ARTICLE pubs.acs.org/IECR
Volumetric GasLiquid Mass Transfer Coefficient in Aerated Stirred Tank Reactors with Dense Floating Solid Particles 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 ‡ Mitsubishi Chemical Engineering Co., Shibaura, Minato-ku, Tokyo 108-0023, Japan ABSTRACT: The effect of floating solid particles on volumetric gasliquid mass transfer coefficients was investigated using a stirred tank of 0.2 m inside diameter (i.d.) with dual four-flat blade disk turbines for solid concentrations up to 50 vol %. Two kinds of floating solids, synthetic adsorbent particles (particle size of 375 μm and wet density of 793 kg m3) and polypropylene particles (particle size of 480 μm and wet density of 854 kg m3) were used. At very low impeller speeds the floating particles formed a stagnant layer on the liquid surface, and none of the solids were dispersed. As the impeller speed was increased, particles were partially dispersed, and the stagnant layer volume was reduced. With further increasing impeller speed, all solids were ultimately dispersed throughout the tank. The gas hold-up and volumetric gasliquid mass transfer coefficient in a baffled or unbaffled stirred tank with dense floating solids particles are measured. The power consumption and gas hold-up decreased with an increase in floating solids concentration. It was found that the presence of floating solid particles significantly reduced the mass transfer coefficient at a given impeller speed. The presence of floating solids increased the apparent viscosity of the slurry and hence probably resulted in increased bubble coalescence tendency enhancing the formation of larger bubbles. They might lead to a decrease in gas hold-up or specific surface area and subsequently induce a significant decrease in the volumetric gasliquid mass transfer coefficient. The experimental data for gas hold-up and volumetric gasliquid mass transfer coefficient are satisfactorily correlated to power consumption, superficial gas velocity, and solid volume fraction.
1. INTRODUCTION Solidliquidgas three-phase, mechanically stirred reactors have been used in a variety of chemical and biochemical industries.1 The solid may be present as a heterogeneous catalyst or as a particulate product of a chemical reaction. There are several applications where solids are lighter than the liquid in food processing, fermentation processes, minerals processing, wastewater treatment, and polymerization reactions.25 For the reliable design and scale-up of solidliquidgas three-phase stirred tank reactors, predictions of gasliquid mass transfer rate are crucial, as well as solid suspension, liquid mixing, and gas dispersion. Although suspension of solids heavier than the liquid has received extensive attention, published work on the floating solids is rather limited. Since it is essential to know the solid particle distributions in stirred tanks for efficient design of the slurry stirred tank reactors, several studies have been published on the suspension or drawdown of floating solids in liquids by agitation.212 Most of them have exclusively examined the impeller speed and power consumption required to just draw down of floating solids from the liquid surface, which are key parameters in determining the design and operation of floating solidliquidgas three-phase stirred tanks. In our previous paper,5 the dispersion of floating solid particles in an aerated stirred tank was examined. We measured the minimum impeller speeds for off-surface (Njsg) and for ultimately homogeneous solid suspension (Nusg) and found that the aeration enhances dispersion of floating particles. We also proposed the onedimensional floating-particle dispersion model, which was successfully applied to predict axial solid particles concentration r 2011 American Chemical Society
profiles. Bao et al.4,10 measured gas hold-ups in floating solidliquidgas three-phase stirred tank and found that gas holdup decreases with increasing floating solids concentration. They used four different buoyant particles, that is, polypropylene particles and powders (Fs = 900 kg m3), low-density polyethylene particles (Fs = 922 kg m3) and high-density polyethylene particles (Fs = 955 kg m3). The maximum solid volume fraction used in their study was 0.15 which is not highly concentrated suspensions of floating solids. However, gasliquid mass transfer in aerated stirred tanks with floating solid particles which is a problem of considerable industrial importance has rarely been studied. Despite many publications on the gasliquid mass transfer in stirred tank reactors with heavy solids, there is little published work on that with floating solid particles. Gentile et al.13 measured the gasliquid mass transfer rate for the threephase system with nonwettable polypropylene particles (dp = 425 μm, Fs = 902 kg m3) and wettable Fillite particles (dp = 130 μm, Fs = 706 kg m3). While the volumetric mass transfer coefficient with 0.1% w/w nonwetted solids was found to fall by a factor of 2 to 3 as compared with the case without solids, that with wetted solids at concentrations up to 2% w/w did not change as compared with the data for water. To the best of our knowledge Special Issue: Nigam Issue Received: November 17, 2010 Accepted: February 25, 2011 Revised: February 23, 2011 Published: March 18, 2011 1938
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Figure 1. Experimental Setup (three distinct zones in the floating solidliquidgas three-phase stirred tank: At higher impeller speeds the stagnant layer and clear liquid zone disappear).
no systematic study appears to have been performed on the gasliquid mass transfer coefficient in floating solidliquidgas three-phase stirred tanks with high solid concentrations. This study was conducted to throw more light on effects of floating solid particles on gasliquid mass transfer in stirred tanks. We measured gas hold-ups and volumetric gasliquid mass transfer coefficients in a stirred tank with floating solid particles for solid particle concentrations up to 50 vol %. Unbaffled stirred tanks are often used for floating solid particles, as the spiral flows are formed and they tend to draw particles into the liquid.14 The vortices cause the liquid surface to be pushed up at the tank wall and sucked down near the impeller shaft. The vortex draws the floating particles into the liquid. In fact, we previously found that the homogeneity of floating-solid dispersion is enhanced with the use of baffles.5 However, Bao et al.4 reported that gas dispersion in a partially baffled floating solidliquidgas three-phase stirred tank is not as effective as when fully baffled. Therefore, effect of baffles on volumetric mass transfer coefficients in a stirred tank with floating solid particles is also examined.
2. EXPERIMENTAL SECTION Figure 1 shows a schematic of the experimental apparatus used in this work. Since the stirred tank and impellers used in this study are the same as those in our previous study,5 only brief description of the experimental setup is presented. Experiments were conducted in a 0.2 m inside diameter (i.d.) cylindrical stirred tank which has an oval bottom with or without four equally spaced vertical baffles having width equal to 1/10th of the tank diameter. The baffles strongly influenced the flow pattern in the stirred tank.1,5,14 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. In our previous study5 we 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 and finally the stagnant layer completely broke up and all the solids were drawn down into the liquid. The height between the liquid free surface and the tangent limit (TL: the transition point from the curved bottom to the vertical wall), H, was maintained as H = DT. The distance between the TL and the tank bottom is 0.25DT. The impeller used in this study was the dual four-flat blade disk turbines (DT) system. The flat disk turbines (DI = 0.4DT) have four blades with width equal to 1/4 of the impeller diameter. Several studies found that radial flow impellers are not energy efficient for solid dispersion.9,11,12 In our previous work,5 the floating solid particles dispersion by the dual DT impeller system was better than that by the dual four-pitched blade downflow disk turbine. In this study, therefore, we used the DT system which discharges radial liquid flows which are converted to axial upward- and downwardflows at the tank wall. They derive suction of solid particles from both top and bottom and as a result improve floating-particle dispersion. The lower impeller clearance from the tank bottom was maintained as 0.25DT as well as the impeller clearance from liquid surface. For φs g 0.2, therefore, the upper impeller was immersed in the floating-solid layer formed on the liquid surface described below. 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 tank bottom. Since Rewatkar et al.15 reported decreases in the critical impeller speed for both gas dispersion and solid suspension for Dring > DI, we used the rather large ring sparger as well as our previous study.5 The most important variables affecting the mixing and mass transfer are the impeller speed and the gas flow rate. In this study, the impeller speed, N, and superficial gas velocity, Ug, were varied from 0 to 12 s1 and from 0 to 0.004 m s1, respectively. The rotational speed of the impellers was varied by means of a variable-frequency drive. The gas flow rate was measured with a rotameter. We previously found that the 1939
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Industrial & Engineering Chemistry Research impeller speed required to maintain good dispersion decreased under gassed condition.5 Gas bubbles formed from the sparger rose vertically were pushed away to the tank wall by 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 up and coalesced during passage through the dense layer. The buoyancy force of large bubbles enhanced the breakup of the stagnant floating-particle layer at the liquid surface. For comparison, several measurements were conducted with the Fullzone impeller (FZ) (Shinko Pantec Co. Ltd., Japan) which is one of large cross-section impellers. The FZ impeller (DI = 0.55DT) consists of two large paddle impellers, and the upper paddle is shifted at 45° in the rotating direction. The detailed design of the FZ impeller used in this study are presented in our previous paper.5 Tap water was used as liquid phase. Experiments were performed in a semibatch manner. 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 vol %. It was found in our previous study5 that at very low impeller speeds the floating particles formed a stagnant layer on the liquid surface and there was a clear liquid zone in the lower part of the tank. With increasing impeller speed, particles were partially dispersed into the liquid phase and the stagnant layer volume was reduced. Floating particles were gradually drawn down into the liquid from the stagnant layer 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, as shown in Figure 1, the tank could be divided in three distinct zones: a stagnant layer of particles, a slurry zone, and a lower clear liquid zone. With an increase in impeller speed, the number of solids particles in the slurry zone increased, and as a result the cloud height also increased. As mentioned above, the top impeller was immersed into the stagnant layer of the floating particles. The particles in the stagnant layer were swept to the periphery by the centrifugal force of the impeller immersed in the floating-solid stagnant layer. With further increasing impeller speed, more solids were dispersed into the liquid, and finally the floating stagnant layer was broken up and all solids were completely dispersed. The slurry zone height approached the tank bottom, and both the stagnant layer volume and the clear liquid height fell to zero. Power consumption, P or Pg, was measured using torque meters (Three-One Motor, Shinnto Sci. Co.). The gas hold-up, εg, was estimated as the increase in volume of the gassed liquid compared with ungassed liquid volume as well as by Bao et al.4,10 The change in liquid volume was measured by observing the height of the surface of the ungassed liquid and aerated liquid. It should be noted that the gas hold-ups in the unbaffled stirred tank could not be measured by observing the change in heights of the surface since a vortex was formed and the free surface was not flat. The dynamic gassing-out method was used to measure kLa in the stirred tank with different aeration rates, impeller speeds, and solids loadings.16,17 The dissolved oxygen concentration (DO) was measured with a fast response polarographic oxygen electrode (YSI Model 57, Yellow Springs Instrument Co., Ohio).17 As well as in the work of Cachaza et al.,18 the delay of the oxygen electrode
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Figure 2. Effect of solid suspension on power consumption in the floating solidliquidgas three-phase stirred tank. (a) Effect of floating solids concentration at Ug = 0.004 m s1(Particle: SA, with baffles). (b) Effect of superficial gas velocity at φs = 0.5 (Particle: SA, with and without baffles, NB: unbaffled). (c) Effect of superficial gas velocity at φs = 0.5 (Particle: PP, with and without baffles, NB: unbaffled).
response was negligible. To avoid the disturbance in the response due to motion of bubbles, the electrode held upside down was attached to a rigid extension rod, and its surface was placed just below the upper impeller. When the baffles were installed, the electrode was placed behind the baffle. The values of kLa obtained by the dynamic gassing-out method in this study included a contribution of mass transfer through the free-surface besides that 1940
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3. RESULTS AND DISCUSSION 3.1. Effects of Floating Solids Loadings on Power Consumption. The power consumption values are plotted in
Figure 2 against the impeller speed. With an increase in impeller speed the power consumption increased. As shown in Figure 2a, the power consumption decreased with an increase in floating solids concentration at a given impeller speed. The largest value of Pg was obtained when no floating particles were present. At N = 12 s1 and Ug = 0.004 m s1, the reduction of power consumption was about 20% with increasing solid concentration from 0 to 0.5. The above findings are contrary to the results for settling solids which are heavier than the liquid.21 The floating particles decreased the apparent density of the slurry (Fslurry = Fsφs þ F(1 φs)). Since the power consumption is proportional to the liquid density, the power consumption decreased as the solid concentration increased. Bao et al.10 found that the solid concentration caused only insignificant change in the power consumption with aeration rate in the solid loading range of 0 to 0.15. The influence of floating solids concentration was more significant at higher impeller speeds. It is clear from Figure 2b and c that the aeration led to a decrease in the power consumption, and the baffles caused rather increased power consumption. The decrease in power consumption due to aeration is because of the formation of cavity behind the impeller blades. For SA particles at φs = 0.5, the aeration at Ug = 0.004 m s1 resulted in almost 30% decrease in the power consumption when N = 12 s1. As shown in Figure 2b and c, the lowering of power consumption due to the absence of baffles was around 35%. Baffles, which create more turbulent motion and convert the transitional liquid motion into axial motion, result in the significant increase in power consumption. 3.2. Effects of Floating Solids Loadings on Gas Hold-up. Gas hold-up is one of the most important parameters critically affecting gasliquid mass transfer rate. The volumetric mass transfer coefficient (kLa) is the product of the liquid-phase mass transfer coefficient (kL) and the specific surface area (a), and a number of factors affect kL and a in different fashions. The gas hold-up gives a useful indication about the specific surface area available for gasliquid mass transfer and depends on many variables such as gas velocity, impeller speed, solid loading, particle diameter, stirred tank configuration, and so on. The values of εg are plotted in Figure 3 against the impeller speed. To clarify three regions for floating solid particles dispersion, that is, N < Njsg, Njsg < N < Nusg, and N > Nusg, values of Njsg and Nusg at different solid concentrations and gas flow rates calculated by the correlations in our previous paper5 are presented in the figure. The correlations for the minimum impeller speed for offsurface floating-particle suspension may be written as5 " #0:45 ðF F Þ l s Njs ¼ Sνl 0:1 g Xs 0:13 dp 0:2 DI 0:85 ð1Þ Fl Figure 3. Effect of solid suspension on gas hold-up in the floating solidliquidgas three-phase stirred tank. (a) Effect of floating solids concentration at Ug = 0.004 m s1 (Particle: SA, with baffles). (b) Effect of superficial gas velocity at φs = 0.5 (Particle: SA, with baffles). (c) Effect of superficial gas velocity at φs = 0.5 (Particle: PP, with baffles).
through the bubble surface. In general, under the air sparged conditions mass transfer through the free-surface is significantly smaller as compared with that through the bubble surface.19,20
for floating solidliquid two-phase systems Ug 3:0 Njsg ¼ Njs 1 þ Ut
ð2Þ
for floating solidliquidgas three-phase systems. In the absence of four fully immersed baffles causing a poor suspension of the floating solids, the following relationship was obtained5 Njsnb or Njsgnb ¼ 1:2 ðNjs or Njsg Þ 1941
ð3Þ
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The terminal floating velocity of solid particles Ut is evaluated by the following equation " #1=3 4 ðFl Fs Þ2 g 2 Ut ¼ dp ð4Þ 225 μl Fl By considering the Reynolds number region in this study, we applied Allen’s law to derive the above equation. It should be noted that the proportional constant in eq 1, S, presented in Table 3 of our previous paper5 should be corrected. For SA particles, the values of S for DT, dual four-pitched blade downflow disk turbines (PDT), Fullzone impeller (FZ), and Maxblend impeller (MB) should be 3.99, 5.45, 2.68, and 2.32, respectively. For PP particles, the values of S for DT, PDT, FZ, and MB should be 4.12, 5.76, 2.61, and 2.53, respectively. We5 previously obtained the correlations for the minimum impeller speeds for ultimately homogeneous floating-particle suspensions. They may be written as " #0:40 ðFl Fs Þ 0:25 g dp 0:47 Xs 0:009 DI 0:80 ð5Þ Nus ¼ Kνl Fl for floating solidliquid two-phase systems Ug 2 Nusg ¼ Nus 1 þ Ut
ð6Þ
for floating solidliquidgas three-phase systems. For the absence of four fully immersed baffles, the following relationship was obtained Nusnb or Nusgnb ¼ 1:3 ðNus or Nusg Þ
ð7Þ
It can be seen that the value of εg increased with increases in N and Ug. This can be attributed to the breakage of the gas bubbles into smaller size with an increase in the impeller speed and gas flow rate. Figure 3a shows that the gas hold-up was significantly affected by the solids volume fraction, with the largest gas holdup values being obtained when no floating solids were present. The gas hold-up decreased as the solid concentration increased at a given impeller speed. The effect of solid loading was particularly significant at higher impeller speeds. At N = 12 s1 and Ug = 0.004 m s1, the solid loading of 50 vol % caused about 35% reduction of gas hold-up. Similar trends have been observed for settling solid particles by several investigators.17,21 This trend coincides with the results reported for floating solid particles by Bao et al.10 The suspended solids leading to an increase of apparent slurry viscosity result in the increased bubble coalescence tendency, the formation of large bubbles having short residence time and then the decrease in gas hold-up. The experimental results in Figure 3 indicate that at low impeller speeds and gas flow rates gas hold-ups were almost constant and with increasing impeller speed gas hold-up significantly increased. The increase in the gas hold-up with increasing N and Ug is presumably due to the enhancement of the overall liquid turbulence causing the bubble break-up.13 The enhancement of bubble break-up might result in the increase in the number of small bubbles and then the increase in the gas hold-up. When the impeller speed was less than the minimum impeller speed for off-surface floating-particle suspension, Njsg, the gas hold-ups were almost constant. Under this dispersion condition, only a part of solid particles were suspended. Beyond the minimum impeller speed for ultimately homogeneous
floating-particle suspension, Nusg, the gas-holdups almost linearly increased with impeller speeds. In this mixing regime, homogeneous dispersions of solid particles occurred. In the regime where Njsg 6 s1). It should be noted that eq 10 was obtained using their experimental data at solids loadings from 0 to 15 vol %, which are rather lower than the solid concentrations ranging from 0 to 50 vol %. The somewhat stronger dependence of N on εg may be attributed to the combination of the larger impeller diameter as compared with the standard configuration26 and the large ring sparger. 3.3. Effects of Floating Solids Loadings on Volumetric Mass Transfer Coefficient. Variations of kLa as a function of impeller speed are presented in Figure 4. As expected the volumetric mass transfer coefficient increased with increasing impeller rotational speed or power input and gas flow rate. More power input and more aeration in their ranges used in this study caused an increase in surface area responsible for gasliquid mass transfer. It can be seen in Figure 4, as well as the results for εg, that for N < Njsg, the kLa coefficients were almost constant. The power input by the impeller, Pg, was mainly used to disperse the solids particles rather than to break up bubbles. In the regime where Njsg < N < Nusg, the kLa coefficients slowly increased with increasing N. For N > Nusg, the kLa coefficients continuously increased with impeller speeds. In this regime, the increase in power input was exclusively used to enhance the bubble break-up resulting in an increase in a and hence kLa. The values of Njsg and Nusg predicted by the correlations proposed in our previous study,5 eqs 17, are given in Figure 4. 1942
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7% of the value obtained for the gasliquid two-phase system. As described above, this was accompanied by the corresponding fall in the gas hold-up to 65% of that for the gasliquid two-phase system. The decrease in kLa with floating solid loading might be due to the increased apparent viscosity of the liquidsolid mixture, which enhanced bubble coalescence, thus decreasing the interfacial area. The extent of decrease in the kLa is more significant as compared with the reduction in the gas hold-up. As well as the present results for floating solid particles, Kawase et al.17 and Conway et al.27 found the kLa decreased with an increase of settling solid loading. Chapman et al.28 also obtained a substantial decrease in kLa at solids loading of 20% by mass. It should be noted that some investigators found complicated effects of the settling solid loading. For instance, Metha and Sharma29 observed that the presence of settling solids decreased and increased kLa coefficients at lower and higher solid concentrations, respectively. Incidentally the volumetric gasliquid mass transfer coefficient kLa in three-phase sparged reactors generally decreases with settling solids concentration.30 The influence of solid particles is primarily reflected in the reduction of specific surface area leading to the reduction of kLa. On the contrary, solid particles may also break up large bubbles formed by bubble coalescence. The bubble break-up causes an increase in a and hence kLa.13 The mechanisms for effects of the presence of floating on kLa coefficients still remain uncertain. It can be seen in Figure 4b and c that the kLa coefficient increased with increased superficial gas velocity. Changing gas flow rate affected the kLa values by changing the gas hold-up and hence the gasliquid interfacial area. At higher gas flow rates, gas hold-ups increased, leading to high a values, which in turn increased the kLa values. The results in Figures 4 b and c indicate that the kLa coefficient decreased with the absence of the baffles at a given impeller speed. This is closely linked in the decrease in power consumption with the absence of the baffles shown in Figures 2 b and c. In Figure 4a the present experimental kLa data are compared with the correlations in the literature. Kawase and Moo-Young31 obtained a theoretical correlation for kLa in non-Newtonian fluids on the basis of Higbie’s penetration theory and Kolmogoroff’s theory of isotropic turbulence. Their correlation for water may be written as F 3=5 ðPg =Fl VL Þ13=20 Ug 1=2 ð11Þ kL a ¼ 0:675Sc1=2 l Ub ðμl =Fl Þ1=4 σ 3=5 Here, the terminal velocity of bubbles in free rise Ub is assumed to be 0.265 m s1.31 van’t Riet32 proposed the following empirical correlation for kLa in water Figure 4. Effect of solid suspension on volumetric gasliquid mass transfer coefficient in the floating solidliquidgas three-phase stirred tank. (a) Effect of floating solids concentration at Ug = 0.004 m s1 (Particle: SA, with baffles). (b) Effect of superficial gas velocity at φs = 0.5 (Particle: SA, with and without baffles, NB: unbaffled). (c) Effect of superficial gas velocity at φs = 0.5 (Particle: PP, with and without baffles, NB: unbaffled).
It is evident from Figure 4a that the presence of floating solid particles drastically reduced the volumetric gasliquid mass transfer coefficient. For N = 12 s1 the kLa value dropped to
kL a ¼ 0:026ðPg =VL Þ0:4 Ug 0:5
ð12Þ
The predictions of these two correlations, eqs 11 and 12, agree reasonably well with the experimental data for gasliquid twophase system (φs = 0). 3.4. Correlations for Power Consumption, Gas Hold-Up, and Volumetric GasLiquid Mass Transfer Coefficient. Correlations were developed for the power consumption, gas hold-up, and volumetric gasliquid mass transfer coefficient in a floating solidliquid gas three-phase stirred tank using results obtained in this study. They are based on the power consumption, superficial gas velocity, and solid concentration. 1943
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(a). Power Consumption. By a regression analysis we developed the following correlation for power consumption in floating solidliquidgas three-phase stirred tanks. Ug 1 ð1 þ 0:5φs Þa1 ð13Þ Pg ¼ P 1 þ NDI Previously we5 obtained the following correlation for the power consumption of the dual DT impellers in floating solidliquid two-phase systems P P ¼ NP Fl N 3 DI 5
ð14Þ
where Np for the dual DT impellers is 4.0. Furthermore, the power consumption values for both floating solidliquid twophase system and floating solidliquidgas three-phase system reduced by 35% without baffles, and the following relationship was obtained Pnb or Pgnb ¼ 0:65 ðP or Pg Þ
ð15Þ
The second and third terms in the right-hand side of eq 13 are introduced as additional terms for effects of aeration and floating solid particles, respectively. The exponents on the solid concentration, a1, obtained by regression of the experimental data for SA and PP particles are 0.3 and 0.1, respectively. Since these exponents are negative, eq 13 indicates the decrease in the power consumption with an increase in the floating solid concentration. In Figure 5, the experimental results are compared with the predictions of the above correlations. The correlations can be found to fit the experimental data with the mean deviation of 16.5%. (b). Gas Hold-Up. The prediction of gas hold-up is very difficult because of the complexity of the hydrodynamics in stirred tanks. Therefore, various investigators have correlated values of gas hold-up in stirred tanks to power consumption per unit volume (Pg/VL) and superficial gas velocity (Ug).16,22 εg ¼ C1 ðPg =VL ÞR1 Ug β1
ð16Þ
where the exponents R1 and β1 range from 0.15 to 0.4 and 0.3 to 0.75, respectively.33 Regression of the data in Figure 3 showed that the proportionality constant is 0.25, and the exponents on power density and superficial gas velocity are 0.40 and 0.75, respectively. By considering the additional term for the effect of floating solid particles which is the same as that in the correlation of Bao et al.10 (eq 10), the resulting correlation may be written as εg ¼ 0:25ðPg =VL Þ0:40 Ug 0:75 ð1 þ φS Þa2
Figure 5. Comparison of predictions of eqs 1315 and experimental data for power consumption in the floating solidliquidgas three-phase stirred tank. (a) Effect of floating solids concentration at Ug = 0.004 m s1 (Particle: SA, with baffles). (b) Effect of superficial gas velocity at φs = 0.5 (Particle: SA, with and without baffles, NB: unbaffled). (c) Effect of superficial gas velocity at φs = 0.5 (Particle: PP, with and without baffles, NB: unbaffled).
ð17Þ
The exponents of (Pg/VL) and Ug in eq 17 are within the range of those in the literature. The exponent on the solid concentration a2 is 1.0 for SA particles and 0.7 for PP particles. The negative exponents on (1 þ φs) indicate that the floating solids reduce εg by causing enhanced bubble coalescence. The exponent a2 for SA particles in eq 17 is somewhat smaller than that for PP particles. Therefore, the presence of SA particles somewhat strongly affects the gas hold-up as compared with PP particles. These values are lower as compared with the exponent of 2 obtained by Bao et al.10 In other words, the influence of floating particles obtained in this study was rather weaker than that of Bao et al.10 1944
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Figure 6. Comparison of predictions of eq 17 and experimental data for gas hold-up in the floating solidliquidgas three-phase stirred tank. (a) Effect of floating solids concentration at Ug = 0.004 m s1 (Particle: SA, with baffles). (b) Effect of superficial gas velocity at φs = 0.5 (Particle: SA, with baffles). (c) Effect of superficial gas velocity at φs = 0.5 (Particle: PP, with baffles).
In Figure 6 the proposed correlation is compared with the present experimental results. The proposed correlation correlates reasonably well the experimental data with the average error of 15.0%. (c). Volumetric GasLiquid Mass Transfer Coefficient. By performing regression analysis on the experimental results, the kLa coefficient in stirred tank reactors has been correlated to the gassed power consumption per unit volume and superficial gas
Figure 7. Comparison of predictions of eq 19 and experimental data for volumetric gasliquid mass transfer coefficient in the floating solid liquidgas three-phase stirred tank. (a) Effect of floating solids concentration at Ug = 0.004 m/s (Particle: SA, with baffles). (b) Effect of superficial gas velocity at φs = 0.5 (Particle: SA, with and without baffles, NB: unbaffled). (c) Effect of superficial gas velocity at φs = 0.5 (Particle: PP, with and without baffles, NB: unbaffled). 1945
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for the solid concentration is introduced into eq 18. The resulting correlation may be written as: kL a ¼ 0:0090ðPg =VL Þ0:50 Ug 0:45 ð1 þ 3:2φS Þa3
Figure 8. Power consumption, gas hold-up, and volumetric gasliquid mass transfer coefficient in the floating solidliquidgas three-phase stirred tank with the Fullzone impeller (Particle: PP and φs = 0.5, with baffles). (a) Power consumption, (b) Gas hold-up, (c) Volumetric gasliquid mass transfer coefficient.
velocity.16,33,34 kL a ¼ C2 ðPg =VL ÞR2 Ug β2
ð18Þ
As summarized by Garcia-Ochoa and Gomez,33 the exponents R2 and β2 range from 0.4 to 1.0 and 0.3 to 0.8, respectively. A single correlation was regressed for the entire range of the operational conditions studied in this work. The correction term
ð19Þ
The coefficients in the above correlation were determined by the regression analysis of the experimental data presented in Figure 4. The proportionality constant is 0.009, and the coefficient in the additional term for the solid concentration is 3.2. The exponents on power consumption per unit volume and superficial gas velocity are 0.50 and 0.45, respectively. The exponents on the solid concentration a3 for SA and PP particles are 3.0 and 0.6, respectively. Since the exponent a3 is negative, eq 19 indicates that the kLa coefficient decreases as the solid concentration increases. The exponent over (1 þ 3.2φs) for SA particles is rather lower than that for PP particles. This result suggests that the influence of floating particles on kLa for SA particles is more drastic as compared with that for PP particles. The exponents of the above equation are within the range of those cited in the literature.33 Figure 7 compares the predictions of the proposed correlation with the experimental data. The agreement is seen to be satisfactory. The average deviation of eq 19 from the experimental data is 23.5%. It should be noted here that the power consumption (Pg/VL) also depends on the solid loadings while the additional term (1 þ 3.2φs)a3 in eq 19 is the main correction factor for the presence of floating solid particles. The influence of the baffles on kLa is also included in the term for the power consumption per unit volume decreased with the absence of the baffles. 3.5. Volumetric GasLiquid Mass Transfer Coefficient with Fullzone Impeller. For reference we measured kLa values with the Fullzone impeller. The liquid flow pattern created by the FZ impeller is characterized by a global axial recirculation flowing downward near the impeller shaft and upward near the tank wall. Figure 8 depicts the experimental results for power consumption, gas hold-up, and volumetric gasliquid mass transfer coefficient with the FZ impeller. It can be seen from Figures 3c and 8b that as expected at the same impeller speeds the gas hold-ups for the FZ impeller were somewhat larger as compared with those for the dual DT impellers. As well as the results for gas hold-ups, kLa values of the FZ impellers in Figure 8c are larger as compared with those of the dual DT impellers in Figure 4c at a given impeller speed. It should be mentioned here that as shown in Figures 2c and 8a the power consumption for the FZ impeller is about 6 times of that for the dual DT impellers at a given impeller speed. Consequently it may be concluded that the FZ impeller is not very effective for gas dispersion and gasliquid mass transfer as compared with the dual DT impellers while the dispersion of floating solid particle of large cross-section impellers is superior to that of small-scale high-speed impellers like disk turbines (Tagawa et al.5). The dual DT impellers were rather capable of breaking the gas into small bubbles and dispersing the bubbles throughout the liquid. Small bubbles having lower rising velocities resulted in larger gas hold-ups and then larger volumetric gasliquid mass transfer coefficients. Therefore, the kLa coefficients of the dual DT impellers were comparable to those of the FZ impeller at a given power consumption.
4. CONCLUSIONS This is the first preliminary study on the gasliquid mass transfer in floating solidliquidgas three-phase stirred tanks. The solid concentration was varied up to 50 vol %. In general, the 1946
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Industrial & Engineering Chemistry Research presence of solids makes gasliquid operation more complicated. The power consumption decreased by the presence of floating particles because of the decreased slurry density. The measured values of εg and kLa were found to decrease with floating solids loading. In particular we found that the dense floating solid particles have a profound effect on gasliquid mass transfer rate. The kLa value dropped by an order of magnitude at φs = 0.5. The considerable reduction in the kLa values is probably due to the reduction in the surface area of the bubbles caused by the addition of floating solid particles. The presence of solids increasing the apparent viscosity of the liquid results in increased bubble coalescence tendency and allows the formation of large bubbles. This leads to a decrease in gas hold-up and subsequently a decrease in kLa. The kLa coefficient was found to decrease with the absence of the baffles. This is closely linked in the decrease in power consumption with the absence of the baffles. The correlations representing the dependences of εg and kLa on process variables were developed. The proposed correlations for gas hold-up and volumetric gasliquid mass transfer coefficient were found to fit the experimental data obtained in the solid loading range from 0 to 50 vol % with the average deviation of 15.0 and 23.5%, respectively. The Fullzone impeller being a large cross-section impeller was found to be not very effective for gas dispersion and gasliquid mass transfer as compared with the dual four-flat blade disk turbine impellers while the dispersion of floating solid particle of large cross-section impellers is superior to that of small-scale high-speed impellers such as disk turbines. The future experiments should be conducted to confirm the findings of the current work. Further work is ongoing to investigate the effect of a number of other parameters including physical properties of floating particles and different impeller configurations.
’ AUTHOR INFORMATION Corresponding Author
*Phone: þ81-49-239-1377. Fax: þ81-49-231-1031. E-mail:
[email protected].
’ NOMENCLATURE a = specific interfacial area, m2 m3 a1, a2, a3 = exponents on solid concentration in eqs 13, 17, and 19, respectively C1, C2 = proportionality constants in eqs 16 and 18, respectively D = diffusivity, m2 s1 DI = impeller diameter, m Dring = ring sparger diameter, m DT = stirred tank diameter, m dp = particle diameter, m g = gravitational acceleration, m s2 H = liquid height above TL, m K = constant in eq 5 kL = mass transfer coefficient, m s1 kLa = volumetric gasliquid mass transfer coefficient, s1 N = impeller speed, s1 Njsg = minimum impeller speed for off-surface floating-particle suspension under gassed condition, s1 Np = Power number (=P/N3DI5Fl) Nusg = minimum impeller speed for ultimately homogeneous floating-particle suspension under gassed condition, s1 P = power consumption, W
ARTICLE
Pg = gassed power consumption, W S = proportional constant in eq 1 Sc = Schmidt number (=μl/FlD) Ub = terminal velocity of bubble in free rise, m s1 Ug = superficial gas velocity, m s1 Ut = terminal floating velocity of particle, m s1 VL = liquid or slurry volume, m3 Xs = solids loading (solid weight/slurry weight) Greek Letters
r1, r2 = exponents on (Pg/VL) in eqs 16 and 18, respectively β1, β2 = exponents on Ug in eqs 16 and 18, respectively εg = gas hold-up φs = average solid volume fraction μl = liquid viscosity, Pa s νl = liquid kinematic viscosity, m2 s1 Fg = gas density, kg m3 Fl = liquid density, kg m3 Fs = solid density, kg m3 Fslurry = density of slurry, kg m3 σ = surface tension, N m1 Subscripts
nb = without baffles
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following eq 4. The corrected version of this paper was published March 22, 2011.
’ NOTE ADDED AFTER ASAP PUBLICATION The version of this paper that was published on March 18, 2011 had minor errors in the caption for Figure 1 and in the text 1948
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