially contained in the sampling tube would not be included in the sample. In the graduated cylinder, the sample was separated into liquid and solid phases and the volume fraction of the solid phase in the sample was determined. All the solid and liquid were then returned to the stirred tank before further experiments were conducted. As shown below, the volume fractions of the solids in the samples were determined and plotted as a function of the impeller speed at which they were obtained. In the resulting plots, the point at which a change in the floating-solid concentration ended corresponds to ultimately homogeneous solids suspension. Although the sample withdrawal method has shortcomings,8,15 this simple technique has been widely used.7,9,16 As described below, when the homogeneous floating-particle suspension was achieved, the solid volume fraction in the sample was nearly coincident with the average solid fraction, φs. This result suggests that the sample withdrawal method used to determine the minimum impeller speeds for ultimately homogeneous floating-particle suspension in this work is reasonable. Incidentally, Kuzmanic and Rusic8 could not obtain the local solids concentration exceeding the average bulk concentration, and therefore they concluded that the withdrawal of a sample from the tank wall could not provide reliable local solids concentrations in a stirred tank. In this study, on the other hand, the local solids concentration exceeding the average bulk concentration was obtained. Of course, replicated data were taken to ensure reliability of the present experimental results. All experiments were performed at least in triplicate and experimental data were reproducible to within (7.5%; the mean values are plotted all the figures. For its simplicity and versatility, this technique has been widely adopted in the industrial practice. A more quantitative measure of suspension performance is provided by the distribution of solids concentration throughout the tank. To measure the axial distribution of floating solids, slurry samples at four different vertical positions were withdrawn from the bulk of a mechanically agitated and aerated mixture at different impeller speeds and gas flow rates using the technique described above. The distances of the four sampling points from the clear free surface were 0.02 (S4), 0.08 (S3), 0.14 (S2), and 0.20 (S1) m, respectively, and their radial positions were about 0.01 m from the tank wall. In the visualization studies for flow and solid particles, the experiments were videotaped. The videotapes were later viewed to evaluate the mixing characteristics. 3. Results and Discussion 3.1. Visual Observations of Floating-Particles Dispersion. When the impeller speed was zero or very low, the floating

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particles formed a stagnant layer on the liquid surface in which agglomeration of particles took place such as the particle pile on the tank bottom observed for settling solids and none of the solids were dispersed into the liquid.12,14,16 There was a clear liquid zone in the lower part of the tank. At the low impeller speeds, particles were partially dispersed into the liquid phase and the stagnant layer volume was slowly reduced as the impeller speed was increased. The forces exerted on the particles are gravity and drag by the fluid. Liquid upflows lift up and liquid downflows draw down the solid particles. Floating particles were gradually drawn down into the liquid from the stagnant layer formed on the liquid surface by the downward liquid flow along the shaft and some of dispersed particles were lifted by the upward liquid flow along the tank wall. Under this condition, the tank could be divided in three distinct regions: an upper stagnant layer of particles, a middle mixed slurry region, and a lower clear liquid layer (Figure 1). With increasing impeller speed the number of solids particles in the cloud or the slurry region where solids were dispersed increased and as a result the cloud height increased. As mentioned above, the upper impellers for the dual small crosssection impeller systems and the upper parts of the large crosssection impellers were immersed into the stagnant layer of the floating particles formed on the liquid surface at lower impeller speeds. The particles in the stagnant layer on the liquid surface were swept to periphery by the centrifugal force of the impeller immersed in the floating-solid layer. We found that the minimum impeller speed for off-surface floating solids increased with increasing immersion depth of the impeller. When the distance of the impeller top from the stagnant layer bottom was large, we observed that distribution of floating solids was very difficult at dense suspension. Therefore, we chose relatively small impeller clearances from liquid surface given above. With further increasing impeller speed, more solids were dispersed into the liquid and the stagnant layer volume was drastically reduced but there were still small stagnant zones behind the baffles where the radial flow component was minimal. As the impeller speed was further increased, the floating clots were broken up and all solids were completely dispersed into the liquid. The cloud height approached the tank bottom, and both the stagnant layer volume and the clear liquid height fell to zero. The stagnant layer of floating solids was significantly affected by the liquid recirculation generated by the impellers. The large cross-section impellers (MB and FZ) created the strong liquid recirculation loop consisting of upward-flows near the tank wall from the tank bottom and spirally downward-flow along the shaft to the tank bottom. It was significantly effective to the break-up of the floating-particle stagnant layer. The four-pitched blade downflow disk turbines (PDT) generated the liquid recirculation similar to that of the large cross-section impellers, but it was rather weaker than that of the large cross-section impellers. In the case of the flat blade disk turbines (DT), radial liquid flows were converted to axial upward- and downwardflows at the tank wall. However, as well as the PDT the liquid reciculation created by the DT was weaker as compared with that created by the large cross-section impellers. The upwardflows affected the break-up of the floating-solids layer and as a result the dispersion of the solids particles. While the liquid recirculation pushed up the particle layer near the tank wall, it pulled down the layer around the shaft. These conflict forces twisted and then broke up the floating-solids layer formed at the liquid surface. Finally particles were dispersed all over the tank.

Figure 4. Power consumption (partcle: SA, φs ) 0.5). (a) Dual PDT impeller. (b) Fullzone impeller.

As described below, the impeller speed required to maintain good solid dispersion decreased under gassed conditions. Gas bubbles formed from the sparger rose vertically were pushed away to the tank wall due to the radial liquid flow created by the impellers. The upward liquid flow near the tank wall pushed up gas bubbles toward the stagnant layer of floating solids. It was observed that small bubbles formed at the sparger rose and coalesced during passing through the dense layer. The buoyancy force of large bubbles enhanced the lift exerted on the floatingparticle stagnant layer near the tank wall and then the break-up of the stagnant floating-particle layer. The baffles strongly influence the flow pattern in the tank.1,2 As also observed by Siddiqui,17 the absence of the baffles led to a poor distribution of the floating particles. When no baffles were used, the flow rotating with the impeller controlled the flow in stirred tank, suppressed radial and axial liquid motions, and then developed the vortex in the center of the tank. With increasing impeller speed the gross central vortex deepened and was wider. It was observed that most floating particles traveled around the tank periphery. As the impeller speed was further increased, the floating solids tended to concentrate in the vortex and the solids were drawn down under the liquid surface by the liquid swirl. More swirls and swells developed over the entire liquid surface and the stagnant layer broke up and more particles sunk. At higher impeller speeds, more particles were drawn down by the stronger downward liquid flow and vortices. At a certain impeller speed, the stagnant layer completely broke up and all the solids were drawn down into the liquid. 3.2. Power Consumption. Power-consumption data were obtained during every solid suspension experiment. Figure 4 shows the typical results of power consumption obtained for solid-liquid two phase and solid-liquid-gas three-phase systems in the stirred tank reactor with PDT and FZ impellers at φs ) 0.5. The data were obtained under the condition in which the impeller speeds were larger than the minimum impeller speed for off-surface floating-particle suspension described

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Table 1. Values of Np in Equation 1 floating particle

DT

SA PP

4.0 4.0

impeller type PDT FZ 2.5 2.0

7.0 6.5

MB 5.0 4.8

below, i.e. N g Njs. With an increase in impeller speed the power consumption increased. For constant impeller speed, the baffles caused rather increased in power consumption and the power consumption decreased slightly with increased superficial gas velocity. Similar results were obtained for DT and MB impellers. Since all of the impellers were operated under turbulent conditions (Re ) NDI2/νl > 9400), the power number (Np ) P/N3DI5Fl) was a function of impeller geometry but almost constant. In other words, the power number was essentially independent of the Reynolds number, and this functionality was characteristic of the turbulent flow regime. Therefore, the power consumption for floating solid-liquid two-phase systems can be calculated by the following equation:

P ) NpFlN3DI5

(1)

Figure 5. Comparison of predictions and data for power consumption (particle: SA, with baffles). Table 2. Minimum Impeller Speeds for Off-Surface Floating-Particle Suspension (floating particles: SA) Ug ) 0 [ms-1] Njs DT PDT

Values of Np in eq 1 for the impellers studied are given in Table 1. It is to be noted that the Reynolds number was calculated using the liquid properties instead of the average slurry properties as well as the literature17,18 since the solids dispersion was not always uniform throughout the tank even for N g Njs. The power consumption decreased due to aeration. It might be due to the formation of cavity behind the impeller blades. Since it was hindered by the dense suspension of fine solid particles, this discussion is based on our previous visual observation in the absence of solid phase.19 The relatively small reduction of power consumption due to aeration indicates that the rather high concentration of solids particles might suppress the cavity formation behind the impeller blades. We introduced an additional term for effects of aeration and obtained the following correlation for the power consumption under the aeration condition, Pg:

( )

Pg ) P 1 +

Ug Ut

(2)

where the terminal floating velocity of solid particles Ut is used to introduce a dimensionless term for the superficial gas velocity Ug and it is given by

[

Ut ) -

]

2 2 4 (Fl - Fs) g 225 µlFl

1/3

dp

(3)

This equation based on the free settling velocity of an isolated sphere is Allen’s law applicable for 0.4 < Rep( ) dp|Ut|/νl) < 500.20,21 The free floating velocities for particles used in this work were in this range of Reynolds number. It should be emphasized here that eq 2 indicated the slight reduction of power consumption due to aeration since the floating velocity obtained by eq 3 is given as negative. For floating solid-liquid two-phase and floating solidliquid-gas three-phase systems without baffles, we obtained the following relationships:

Pnb or Pgnb ) 0.65 × (P or Pg)

(4a)

FZ MB

with baffles without baffles with baffles without baffles with baffles without baffles with baffles without baffles

[s-1]

3.00 4.17 3.83 4.17 1.00 1.67 1.30 1.67

Ug ) 1.00 × 10-3 [ms-1]

P at Njs [W]

Njsg [s-1]

P at Njsg [W]

0.63 0.72 0.41 0.46 0.11 0.21 0.12 0.16

1.67 3.83 2.50 3.33 1.00 1.33 1.00 1.33

0.03 0.50 0.14 0.22 0.08 0.12 0.03 0.07

for the dual small cross-section impellers (DT and PDT)

Pnb or Pgnb ) 0.50 × (P or Pg)

(4b)

for large cross-section impellers (MB and FZ). The decrease of power consumption in the presence of baffles was reasonably correlated by the above correlation. The extent of lowering due to the absence of baffles for the large crosssection impellers was 15% larger as compared with that for the small cross-section impellers. In Figure 5, the experimental results in the presence of baffles are compared with the predictions of the above correlations. The correlations were found to fit the experimental data with the correlation coefficient of 0.90. Similar results were obtained for the power consumption data in the absence of the baffles. The predictions of the proposed correlations are also presented as solid and broken lines in Figure 4. 3.3. Minimum Impeller Speeds for Off-Surface FloatingParticle Suspension. At low impeller speeds, as described above, all solid particles were near the free surface. As rotational speed was increased, partial particle suspension occurred. A further impeller speed increase suspended more particles into the liquid, and the stagnant floating-particle layer volume fell to zero at just-suspended conditions (N/Njs ) 1). In Table 2 the experimental results for SA particles at φs ) 0.5 in aerated and unaerated systems are presented to illustrate the effect of impeller design on the minimum drawndown agitation requirements. It was found that Njs and Njsg for the large cross-section impellers were smaller than those for the smaller cross-section impellers under both aerated and unaerated conditions. The large cross-section impellers were also found to have rather lower power requirements to achieve just-suspended conditions as compared with the small cross-section impellers. Under the aeration conditions the decrease in minimum impeller speed required for off-surface solid suspension was observed. As described previously, bubbles which were dispersed by the impellers and rose near the tank wall pushed up the floatingparticle stagnant layer and enhanced its break-up. As a result

Ind. Eng. Chem. Res., Vol. 45, No. 2, 2006 823 Table 3. Values of S in Equation 5 impeller type PDT FZ

floating particle

DT

SA PP

1.10 × 9.30 × 103

1.50 × 1.30 × 104

104

MB

7.39 × 5.90 × 103

104

103

6.38 × 103 5.70 × 103

the aeration decreased the minimum impeller speed for offsurface solid suspension. This is contrary to the results for offbottom settling solids of Dutta and Pangarkar22 and Chapman et al.23 and for off-surface floating solids of Bakker and Frijlink.4 Although the decrease in power consumption due to cavity formation behind the impeller blades occurred, it might be insignificant as mentioned previously. On the basis of Zwietering’s approach which a number of investigators have applied,2,22,24 we proposed the following correlation for the minimum impeller speed required keeping the floating solids just suspended in solid-liquid two-phase systems:

[

]

(Fl - Fs) Fl

Njs ) Sνl0.1 g

0.45

Xs0.13dp0.2DI-0.85

(5)

The parameter S is a function of impeller type and system geometry, and values of S for all impellers used in this work are given in Table 3. It can be seen from the values of S for SA and PP particles in Table 3 that latter particles produced an earlier onset of solids dispersion. The dual PDT impeller system was found to require the largest minimum impeller speed for off-surface floating-particle suspension among the impeller configurations studied. Instead of mass percentage used in the original correlation of Zwietering25 mass fraction Xs was used to represent solid loadings in this work. The functional dependence is identical to that of the correlation proposed by Zwietering.25 As observed for off-bottom settling particles, the value of the exponent of Xs was 0.13 and solids loading insignificantly influenced the just off-surface floating-particle suspension. The decrease of minimum impeller speed under gassed conditions was correlated well by the following correlation:

( )

Njsg ) Njs 1 +

Ug Ut

3.0

(6)

A linear fit suggested an exponent over (1 + Ug/Ut) of 3.0. Since Ut is negative, eq 6 indicates the decrease in the Njsg values with an increase in the gas velocity. Bao et al.11 measured the critical minimum impeller speed to just draw floating particles by varying the gas velocity in the range of 0 to 0.024 m/s and found that Njsg first increased slightly and then decreased with an increase in gas flow rate. It should be pointed out that in their study the particle loadings were less than 15 volume%, being rather smaller than that in this study. Furthermore, they used polypropylene beads of diameter ranging from 3 to 4 mm, which are rather larger than those used in this study. The omission of the four fully immersed baffles led to a poor suspension of the solids and required a higher impeller speed to draw down the floating solids. In general, baffles are recommended for off-bottom settling-particle suspension involving solids which are heavier than the liquid since they convert the swirling liquid motion into axial fluid motion, helping lift and suspend the solids.1,2 For floating solids, however, fully immersed baffles are not recommended for solid suspension.3,5 Joosten et al.3 found that partial baffles were suitable for dispersion of floating particles as compared with standard full

Figure 6. Comparison of predictions and data for minimum impeller speeds for off-surface floating-particle suspension for solid-liquid two-phase and solid-gas-liquid three-phase systems (particle: SA and PP, φs ) 0.5, with baffles).

baffles. In this study, baffles led to slightly better dispersion of the floating solids and the existence of baffles caused a decrease in the minimum impeller speed for off-surface solid suspension. For the large cross-section impellers, the absence of baffles practically had no effect. The floating-particle suspension for the small cross-section and large cross-section impellers depressed by fully immersed baffles could be described using the following correlation:

Njsnb or Njsgnb ) 1.2 × (Njs or Njsg)

(7a)

for the dual small cross-section impellers (DT and PDT)

Njsnb or Njsgnb ) 1.0 × (Njs or Njsg)

(7b)

for the large cross-section impellers (FZ and MB). Figure 6 compares the predictions of eqs 5-7 and the present experimental data with baffles (Njs and Njsg). Reasonable agreement was found. The data of the minimum impeller speeds for off-surface floating particles in the absence of baffles were also reasonably correlated with the proposed equation. The mean deviation for the experimental data from the predictions of the above correlations is 13.3%. 3.4. Minimum Impeller Speeds for Ultimately Homogeneous Floating-Particle Suspension. Figure 7 illustrates typical plots of the volume fraction of solid particles (SA particles) in the sample taken from the bulk of the mixture at four different vertical positions (S1-S4) against the corresponding impeller speed (N > Njs or Njsg) in the stirred tank with the FZ impeller. Similar plots were found for other impellers and the PP particles. As expected, homogeneous dispersions occurred at impeller speeds higher than the minimum impeller speeds for off-surface floating-particle suspension. At Njs < N < Nus, the solid concentrations near the liquid surface (S4 and S3) were higher than the average solid fraction φs while those near the tank bottom (S2 and S1) were rather lower than φs. This distribution is contrary to that for settling particles.14 As impeller speed was increased, the floating particles were rapidly drawn down and the solid concentrations near the liquid surface and the tank bottom sharply decreased and increased, respectively. As the impeller speed was further increased, the solid concentrations leveled off and approached the ultimate solid distributions. When the homogeneous solid dispersion was achieved, the solid concentrations withdrawn from four different locations nearly coincided with each other. This fact suggests that the sampling technique used to measure solid concentration is reasonable.

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Figure 8. Effect of aeration on minimum impeller speeds for ultimately homogeneous solid suspension (particle: SA, φs ) 0.5) (a) with baffles, (b) without baffles. Table 4. Values of K in Equation 8

Figure 7. Minimum impeller speeds for ultimately homogeneous solid suspension for solid-liquid two-phase and solid-gas-liquid three-phase systems with the Fullzone impeller (particle: SA, φs ) 0.5). (a) With baffles, Ug ) 0 ms-1. (b) With baffles, Ug ) 0.001 ms-1. (c) Without baffles, Ug ) 0 ms-1. (d) Without baffles, Ug ) 0.001 ms-1.

Under aeration conditions, as shown in Figure 7, as N increased, the solid concentrations of the samples taken from the location S4 leveled off but often did not reach φs. This indicates that the ultimate solid concentration was accomplished but the completely homogeneous or uniform suspension of floating solid particles throughout the stirred tank could not be achieved. Figure 8 illustrates the typical results for effects of aeration on Nus of SA particles at φs ) 0.5. Aeration contributed to a decrease of Nus unlike the results for settling particles.12 As mentioned above, bubble motion broke the floating-particle layer

floating particle

DT

impeller type PDT FZ

MB

SA PP

0.56 0.40

0.81 0.45

0.32 0.25

0.38 0.28

formed at the liquid surface and enhanced motion of floating particles. This result is inconsistent with the data for buoyant particles obtained by Bao et al.11 This may be attributed to different impeller designs and size and volume fraction of solid particles. On the basis of the correlation for settling particles proposed by Dohi et al.,12 we correlated the present experimental data of Nus for the floating particles as follows:

[

]

(Fl - Fs) Fl

Nus ) Kνl-0.25 g

0.40

dp0.47Xs0.009DI-0.80

(8)

The exponents were same for all impellers, and this functional relationship was identical with that obtained for settlingparticles12 except the exponent of Xs. Nus is nearly independent of Xs and the exponent on Xs for floating particles is 0.009 instead of 0.22 for settling particles.12 In other words, an increase in Xs has a negligible influence on Nus for floating particles. Values of K in eq 8 for all impellers used in this work are given in Table 4. As mentioned above, aeration led to a reduction of the minimum impeller speed for ultimately homogeneous floating-particle suspension. Under sparged conditions, the

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dimensional floating-particle dispersion model is27

∂C ∂2 C ∂C ) Des 2 + Us ∂t ∂z ∂z

(11)

The solution of eq 11 for operations being batchwise with respect to liquid phase may be written as:27

φs′ Pes C z ) ) exp -Pes Cav φs 1 - exp(-Pes) H

(

)

(12)

where Peclet number for solid dispersion characterizing the solid distribution in the stirred tank is defined as:

Pes )

Figure 9. Comparison of predictions and data for minimum impeller speeds for ultimately homogeneous solid suspension for solid-liquid two-phase and solid-gas-liquid three-phase systems (particle: SA).

dispersion of the floating solids was enhanced by the motion of bubbles. The decrease in Nus due to aeration was correlated by the following correlation:

( )

Nusg ) Nus 1 +

Ug Ut

-UsH Des

(13)

The solid particle Peclet number defined by eq 13, Pes, represents the degree of solid dispersion in the liquid, and smaller value of Pes indicates better solid dispersion. Since the floating particles have upward velocity due to the buoyancy force effect, the hindered solids floating velocity Us in eq 13 is negative as presented below, and as a result Pes is positive. On the basis of the assumption that the solid-phase dispersion is equal to the liquid-phase dispersion,8 since the eddy diffusivity has been shown to be proportional to NDI2 in the turbulent flow region,29 we assumed the following dependency:

2

Previously, we12 examined Nusg for settling particles and the exponent for (1 + Ug/Ut) was 0.15 which is much smaller than that for floating particles in this study. We found that the fully immersed baffles improved floatingparticle suspension for the small cross-section impellers by 30%. For large cross-section impellers, the absence of baffles had minor effect on the minimum impeller speeds for ultimately homogeneous suspension. The following correlations under the absence of baffles were obtained:

Nusnb or Nusgnb ) 1.3 × (Nus or Nusg)

(10b)

for the large cross-section impellers (FZ and MB). Figure 9 shows the relationship between the experimental data and predicted values of Nus or Nusg for SA particles. It is seen that the proposed correlations fit the experimental results with the correlation coefficient of 0.97. Similar agreement was obtained for PP particles. 3.5. A One-Dimensional Model for Floating-Solids Concentration Profile. One of phenomenological approaches to modeling the solids distribution in agitated slurries is a onedimensional model in which no radial gradients of solids concentration are assumed. It has been widely and successfully used to describe solids concentration profiles in stirred tanks.26-28 When particles are suspended in a liquid by fluid motion induced by an impeller, particle concentration gradients exist. Unless the impeller speed is very high, floating-particle concentrations are higher at the free surface (z ) H) than at the bottom (z ) 0). This distribution for floating-particle concentration is contrary to that for settling-particle concentration.26-28 The proposed one-

(14)

The measurements of solid distribution were used to determine the particle Peclet numbers. Since the velocity distribution of liquid flow responsible for solid suspension is very complicated, we obtained the following empirical correlation for a characteristic velocity of floating particles moving in a stirred tank, Us, using the experimental data instead of the terminal floating velocity of solid particles, eq 3.

CuRe-3.5 Us ) -

(10a)

for the dual small cross-section impellers (DT and PDT)

Nusnb or Nusgnb ) 1.0 × (Nus or Nusg)

Des ∝ NDI2

(9)

( )[

]

Fg (Fl - Fs) g dpD I Fd Fl νl

(15)

where the drag force, Fd, and the buoyancy force, Fg, are given as

Fd ) dp2FlUt2

(16)

Fg ) dp3g(Fl - Fs)

(17)

and

respectively. It should be noted that the hindered velocity for floating particles, Us, is negative contrary to the sedimentationdispersion model for settling particles.27 In many previous studies,8,16,30 incidentally, Us was one of adjustable parameters. Recently, Pinelli et al.31 presented an empirical correlation for the effective particle velocity in the stirred tank as a function of the terminal velocity, Kolmogoroff micro length scale, and particle diameter. To obtain a good fit between the data and model predictions for the solid concentration distribution, the adjustable parameter Cu was varied and then the particle Peclet number was calculated using eqs 13 and 15. Values of Cu in eq 15 are presented for all impellers and solid particles studied in

826

Ind. Eng. Chem. Res., Vol. 45, No. 2, 2006 Table 6. Values of r in Equation 19 impeller type PDT FZ

floating particle

DT

SA PP

1.2 × 3.0 × 102 103

6.7 × 2.5 × 102 102

MB

2.5 × 1.5 × 102 102

6.0 × 102 2.0 × 102

The variation of Peclet number under aeration was found to be proportional to (1 + Ug/Ut)7 and we have

( )

Pesg ) Pes 1 +

Ug Ut

7

(18)

For floating particles, Ut is negative as given by eq 3. The relationship of Peclet number for the absence of baffles was obtained as:

Pesnb or Pesgnb ) R × (Pes or Pesg)

Figure 10. Effect of power consumption on floating-particle Peclet number (particle: SA, φs)0.5) (a) with baffles, (b) without baffles. Table 5. Values of Cu in Equation 15 floating particle

DT

SA PP

2.24 × 104 1.36 × 105

impeller type PDT FZ 1.39 × 105 3.96 × 104

8.65 × 103 7.55 × 103

MB 6.73 × 103 6.75 × 103

Table 5. The values of Cu for the dual PDT impellers were larger than those for other impellers since as described below the PDT provided rather poor dispersion of floating particles in the stirred tank. It should be noted that for all practical purposes floatingsolid dispersion might be taken to be almost independent of solid loading or solid concentration. The typical variation of Pe with power consumption at φs ) 0.5 for all impellers studied is illustrated in Figure 10. The particle Peclet number drastically decreased with power consumption or impeller speed. The Pe value was found to decrease with aeration. It is clear from Figure 10 that the Pe values obtained for the large cross-section impellers (closed symbols) were substantially smaller than those obtained with the small cross-section impellers (open symbols) at a given power consumption. The PDT impeller was the worst performance for uniform floating-particles dispersion among the various impellers used in this work and could not generate the desired flow patterns in the liquid for drawing floating solids down into the liquid. The axial downward-liquid flow in the vicinity of the impeller shaft created by the dual PDT impellers was less useful to draw down floating solids as compared with the radial flow converted to strong axial upward-liquid flow near the tank wall created other impeller configurations.

(19)

Values of constant R in eq 19 for all impellers and solids studied are given in Table 6. By use of eqs 13-19, it is possible to estimate Peclet number for the floating solid particles. We measured local solid concentrations at four different heights in the tank. The typical variations of the normalized local dimensionless solid concentration or local solid volume fraction, φs′/φs, with axial distance in the tank with DT and FZ at impeller speeds higher than the minimum impeller speeds for off-surface floating-particle suspension are presented in Figure 11. Similar results were also obtained for PDT and MB impellers. As can be seen, the dimensionless solid concentration normalized by the average solid volume fraction, φs, lied above and below 1 near the liquid surface and near the tank bottom, respectively. This distribution for floating particles is opposite to that for settling particles.16,17,26 At low impeller speeds, the solid suspension is not complete and particles are only partially dispersed. Under this condition, the rather significant concentration gradient appeared. As the impeller speed is increased, larger quantities of particles were suspended, thus increasing the average suspended concentration. The concentration of floating solids continuously decreased from the liquid surface to the tank bottom. It can be seen from Figure 11 that higher impeller speeds and higher gas velocities tended to give more uniform solid distributions. With the use of baffles the homogeneity of floating-solid dispersion was enhanced. The variation of solid concentration with impeller speed was similar for all solid loadings tested. Good overall agreement existed between the model predictions given as solid lines in the figure and the experimental data. Conclusions Dispersion of floating solid particles has been examined in the stirred tank reactor with dual small cross-section impellers and large cross-section impellers over a wide range of operating conditions. The minimum impeller speeds for off-surface floating-particle suspension were found to decrease with aeration since bubbles rising near the tank wall enhanced the breakup of the floatingparticle stagnant layer formed on the liquid surface and then the dispersion of floating particles into the liquid. The minimum impeller speeds for ultimately homogeneous floating-particle suspension also decreased with aeration. For good dispersion of floating particles, the key point is how to quickly break-up the stagnant layer of particles formed on the liquid surface.

Ind. Eng. Chem. Res., Vol. 45, No. 2, 2006 827

Figure 11. Axial distribution of floating solids dimensionless concentration (φs′/φs) in the stirred tank (particle: SA, φs ) 0.5). (a) Dual DT impeller. (b) Fullzone impeller.

828

Ind. Eng. Chem. Res., Vol. 45, No. 2, 2006

The fully immersed baffles improved floating-particle suspension for the small cross-section impellers but had little effects for large cross-section impellers. The Peclet numbers for floating-particle dispersion in the onedimensional dispersion model were successfully correlated to impeller speed, power consumption, and geometric and physical parameters. Reasonable agreement between the experimental results and the model predictions for axial concentration profiles of floating solid particles in the stirred tank was obtained. This suggests the applicability of the proposed one-dimensional floating-dispersion model. It was found that the large crosssection impellers could disperse completely floating particles into the liquid with less power consumption or agitated speed as compared with the dual small cross-section impeller systems studied in this work. At this stage no detailed attempt has been made to elucidate effects of design and location of gas sparger and impeller clearances from the tank bottom and the liquid surface. Additional work in this area should be pursued. The wettability of the particles may significantly affect dispersion of floating particles.32 This important aspect should be considered in our future work. Nomenclature C ) solids concentration, kg m-3 Cav ) average bulk solids concentration, kg m-3 Cu ) constant in eq 15 C h ) dimensionless solids concentration (C/Cav) Des ) solid particle dispersion coefficient, m2 s-1 DI ) impeller diameter, m Dring ) ring sparger diameter, m DT ) stirred tank diameter, m dp ) particle diameter, m Fd ) drag force, N Fg ) buoyancy force, N g ) gravitational acceleration, ms-2 H ) liquid height above T. L., m K ) constant in eq 8 N ) impeller speed, s-1 Njs ) minimum impeller speed for off-surface floating-particle suspension, s-1 Np ) Power number ()P/N3DI5Fl) Nus ) minimum impeller speed for ultimately homogeneous floating-particle suspension, s-1 P ) power consumption, W Pg ) gassed power consumption, W Pes ) solid particle Peclet number ()-UsH/Des) Re ) impeller Reynolds number ()NDI2/νl) Rep ) particle Reynolds number ()dp|Ut|/νl) S ) constant in eq 5 t ) time, s Ug ) superficial gas velocity, ms-1 Us ) characteristic velocity of floating particle in stirred tank, ms-1 Ut ) terminal floating velocity of particles, ms-1 Xs ) solids loading (solid weight/slurry weight) z ) axial coordinate, m Greek Letters φs ) average solid volume fraction φs′ ) local solid volume fraction µl ) liquid viscosity, Pa‚s νl ) liquid kinematic viscosity, m2 s-1

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ReceiVed for reView May 31, 2005 ReVised manuscript receiVed October 19, 2005 Accepted November 2, 2005 IE050634K