Comparison of Continuous Blend Time and Residence Time

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Ind. Eng. Chem. Res. 2008, 47, 3532-3539

Comparison of Continuous Blend Time and Residence Time Distribution Models for a Stirred Tank Vesselina Roussinova and Suzanne M. Kresta* Department of Chemical and Materials Engineering, UniVersity of Alberta, Edmonton, Alberta T6G 2G6, Canada

In continuous operation, mixing in a stirred tank is often characterized by the residence time distribution (RTD) curves and the mean residence time (V/Q). The RTD is a measure of the history of the fluid element flowing through the reactor rather than a measure of the local mixing conditions inside the vessel. In this study, additional information about local mixing is obtained by taking measurements inside the vessel. The variance of concentration fluctuations from three probes (two located inside the tank and one at the outlet) is used to determine the continuous blend time (θcnts). At the limiting condition of a slow feed rate relative to the batch blend time, the CSTR is ideal, but at high flow rates the mixing inside the vessel deviates by up to 50% from the ideal case. Three design guidelines are recommended for designs where ideal mixing conditions are required. First, a line from the inlet to the outlet should pass through the impeller. Second, the feed velocity should decay to the mean impeller suction velocity by the time the feed reaches the impeller for the case of surface feed above a downpumping impeller. Third, the ratio of the mean residence time (V/Q) to the batch blend time (θb) should be at least 10. Additional guidelines will be needed for tank configurations where the feed(s) and/or outlet(s) are located on the side of the vessel. Introduction Stirred tanks in both batch mode and continuous mode are widely used in industry. In the batch case, the blend time depends only on the impeller speed, diameter, and power number and the size of the impeller relative to the size of the tank. Correlations for batch blend time are well established.1 The situation becomes more complicated in the case of the continuous stirred tank (CST, or where the vessel is a reactor, the CSTR) due to the flow through the tank. To describe the blend time in the continuous case, it is often assumed that the reactor behaves ideally, which means that the concentration everywhere in the tank is equal to the outlet concentration and the fluid has a mean residence time equal to the tank volume divided by the volumetric flow rate through the tank (V/Q). In reality, the CSTR can easily deviate from ideal conditions if the batch blend time approaches the mean residence time, or if the inlet and outlet locations are poorly selected. Nonideal mixing conditions cause operating problems in many applications, from dosing of chlorine and flocculants in water treatment to excessive byproduct formation in reactors. In the past decade, the level of knowledge of the fluid dynamics in stirred tanks has been significantly improved. The flow patterns for different impeller and tank geometries in the turbulent regime (Re > 20 000) have been measured and documented in numerous papers, and blend time equations for mechanical agitators and jet mixers have been developed from a Corrsin analysis of turbulent mixing2,3 and verified over a wide range of tank sizes for both turbulent and transitional flow.1 Ruszkowski and Muskett4 reviewed the experimental procedures for measuring the blend time, and they are among the first who attempted to fit the experimental data obtained from the batch stirred tank to a physical model. They measured the conductivity change in the tank when a pulse of electrolyte is injected. For each experiment the time history of conductivity * To whom correspondence should be addressed. Tel.: (780) 4929221. Fax: (780) 492-2881. E-mail: [email protected].

Figure 1. Probes and injection positions for batch configuration. Injection position at probe 0 r ) 100 mm, z/T ) 0.90; at probe 1 r ) 100 mm, z/T ) 0.80; at probe 2 r ) 100 mm, z/T ) 0.70; at probe 3 r ) 100 mm, z/T ) 0.40.

at each probe was obtained. The recording started at the time when the pulse was injected, and it finished when the conductivity reached a steady value. The data analysis of the combined concentration variance of all probes was used as a measure of the mixing performance. The authors were able to define blend time as the time needed for the normalized concentration variance to decay to within 5% the final mean concentration. At this point 95% of the total change in concentration has been achieved. This definition makes it possible to compare different impellers and different mixing conditions. Grenville et al.5 continued the work and were able to define the blend time in round tanks for fully turbulent conditions when (Re > 6370/Np1/3)

Nθb )

5.2 T 2 Np1/3 D

()

(1)

In eq 1, N is the rotational speed of the impeller in rotations per second, Np is the power number, T is the tank diameter, and D is the impeller diameter. The form of the correlation was experimentally confirmed by Nienow6 and by Kresta et al.,3 who extended its application to square tanks.

10.1021/ie070955r CCC: $40.75 © 2008 American Chemical Society Published on Web 12/15/2007

Ind. Eng. Chem. Res., Vol. 47, No. 10, 2008 3533

Figure 2. (a) CSTR experimental setup; (b) injection location and position of the spectrophotometer probes. Injection position at probe 0 r ) 60 mm, z/T ) 0.90; at probe 1 r ) 100 mm, z/T ) 0.75; at probe 2 r ) 100 mm, z/T ) 0.75; at outlet probe 3 r ) 0 mm, z/T ) 0.0.

Figure 3. Response of spectrophotometer probes to a pulse injection of crystal violet dye (A310 impeller, Ts ) 0.280 m, D ) 0.134 m, N ) 150 rpm).

CSTRs are most often characterized using residence time distribution (RTD) models.7,8 The nonideality is generally modeled as arising from three possible factors: short circuiting, dead zones, and plug flow. When short circuiting is present, some of the fluid leaves the system immediately without mixing with the bulk. Dead zones reduce the effective volume of the tank and prolong the residence time of some of the fluid elements. Plug flow allows some of the liquid to pass through the reactor in a piston flow manner with a fixed residence time. The complexity of the models is determined by the number of parameters involved. The parameters can be evaluated by measuring the residence time distribution of a pulse injection at the inlet, or a step change in inlet concentration. A good model reflects the physical reality with the minimum number of

Figure 4. Decay of variance vs time for three probes for the data shown in Figure 3. The blend time is the time needed for the total concentration variance to drop to within 5% of the final mean concentration. Normally this will be dominated by the worst mixed point in the tank.

parameters required. This is somewhat difficult to achieve because the RTD will not reveal the sequence of the flow through various regions inside the vessel, and many different parametric models will produce the same RTD. Few papers examine nonideal mixing in continuous flow systems directly, although it is clear that aspects of the design such as the location of the incoming and outgoing streams and flow rate through the vessel will impact the quality of mixing. Rules of thumb are widely used, such as “a line from the inlet to the outlet should pass through the impeller” and “the residence time should be (some multiple of) the batch blend time.”23 The value of the multiplier is not well established, although recent

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Ind. Eng. Chem. Res., Vol. 47, No. 10, 2008

Figure 5. Blend time correlation for two round tanks: large tank T ) 0.240 m (open symbols) and small tank T ) 0.140 m (solid symbols).

work shows that it depends on both the impeller and the inlet stream momentum.9 In this study, the concept of homogeneity for a continuous flow system is revisited. The mixing time in a CSTR (θcnts) is determined using both the concentration at the outlet and local concentration probes located at several points inside the vessel. The main purposes of the present study are (1) to verify the existing correlation for a batch tank (eq 1), (2) to determine the blend time in the continuously fed CSTR and provide a limiting ratio of the mean residence time (V/Q) to the batch blend time (θb) that ensures effective operation of the CSTR, and (3) to investigate the interaction between feed stream velocity and impeller rotational speed and the effect of this ratio on the continuous blend time. Mixing Time Experiments The most common methods for mixing time measurements in stirred tanks are conductivity probes,10-12,20 decolorization techniques,13,14 and nonintrusive laser induced fluorescence measurements.15,16 This work uses spectrophotometer probes to measure concentration fluctuations. This approach was successfully developed and applied by Lee and Brodkey17 and Nye and Brodkey,18 who measured the scalar concentration fluctuations in turbulent pipe flow. The spectrophotometer method is easy to implement but suffers from the disadvantage of being an intrusive technique, in which case the probes will have some effect on the flow field and the mixing. It is assumed, however, that any disturbance introduced by the probes will be insignificant as far as the measurement of the decay of concentration is concerned. Spectrophotometer. Blend times were measured using an Ocean Optics spectrophotometer equipped with four probes.19 Each probe consists of a pair of 300 µm diameter optical fibers, one for illumination and the other for collection of transmitted light. The probe is 127 mm in length with an outer diameter of 6.35 mm. At the end of the probe the light travels from the illumination fiber across 2 mm of fluid to a mirror. The light reflects back through a focusing lens onto the collection fiber. The advantage of the probe is its compact optical design, but

the tradeoff is that the probe measures both the transmitted light and the backscattered light from the sample and has internal reflections that limit the dynamic range of the measurement. A halogen lamp with a spectral range from 360 nm to 2 µm was used as the light source. The collected light is converted to concentration using Beer’s absorption law, which states that for a given path length

I ) exp(-C1Cm) I0

(2)

where I and I0 denote the attenuated and incident light intensities and Cm denotes the concentration. The probes used have a finite volume, so the measured value of Cm is an average over the path length of the light. C1 is the molar absorptivity, which is a constant for a given wavelength and tracer compound. The calibration curve for crystal violet dye returned a constant molar absorptivity (C1) over a range of concentrations from 0 to 20 mg/L. Batch Experiments. Batch blend time experiments were carried out in cylindrical tanks to verify the experimental method. Two different tank diameters were used: T1 ) 0.240 m and T2 ) 0.140 m. Four full length baffles of width T/10 were separated by 90° around the wall of the vessel. The height of the liquid was held equal to the diameter of the tank (H ) T). Five different impellerssfour axial impellers (45° PBT, A310, HE3, and flat blade turbine with four blades) and one radial impeller (Rushton turbine)swere used. All experiments were performed at an impeller off-bottom clearance of C ) T/2. The flow was always in the fully turbulent regime with impeller Reynolds numbers greater than Re ) ND2/ν > 20 000. The batch blend time was measured by placing four probes inside the vessel and measuring the absorption of the light by the dye. In Figure 1 the four probe locations are shown. Crystal violet dye with a concentration of 3.4 mg/L and a volume of 5 mL was deposited near probe 0. The reading from this probe was used to determine the time when the dye was first introduced in the tank. The response curves from probes 1, 2, and 3 were used to calculate the blend time. To obtain accurate blend time measurements, at least one probe must be located


Figure 6. Semilog plot of the calculated variance from (a, top) outlet probe and (b, bottom) from all three probes at N ) 100 rpm (A310 impeller D ) 0.56T, Q ) 20 L/min). The straight line is the predicted response for ideal mixing.

in the worst mixed region of the tank. This location is determined using several initial experiments where blending is observed using a tracer dye and the probe locations are changed until the maximum blend time probe locations are determined. Visual observations and flow patterns are used to select probe locations. CSTR Experiments. The CSTR is a standard flat-bottomed cylindrical tank with diameter T ) 0.240 mm and four rectangular baffles of width T/10. Three axial impellers (45° PBTD, A310, and HE3) and one radial impeller (Rushton turbine) were used. The off-bottom clearance was kept constant at C ) T/3 for all impellers studied. The inlet tube was placed 20 mm below the liquid surface at r ) 60 mm from the shaft. The outlet is at the center of the bottom of the tank. The continuous liquid feeding system is shown in Figure 2a. Two progressing cavity pumps with a power of 1 hp and capacity up to Q ) 20 L/min maintained a steady liquid height inside the tank. A reservoir supplied the tank continuously with crystal violet dye at a concentration of 3.4 mg/L. Figure 2b shows the position of the spectrophotometer probes for the continuous experiments. The probe locations were selected using the same method described for the batch blend time experiments. Probe 0 is located in the feed pipe, and it is

used to determine the time when the dye is first introduced in the tank. The distance from the probe to the liquid surface is very small, so the lag time is neglected. The blend time in the continuous system is calculated based on the response from two probes located inside the vessel and one probe at the outlet. The concentration change at the outlet is compared to the ideal concentration change predicted for a perfectly mixed tank. For all experiments the inlet pipe Reynolds number was greater than 5000 and the impeller was operated in the fully turbulent regime at an impeller Reynolds number Re ) ND2/ν > 20 000. Data Analysis To find the blend time, the variance in concentration was calculated as a function of time. Figure 3 shows a typical set of dynamic response curves for four spectrophotometer probes in a batch experiment. When the dye is introduced close to the injection probe, the probe saturates and it takes a much longer time to return to its new steady state. If the response of this probe is included in the calculation of the blend time the repeatability of the experiment is very poor, so the injection probe is only used to determine the time when the dye is released in the system.

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The data analysis closely follows that described by Ruszkowski.20 The zero concentration level is subtracted from each probe response, and the resulting concentrations are normalized with the final concentration, or the mean concentration in the vessel at t ) ∞. Each normalized signal starts from a concentration Cm(t)0) ) 0 and changes over time to the final concentration of Cm(t)∞) ) 1.0. The variance is then defined as

σ2 )

1

M

∑ (Cm(t) - 1)2 M m)1

(3)

where M is the number of probes and Cm(t) is the current value of the normalized response for a given probe. The variance defined with eq 3 gives a space average over the three probes without no averaging over time. Note also that the variance as defined here is not the population variance, due to the small number of probes used. It also violates the definition of sample variance, since the result is divided by M (the number of probes), not (M - 1), the degrees of freedom. The assumption made in this calculation is that one of the probes is placed in the worst mixed point in the tank, and therefore the variance is representative of the population, even with the small number of probes used. The blend time is defined as the time when the variance reaches 95% of its final value, as shown in Figure 4 for the batch case. The variance expresses the decay of the concentration fluctuations after the addition of tracer. The log of the variance can range from 0 for a completely unmixed system (Cm(t) ) 0) to -∞ for a perfectly mixed system (Cm(t) ) 1). The 95% blend time is then defined as the time when the last concentration fluctuation drops below the 95% line (log(σ2) ) -2.6) for the last time. Results Batch Blend Time. The blend time data agree well with the correlation proposed by Grenville et al.5 as shown in Figure 5. At each rotational speed the blend time point on the figure is the average of six experiments. Individual values never varied by more than 8% from the mean. The slope obtained for two sizes of tank and six impellers is 5.80 with a correlation coefficient r2 of 0.966. This is a somewhat higher value of the coefficient than the value of 5.2 reported by Grenville and Nienow (p 509),1 but falls within the 10% standard deviation reported for the coefficient. These results were considered sufficient validation of the spectrophotometer probes, and experiments then progressed to the continuous case. Blend Time in a CSTR. If a perfectly mixed CSTR with a fluid volume V and a volumetric rate Q is disturbed by a step increase in concentration at the inlet (C0(t)0) ) 0 and C0(t>0) ) C0), then the concentration at the outlet will increase as

C ) C0(1 - e-(Qt/V))

(4)

One can define a 95% blend time (θRTD) based on the outlet probe concentration in an analogous way to the batch blend time:

θRTD )

(

)

C0 V V V ) ln(20) ) 3 ln Q C0 - 0.95C0 Q Q

(5)

giving an ideal 95% blend time for a perfectly mixed CSTR equal to 3 times the mean residence time. The continuous blend time θcnts is the experimental result obtained by calculating the variance from all three probes, two inside the vessel and one at

Figure 7. Semilog plot of the calculated variance from (a, top) outlet probe and (b, bottom) from all three probes at N ) 500 rpm (A310 impeller, D ) 0.56T, Q ) 20 L/min). The straight line is the predicted response for ideal mixing.

the outlet, and calculating the blend time at 95% homogeneity in exactly the same way as the batch blend time in eq 3 and Figure 4. At θcnts,

log(σ2) ) log

[

1

M

∑

]

(Cm(θcnts) - 1)2 M m)1 ) log[(-0.05)2] ) -2.6

(6)

In Figure 6a, the decay in normalized concentration deviation for the single outlet probe is compared with eq 4 for the ideal CSTR. Figure 6b shows the same comparison for the normalized decay of variance over all three probes. The experimental configuration used for Figure 6 has a mean residence time of 32 s, twice the blend time in the tank. The volumetric feed rate of 20 L/min is 1/10 the pumping capacity of the impeller. For both the single probe and the decay of variance, there are significant deviations from the ideal case. Following the discussion by Levenspiel,7 the shape of the RTDs suggests that there is short circuiting from the inlet to the outlet, which delays the rise in concentration in the tank. Figure 6b, which includes information about local variance inside the tank, shows a 50% deviation from ideality. This is much larger than the deviation in Figure 6a (38% deviation), confirming the limitations of a single exit probe as an indicator of mixing conditions inside the tank. In Figure 7, the analysis is repeated with the same tank configuration and inlet flow rate, with an impeller speed which is 5 times higher. In this case, the residence time is equal to 10 blend times, and the impeller pumping capacity is 50 times the


Figure 8. (a) Comparison of the time to reach 95% of the final concentration at the outlet with the theoretical value of 3(V/Q). (b) Dimensionless experimental blend time, θcnts/θb, vs calculated theoretical blend time, ln(20)(V/Q)/θb.

inlet flow rate. Comparison of Figure 7a with Figure 7b shows that when the blend time is decreased to 1/10 of the mean residence time, there is no difference between the outlet condition and the variance decay inside the tank, although in both cases the time to reach 95% of the final concentration differs from the ideal material balance by 35%. As in Figure 6, this deviation could be attributed to a combination of short circuiting through the center of the tank and more stagnant regions close to the surface, but there is not sufficient local concentration data to verify this explanation. Figure 8 combines the percent deviation results shown in Figures 6 and 7 for a range of tank geometries, inlet flow rates, and blend times. In Figure 8a, the outlet probe is used to follow the 95% rise in concentration. The combined results cover a wide range of residence times, from 30 to 330 s. There is an error of approximately 10% of the expected rise time at small residence times, with somewhat better agreement at long residence times. Figure 8b shows the results when three probes are used. In order to collapse the data for different impeller speeds, both the theoretical and the measured decay times are normalized with the batch blend time. Both figures show a

systematic deviation from the ideal blend time for small values of V/Q, or for small values of the ratio (V/Q)/θb. The data also show the expected shift toward the ideal result at large values of (V/Q)/θb. Focusing now only on the deviation from ideality for the case of three probes, Figure 9 shows the absolute percent difference:

%)

|

|

θcnts - θRTD × 100 θRTD

(7)

with increasing ratios of mean residence time to batch blend time. The general trend observed for all impellers is that for small (V/Q)/θb the absolute deviation from ideal mixing increases, and for a mean residence time less than 10 blend times the error increases rapidly, in some cases up to 50%. At high feed rates and low intensity of agitation, the mixing is poor. Conversely, as the mean residence time increases past 15 blend times, the mixing in the tank approaches the ideal case. Effect of Feed Stream Velocity. An alternate analysis for the percent error for this configuration is based on the analysis of a high-speed feed jet at the surface which is injected above

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of the power number in the scaling based on batch blend time. Both length scales (Lt and T) are held constant for this set of experiments. Both the power number and the ratio of D/df vary over a substantial range in the data set, and for both variables, the data collapse more cleanly for the blend time analysis than the jet velocity analysis. A third scaling based on the balance between the momentum of the feed jet and the momentum flux at the impeller was suggested by Grenville and Musgrove,22 but this data set is not well configured to test this third approach. Conclusions

Figure 9. The absolute percent deviation from ideal mixing increases dramatically as the mean residence time drops below 10 batch blend times.

Figure 10. Balancing the feed jet velocity with the impeller suction velocity provides better performance as the feed velocity gets smaller. However, the data do not collapse well enough to support a general model based on this criterion.

the impeller suction flow. In this case, Bhattacharya and recommend limiting the velocity of the feed jet to

Usuction 0.25π N D ) (L - 4df) g 1 Ujet 5.8 Vf df t

Kresta21

(8)

where Usuction is the suction velocity above the impeller, equal to 0.25(πND) by a material balance on the impeller, and Ujet is the velocity of the jet when it reaches the impeller, a distance Lt from the point of injection. The diameter of the feed pipe, df, determines the characteristic length scale of the jet decay and the feed velocity, Vf. The percent error is plotted against this criterion in Figure 10. These results do not collapse nearly as well as for the analysis based on (V/Q)/θb. To consider the physical basis for the difference, the ratio (V/Q)/θb can be restated in terms of the feed jet variables:

()

1 N D2 V/Q ) TNp1/3 θb 5.8 Vf df

(9)

There are two differences between these scaling equations which can be evaluated for the current set of experimental data. The first is the exponent on D/df, and the second is the inclusion

The results of this study confirm the form of the batch blend time correlation reported previously in the literature, suggesting a somewhat higher value of the constant than the value of 5.2 initially reported by Grenville et al.5 Experiments with multiple probes showed the importance of local mixing in continuous operations. The period of time when deviation from perfect mixing was observed at the outlet was often less than the time required to reach 95% of the final concentration throughout the tank volume, supporting the use of multiple probes to measure blend times. For small values of (V/Q)/θb, the continuous blend time was typically 30% longer than the prediction of the perfectly mixed CSTR model. When the impeller speed is increased, thus decreasing the batch blend time, the mixing inside the tank improves and the continuous blend time drops. When the mean residence time in the tank drops below 10 batch blend times, the mixing time in the tank deviates by up to 50% from the ideal CSTR model. For a feed at the top center of the tank and an outlet at the bottom center, a mean residence time of 15 batch blend times or more is needed to approach the ideal condition. These results support the recommendation that continuous stirred tanks be designed to have a mean residence time of at least 10 batch blend times. If the local mixing is critical, a more conservative value should be selected. For feed and outlet configurations other than the one studied here, somewhat different results may be obtained. Acknowledgment The authors would like to acknowledge Deming Mao, who carried out the original experiments; Dallas Chapple, who designed and built the apparatus; and Lightnin and NSERC, who funded this work under a strategic grant. Nomenclature C ) impeller off-bottom clearance (m) C1 ) molar absorptivity Cm ) dye concentration at probe m (mg/L) df ) inlet diameter (m) D ) impeller diameter (m) I, I0 ) light intensity (lm) Lt ) transit distance from the feed point to the impeller suction surface (m) M ) number of probes N ) impeller rotational speed (rpm or rps) Np ) power number Q ) flow rate (m3/s) Re ) Reynolds number (ND2/ν for a stirred tank, Vfdf/ν for the feed pipe) t ) time (s) T ) tank diameter (m) Ujet ) feed jet velocity at the point where the feed jet reaches the impeller (m/s)


Usuction ) axial velocity at the impeller suction surface (m/s) V ) tank volume (m3) Vf ) feed jet velocity at the feed pipe outlet (m/s) z ) axial coordinate (m) Greek Symbols θb ) batch blend time (s) θcnts ) continuous blend time (s) θRTD ) mean residence time (s) ν ) kinematic viscosity (m2/s) σ ) standard deviation Literature Cited (1) Grenville, R. K.; Nienow, A. W. Blending of Miscible Liquids. In Handbook of Industrial Mixing; Paul, E. L., Atiemo-Obeng, V., Kresta, S. M., Eds.; Wiley: New York, 2004. (2) Corrsin, S. The isotropic turbulent mixer II: Arbitrary Schmidt number. AIChE J. 1964, 9, 870-877. (3) Kresta, S. M.; Mao, D.; Roussinova, V. T. Batch blend time in square stirred tanks. Chem. Eng. Sci. 2006, 61, 2823-2825. (4) Ruszkowski, S. W.; Muskett, M. J. Comparative mixing times for stirred tank agitators. Proceedings of the 5th European Conference on Mixing; BHRA: Cranfield, U.K., 1985; pp 89-104. (5) Grenville, R.; Ruszkowski, S.; Garred, E. Blending of Miscible Liquids in the Turbulent and Transitional Regimes. Presented at the 15th NAMF Mixing Conference, Banff, Canada; 1995; Paper 1.5. (6) Nienow, A. W. On impeller circulation and mixing effectiveness in the turbulent flow regime. Chem. Eng. Sci. 1997, 52, 2557-2565. (7) Levenspiel, O. Chemical Reaction Engineering; Wiley: New York, 1972. (8) Nauman, E. B.; Buffham, B. A. Mixing in Continuous Flow Systems; Wiley: New York, 1983. (9) Aubin, J.; Kresta, S. M.; Bertrand, J.; Xuereb, C.; Fletcher, D. F. Alternate operating methods for improving the performance of continuous stirred tank reactors. Chem. Eng. Res. Des. 2006, 84, 569-582. (10) Shiue, S. J.; Wong, C. W. Studies on homogenization efficiency of various agitators in liquid blending. Can. J. Chem. Eng. 1984, 62, 602609.

(11) Sano, Y.; Usui, H. Interrelations among Mixing time, Power Number and Discharge flow Rate Number in Baffled Mixing Vessels. J. Chem. Eng. Jpn. 1985, 18, 47-52. (12) Mahouast, M. Concentration fluctuations in a stirred reactor. Exp. Fluids 1991, 11, 153-160. (13) Brennan, D. J.; Lehrer, I. H. Impeller mixing in vessels: experimental studies on the influence of some parameters and the formulation of a general mixing time equation. Trans. Inst. Chem. Eng. 1976, 54, 139152. (14) Hass, V. C.; Nienow, A. W. A new axially conveying stirrer for dispersion of gas in liquids. Chem. Ing. Tech. 1989, 61, 152-154. (15) 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. (16) Houcine, I.; Vivier, H.; Plasari, E.; David, R.; Villermaux, J. Planar laser induced fluorescence technique for measurements of concentration fields in continuous stirred tank reactors. Exp. Fluids 1996, 22, 95-102. (17) Lee, J.; Brodkey, R. S. Turbulent motion and mixing in a pipe. AIChE J. 1964, 10, 87-193. (18) Nye, J. O.; Brodkey, R. S. Light probe for measurement of turbulent concentration fluctuations. ReV. Sci. Instrum. 1967, 38, 26. (19) OceanOptics. Operating Manual and User’s Guide: S2000 Miniature Fiber Optic Spectrometers and Accessories. (20) Ruszkowski, S. A Rational Method for Measuring Blending Performance and Comparison of Different Impeller Types. Proceedings of the 8th European Conference on Mixing. Inst. Chem. Eng. Symp. Ser. 1994, No. 136, 283-292. (21) Bhattacharya, S.; Kresta, S. M. Reactor performance with high velocity surface feed. Chem. Eng. Sci. 2006, 61, 3033-3043. (22) Grenville, R. K.; Musgrove, M. E. Comparison of Blend Times in Agitated and Jet Mixed Vessels: The Role of Momentum; Fluid Mixing Processes Consortium Steering Committee Meetings; September 1998. (23) Clark, M. M.; Srivastava, R. M.; Lang, J. S.; Trussell, R. R.; Mccollum, L. J.; Bailey, D.; Christie, J. D.; Stolarik, G. Selection and Design of Mixing Processes for Coagulation: American Water Works Association, Research Foundation: Denver, CO, 1994.

ReceiVed for reView July 13, 2007 ReVised manuscript receiVed October 9, 2007 Accepted October 10, 2007 IE070955R

Comparison of Continuous Blend Time and Residence Time

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