Mass-Transfer Characteristics of Surface Aerators and Gas-Inducing

Jyeshtharaj B. Joshi , Nandkishor K. Nere , Chinmay V. Rane , B. N. Murthy , Channamallikarjun S. Mathpati , Ashwin W. Patwardhan , Vivek V. Ranade...
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Ind. Eng. Chem. Res. 2004, 43, 2765-2774

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GENERAL RESEARCH Mass-Transfer Characteristics of Surface Aerators and Gas-Inducing Impellers Swapnil S. Patil, Niteen A. Deshmukh, and Jyeshtharaj B. Joshi* Institute of Chemical Technology, University of Mumbai, Matunga, Mumbai 400 019, India

Liquid-side mass-transfer coefficients (kLa) were measured in surface aerators and self-inducingtype reactors. The measurements were made in 1.0- and 1.5-m-i.d. cylindrical and 8.2 × 8.2-m square tanks using physical absorption of oxygen. The effect of liquid submergence was investigated in detail. Further, the effects of the diameter of the tank, the ratio of the impeller diameter to the tank diameter, and the clearance of the impeller from the tank bottom were also studied. Three different impeller designs were investigated as surface aerators. Single and multiple impellers were employed in the case of self-inducing reactors. The power consumption was varied in the range of 30-1000 W/m3. Suitable correlations were developed for both types of reactors. 1. Introduction Entrainment of gas from a gas-liquid surface is known as surface aeration. Stirred reactors designed for this type of gas-liquid contact are called surface aerators (SAs). For effective aeration, the impeller is located near the free liquid surface. Surface aerators are very widely used for the treatment of wastewater by biological oxidation. The important functions of surface aerators include oxygen transfer, liquid phase mixing to ensure oxygen availability in all parts of the contactor, and suspension of microorganisms. In addition to these applications, there are many reactions, such as hydrogenation, alkylation, oxidation, etc., in which conversion per pass can be low. For these cases, recycling of the unreacted gas from the headspace can be achieved internally with the help of surface aeration. During the past 30 years, substantial work has been reported on surface aerators in efforts to (1) understand the mechanism of surface aeration, (2) estimate the critical conditions for the onset of aeration, and (3) elucidate the effects of various parameters on the masstransfer rates. There are three distinct regimes in the aeration process. At lower impeller speeds, the liquid surface is visually distinct, or bubbles are not present in the liquid. Under these conditions, mass transfer across the interface occurs by the mechanism of surface renewal by turbulent eddies in the liquid. At higher impeller speeds, larger eddies are formed near the interface, and these eddies can entrap bubbles by overcoming the resistance of surface tension. The speed at which the entrapment begins is called the critical impeller speed for surface aeration (NC). The gas-liquid interface (a) available for mass transfer increases many fold as a result of surface aeration. The intensity and frequency of the eddies depend on the tank geometry, the impeller geometry, the ratio of the impeller diameter * To whom correspondence should be addressed: E-mail: [email protected].

to the tank diameter, the position of the impeller in the tank, the impeller speed, and the properties of the liquid such as its surface tension and viscosity. The entrapped bubbles are drawn into the bulk by the downflow of liquid. The bubbles can then escape in the regions of upward or weak downward liquid flows. Thus, the fractional gas hold-up increases with increasing impeller speed. However, at a certain impeller speed, denoted as NF, the impeller becomes flooded with gas. Under flooding conditions, there is a reduction in power consumption and liquid circulation and, hence, in the overall gas hold-up. A drop in the mass-transfer rate also results. In the range of impeller speeds NC < N < NF, the mass-transfer coefficient increases with increasing power consumption per unit volume. In the published literature, mass-transfer characteristics are reported in this speed range. The reported correlations are summarized in Table 1. Correlations reported for small-scale tanks (T < 0.5 m), which have limited applicability in the design of full-scale aerators, are not considered here. Zlokarnik1 has used disk turbine and different variation of radial impeller designs and reported that aerators with blades open from below are more effective than those with blades that are fully enclosed from both top and bottom. Further, even though the role of impeller submergence (S, see Figure 1) has been identified as an important parameter, it has not been systematically investigated. Backhurst et al.2 carried out experiments in pilot-scale square tanks of dimensions 0.46 × 0.46, 0.76 × 0.76, and 1.52 × 1.52 and full-scale tanks of dimensions 13.41 × 13.41 (square) and 10.47 × 17.67m (rectangular). The tanks were unbaffled. The impellers were of vane-disk-turbine type having 4-16 blades. The effect of impeller submergence (h ) S + W/2) at constant liquid height (H) was found to be dramatic.2 As the submergence was increased, the rate of oxygenation per unit power consumption (R/P) was found to increase to S/D ) 0.1 or S ) W/2, whichever is less. A further

10.1021/ie030428h CCC: $27.50 © 2004 American Chemical Society Published on Web 04/23/2004

2766 Ind. Eng. Chem. Res., Vol. 43, No. 11, 2004 Table 1. Correlations for Mass-Transfer Coefficient in Surface Aerators investigator

impeller type

system geometry

correlation

Zlokarnik1

four-bladed Ruston turbine

T ) 0.2-4.3 m, D/T ) 1/6-1/4

Y ) 1.41 × 10-4Fr1.205Ga0.115 Fr ) 0.02-0.34, Ga ) (1.5 × 109)-(2 × 1011)

Backhurst et al.2

vane-disk turbine

pilot-scale tanks: square, L ) 0.46, 0.76, 0.52 m D ) T/5, N ) 0-5.8 (s-1), [A*] ) 9.1 mg/L at t′) 20 °C

R ) 2.78 × 10-7(D[A*]D0)Re1.90Fr0.15

full-scale tanks: square, L ) 13.41 m; rectangular 10.47 × 17.67 m Ognean3

radial impeller closed from bottom

square tanks: L ) 8, 6, 4 m D/L ) 1/8, H/D ) 3

increase in the submergence resulted in a reduction in R/P such that this ratio eventually approached 0 when S/D was around 1. Backhaurst et al.2 developed two separate relations for estimating oxygen absorption rates (R) for the pilot-scale and full-scale tanks up to the optimum submergence (Table 1). Zlokarnik1 has reported the effect of submergence on the power number (NP) but not on the mass-transfer characteristics. Ognean3 has reported the mass-transfer characteristics at optimum submergence. Ognean3 observed different mass-transfer coefficients at different locations but considered only the maximum values. Also, Ognean3 did not mention the optimum submergence for the given impeller design. The second important parameter is the scale of the aerator or tank diameter (T). With increasing tank diameter, the value of R/P was found to decrease.2 Matsumura et al.4 also reported a decrease in interfacial area per unit volume with increasing tank diameter (a ∝ T-2.15). With increasing tank diameter, the liquid velocity near the tank walls at the liquid surface decreases, which can result in partial gas dispersion. Backhurst et al.2 and Wu8 reported partial gas dispersion in the case of surface aeration, particularly when the impeller is near the gas-liquid surface.

( )( )

()

where R ) kLa[A*]V 3

-x′

5

P ) 6.2F N D Fr

0.45

T D

0.20

S+

H

0.27

S+

W 2

n n8

()

0.20

T D

0.05

y′

H

s-1)

x′) 0.5 (N e 2.5 or 0.43 (N > 2.5 s-1), y′ ) 1.0 [H/(S + W/2) g 12] or 1.38 [H/(S + W/2) < 12] -5

R ) 2.78 × 10

(

)

W S+ 2 2.6 2,6 1 + 0.84 T VP H

S + W/2 2.6 2.4 T VP H

P ) 417

Y ) 8 × 10-6Fr1.07Ga0.2

A third important parameter is the impeller clearance (C), which is the distance between the bottom of the tank and the middle of the impeller blade (Figure 1). The effect of this parameter can also be viewed as the effect of the total liquid height (H ) S + C) at constant impeller submergence (S). Takase et al.5 carried out experiments at just-submerged condition and found that a vortex was formed for liquid heights of H < 0.38D. The mass-transfer rate was found to increase in the range of 0.38D < H < 1.2D and to be independent of the liquid height in the range of 1.2D < H < 4D.5 For constant impeller submergence, Zlokarnik1 found a relatively greater effect of the liquid height on the masstransfer rate than on the power consumption. The primary liquid circulation did not vary much with liquid height. However, the tank base and tank walls affect the secondary liquid circulation. The power consumption is strongly dependent on the primary liquid circulation, whereas the total liquid circulation affects the overall mass-transfer rate in the tank because of its ability to distribute the bubbles and increase the gas hold-up. Backhurst et al.2 found that the mass-transfer rate per unit power consumption (R/P) was optimum at an impeller clearance of 2D and that, with a further increase in C, the value of R/P decreased. Backhurst et al.2 and Takase et al.5 reported different effects of impeller clearance. Given that Backhurst et al.2 covered a wide range of reactor scales, their results are more important for scale-up than those of Takase et al.5 Different types of correlations are reported to account for the effect of aerator scale. Fuchs et al.6 reported that, at the same value of P/V, the value of kLa decreases with increasing aerator scale. They proposed the following correlation

kLa ) R(P/V)β where Figure 1. Experimental setup. H ) liquid height, C ) impeller clearance from the tank bottom, T ) tank diameter, P-n ) dissolved oxygen probe position, where n ) 1-3.

W 2

( )

() () n n8

D H

R)

(kLa)V(0) [PV(0)/V(0)]βV(0)

(1)

Ind. Eng. Chem. Res., Vol. 43, No. 11, 2004 2767

and

Table 2. Dimensions of Tanks

β ) βV(0)[V/V(0)]-0.3

For the scale-up of given gas-liquid system, Fuchs et al.6 recommended the following procedure: As the first step, make measurements at the pilot scale (V(0) > 0.2 m3), and calculate the value of β from a log-log plot of kLa versus P/V(0). Let the value of β for the pilot scale be called βV(0). Then, calculate the values of R and β for the gas-liquid system under consideration using eq 2. The scale-up for the same system and for geometrically similar vessels can then be made using eq 1. For proper scale-up, Fuchs et al.6 showed that vessels smaller than 0.2 m3 did not give satisfactory results. Zlokarnik1 correlated the mass-transfer coefficient as

Y ) k′FriGaj

(3)

where Y ) kLaV(ν/g2)1/3/D3 is the sorption number and Ga ) Re2/Fr ) D3g/v2 is the Galilei number. The Galilei number was introduced because it is independent of the impeller speed and, for a given liquid, it changes only with the impeller diameter. Zlokarnik1 obtained the following values for the constants in eq 3: k′ ) 1.4 × 10-4, i ) 1.205, and j ) 0.115. Ognean3 used a correlation similar in form to that of Zlokarnik1 and obtained the constants k′ ) 8 × 10-6, i ) 1.07, and j ) 0.2 (Table 1). The correlations mentioned above permitted the scale-up of aerators having the same type of impeller design and the constants reported for other types of impeller design are1 i ) 0.95 and j ) 0.033. To compare different aerator types and to determine optimum operating conditions, a procedure was suggested that used the following dimensionless parameter1

D0.5 2 5 1/6 F(ν g ) P

E* ) YNP-1Fr-3/2 ) kLa

(4)

where E* is the dimensionless efficiency and Y is the sorption parameter. Ognean7 modified the sorption number by using the equivalent dimension De in place of impeller diameter D

De ) (P/FgND2)1/2 Y0 )

and

AV ) De3/V

(5)

( ) ( )( )

kLaV ν De3 g2

1/3

)

Fr0 )

Cylindrical Tank tank diameter (T) 1.0 and 1.5 m baffle width 0.1T (fully baffled) number of baffles 4 construction material acrylic cylindrical vessels and flat bottom

(2)

kLaV 1 (D3N 3/2)(F3/2g5/6ν1/3) 1/2 P P (6) N 2De N 3/2P1/2 ) 3/2 1/2 g g F D

where the dimensionless number AV represents the effect of power consumption per unit volume and De3 was considered as an “active volume”. In this way, the author was attempting to correlate the mass-transfer coefficient directly with the power consumption. Ognean7 found that the value of Y0 increases with increasing Fr0 and asymptotically reaches a constant value. Irrespective of impeller design and impeller dimensions, the maximum value of Y0 was found to be approximately 5 × 10-3. When two different impeller designs with the same diameter and speed of rotation reach the maximum value of Y0, it was found that the one that has a higher power consumption gives a greater efficiency.3 For two aerators having the same impeller design but

Square Tank tank dimensionsa 8.229 × 8.229 × 2.43 m number of baffles 0 construction material cement concrete a

Length x width x depth.

different diameters and the same parameters as above, different efficiencies were obtained, and the difference was shown to be the function of D-0.5. However, a simple relationship between Y0 and Fr0 could not be established.3 The relations found in the literature1 show a reduction in the value of R/P with proportionalities ranging from D-0.155 to D-0.5. Backhurst et al.2 gave an optimum condition in the form of DN1.51 ) constant. The specific power was recommended to be >15 W/m3 so that the bottom velocities are at least 0.15 m/s. The optimum ratio of impeller diameter to tank diameter was found to be 0.2. The authors recommended that the depth H be less than 2D. Any further increase in H was found to reduce R/P.2 From the preceding discussion, it can be seen that all of the investigators mentioned used a disk turbine and its variation; however, it is known that axial flow impellers are also used in commercial applications of SAs. Even though the role of impeller submergence has been identified as an important parameter, it has not been systematically investigated. Further, although the effect of impeller clearance has been studied, the effect of impeller clearance for different D/T ratios has not. In addition, we considered it useful to analyze all of the published information in this area and present it in the form of a coherent correlation. To bridge knowledge gaps, we consider a wide range of impeller diameters, clearances, submergences, and total volumes (0.4-125 m3). For aerobic biological oxidation, self-inducing reactors (SIRs) are known to be superior to surface aerators. The reported correlations for such reactors were developed using small equipment and cannot be used to design full-scale tanks. Hence, to develop a correlation applicable for commercial-size effluent treatment plants, some additional work is needed. In view of the abovementioned status of the literature, it was considered desirable to investigate the effects of all of the above parameters on mass-transfer coefficients for self-inducing reactors as well. It was also considered desirable to establish the comparative performance of self-inducing reactors and surface aerators. 2. Experimental Section Experiments were performed in 1.0- and 1.5-m-i.d. cylindrical tanks and in an 8.2 × 8.2-m square tank. The experimental setup for the surface aerator is shown in Figure 1. The cylindrical tanks were baffled, whereas the square tank was unbaffled. Further details are listed in Table 2. In the case of surface aerators, three impeller designs were used, namely, a pitched blade downflow turbine (PBTD), a pitched blade upflow turbine (PBTU), and a standard disk turbine (DT). The dimensions of these impellers are reported in Table 3. The self-

2768 Ind. Eng. Chem. Res., Vol. 43, No. 11, 2004

Simultaneous solution of eqs 10 yields

Table 3. Impeller Geometry tank diameter(s) (m)

impeller design

impeller diameter, D (m)

blade width (m)

blade length (m)

impeller blade angle (°)

PBTD DT PBTU PBTU

0.33 0.33 0.33 0.20

0.3D 0.2D 0.3D 0.3D

0.42D 0.25D 0.42D 0.42D

45 90 45 45

1.5

PBTD PBTU DT

0.50 0.50 0.50

0.3D 0.3D 0.2D

0.45D 0.45D 0.25D

45 45 90

8.2 × 8.2

PBTD

1.6

0.1D

0.48D

45

1.0 and 1.5

(7)

where [A]M is the dissolved oxygen concentration in the reactor at time t and [A*]M is the saturation concentration of oxygen in water in the reactor. The latter concentration was measured by allowing aeration to proceed until a constant value had been attained. kLa is the liquid-side mass-transfer coefficient. Experiments on oxygen probes used in our work showed that the probes gave first-order responses, with time constants of around 5 s. The expression for this kind of probe can be written as

d[A]P/dt ) kP([A]M - [A]P)

(8)

where [A]P is the oxygen concentration measured by the probe and kP is the probe constant. The values of the latter depend on the transport characteristics of the probe membrane, the nature of the electrolyte layer, and the electrochemical reaction at the cathode surface. We now introduce the following dimensionless quantities

XP )

[A*]P - [A]P

,

[A*]P - [A]P0

XM )

[A*]M - [A]M [A*]M - [A]M0

(9)

Then, eqs 7 and 8 can be rewritten in dimensionless form as

dXM/dt ) -kLaXM,

dXP/dt ) kP(XM - XP)

(11)

The value of kP needed to solve eq 11 for kLa can be determined from the probe response to a step input. For example, one could apply a negative step input by transferring the probe from a container of water saturated with dissolved oxygen ([A]M ) [A*]) to a container of oxygen-free sulfite solution ([A]M ) 0) and noting the probe reading. For this case, eqs 10 become

inducing impeller was of stator rotor type with a standpipe.9 The stator had 12 vanes, an internal diameter of 1.055D, a diffuser width of 0.133D, and a diffuser height of 0.233D. The self-inducing impeller was a pitched blade downflow turbine (PBTD). In the case of the multiple self-inducing impeller system, the second impeller was a pitched blade upflow turbine (PBTU) having a diameter (D2) of 0.6D. The mass-transfer coefficient was measured by the unsteady-state oxygen absorption method. The tap water (at a temperature of 23-30 °C) was deoxygenated by chemical reaction with sodium sulfite. A dissolved oxygen meter was used to measure the rate of oxygenation. The amount of dissolved sodium sulfite was too small to change mass-transfer properties of the water. The rate of oxygen transfer is given by

d[A]M/dt ) kLa([A*]M - [A]M)

kPe-kLat - kLae-kPt XP ) kP - kLa

(10)

In these expressions, [A]P0 and [A]M0 represent the concentrations of dissolved oxygen at time t ) 0, and [A*]P represents the probe saturation concentration. Note that [A]P0 ) [A]M0 and [A*]P ) [A*]M.

d[A]P/dt ) kP([A*]P - [A]P) dXP/dt ) kPXP

(12)

Equations 12 represent a special case of eqs 10 where XM is replaced by X/P. kP values for the probe were checked before and after each set of experiments. Variations in kP values were not significant. From each aeration experiment, a set of values of XP(actual) (called XPA) was obtained as a function of time. After the concentration and time had been noted, the zero time, t0, and the corresponding oxygen concentration, [A]P0, were shifted to the point at which the concentration was observed to begin increasing. By assuming a value of kLa, the value of XP(equation) (XPE) for a given time was calculated with eq 11. Then, the value of the error for a given kLa and a given time was calculated according to

error )

(

)

XPA - XPE XPA

2

(13)

The total_error was calculated by adding the values of error (eq 13) for the experimental set in the saturation range of 20-80%. The value of kLa for given set of experiments was calculated by minimizing the total_error (iterative calculation of above procedure) using the goldensection optimization algorithm. The mass-transfer coefficient measured is for the water temperature t′ °C (around 23-30 °C) at the experimental conditions. The calculated mass-transfer coefficient was then normalized to a temperature of 20 °C by the following relation2

kL20a ) 1.02(20-t′)ktL′a

(14)

Visual observations showed that the gas was not dispersed throughout the tank. Most of the gas bubbles were present in the top portion of the reactor (for both SIRs and SAs), and bottom portion was practically bubble-free. Under these conditions, at a given point, the rate of change in oxygen concentration is due to the combined effects of the mass-transfer rate and the liquid circulation rate. The value of kLa was calculated with the assumption that the liquid phase was completely mixed. To confirm the liquid-phase mixing behavior, the oxygenation conditions (and hence kLa) were measured at different points (Figure 1): near the tank bottom, at the tank wall (practically bubble-free region), and near the gas-liquid interface (P-1); at the tank wall (P-2); and near the impeller (P-3). Gas was always dispersed at P-2 and P-3. It was observed that, in the range of impeller speeds NC < N < NF, the value of kLa was practically the same at all three points (Figure 2). The

Ind. Eng. Chem. Res., Vol. 43, No. 11, 2004 2769

Figure 2. Mass-transfer coefficients at different probe locations: ], P-1 at tank bottom; ×, P-2 at tank wall in the impeller plane; 4, P-3 near the impeller

average difference in the kLa value (1.0- and 1.5-m-i.d. tanks) was within 3%, whereas the maximum difference was within 8%. In the case of the 1- and 1.5-m-diameter tanks, the kLa value was measured with probe at P-1. In the case of the large-scale square tank, the average difference in kLa values was within 10%. Therefore, in the case of the large-scale square tank, the oxygenation rate was measured at three different locations, and the average value of kLa was estimated. In the case of the 1- and 1.5-m-diameter tanks, the power consumption was calculated by measuring the load on the frictionless torque table. In the case of the large-scale square tank, the power consumption was calculated by measuring the power consumed by the motor and estimating the efficiency of the motor, belt, pulley, and gears for given conditions. 3. Results 3.1 Impeller Submergence. The performance of surface aerators as well as self-inducing reactors is known to depend on the impeller submergence (S). Therefore, the effect of impeller submergence was investigated systematically. In SA as well as SIR the

gas bubbles are entrapped into the surface waves and eddies formed by the impeller. With increasing submergence, the number of eddies at gas-liquid interface are decreased. In the case of pitched blade downflow turbine (PBTD), entrapped bubbles are carried downward by the liquid flow generated by the impeller. The dispersion in this case is entirely of the gas-in-liquid type (Figure 3B). Unlike the PBTD, the pitched blade upflow turbine (PBTU) pumps liquid upward and discharges a liquid jet in the air (Figure 3A). The disk turbine (DT) also discharges a liquid jet (Figure 3C). The centrifugal force due to the strong tangential velocity is the cause for jet formation from the DT. As shown in Figure 3A and C, the jet gives rise to a liquid-in-gas dispersion. Further, when the liquid trajectory hits the liquid surface, bubbles are entrapped, resulting in a gas-in-liquid type dispersion. A decrease in impeller submergence results in stronger surface waves and/or forceful liquid jets. However, the liquid circulation velocity increases with increasing submergence. Further, for the PBTD and DT impellers, a vortex is formed. The vortex size increases as the impeller approaches the liquid surface. The combined effect of bubble entrapment, vortex size, and liquid circulation results in a maximum value of kLa with respect to S (Figure 4B and C). For the PBTD and DT impellers, the maximum was observed at the submergence of 0.2D, and the optima were found to be independent of P/V (Figure 5B and C). The PBTU impeller pumps the liquid in the upward direction. This upward flow prevents the formation of a vortex. Further, for the PBTU impeller, increasing the impeller submergence reduces the ability of the impeller to form a jet. This, in turn, decreases the surface aeration. The maximum jet size was observed when all of the impeller blades were just submerged in the water. The submergence showing maximum value of kLa was found to be 0.12D (Figures 4A and 5A). Backhurst et al.2 made similar observations in the case of a vane-disk turbine. In the case of SIR, the stator protects the forced vortex, and irrespective of impeller submergence, the gas-liquid interface can approach very near to the impeller (provided N > NC, Figure 3D). Hence, at relatively high impeller speed N > 2NC, bubble entrapment and subsequent transport become essentially independent of S. However, at impeller speeds compa-

Figure 3. Schematic representation of gas dispersion in surface aerator with different impeller designs and self-inducing impeller: (A) surface aerator with pitched blade upflow turbine, (B) surface aerator with pitched blade downflow turbine, (C) surface aerator with disk turbine, (D) self-inducing reactor with single impeller.

2770 Ind. Eng. Chem. Res., Vol. 43, No. 11, 2004

Figure 4. Effect of impeller submergence on mass-transfer coefficient (T ) 1.5 m, D ) T/3, C ) 1.75D); N (s-1) ) ], 1.17; 0, 1.5; 4, 2; ×, 2.5: (A) surface aerator with pitched blade upflow turbine, (B) surface aerator with pitched blade downflow turbine, (C) surface aerator with disk turbine, (D) self-inducing reactor with single impeller.

Figure 5. Effect of impeller submergence on mass-transfer coefficient at various levels of power consumption per unit volume (T ) 1.5 m, D ) T/3, C ) 1.75D); S/D ) ] 0.0, 0 0.12, 4 0.2, × 0.3, * 0.4; (A) surface aerator with pitched blade upflow turbine, (B) surface aerator with pitched blade downflow turbine, (C) surface aerator with disk turbine, (D) self-inducing reactor with single impeller.

rable to NC (NC < N < 1.25NC), a slight maximum was observed (Figure 4D). From Figure 5D, it can be seen that the effect of impeller submergence is much less pronounced in self-inducing reactors than in surface aerators. A comparison of impeller designs for the SAs at their respective optimal impeller submergences and the SIR with a single impeller at a just-submerged position is shown in Figure 6. In the SA category, at all levels of power consumption, the PBTD design can be seen to give higher values of kLa than the other impeller designs in the SA. Because the PBTD design was found to be superior to the other SA designs, the effects of the other parameters are discussed only for PBTD impellers. The other impellers were found to exhibit similar sensitivities to various parameters, although the value of kLa was always higher for the PBTD design in the SA category. However, Figure 6 also shows that the SIR design is superior to the SA-PBTD design. 3.2. Effect of Tank Diameter. The effect of tank diameter was investigated at the optimum impeller submergence in the SA and at the just-submerged

Figure 6. Comparison of impeller designs in surface aerator and self-inducing reactor (with single impeller) (T ) 1.5 m, D ) T/3, C ) 1.75D): ], SA-PBTU; 0, SA-PBTD; 4, SA-DT; ×, SIRsingle.

position for the SIR with a single impeller. The experiments were carried out in the geometrically similar 1and 1.5-m-diameter tanks. It was observed that the kLa values were higher in the 1-m-diameter tank than in the 1.5-m-diameter tank in both cases (Figure 7).

Ind. Eng. Chem. Res., Vol. 43, No. 11, 2004 2771

Figure 7. Effect of tank diameter (S ) just submerged, D ) T/3, C ) 1.75D); T ) ], 1 m; 0, 1.5 m: (A) surface aerator with pitched blade downflow turbine, (B) self-inducing reactor with single impeller.

Figure 9. Effect of impeller clearance (S ) just submerged): (A) Surface aerator with pitched blade downflow turbine, T ) 1 m, D/T ) 0.33, C/D ) ], 1.76; 0, 1.98; 4, 2.42. (B) Surface aerator with pitched blade downflow turbine, T ) 1.5 m, D/T ) 0.2, C/D ) ], 1.23; 0, 1.77; 4, 2.44. (C) Self-inducing reactor with single impeller, T ) 1.5 m, D/T ) 0.2, C/D ) ], 1.21; 0, 1.67.

Figure 8. Effect of impeller diameter (S ) just submerged, T ) 1.5 m, C ) 1.75D); D ) ], T/3; 0, T/5: (A) surface aerator with pitched blade downflow turbine, (B) self-inducing reactor with single impeller.

3.3. Effect of Impeller Diameter. The effect of the impeller diameter was studied with T/3 and T/5 impellers (Figure 8). In the lower range of power consumption (P/V < 100 W/m3), the T/5 SA impeller was found to exhibit relatively high values of kLa. However, as the power consumption increased beyond 100 W/m3, the rate of increase in kLa with respect to P/V was diminished as a result of of poor liquid circulation. This effect could be visually observed in terms of the gas dispersion characteristics. For P/V > 100 W/m3, the gas hold-up in the top portion was found to increase with P/V, but the depth of gas dispersion was found to decrease. Increasing the power consumption further, the impeller of T/5 diameter became flooded, and the value of kLa decreased (P/V > 150 W/m3). The kLa values of the T/3

impeller were found to be higher. A similar trend was observed in the case of the SIR. For the same impeller design with different impeller diameter P/V ∝ Df, where f > 0 and f ) 2 for singlephase systems. However, QL/(P/V) ∝ Dm, where m > 0 and m ) 1 for single-phase systems. At a given value of P/V, the impeller with the lower diameter has a higher speed and entraps gas at a higher rate. However, the liquid circulation capacity of the impeller with the greater diameter is high. At conditions of lower P/V, the gas hold-up around the impeller is less, and the impeller having the lower diameter shows better performance because of its higher gas entrapment characteristics. At conditions of higher P/V, the gas dispersion is an important parameter for better performance; if the gas dispersion is too low, the impeller can also become flooded as a result of poor liquid circulation. Higher gas dispersion can be achieved by the impeller with the greater diameter. 3.4. Effect of Impeller Clearance. The effect of impeller clearance (C) at constant impeller submergence (S) is shown in Figure 9. With the T/3 impeller, C was varied from 1.76D to 2.42D. In this range, kLa was found to be higher at the clearance of 1.98D than at the clearances of 1.76D and 2.42D (Figure 9A). For the T/5 impeller, the clearance was varied in the range of (1.232.44)D (Figure 9B). The value of kLa was found to decrease continuously with increasing clearance. The effect of impeller clearance for a single-impeller SIR of

2772 Ind. Eng. Chem. Res., Vol. 43, No. 11, 2004

Figure 10. Effect of tank diameter in self-inducing reactor with multiple-impeller system (D ) T/3, S ) just submerged): T ) ], 1 m; 0, 1.5 m.

values of kLa than the surface aerators. It can also be seen that, up to 150 W/m3, the self-inducing singleimpeller reactor offers about 27% higher kLa than the surface aerators. When the value of P/V is greater than 150 W/m3, the multiple-impeller inducing system can be seen to be superior even to the single-impeller inducing system. However, at lower values of P/V (