Effect of Blade Shape on the Performance of Six-Bladed Disk Turbine

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Ind. Eng. Chem. Res. 2000, 39, 203-213

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Effect of Blade Shape on the Performance of Six-Bladed Disk Turbine Impellers Jorge M. T. Vasconcelos,* Sandra C. P. Orvalho, Ana M. A. F. Rodrigues, and Sebastia˜ o S. Alves Center for Biological and Chemical Engineering, Chemical Engineering Department, Instituto Superior Te´ cnico, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal

Different modifications of the Rushton turbine were studied in a dual-impeller agitated tank (T ) 0.4 m), to find the effect of blade form on power draw, turbulent dispersion, gas handling capacity, mixing, gas holdup, and mass-transfer rate performance under turbulent agitation in an air-water system. Blade streamlining was found to lead to a lower ungassed power number, a higher gas flow number before flooding, and increased insensitivity of impeller power dissipation to the gassing rate. This is consistent with the formation of smaller trailing vortices and ventilated cavities behind the blade. At the same power input and superficial gas velocity, however, the different impellers provided the same mixing time t0.05, gas holdup G, and specific mass-transfer coefficient KLa. Each of these variables correlates with the specific power input PG/VL, clearly suggesting that a better performance may be expected after retrofitting of Rushton turbines with streamlined impellers. Introduction Agitation is one of the important factors in the chemical and biochemical reaction processes. Gasliquid processes in particular, like fermentation and a variety of oxygenation and hydrogenation processes, need a large gas handling capacity and an effective gas dispersion for generating as large an interfacial area as possible. Disk turbines are radial-flow impellers that are particularly suitable for gas-liquid dispersion through mechanical agitation. This is so not only because the disk collects the gas underneath and forces it into the high shear zone near the blades where bubble formation occurs,1 but also because it eliminates the flow instabilities shown by open-blade turbines.2 The standard Rushton turbine is a six-bladed disk turbine and one of the most usual impellers found in the industry. Some weaknesses of the Rushton turbine as an ideal gas disperser have, however, been identified. First, there is an important fall in power demand after gas is introduced, usually more than 50% of the ungassed value. This represents an inconvenience for power prediction, but above all it means a loss of potential for heat and mass transfer.3 Second, the gas handling capacity of the Rushton turbine is handicapped by flooding occurring at relatively low gas flow numbers.4 Both disadvantages are due to the formation of high-speed, low-pressure trailing vortices at the rear of the blades5,6 which are associated with the phenomenon of boundary layer separation.7 Under gas dispersion, the low-pressure core of the trailing vortices attracts gas bubbles, which coalesce to form ventilated cavities behind the blades.8 These cavities not only lead to an increase in pressure and thus to an important fall in power relative to the ungassed situation,9 but also control turbine hydrodynamics and dispersion characteristics.10 The size and rotation of the trailing vortices * To whom correspondence should be addressed. Fax: 351.21 849 9242. E-mail: [email protected].

were found to be influenced by both blade number11 and blade curvature.10 Therefore, the blade shape may affect the ease of formation of the ventilated cavities and reduce their size in such a way that, even under gassing, power can remain high.12 Since the early papers on mixing research, different designs other than the traditional flat-blade Rushton turbine have been considered, like the arrowhead disperser,13,14 the curved-blade turbine,14,15 or, more recently, the divided, inclined blades turbine.16 In one of the earliest studies on a modified Rushton impeller, van’t Riet et al.10 presented results on the performance of convex and concave designs. Flattened power curves and improved gas handling capacity were obtained with a concave-blade turbine which led the authors10 to propose it as an attractive alternative. The same was done by Warmoeskerken and Smith12 while also claiming higher gas-liquid mass-transfer rates compared to the Rushton turbine, contrary to previous results by Smith.17 Other studies on concave/convex turbines have appeared since then,18 and several commercially available impellers were developed based on a similar design, like the Chemineer CD-619 and the parabolic-blade Scaba 6SRGT3,20 or ICI Gasfoil21 agitators. These new radial-flow impellers are preferably used nowadays as bottom gas dispersers in multiple agitators with axialflow impellers in the upper positions.22 Advantages have also been claimed for them in gas dispersion and solids suspension combined operations,23 as well as in gas dispersion in highly viscous liquids.24 The perforated-blade design was a different approach tried without success by van’t Riet et al.10 for modifying the Rushton turbine. It has recently been reported,25 however, that a perforated blade could significantly improve the oxygen-transfer efficiency, as well as the discharge efficiency of the Rushton impeller. The aim of this paper is to compare different sixbladed disk turbine designs, to define the best performing alternative for retrofitting operating Rushton turbine agitators. One of the important requirements for

10.1021/ie9904145 CCC: $19.00 © 2000 American Chemical Society Published on Web 12/09/1999

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Figure 1. Schematic diagram of the tank configuration and experimental setup.

retrofitting is that neither the agitator driver nor the drive assemblies be modified. This means that the new impeller is also of the radial-flow type, so that the modified blade must keep its symmetry relative to the disk. Different degrees of reduction of the boundary layer separation area in the blade rear were designed. Following an increasing order of expected streamlining of the blade wake, angled, semicircle, and lancet profiles were established as logical choices. Another important requirement was that retrofitting should enable as much of the power available to the motor as possible to enhance mass transfer across the whole speed and power input range. The performance criterion was, therefore, the minimization of power draw sensitivity to the gassing rate. A final requirement was that the retrofitting should not affect significantly the mixing efficiency of the agitator. Most large-capacity units are equipped with multiple impeller agitators, because of favorable power distribution, dispersion uniformity, gas handling, heat transfer, and cost. Therefore, because the mixing efficiency in these units is largely controlled by material exchange between stages, a double-impeller arrangement was used in this work. Experimental and Methods The experimental work was carried out in a flatbottomed cylindrical vessel made of transparent Perspex with internal diameter T ) 0.392 m, provided with four equispaced full baffles of width T/10, as shown in Figure 1. The tank was encased in a water jacket of the same material, for distortion-free flow visualization. The working liquid was tap water, with depth H giving an

aspect ratio H/T equal to 2. Compressed air was introduced in the tank through a 60-mm-diameter sparger at T/10 from the bottom. The air flow rate was measured by calibrated rotameters, ranging up to 1.0 vvm (volume per volume per minute) and thus giving a maximum superficial gas velocity of 0.013 m/s typical of many industrial processes. Agitation was provided by different sets of dual six-bladed disk turbines driven by a variable-speed motor. A standard Rushton turbine with diameter D ) T/3, as the reference impeller, and six other modified blade models were studied. For every turbine type, the rotational speed was such that the specific ungassed power input was 0.125, 0.25, 0.5, 1.0, 2.0, and 4.0 kW/m3 (see Table 1). The bottom clearance of the lower turbine was T/2, and the clearance between impellers was T (see Figure 1). Under these conditions, the bottom plays no role in the power drawn,26 the turbines generate two independent parallel-flow patterns27 and the tank behaves like two stacked single tanks.28,29 A perforated flat-bladed turbine was manufactured in accordance with the design of Roman et al.25 having the same size as the Rushton turbine. Other nonflat profile shapes were designed, as shown in Figure 2. A semicylindrical blade was manufactured, which can be operated either as a concave or as a convex turbine (see Figure 2). Except for the angled-90° blade, also driven in both directions, the other models were studied with the hollow face only forward driven (see Figure 2). Disk diameter, blade and disk thickness, and vertical projected area of the blade were the same in all models as in the standard Rushton turbine (see Figure 3). Because the characteristic impeller dimension D is the diameter swept by the outermost protruding edge of the blade, D depends not only on the blade shape but also on its mounting on the disk. The blades were mounted radially, with the front and rear edges equidistant from a vertical radial plane, except for lancet-II, where the latter is coincident with its front face (see Figure 2). Values of D are shown in Table 1. Power. The agitator power draw P was calculated, according to its definition, from the resistant torque M applied to the impeller, multiplied by the angular velocity 2πN. The torque was measured with an estimated precision of (1% using inductive torquemeters Vibrometer TG-0,5/BP or TG-0,2/BT. The rotational speed N was measured using a Cole Parmer digital photoelectric tachometer with an accuracy of (0.008 s-1. Flooding. The flooding regime is the condition under which the agitation is not sufficiently intense for the impeller to disperse the gas conveniently, either because N was decreased or because QG was increased. As the air flow rate increased at constant rotational speed, a condition was visually detected for which the air flowing into the impeller started rising along the shaft by following a helical path. This was considered to be the flooded condition. Interstage Exchange Rate. The ungassed interstage exchange rate Qi was measured using a flowfollower counting technique as elsewhere.30 A number of 1-5 neutraly buoyant particles with diameter 3-5 mm were dispersed in the tank volume VL. During the elapsed time t, the p particles cross the midway plane between the impellers a total number of times nc in each direction. According to the average residence time

Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000 205 Table 1. Impeller Data

impeller type Rushton angled-90° (hollow) angled-90° (edge) concave convex angled-60° lancet-I lancet-II perforated

ungassed rotational speed values N (s-1) corresponding to the power following ungassed specific power input PU/VL (kW/m3) diameter number D (m) NP 0.125 0.25 0.5 1.0 2.0 4.0 0.131 0.131 0.131 0.131 0.131 0.133 0.132 0.138 0.131

5.8 3.9 3.9 2.9 3.6 2.3 1.9 1.7 2.5

3.0 3.4 3.4 3.8 3.5 4.0 4.3 4.4 4.0

3.8 4.3 4.3 4.7 4.4 5.1 5.4 5.5 5.0

4.7 5.4 5.4 6.0 5.6 6.4 6.8 7.0 6.3

6.0 6.8 6.8 7.5 7.0 8.1 8.6 8.8 8.0

7.5 8.6 8.6 9.5 8.8 10.1 10.8 11.0 10.0

9.5 10.9 10.8 11.9 11.1 12.8 13.6 13.9 12.6

ungassed interstage exchange number Fli 0.60 ( 0.04 0.54 ( 0.02 0.52 ( 0.03 0.43 ( 0.03 0.53 ( 0.04 0.43 ( 0.02 0.40 ( 0.03 0.33 ( 0.02 0.48 ( 0.02

ungassed mixing number θ0.05

exponent in t0.05 versus (PG/VL)a regression (eq 9) R

95 ( 2 96 ( 3 111 ( 5 117 ( 4 112 ( 5 120 ( 3 134 ( 7

-0.27 ( 0.03 -0.24 ( 0.03

123 ( 1

-0.26 ( 0.03

-0.27 ( 0.03 -0.29 ( 0.04 -0.29 ( 0.03

Figure 3. Common front view (full lines) and basic dimensions of the different blades. Front views of particular blade designs are superimposed as dashed lines.

which the specific conductivity of the liquid K(t) is definitely within

K(t0.05) ) K(∞) ( 0.05 [K(∞) - K(0)]

(2)

where K(0) and K(∞) are the initial and final specific conductivity values, respectively. The mixing time t0.05 was obtained with an estimated accuracy of (1 s from at least three measurements, each one varying less than 4% from the mean. Mixing time experiments were not performed at speeds giving power inputs higher than 2.0 kW/m3 (see Table 1) because of precision problems. Holdup. The fractional gas holdup G was measured by comparing the gassed and ungassed liquid heights, HG and H, respectively: Figure 2. Schematic end view of the blade profiles studied (dashpoint line represents a vertical radial plane).

concept, Qi is given by

Qi )

ncVL pt

(1)

For a minimum of 300 crossings, Qi measurements were reproducible within (10%. Mixing Time. Mixing time was measured with a dual-impeller configuration, using the electrical conductivity method31 with NaCl as the tracer. A conductivity meter was used in the range 0.2 S/m, fitted with a measuring cell of constant 1 cm-1 fixed near the bottom (Figure 1). A pulse of a saturated NaCl solution was added at the surface, giving an increment of nearly 0.02 S/m on the average specific conductivity. The mixing time t0.05 was defined as the time required for the conductivity fluctuations to become less than 5% of the total conductivity jump, so that t0.05 is the time for

G ) (HG - H)/HG

(3)

where HG was determined visually with repetitivity within (10%. Volumetric Oxygen-Transfer Coefficient KLa. The overall volumetric mass-transfer coefficient KLa was measured at 25 ( 0.5 °C using the peroxide decomposition steady-state technique with manganese dioxide as the catalyst.32 Measurements of the dissolved oxygen concentration CL were performed using two oxygen meters WTW Oxi340 equipped with galvanic probes WTW CellOx 325. The probes were positioned at midheight of the tank (Figure 1). This gives a representative value of CL which was shown by Nocentini33 to be quite suitable for the evaluation of KLa using dynamic methods, provided that perfectly mixed liquid and gas plug flow are assumed and the gas Pe´clet number is PeG > 5. Not only is the latter condition met under the operating conditions in this work,34 but also errors due to simple model assumptions are comparatively smaller

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with steady-state methods, like the one used here, than in the dynamic case. Furthermore, because all impellers are likely to be equally affected by residual errors, these are not significant for comparison purposes. The KLa value was calculated from

KLa )

Qperoxide 2VL∆logC

(4)

where Qperoxide is the peroxide molar addition rate to the liquid volume VL and ∆logC is the logarithmic mean difference between the oxygen concentration in the bulk, CL, and the one in equilibrium with the gas. The outlet oxygen concentration in the gas phase was calculated assuming a constant volumetric gas flow rate across the vessel, QG, which is accurate within (5%. KLa was determined at least twice under the same experimental conditions with a reproducibility within (20%. Results and Discussion Power Draw. The individual ungassed power number NP, which is a characteristic of turbine type, was determined from the power P required to drive n independent impellers of diameter D at the rotational speed N, according to the definition

NP )

P nFN3D5

(5)

where F is the liquid density. Independent measurement of dual- and single-impeller arrangements confirmed that, within (1%, NP had the same constant value under a turbulent regime for both the upper and the lower turbine. This was verified up to the point where air entrainment by highly turbulent surface vortices impaired the power draw of the upper impeller. NP data in Table 1 confirm that form drag typically dominates the total drag force exerted by the rotating impeller under turbulent flow.35 Because power dissipation is determined by the size and rotation of the pair of trailing vortices behind the blade,5,6 the power number must be lower for streamlined blades, where boundary layer separation7 was retarded and therefore trailing vortices were reduced.36 This is the reason why, in Table 1, the Rushton turbine presents the highest NP value and the lancet turbines the lowest ones. Gassed power characteristics were obtained for the various turbines under constant rotational speed corresponding to ungassed power inputs of 0.125, 0.25, 0.5, 1, 2, and 4 kW/m3 (see Table 1). The gas rate was then increased stepwise up to 1.0 vvm, except when flooding of the lower turbine occurred first. Power characteristics for the extreme N values are shown in Figure 4 as plots of the power ratio PG/PU versus air flow rate QG. Some of the plots in Figure 4a do not extend to the full range of QG because of the onset of flooding at low N. It is clear from Figure 4 that blade shape determines turbine behavior as regards the aerated power draw. For the convex and the angled-90° (edge forward) turbines, the power fall with increasing air flow rate is more or less as sharp as that for the Rushton turbine. Because this is due to the formation of large gas cavities behind the blades, the power drop will be lower if their tendency to form is reduced.3 This is what happens in the concave turbine,12 and angled-60° turbine and, in particular, both lancet turbine models (see also Saito et al.3). In these cases, the blade profile produces much smaller

Figure 4. Power characteristics under the extreme values of constant rotational speed N (N data for each impeller in Table 1).

low-pressure regions in the near wake of the blade, thus much smaller cavities, if any, whence the power ratio is much more insensitive to air throughput. The performances of the angled-90° (hollow) and perforated blade turbines were between the extreme cases. A rough correlation may therefore be assumed between blade profiling (Figure 2) and a tendency to cavity formation that explains the results in Figure 4. Moreover, because the sensitivity of power draw to the gas rate is connected to form drag, it is not surprising to find out that it correlates as well with power number (see Table 1). Figure 4 shows an effect of smoothing and flattening of the single-impeller characteristic curve when the dual configuration is used. This is due to the distribution of gas across the upper stage without affecting the upper impeller to the same extent as the lower one. At low gassing rates, Figure 4 exhibits the gassed power of concave blade and both lancet blades rising above the ungassed value. This phenomenon was explained by Myers et al.22 for axial-flow impellers when sparge rings smaller than the impeller were used. For radial-flow

Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000 207

impellers, cases of initial power rising have also been reported, but without explanation.3,10,12 Results of Mehtras et al.18 for concave/convex turbines are consistent with data in this work. Also, van’t Riet et al.10 have found the performance of the perforated blade to be more or less similar to that of the standard blade, except for a smaller NP, as in this work. Results show that, at specific power inputs up to the typical industrial value of 4 kW/m3, the power reduction on gassing is negligible for the lancet-bladed turbines. Agitator retrofitting with impellers like these, whose power draw is not sensitive to gassing, is interesting at least in the sense that the need is eliminated of taking appropriate safety precautions to prevent overloading of fully loaded agitator drives when gas is interrupted. Flooding. Figure 4a shows that lancet, angled-90° (hollow forward) and concave impellers were able to handle an air flow rate at least 3 times greater than the Rushton turbine before they flooded. As detailed further on, impellers which are able to handle high values of the superficial gas velocity vG without flooding offer advantages for gas holdup and KLa enhancement. Besides, because their power number is lower, they can be used at larger impeller-to-tank diameter D/T to get the same power input (see eq 5). According to the flooding point correlation by Nienow et al.,4 larger D/T contributes to a further increase of the gas handling capacity before flooding compared to smaller impellers. Interstage Exchange Rate. The liquid exchange rate between stages, Qi, was found to be proportional to the rotational speed N. This is in accordance with what had already been established for multi-Rushton turbine agitated tanks in the turbulent regime.30 Analysis of the values of the interstage exchange number Fli ) Qi/ND3 shown in Table 1 needs some comments. The net flow of liquid through any cross section of the tank, hence between the upper and lower stages, must be zero. Therefore, given the symmetry of the flow patterns relative to the horizontal plane separating the stages,29 the time-averaged value of the vertical velocity vector at any point in such a plane must also be zero. This means that the exchange of liquid between the agitation stages, rather than being due to convection, is caused by fluctuations of the instantaneous velocity vector in the z direction. This explains why Fli was found elsewhere37 to decrease progressively with decreasing Reynolds number Re, down to a point near Re ) 200 where it felt abruptly about 2 orders of magnitude as laminar flow approached. Because velocity fluctuating components are related with turbulence intensity,1 a correlation was therefore expected to hold between the dimensionless exchange number Fli and the dimensionless power NP, which is assumed to represent the turbulence in the bulk of the tank. Such an assumption relies on the fact that turbulence is characterized, not by the average power input per unit mass  but rather by its maximum local value in the impeller region max, which is a function of the power number NP, as shown by Zhou and Kresta.38 Figure 5 clearly shows a strong correlation between Fli and NP data in Table 1. The following power regression has a correlation coefficient of 0.94:

Fli ) 0.29NP0.43

(6)

The physical significance of eq 6 is that single-phase mass exchange between stages is correlated with turbulence generation.

Figure 5. Correlation of ungassed interstage exchange number Fli and power number NP.

Mixing Time. The ungassed mixing time t0.05 for a dual impeller was found to vary inversely with the rotational speed N, except when mixing was slowed by the onset of surface aeration. Under turbulent agitation, constant dimensionless mixing time θ0.05 ) Nt0.05 is a theoretical prediction from dimensional analysis39 which had already been verified elsewhere30 with a variety of multiple Rushton impeller configurations and sizes. Table 1 shows θ0.05 results. At the same rotational speed, the Rushton turbine has the lowest mixing time, but because it is also the impeller with the highest NP (see Table 1), this result simply reflects its drawing of more power. A mixing number of 95 ( 2 for the Rushton turbine (Table 1) agrees with 92 ( 3 and 90 ( 2 reported elsewhere30 for dual Rushton impellers in tanks of the same geometry with 0.29 and 0.49 m diameter, respectively. As suggested in the previous section, mixing with multiple-radial-flow impellers is controlled by the turbulence-dependent mass exchange between stages. This is a slower process than the convective transport phenomena inside the agitation stage.30 It is thus not surprising to find out, as in Figure 6, that the mixing number θ0.05 correlates with the interstage exchange number Fli, leading to

θ0.05 ) 0.66 × 102Fli-0.75

(7)

with correlation coefficient 0.88. Equations 6 and 7 imply that θ0.05 correlates with Np, a conclusion which is consistent with the thesis of Kresta40 that the local energy dissipation rate max, thus Np,38 is one of the keys to modeling for blend time. A correlation is

θ0.05 ) 0.16 × 103NP-0.31

(8)

with correlation coefficient 0.92. From dimensional analysis, in a turbulent regime, both θ0.05 ) Nt0.05 and NP are constant characteristic quantities of a given impeller geometry.39 Therefore, from eq 5, the ungassed mixing time t0.05 must be related to the ungassed specific power input PU/VL under the

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Figure 6. Correlation of ungassed mixing number θ0.05 and interstage exchange number Fli.

following general form:

( )

t0.05 ) k

P VL

R

(9)

where, in this case, k is a characteristic constant dependent on impeller design, P ) PU, and R ) -1/3. However, when the ungassed t0.05 and PU data of all impellers are used, an average optimized value equal to 0.15 × 103 (kg/m)1/3 is found for k with a correlation coefficient 0.98. Considering that this result involves all turbines, it means that their single-phase mixing efficiency is the same. This seems to confirm the deduction from turbulence theory that all types of impellers of equal diameter are equally energy efficient in achieving overall homogenization.41 Because power input per unit volume controls the turbulence in the microscale range, eq 9 is indeed consistent with the conclusion by Nienow41 that turbulence-based mixing time equations42,43 are superior to the ones based on the bulk flow generation approach. These imply different mixing efficiencies for different types of impellers.44 The turbulence-based correlations by Ruszkowski42 or Grenville et al.,43 established for blending in single-impeller systems, give a lower k value in eq 9 than in this work. This is not surprising, because multiple radial-flow impellers are less efficient because of liquid compartmentalization in an increased number of recirculating flows.30,45 Gassed mixing time results were plotted in Figure 7 against power input per unit volume PG/VL. Five different sets of data points are represented as jointed lines for each impeller. Each set corresponds to a different value of a parameter of rotational speed N yielding under ungassed conditions specific power inputs PU/PL of approximately 0.125, 0.25, 0.5, 1, and 2 kW/m3. Black symbols in Figure 7 represent ungassed experiments. A common line of slope -1/3 is superimposed on every graph representing the regression line of all ungassed data according to eq 9 with R ) -1/3 and optimized k value as mentioned above. White symbols in Figure 7 stand for gassed data, obtained as QG was increased under constant N from the ungassed condition onward. As seen from the plots, there is a general trend of decreasing in mixing time t0.05 with an increase in

Figure 7. Mixing time results. Lines represent regression of all ungassed data (black symbols).

specific power input PG/VL. However, it is very doubtful to accept the thesis36,41 that t0.05 data should follow the

Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000 209

Figure 8. Regression of mixing time data of individual impellers in the agitator-controlled regime, as a function of PG/VL (eq 9). Error bars correspond to 95% confidence intervals associated with the extreme cases (perforated and angled-90° or -60° turbines).

gradient -1/3 implied by single-phase mixing correlations like Ruszkowski’s.42,43 Mixing time data of Figure 7 clearly show that, for low N (low PG/VL), t0.05 either increases or stays constant with PG/VL. This situation corresponds to the gas-controlled regime of the tank, resulting from the trade-off between the competitive agitator mechanism and aeration mechanism of flow generation.30,46 The opposite situation is shown in Figure 7 for high N (high PG/VL), where t0.05 increases with QG. This is the agitator-controlled regime, which was the only one taken into consideration by Nienow36,41 while suggesting the general validity of Ruszkowski’s correlations.42,43 Even under this condition, however, if the power draw is insensitive to the gassing rate (vertical jointed lines in Figure 7), t0.05 varies significantly with QG although PG/VL stays constant. Mixing time data in this work decidedly do not support Nienow’s suggestion.36,41 Under the above circumstances, the comparison of gassed data is not straightforward. As an option, only the agitator-dominated regime was considered, excluding points in Figure 7 that do not correspond to t0.05 increasing with QG. Regression of t0.05 data against PG/ VL according to eq 9 with P ) PG yields the R values shown in Table 1. Gassed R exponents are clearly higher than the theoretical ungassed value -1/3. The individual regression lines were plotted in Figure 8, including the 95% confidence intervals corresponding to the impellers with the highest and lowest t0.05 respectively the perforated and the angled-90° or -60° turbines. As seen from Figure 8, every regression line falls within the overlapping band of uncertainty common to all impellers. This means that the different impellers give approximately the same average mixing performance at the same power input, under the agitator-controlled regime. This result agrees with the finding by Saito et al.3 that the 6SRGT agitator and the standard Rushton turbine have the same mixing efficiency. Similarly, mixing times for the Rushton turbine and so-called “bucket” (concave) impeller were also found to be identical by Distelhoff et al.47 Because only radial-flow impellers were compared in this work, it is not legitimate to conclude that mixing times are independent of impeller type in general. Indeed, according to both conventional theory44,48 and recent studies,47 the type

Figure 9. Holdup results. Lines represent the overall correlation (eq 10).

of flow field generated is expected to play a considerable role on mixing. The effect of flow may even explain why mixing time was found in this work to vary with gas rate for a given power input. Holdup. Holdup results are plotted in Figure 9 against the specific power input PG/VL with gassing flow rate QG as a parameter. At the same power input and gas flow rate, the holdup is approximately independent of impeller design within experimental error. Experimental measurements were correlated in terms of PG/ VL and the superficial gas velocity vG as follows:

G ) 0.10

( ) PG VL

0.37

(vG)0.65

(10)

with deviations within (30% and correlation coefficient 0.989. Equation 10 is represented in Figure 9 by parallel lines corresponding to different values of QG in vvm. Correlating eq 10 is very similar to that proposed by Nocentini et al.49 with triple- and quadruple-Rushton turbines (see Table 2). Other correlations for air-water systems are those by Linek et al.,50 for stages 2-4 with quadruple-Rushton turbines, or Bouaifi et al.,51 Pinelli et al.,52 and Smith53 with varying multiple-impeller geometries. Table 2 assesses how well such correlations fit the experimental data in this work. Results in this work confirm the finding by Saito et al.3 that the parabolic-blade-shaped 6SRGT and the Rushton impeller give the same gas holdup at the same power input and superficial gas velocity. The same has been reported in the literature for the concave and Rushton turbines in one-, two-, and four-impeller systems,19,54 although in one paper19 differences were admitted that would not be disclosed by the measurement accuracy. In line with the latter position, it has also been reported that the convex disk turbine gives higher holdup per unit power consumption than the concave disk turbine.18 Contrary to the results in water and low-viscosity media, strong differences were found recently in highly viscous Newtonian liquids between the gas holdup behavior of four disk-type impellers, namely Rushton, concave, 6SRGT, and parabolic-bladed turbines.24

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Table 2. Correlations for Holdup Compared to Experimental Data error (%) correlation

reference

G ) 0.10(PG/VL)0.37(vG)0.65 G ) 8.35 × 10-2(PG/VL)0.375(vG)0.62 G ) Ct(PG/VL)0.24(vG)0.65 (best fit: Ct ) 0.268) G ) 0.285[(PG + vGFg)/VL]0.303(vG)0.732 G ) 0.223(PG/VL)0.264(vG)0.699 G ) 1.25 × 10-2(Re × Fr × FlG)0.35(D/T)1.25

this work Nocentini et al.49 Bouaifi et al.51 Linek et al.50 Pinelli et al.52 Smith53

range

average -31 -29 -40 -36 -55 -59

25 27 54 63 7 28

7 7 13 19 21 37

Table 3. Parameters of KLa Correlating Equation 11 C

A

B

impeller

mean

error (95%)

mean

error (95%)

mean

error (95%)

corr coeff R

Rushton perforated angled-90° (hollow) concave angled-60° lancet-II overall

0.0083 0.0032 0.0054 0.0113 0.0050 0.0080 0.0062

0.0016 0.0007 0.0015 0.0021 0.0011 0.0019 0.0010

0.62 0.66 0.68 0.63 0.64 0.68 0.66

0.02 0.02 0.03 0.02 0.02 0.02 0.01

0.49 0.41 0.52 0.57 0.46 0.60 0.51

0.02 0.03 0.03 0.02 0.03 0.03 0.02

0.997 0.995 0.993 0.998 0.997 0.997 0.989

Finally, it must be stressed that increased holdup before flooding is obviously expected, from eq 10, after retrofitting with any of the impellers studied for which (i) the ungassed power falls less on gassing or (ii) flooding occurs at higher gas flow number FlG ) QG/ ND3, as compared to the Rushton turbine.4 Mass Transfer. By analogy with gas holdup, which may be considered an indication of the gas-liquid masstransfer ability of the system, volumetric mass-transfer coefficient KLa could also be expected not to depend on impeller design. KLa was measured under the same operating conditions as holdup (see Figure 9). The different sets of KLa data were correlated separately for each impeller in terms of PG/VL and the superficial gas velocity vG, according to the well-known equation:55

( )

KLa ) C

PG A (vG)B VL

(11)

Table 3 summarizes the nonlinear regression analysis of the different data sets, yielding the adjusted values of parameters A, B, and C. Results show overlapping of all 95% confidence intervals associated with the individual correlations. Consequently, the overall regression of all KLa data (bottom line in Table 3) still represents satisfactorily the performance of the different impellers, with a correlation coefficient R ) 0.989 and an average error 9%. This is illustrated in Figure 10 just for the extreme values of QG, the overall regression being shown by full lines, while dashed lines stand for its associated error interval at 95% confidence level. When thus compared, the impellers appear to behave similarly, for their differences derive entirely from experimental errors. Rushton and concave impellers are the only impellers compared in the literature, by Smith and co-workers,12,17,19 but conclusions are somehow contradictory. The conclusion from this study is that KLa does not depend significantly on the impeller types studied. This result confirms the suggestion by van’t Riet,55 followed by other authors,3,17,21,36 that power input and gassing rate, rather than agitator type, are decisive concerning mass-transfer efficiency. It is thus not surprising to find out that the generalized correlation obtained by van’t Riet for water, in his survey of literature data,55 fits reasonably KLa results in this work, independently of

Figure 10. KLa results for the extreme values of constant air flow rate QG. Full lines represent the overall correlation (eq 11 and Table 3). Dashed lines stand for 95% confidence interval.

blade design. In Table 4, other correlations from works in the literature dealing with multiple-Rushton turbines,49,50,56,57 multiple-impeller geometries,53 and, specifically, concave-blade disk impellers,19 are listed and compared to KLa data in this work. Despite the fact that KLa does not depend on blade design, it must be emphasized that improved KLa can be obtained with those impellers for which (i) the power ratio is less sensitive to the gassing rate, because a higher proportion of ungassed power dissipation is still available as PG/VL, (ii) higher values of vG can be

Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000 211 Table 4. Correlations for KLa Compared to Experimental Data error (%) correlation

reference

KLa ) 6.2 × 10-3(PG/VL)0.66(vG)0.51 KLa ) 0.026(PG/VL)0.4(vG)0.5 KLa ) 0.015(PG/VL)0.6(vG)0.6 KLa ) 1.25 × 10-4 (D/T)2.8 (Fr)0.6 (Re)0.7 (FlG)0.45 (D/g)-0.5 KLa ) 8.61 × 10-3[(PG + vGFg)/VL]0.637(vG)0.54 KLa ) 1.5 × 10-2(PG/VL)0.59(vG)0.55 KLa ) 0.0218(PG/VL)0.50(vG)0.60 KLa ) 2.38(PG × 10-3/VL)0.58(vG)0.70

this work van’t Riet55 Bakker et al.19 Smith53 Linek et al.50 Nocentini et al.49 Bouaifi and Roustan56 Wu et al.57

handled without flooding, or (iii) the power number is lower, because, considering the case of shear-thinning fluids as in biotechnology, higher speed is needed to get the same power input; therefore, lower apparent viscosity is obtained and, consequently, enhanced KLa is achieved. Retrofitting. Retrofitting of Rushton turbines with radial-flow impellers which do not lose power on gassing is advantageous, first, because power is fully available under any gassed conditions to enhance the rates of transport processes in the reactor and, second, because gas-handling capacity is increased. Equations 9-11 clearly show that keeping high values of PG/VL under gassing reduces t0.05, while increasing G and KLa. As seen before, the insensitivity of power draw to gas rate is correlated with low power number. Assuming that retrofitting is done at equal power, the decision on keeping equal diameter or equal speed depends on the expected effects on mixing, shear, and gas-handling ability. Retrofitting at equal power and diameter needs some allowance from the mechanical drive system. From eq 5, lower NP implies higher N, which means also lower torque (P definition). However, according to eq 9, ungassed mixing time t0.05 must be rigorously the same as before. Retrofitting under these conditions is clearly uninteresting or even harmful to shear-sensitive media, unless higher shear rate is preferred, as possibly in the case of shear-thinning liquids. The alternative retrofitting at equal power and speed means equal torque (P definition). According to eq 5, lower NP implies larger D:

Dnew ) DRushton

(

)

NP,Rushton NP,new

1/5

(12)

One important advantage of larger D is increasing further the gas-handling capacity of the impeller before flooding.4 If the lancet-II turbine is chosen as the new impeller, its diameter Dnew will be almost 30% larger than before, almost doubling the gas-handling ability of the system. The new mixing time is estimated from the new value T/Dnew ) 2.3. First, the ungassed θ0.05 of dual Rushton turbines of the same size as the new impeller is calculated from its correlation with T/D.30 θ0.05 is obtained equal to 93 for T/D ) 3 (compare with 95 in Table 1) and equal to 59 for T/Dnew ) 2.3. Afterward, the mixing number of the new impeller is estimated from eq 8:

θnew ) θRushton

(

NP,new NP,Rushton

)

-0.31

(13)

From eq 13, the new lancet-II impellers give an ungassed mixing number θnew ) 90, only slightly lower than the actual one, a result that supports Nienow’s

range 41 42 59 80 66 85 17 160

average -24 -55 -26 -45 -16 -7 -54 -5

9 27 12 22 13 24 27 47

opinion41 on the use of larger low-power number impellers being less effective for enhancing mixing than often suggested. The new interstage exchange rate is evaluated from its relationship with the impeller diameter, Qi ) FliND3, i.e.

(

Fli,new Dnew Qi,new ) Qi,Rushton Fli,Rushton DRushton

)

3

(14)

Fli,new for the new impeller is calculated from Fli for the Rushton impeller of the same size (T/Dnew ) 2.3). This is obtained from another simple correlation previously published,30 stating that Fli ≈ 0.2T/D. When this is combined with eqs 6, 12, and 14, a new interstage exchange rate Qi,new is obtained having practically the same value as before, which confirms the little change in the ungassed mixing time. The advantages of retrofitting the Rushton turbines with impellers of flattened power characteristics are thus fully evident only under gassed conditions. Conclusions Blade form influences the performance of six-bladed disk turbines of the radial-flow type. Modification of the flat geometry of the Rushton blade affects pressure and velocity fields in the blade vicinity. Different degrees of power dissipation can thus be obtained at the same rotational speed under either ungassed or gassed conditions. Angled (60° and 90°), semicircular, and lancet shape profiles, studied in dual-impeller configuration, show that improved blade streamlining lowers the impeller power number, causes lesser ungassed power fall on gassing, and retards impeller flooding. Dimensionless correlations under ungassed conditions, between the power number Np and both the interstage exchange number Fli ) Qi/ND3 and the mixing number θ0.05 ) Nt0.05, suggest that mixing in multiple radial-flow impeller systems is controlled by turbulence. Turbulent dispersion, mixing, gas dispersion, and gas-liquid mass-transfer change in accordance with the energy dissipation rate achieved by the different impellers. However, at equal power and gassing rate, no distinction could significantly be established between the various designs regarding mixing time, gas holdup, and KLa. Retrofitting of working Rushton turbine agitators with impellers such as the lancet-blade turbine whose power draw is practically insensitive to gassing rate is recommended, because more power is available for mixing, gas dispersion, and interphase mass transfer for a given driving system. Retrofitting at equal power and speed implies larger diameter, which enhances the gas-handling capacity of the agitator.

212

Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000

Acknowledgment This work was supported by JNICT Project PBIC/C/ BIO/1988/95 and JNICT Grant BJI/2575 (A.M.A.F.R.). The excellent manufacturing of the impellers by Vasco N. Fred of the Mechanical Engineering Department of IST is acknowledged with thanks. Nomenclature A, B, C ) parameters of KLa correlation (eq 11) C ) concentration, mol m-3 CG ) oxygen concentration in the gas phase, mol m-3 CL ) dissolved oxygen concentration, mol m-3 Ct ) fitted constant of correlation by Bouaifi et al.51 (Table 2) D ) impeller diameter, m DG ) dispersion coefficient for the gas phase, m2 s-1 Fli ) ungassed interstage exchange number ()Qi/ND3) FlG ) gas flow number ()QG/ND3) Fr ) Froude number ()N2D/g) g ) gravitational acceleration, m s-2 H ) liquid depth, m k ) constant parameter of eq 9, kg1/3 m-1/3 K ) specific electrical conductivity, S m-1 ()Ω-1 m-1) KLa ) overall volumetric gas-liquid mass-transfer coefficient, s-1 M ) torque, N m n ) number of impellers N ) rotational speed, s-1 nc ) number of crossings of the flow-follower in each direction NP ) impeller power number (eq 5) P ) agitation power (P ) 2πMN), W p ) number of flow-follower particles PeG ) gas Pe´clet number ()vGH/GDG) QG ) volumetric gas flow rate, m3 s-1 or vvm (gas volume per liquid volume per minute) Qi ) ungassed interstage exchange rate, m3 s-1 Qperoxide ) hydrogen peroxide molar flow rate, mol s-1 R ) correlation coefficient Re ) Reynolds number ()FND2/m) T ) tank diameter, m t ) time, s t0.05 ) mixing time to 5% deviation from homogeneity, s vG ) superficial gas velocity, ms-1 VL ) liquid volume, m3 Greek Letters R ) negative parameter of eq 9  ) power input per unit mass (specific energy dissipation rate), W kg-1 G ) volumetric gas fraction (holdup) µ ) liquid viscosity, kg m-1 s-1 F ) liquid mass density, kg m-3 θ0.05 ) dimensionless mixing time or mixing number ()Nt0.05) Subscripts G ) gas phase or gassed condition L ) liquid phase max ) maximum value new ) referred to a new impeller Rushton ) referred to the Rushton impeller U ) ungassed condition

Literature Cited (1) Tatterson, G. B. Fluid Mixing and Gas Dispersion in Agitated Tanks; McGraw-Hill: New York, 1991; pp 19-20, 125151, and 419-434.

(2) Mishra, V. P.; Joshi, J. B. Flow Generated by a Disc Turbine: Part III: Effect of Impeller Diameter, Impeller Location and Comparison with Other Radial Flow Turbines. Chem. Eng. Res. Des., Part A 1993, 71, 563-573. (3) Saito, F.; Nienow, A. W.; Chatwin, S.; Moore, I. P. T. Power, Gas Dispersion and Homogenisation Characteristics of Scaba SRGT and Rushton Turbine Impellers. J. Chem. Eng. Jpn. 1992, 25 (3), 281-287. (4) Nienow, A. W.; Warmoeskerken, M. M. C. G.; Smith, J. M.; Konno, M. On the Flooding-Loading Transition and the Complete Dispersal Condition in Aerated Vessels Agitated by a Rushton Turbine. Proceedings of the 5th European Conference on Mixing, Wu¨zburg, Germany, 1985; BHRA: Cranfield, U.K., 1985; pp 143154. (5) van’t Riet, K.; Smith, J. M. The Trailing Vortex System Produced by Rushton Turbine Agitators. Chem. Eng. Sci. 1975, 30, 1093-1105. (6) Yianneskis, M.; Whitelaw, J. H. On the Structure of the Trailing Vortices around Rushton Turbine Blades. Chem. Eng. Res. Des., Part A 1993, 71, 543-550. (7) Schlichting, H. Boundary Layer Theory; Pergamon Press: London, 1955; pp 22-32. (8) van’t Riet, K.; Smith, J. M. The Behaviour of Gas-Liquid Mixtures near Rushton Turbine Blades. Chem. Eng. Sci. 1973, 28, 1031-1037. (9) Bruijn, W.; van’t Riet, K.; Smith, J. M. Power Consumption with Aerated Rushton Turbines. Chem. Eng. Res. Des. 1974, 52, 88-104. (10) van’t Riet, K.; Boom, J. M.; Smith, J. M. Power Consumption, Impeller Coalescence and Recirculation in Aerated Vessels. Chem. Eng. Res. Des. 1976, 54, 124. (11) Lu, W.-M.; Yang, B.-S. Effect of Blade Pitch on the Structure of the Trailing Vortex around Rushton Turbine Impellers. Can. J. Chem. Eng. 1998, 76, 556-561. (12) Warmoeskerken, M. M. C. G.; Smith, J. M. The Hollow Blade Agitator for Dispersion and Mass Transfer. Chem. Eng. Res. Des. 1989, 67, 193-198. (13) Foust, H. C.; Mack, D. E.; Rushton, J. H. Gas-Liquid Contacting by Mixers. Ind. Eng. Chem. 1944, 36 (6), 517-522. (14) Rushton, J. H.; Costich, E. W.; Everett, H. J. Power Characteristics of Mixing Impellers: Part I. Chem. Eng. Prog. 1950, 46 (8), 395-404. (15) Wong, C. W.; Huang, C. T. Flow Characteristics and Mechanical Efficiency in Baffled Stirred Tanks with Turbine Impellers. Proceedings of the 6th European Conference on Mixing, Pavia, Italy, 1988; BHRA, Cranfield, U.K., 1988; pp 29-34. (16) Kamienski, J. Mixing power of turbine-type impellers with divided, inclined blades. Int. Chem. Eng. 1990, 30 (3), 517-525. (17) Smith, J. Dispersion of Gases in Liquids: The Hydrodynamics of Gas Dispersion in Low Viscosity Liquids. In Mixing of Liquids by Mechanical Agitation; Ulbrecht, J. J., Patterson, G. K., Eds.; Gordon & Breach: New York, 1985; pp 139-201. (18) Mehtras, M. B.; Pandit, A. B.; Joshi, J. B. Effect of Agitator Design on Hydrodynamics and Power Consumption in Mechanically Agitated Gas-Liquid Reactors. Proceedings of the 8th European Conference on Mixing; IChemE Symposium Series No. 136; Institution of Chemical Engineers; Rugby, U.K., 1994; pp 375-382. (19) Bakker, A.; Smith, J. M.; Myers, K. J. How to Disperse Gases in Liquids, Chem. Eng. 1994, 101 (12), 98-104. (20) Galindo, E.; Nienow, A. W. Performance of the Scaba 6SRGT Agitator in Mixing of Simulated Xanthan Gum Broths. Chem. Eng. Technol. 1993, 16, 102-108. (21) Cooke, M.; Middleton, J. C.; Bush, J. R. Mixing and Mass Transfer in Filamenteous Fermentations. Proceedings of the 2nd International Conference on Bioreactor Fluid Dynamics, Cambridge, U.K.; BHRA: Cranfield, U.K., 1988; pp 37-64. (22) Myers, K. J.; Russell, M. I.; Bakker, A. Gassed Power Draw of Mixed Impeller Systems. Can. J. Chem. Eng. 1997, 75, 620625. (23) Hjorth, S. Agitation in Gassed Magnetite Suspensions. Proceedings of the 8th European Conference on Mixing; IChemE Symp. Series No. 136; Institution of Chemical Engineers: Rugby, U.K., 1994; pp 293-300. (24) Khare, A. S.; Niranjan, K. An Experimental Investigation into the Effect of Impeller Design on Gas Hold-up in a Highly Viscous Newtonian Liquid, Chem. Eng. Sci. 1999, 54, 1093-1100.

Ind. Eng. Chem. Res., Vol. 39, No. 1, 2000 213 (25) Roman, R. V.; Tudose, Z. R.; Gavrilescu, M.; Cojocaru, M.; Luca, S. Performance of Industrial Scale Bioreactors with Modified RUSHTON Turbine Agitators. Acta Biotechnol. 1996, 16 (1), 4356. (26) Armenante, P.; Chang, G.-M. Power Consumption in Agitated Vessels Provided with Multiple-Disk Turbines. Ind. Eng. Chem. Res. 1998, 37, 284-291. (27) Rutherford, K.; Lee, K. C.; Mahmoudi, S. M. S.; Yianneskis, M. Hydrodynamic Characteristics of Dual Rushton Impeller Stirred Vessels. AIChE J. 1996, 42 (2), 332-346. (28) Micale, G.; Brucato, A.; Grisafi, F.; Ciofalo, M. Prediction of Flow Fields in a Dual-Impeller Stirred Vessel. AIChE J. 1999, 45 (3), 445-464. (29) Mishra, V. P.; Joshi, J. B. Flow Generated by a Disc Turbine: Part IV: Multiple Impellers. Chem. Eng. Res. Des., Part A 1994, 72, 657-668. (30) Vasconcelos, J. M. T.; Alves, S. S.; Barata, J. M. Mixing in Gas-Liquid Contactors Agitated by Multiple Turbines. Chem. Eng. Sci. 1995, 50 (14), 2343-2354. (31) Kramers, H.; Baars, G. M.; Knoll, W. H. A Comparative Study on the Rate of Mixing in Stirred Tanks. Chem. Eng. Sci. 1953, 2, 35-42. (32) Vasconcelos, J. M. T.; Nienow, A. W.; Martin, T.; Alves, S. S.; McFarlane, C. M. Alternative Ways of Applying the Hydrogen Peroxide Steady-State Method of KLa Measurement. Chem. Eng. Res. Des., Part A 1997, 75, 467-472. (33) Nocentini, M. Mass Transfer in Gas-Liquid, MultipleImpeller Stirred Vessels: a Discussion about Experimental Techniques for KLa Measurement and Models Comparison. Chem. Eng. Res. Des., Part A 1990, 68, 287-294. (34) Nocentini, M.; Pinelli, D.; Magelli, F. Analysis of Gas Behavior in Sparged Reactors Stirred with Multiple Rushton Turbines: Tentative Model Validation and Scale-up. Ind. Eng. Chem. Res. 1998, 37, 1528-1535. (35) Tay, M.; Tatterson, G. B. Form and Skin Drag Contributions to Power Consumption for the Pitched-Blade Turbine. AIChE J. 1985, 31 (11), 1915-1918. (36) Nienow, A. W. Gas-Liquid Mixing Studies: a Comparison of Rushton Turbines with some Modern Impellers. Chem. Eng. Res. Des., Part A 1996, 74, 417-423. (37) Vasconcelos, J. M. T.; Barata, J. M.; Alves, S. S. Transitional Mixing in Multiple-Turbine Agitated Tanks, Chem. Eng. J. 1996, 63, 53-58. (38) Zhou, G.; Kresta, S. M. Impact of Tank Geometry on the Maximum Turbulence Energy Dissipation Rate for Impellers. AIChE J. 1996, 42 (9), 2476-2490. (39) Bird, R. B.; Stewart, W. S.; Lightfoot, E. N. Transport Phenomena; John Wiley & Sons: NewYork, 1960; pp 205-206 and 582-583. (40) Kresta, S. Turbulence in Stirred Tanks: Anisotropic, Approximate, and Applied. Can. J. Chem. Eng. 1998, 76, 563574. (41) Nienow, A. W. On Impeller Circulation and Mixing Effectiveness in the Turbulent Flow Regime. Chem. Eng. Sci. 1997, 52 (15), 2557-2565. (42) Ruszkowski, S. A Rational Method for Measuring Blending Performance, and Comparison of Different Impeller Types. Proceedings of the 8th European Conference on Mixing; IChemE Symposium Series No. 136; Institution of Chemical Engineers: Rugby, U.K., 1994; pp 283-291. (43) Grenville, R.; Ruszkowski, S.; Garred, E. Blending of Miscible Liquids in the Turbulent and Transitional Regimes. Paper of the 15th NAMF Mixing Conference, MIXING XV, 1995 (29 pages).

(44) Ranade, V. V.; Bourne, J. R.; Joshi, J. B. Fluid Mechanics and Blending in Agitated Tanks. Chem. Eng. Sci. 1991, 46 (8), 1883-1893. (45) Komori, S.; Murakami, Y. Turbulent Mixing in Baffled Stirred Tanks with Vertical-Blade Impellers. AIChE J. 1988, 34 (6), 932-937. (46) Vasconcelos, J. M. T.; Alves, S. S.; Nienow, A. W.; Bujalski, W. Scale-up of Mixing in Gassed Multi-Turbine Agitated Vessels. Can. J. Chem. Eng. 1998, 76, 398-404. (47) Distelhoff, M. F. W.; Marquis, A. J.; Nouri, J. M.; Whitelaw, J. H. Scalar Mixing Measurements in Batch Operated Stirred Tanks. Can. J. Chem. Eng. 1997, 75, 641-652. (48) Oldshue, J. Y. Fluid Mixing Technology; McGraw-Hill: New York, 1983; pp 72-93. (49) Nocentini, M.; Fajner, D.; Pasquali, G.; Magelli, F. GasLiquid Mass Transfer and Hold-up in Vessels Stirred with Multiple Rushton Turbines: Water and Water-Glycerol Solutions. Ind. Eng. Chem. Res. 1993, 32, 19-26. (50) Linek, V.; Moucha, T.; Sinkule, J. Gas-Liquid Mass Transfer in Vessels Stirred with Multiple ImpellerssI. GasLiquid Mass Transfer Characteristics in Individual Stages. Chem. Eng. Sci. 1996, 51 (12), 3203-3212. (51) Bouaifi, M.; Roustan, M.; Djebbar, R. Hydrodynamics of Multi-stage Agitated Gas-Liquid Reactors. MIXING IXsRecent Advances in Mixing Proceedings of the 9th European Conference on Mixing; Groupe Franc¸ ais de Ge´nie des Proce´de´s: Nancy, France, 1997; pp 137-144. (52) Pinelli, D.; Nocentini, M.; Magelli, F. Hold-up in Low Viscosity Gas-Liquid Systems Stirred with Multiple Impellers. Comparison of different Agitators Types and Sets. Proceedings of the 8th European Conference on Mixing; IChemE Symposium Series No. 136; Institution of Chemical Engineers: Rugby, U.K., 1994; pp 81-88. (53) Smith, J. M. Simple Performance Correlations for Agitated Vessels. Proceedings of the 7th European Conference on Mixing, Brugge, Belgium, 1991; Royal Flemish Society of Engineers: Belgium, 1991; Part I, pp 233-241. (54) Myers, K. J.; Fasano, J. B.; Bakker, A. Gas Dispersion using Mixed High-Efficiency/Disc Impeller Systems. Proceedings of the 8th European Conference on Mixing; IChemE Symposium Series No. 136; Institution of Chemical Engineers: Rugby, U.K., 1994; pp 65-72. (55) van’t Riet, K. Review of Measuring Methods and Results in Nonviscous Gas-Liquid Mass Transfer in Stirred Vessels. Ind. Eng. Chem. Process Des. Dev. 1979, 18 (3), 357-364. (56) Bouaifi, M.; Roustan, M. Bubble Size and Mass Transfer Coefficients in Dual-Impeller Agitated Reactors. Can. J. Chem. Eng. 1998, 76, 390-397. (57) Wu, H.; Arcella, V.; Malavasi, M. A Study of Gas-liquid Mass Transfer in Reactors with Two Disk Turbines. Chem. Eng. Sci. 1998, 53 (5), 1089-1095.

Received for review June 11, 1999 Revised manuscript received October 7, 1999 Accepted October 12, 1999 IE9904145