Hydrodynamics in Three-Phase Stirred Tank Reactors with Non

Hydrodynamics in Three-Phase Stirred Tank Reactors with Non-Newtonian Fluids. Yoshinori Kawase*, Kazuhiro Shimizu, Takae Araki, and Tatsuya Shimodaira...
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Ind. Eng. Chem. Res. 1997, 36, 270-276

Hydrodynamics in Three-Phase Stirred Tank Reactors with Non-Newtonian Fluids Yoshinori Kawase,* Kazuhiro Shimizu, Takae Araki, and Tatsuya Shimodaira Biochemical Engineering Research Center, Department of Applied Chemistry, Toyo University, Kawagoe, Saitama 350, Japan

Hydrodynamic characteristics have been studied in three-phase stirred tank reactors with nonNewtonian fluids. Critical impeller speeds for solid suspension and liquid-phase mixing times were measured. With increasing gas flow rate, solid loading, and non-Newtonian flow behavior, the critical impeller speed for solid suspension increased. The experimental data for nonNewtonian fluids were reasonably correlated by the available equations generalized by replacing the Newtonian viscosity by the apparent viscosity for a non-Newtonian fluid. An increase in the liquid-phase mixing time due to solid loading was obtained in both Newtonian and nonNewtonian fluids. Although the introduction of gas caused a decrease in the mixing time for water, the mixing time in non-Newtonian fluids increased by the gas dispersion. The model for liquid-phase mixing time based on the energy dissipation rate fit the experimental data reasonably. Introduction Mechanically agitated stirred tank reactors have been widely used in the chemical, biochemical, and pharmaceutical industries. In the literature, therefore, there has been much attention paid to hydrodynamics in stirred tank reactors (Shah, 1992). Nevertheless, relatively little information is available on the mixing in mechanically agitated solid-gas-liquid three-phase tank reactors. While the solid suspension has been studied in the past for the solid-liquid two-phase systems, few studies have been reported in the literature regarding the solid-gas-liquid three-phase systems. Subbaroa and Taneja (1979), Chapman et al. (1983), Rewatkar et al. (1991), and Dutta and Pangarkar (1995) measured the critical impeller speed for complete particle suspension under gassed conditions. Chapman et al. (1983) proposed an empirical correlation. The nature of mixing in three-phase stirred tanks is very complicated, and the critical impeller speed may depend on several parameters such as superficial gas velocity, particlesettling velocity, impeller design, impeller diameter, sparger design, and its location. The published literature does not give sufficient elucidation regarding the solid suspension in three-phase stirred tank reactors. The liquid-phase mixing time is very useful for obtaining an overall idea regarding the average flow in stirred tank reactors. In spite of its prime importance, however, only limited work has addressed liquid-phase mixing in solid-gas-liquid three-phase stirred tank reactors. Dutta and Pangarkar (1995) reported the data for liquid-phase mixing time in multi-impeller threephase agitated contactors. Only a few measurements on critical impeller speed for particle suspension and liquid-phase mixing time in non-Newtonian fluids have been published. Recently, Kushalkar and Pangarkar (1995) experimentally measured the critical impeller speed for solid suspension in non-Newtonian fluids. In spite of the fact that many reactants represent non-Newtonian flow behaviors, a knowledge of the effects of non-Newtonian flow behav* To whom correspondence should be addressed. Phone: +81-492-39-1377. Fax: +81-492-31-1031. E-mail: bckawase@ krc.eng.toyo.ac.jp. S0888-5885(96)00452-6 CCC: $14.00

iors on hydrodynamics in solid-gas-liquid three-phase stirred tank reactors is severely limited at present. Therefore, it is desirable to undertake a study of liquidand solid-phase mixing in three-phase stirred tank reactors with non-Newtonian fluids. The objective of the present study is to examine the influence of nonNewtonian flow behaviors on hydrodynamics in threephase stirred tank reactors. Experimental Section The experimental setup is shown schematically in Figure 1. Experiments were carried out in a 0.2 m diameter mechanically stirred tank fitted with a flat bottom, four 0.02 m (b/DT ) 0.1) wide baffles, and a ring sparger having 20 holes of 1 mm diameter. Six bladed disk turbines (DI ) DT/2 and DT/3) and six 45°-pitched turbine downflows (DI ) DT/2 and DT/3) were used in this study. Details of the impeller design are given in Table 1. The impeller clearance from the tank bottom was 1/3 of the tank diameter. The ring sparger had a diameter equal to 0.8(DT/3) and was located at a distance DT/6 above the tank bottom. Table 2 summarizes the physical properties of the liquids used in this study at room temperature (295.15299.15 K). The actual physical properties were measured individually for each experiment. Tap water was used as a Newtonian liquid. The aqueous solutions of carboxymethylcellulose (CMC) (Daiseru Chem. Co.) and xanthan gum (XG) (Sigma Chem. Co.) were used to study the effect of non-Newtonian flow behaviors. Their rheological properties were assumed to be represented by a power-law model:

τ ) Kγ˘ n

(1)

Rheological measurements were carried out using a coaxial cylinder viscometer (B-type viscometer, Tokyo Keiki Co.) at shear rates of 1.68-79.2 s-1. Liquid densities were measured with a pycnometer. Three types of polymeric cylindrical particles were employed (Table 3). Since the use of solid-gas-liquid three-phase reactors containing low-density particles is finding many applications in biotechnology processes, low-density particles were used in this study. Experiments were carried out in a semibatch manner with © 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 271

curve for pH is shown in Figure 2. In this study the liquid-phase mixing time was defined as the time required to achieve 95% homogeneity. Power consumption was measured using a torque meter fitted to the shaft, and the impeller speed and power input were indicated on the signal indicator unit (Three-One Motor RX, Shinnto Sci. Co.). Results and Discussion

Figure 1. Experimental setup. Table 1. Details of Impellers impeller

no. of blade

DT1 DT2

6 6

PTD1 PTD2

6 6

diameter (m)

blade width (m)

blade length (m)

Disk Turbine 0.096 0.020 0.066 0.0135

0.025 0.017

45°-Pitched Turbine Downflow 0.096 0.020 0.066 0.0135

0.025 0.017

Table 2. Rheological Properties of Liquids at Actual Test Conditions

water 0.5 wt % CMC 0.3 wt % xanthan gum

density (kg m-3)

flow index

consistency (Pa sn)

999 1001 1000

1 0.86 0.218

0.000 95 0.212 1.86

Table 3. Particles Used in This Study (Shape: Cylindrical)

particle A (poly(vinyl chloride)) particle B (poly(vinyl chloride)) particle C (polycarbonate)

density (kg m-3)

diameter (m)

length (m)

1430 1200 1030

0.004 0.002 0.002

0.002 0.004 0.003

known volumes of liquid and solid forming the batch through which air was continuously sparged. The air flow rate was measured with a precalibrated rotameter. The gas rates used were between 5 and 15 L min-1, corresponding to 0.8-2.4 vvm (volumetric gas flow rate (m3 min-1)/liquid volume (m3)). The critical impeller speed for the suspension of solid particles was obtained using visual observations (Zwietering, 1958). At this speed no particles remained on the tank bottom for more than 1 or 2 s. The values of liquid-phase mixing time were obtained by transient pH measurements (Pandit and Joshi, 1983). The point of pulse addition was the top of the dispersed height (the injection point is shown in Figure 1). The quantity of the pulse was less than 1/100 of the bulk liquid volume in the tank. A pH electrode was placed between the impeller region and baffles at a position giving the least noisy signal. The pH responses were recorded with a chart recorder. A typical response

Critical Impeller Speed for Solid Suspension: NJS and NJSg. Figure 3 shows variation of critical impeller speed for solid suspension, NJS and NJSg, with superficial gas velocity, Usg. An increase of the critical impeller speed with increasing gas flow rate is evident from the figure. However, the extent of increase decreased at higher gas velocities. Sircard et al. (1980), Chapman et al. (1983), and Dutta and Pangarkar (1995) obtained similar trends with the present results. The increase in impeller speed required for complete solid suspension under a gassed condition is mainly due to the decrease in power resulting from cavity formation behind the impeller blade. A larger power requirement is required to cause suspension of solid particles under aerated conditions than that under unaerated conditions, suggesting that the gas presence has an additional effect besides a reduction of liquid flow from the impeller region, in damping local turbulence and velocities near the tank bottom. The presence of a sparger may obstruct liquid flow effective to solid suspension and reduce turbulence generated by an impeller. Furthermore, the liquid flow directed toward the tank bottom, which is more efficient for solid suspension compared with the upward liquid flow, may be suppressed by the upward liquid flow generated by bubble rising. Although in general the axial flow impellers are known to be efficient for solid suspension (Rao et al., 1988), in this work the disk turbine required lower impeller speed to suspend solids compared with the pitched-blade turbine downflow. This discrepancy may be due to different designs of impellers. Furthermore, the ring sparger positioned between the impeller and the tank bottom might not only obstruct downward flow but also reduce turbulence available for solid suspension. Visual observations of particle motion near the tank bottom suggested that the PTD used in this study did not generate strong downflow. It is mentioned, incidentally, that Rewatkar et al. (1991) found effects of blade width and blade thickness on critical impeller speed. It is also seen from the figure that the critical impeller speeds for solid suspension increased with an increase in liquid viscosity. This trend is consistent with the prediction of Zwietering’s (1958) correlation. Zwietering (1958) proposed the following empirical correlation to predict the critical impeller speed of agitation required for the complete suspension:

NJS )

S(µl/Fl)0.1dp0.2(g∆F/Fl)0.45X0.13 DI0.85

(2)

where S is a function of impeller type and system geometry and the values of S are represented in the paper of Zwietering (1958). It is seen from Figure 3 that the variation of the critical impeller speed with gas flow rate for the CMC solution is somewhat larger than that for water. Frijlink et al. (1990) pointed out that the increase of the critical impeller speed for solid suspension when gas is intro-

272 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997

Figure 2. Typical response curve for CMC at Qg ) 5 L min-1 and N ) 7 s-1.

Figure 3. Effect of gas flow rate on the critical impeller speed for solid suspension (particle B, 5 vol %).

duced is strongly related to the power reduction caused by cavity formation. Certainly, the reduction in power consumption due to aeration results in the formation and periodic shedding of gas cavities behind the impeller, and the size and stability of the cavities may be affected by non-Newtonian flow behaviors. Under the range of experimental conditions covered in this work, however, the reduction in power consumption for the CMC was about 47%, which was almost same as that for water. Since direct measurements of the size of cavities and the frequency cavity shedding were not performed in this work, no quantitative explanation for the effects of non-Newtonian flow behaviors on the variation of NJSg with Usg is impossible. In spite of its higher consistency index K or viscosity, the values of NJS and NJSg for the xanthan gum solution are smaller than those for the CMC solution. This may be due to

stronger shear thinning and viscoelasticity of the xanthan gum solution. The viscosity of Newtonian liquids reduces the liquid flow generated by the impeller, and as a result the values of NJS and NJSg increase. On the other hand, shear thinning enhances liquid flow near the impeller available for solid suspension. The apparent viscosity of shear-thinning liquids decreases with increasing shear rate. Since the impeller creates high shear rates, the apparent viscosity of a shear-thinning fluid in the vicinity of the impeller is rather low and mixing is relatively good. For non-Newtonian fluids, there is a wide distribution of apparent viscosity in stirred tank reactors. It makes hydrodynamic characteristics very complicated. The resulting changes in NJS and NJSg depend on whether the viscosity decreases or the shear thinning increases the tendency of solid suspension. It should be noted that Chapman et al. (1983) observed no measurable effect on NJSg with increasing the kinematic viscosity from 10-6 to 5 × 10-6 m2 s-1. The variation of the critical impeller speed with solid loading in solid-gas-liquid three-phase systems is depicted in Figure 4. The values of NJSg for both Newtonian and non-Newtonian fluids increase slightly with an increase in solid loading in the range 5-15 vol % as well as the results reported by Rao et al. (1988) and Dutta and Pangarkar (1995). Zwietering’s (1958) correlation, eq 2, also suggests that the exponent of X is 0.13 and an increase in NJS with increasing solid loading is very small. With an increase in solid loading, the liquid flow generated by the impeller might decrease due to the energy dissipation at the solid-liquid interface. Figure 5 compares eq 2 with the present data for the solid-liquid two-phase systems. For non-Newtonian fluids, the Newtonian viscosity µl in eq 2 is replaced by the apparent viscosity defined as

µA ) K(ksN)n-1

(3)

Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 273

Figure 4. Effect of solid loading on the critical impeller speed for solid suspension (particle B, Qg ) 5 L min-1).

Figure 6. Comparison of experimental results and eq 4 for the critical impeller speed for a solid suspension in a gas-solid-liquid system.

Chapman et al. (1983) proposed the following correlation for a solid-gas-liquid three-phase stirred tank reactor

∆NJS ) NJSg - NJS ) 0.94Qg

Figure 5. Comparison of experimental results and eq 2 for the critical impeller speed for a solid suspension in a solid-liquid system.

This relationship was proposed by Metzner and Otto (1957), and the values of ks are given in the books of Skelland (1967, 1983). The surface-to-volume mean diameter was used as the particle diameter, dP. For reference, the data in Newtonian systems of Narayanan et al. (1969) and Rao et al. (1988) are also plotted in Figure 5. On the whole, reasonable agreement can be found. Recently, Kushalkar and Pangarkar (1995) measured the critical impeller speed for complete solids suspension in non-Newtonian CMC liquids (n ) 0.9850.633; K ) 0.0058-0.1350 Pa sn). In Figure 5, their data with benzoic acid granules for disk turbine impellers are compared with eq 2. It can be seen that their data lie within 30% of the correlation. It should be noted, as pointed out by Rewatkar and Joshi (1991), that the critical impeller speeds for Newtonian fluids reported by different investigators deviate in the range -25 to +70% from Zwietering’s predictions, eq 2.

(4)

where Qg is in vvm. We extend this correlation for Newtonian fluids to non-Newtonian fluids by replacing the Newtonian viscosity µl appearing in the term of NJS with the apparent viscosity µA given by eq 3. In other words, the influence of non-Newtonian flow behaviors on the critical impeller speed is assumed to be insignificantly affected by the gas sparging. The predictions of eqs 2-4 are compared with the present data for Newtonian and non-Newtonian fluids in Figure 6. The somewhat discrepancy between eqs 2-4 and the present work with regard to the impeller size can be seen. As pointed out by Skelland and Dimmick (1969), the discrepancy may be due to the distribution of the apparent viscosity in the stirred tank reactor which depends on non-Newtonian characteristics and impeller diameters and speeds. For comparison, the data in three-phase systems with non-Newtonian CMC solutions of Kushalkar and Pangarkar (1995) are also plotted in Figure 6. Reasonable agreement can be found. It is seen from Figures 5 and 6, however, that the influence of particle sizes on NJS and NJSg in their experiments is somewhat larger than that predicted by eqs 2 and 4. Liquid-Phase Mixing Time: θM. Values of liquidphase mixing time in CMC aqueous solution plotted against impeller speed are shown in Figure 7. The value of θM decreases with an increase in impeller speed N. It is also seen from Figure 7 that the value of θM has higher values owing to the presence of solid particles. This result coincides with that for solid-liquid two-phase systems reported by Rao and Joshi (1988). As the impeller speed increases, more and more solid particles become suspended. An increasing amount of energy is spent at the solid-liquid interface, and as a result less energy is available for liquid-phase mixing. Therefore, the liquid-phase mixing times for solidliquid systems lie somewhat above those of the liquid

274 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997

Figure 7. Effect of impeller speed on mixing time in CMC solution (particle A).

mixing time up to a certain gas flow rate, but at the impeller speeds above the critical impeller speed the introduction of gas increases the mixing time. According to the empirical correlation for the prediction of critical impeller speed proposed by Van Direndonck et al. (1968), most impeller speeds in the present study are below the critical impeller speed. It implies that as expected the present results for mixing time obtained above the critical impeller speed coincide with the results of Pandit and Joshi (1983). In the case of CMC aqueous solution, the introduction of gas increased the mixing time. Because of cavity formation behind the impeller, the intensity of eddy motion decreased and turbulent energy dissipation was reduced, and as a result a relatively substantial increase of the mixing time compared with that of pure liquid phases resulted at lower impeller speeds. In viscous non-Newtonian fluids, rather stable cavities were formed behind the impeller. In the region of N > 7 s-1, the influence of gas dispersion became weak because of the breakup of the cavity. At higher impeller speeds, the liquid flow generated by the impeller controlled liquidphase mixing instead of the liquid flow produced by the aeration. Dutta and Pangarkar (1995) found a maximum in the θM vs N curve at the critical speeds for solid suspension and for complete gas dispersion. In this work, we could not obtain maximum liquid-phase mixing time. It is also understood from Figure 8 that the mixing times for water were shorter than those in CMC solution. The experimental data for the liquid-phase mixing in three-phase stirred tank reactors are analyzed on the basis of simplified model. Kawase and Moo-Young (1989) developed a correlation for the mixing time in a stirred tank on the basis of Kolmogoroff’s theory of isotropic turbulence. Their correlation for a singlephase system may be written as a function of the energy dissipation rate as follows:

θM ) Figure 8. Effect of liquid property on mixing time (gas-liquid system).

alone. As shown in Figure 7, an introduction of gas results in the slightly larger liquid-phase mixing time as compared with the nonaeration systems. Figure 8 depicts effects of aeration on liquid-phase mixing time in water and CMC solution. For water, the value of θM in the presence of aeration is lower than in liquid alone. The liquid-phase mixing time in water at low impeller speed decreased due to aeration. In other words, the liquid-phase mixing process at lower N might be rather controlled by the gas flow rate. In fact visual observation indicated that at low impeller speed and high gas flow rate bubble column behavior was predominant. As the gas flow rate increased, therefore, the liquid-phase mixing time decreased. At higher impeller speeds, stirred tank behavior completely controlled the liquid mixing and the influence of gas injection was insignificant. In this impeller speed region, the liquid mixing was mainly caused by the impeller pumping flow rather than the gas dispersion. Einsele and Finn (1980) measured blending or mixing time in the 0.28 m i.d. stirred tank using the pH response technique. Their results suggested that the mixing time increases due to the introduction of gas, unlike the present results. On the other hand, Pandit and Joshi (1983) found that at low impeller speeds the introduction of gas reduces

2DT2 ) 6.35 × 2(5n-2)/3nDT2/3-1/3 EZ

(5)

It is assumed that the above correlation is applicable even to two- and three-phase systems by using the energy dissipation rate  for the systems. Substitution of the values of the energy dissipation rate measured or predicted into eq 5 provides the estimation of the liquid-phase mixing time θM. In this study, the measured energy dissipation rates were used to estimate the mixing times in one-, two-, and three-phase systems. The functional form of this equation is same as that of Mersmann’s (1985) correlation. Incidentally, it is also possible to evaluate the axial dispersion coefficients Ez using eq 5. Values of θM predicted by eq 5 and observed values for unaerated systems of liquid alone are depicted in Figure 9. The experimental results of Pandit and Joshi (1983), Rao and Joshi (1988), Abrardi et al. (1990), and Rewatkar and Joshi (1993) for liquid single-phase systems are also compared with eq 5. It can be seen that the agreement between predicted values of θM and the experimental values of θM in the absence of gas and solid is good. Figure 10 compares the data of liquid-phase mixing time for gas-liquid two-phase systems with eq 5. Typical experimental data for θM in gas-liquid twophase systems reported by Abrardi et al. (1990), Rewatkar and Joshi (1993), and Satoh et al. (1995) are also

Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 275

Figure 9. Comparison of experimental data and eq 5 for mixing time in liquid single phase (impeller in this study: DT1). Figure 11. Comparison of experimental data and eq 5 for mixing time in gas-solid-liquid three phase (impeller in this study: DT1).

Figure 10. Comparison of experimental data and eq 5 for mixing time in gas-liquid two phase (impeller in this study: DT1).

shown for comparison. On the whole, reasonable agreement can be found. A comparison between the data and eq 5 for the liquid-phase mixing time in gas-liquid-solid threephase systems is shown in Figure 10. Satisfactory agreement is seen between the experimental data for water and CMC aqueous solution and the predictions of eq 5. Rao and Joshi (1988) measured liquid-phase mixing times in mechanically agitated tanks of diameter 0.57 and 1.0 m. Tap water was used as the liquid phase, and quartz particles (Fs ) 2520 kg m-3) were used as the solid phase. It is seen from Figure 10 that the data of Rao and Joshi (1988) can be also reasonably correlated by eq 5. Conclusions Experimental data on the critical impeller speed for solid suspension and liquid-phase mixing time have been obtained in the three-phase stirred tank reactor with non-Newtonian fluids.

The critical impeller speeds for solid suspension for non-Newtonian fluids were found to be higher than those for water. While the increase in viscosity led to an increase in NJS and NJSg, the increase in shearthinning anomaly caused a decrease in NJS and NJSg. As an overall effect of these contraries, the critical impeller speed for solid suspension may decrease or increase. Aeration of the solid suspension in nonNewtonian liquids resulted in an increase of the critical impeller speed as well as that in water. The correlations for NJS and NJSg which were obtained by modifying the existing correlations for Newtonian fluids fit the data for non-Newtonian fluids reasonably well. An increase in the liquid-phase mixing time due to solid loading was obtained in both Newtonian and nonNewtonian fluids. The introduction of gas caused a decrease in the mixing time for water. On the other hand, the mixing time in non-Newtonian fluids increased by the gas dispersion. The model for liquidphase mixing time based on the energy dissipation rate correlated with the experimental data successfully. Further systematic investigations on effects of nonNewtonian flow behaviors on hydrodynamics will be required to increase confidence in the design and scaleup of three-phase stirred tank reactors with nonNewtonian media. Nomenclature b ) buffle width (m) C ) distance between sparger and tank bottom (m) dP ) particle diameter (m) DI ) impeller diameter (m) DT ) reactor diameter (m) EZ ) axial dispersion coefficient (m2 s-1) g ) gravitaional acceleration (m s-2) h ) impeller clearance from reactor bottom (m) H ) liquid height from reactor bottom (m) ks ) constant in eq 3 K ) consistency index in power-law model (Pa sn) n ) flow index in power-law model N ) impeller speed (s-1) NJS ) critical impeller speed for a solid suspension in solid-liquid two-phase system (s-1)

276 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 NJSg ) critical impeller speed for a solid suspension in solid-gas-liquid three-phase system (s-1) Qg ) gas flow rate (vvm) S ) proportionality constant in eq 2 Usg ) superficial gas velocity (m s-1) X ) solid loading (wt %) ∆NJS ) NJSg - NJS (s-1) ∆F ) density difference between particles and liquid (kg m-3)  ) energy dissipation rate (W kg-1) γ˘ ) shear rate (s-1) µl ) liquid viscosity (Pa s) µA ) apparent liquid viscosity (Pa s) ν ) kinematic viscosity (m2 s-1) θM ) mixing time (s) Fl ) liquid density (kg m-3) Fs ) solid density (kg m-3) τ ) shear stress (Pa)

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Received for review July 29, 1996 Revised manuscript received October 23, 1996 Accepted October 23, 1996X IE960452D X Abstract published in Advance ACS Abstracts, December 15, 1996.