2984
Ind. Eng. Chem. Res. 1997, 36, 2984-2989
An Experimental Study To Characterize Imperfect Macromixing in a Stirred Semibatch Reactor A. W. Nienow,* S. M. Drain, A. P. Boyes, and K. J. Carpenter† The School of Chemical Engineering, The University of Birmingham, Birmingham B15 2TT, U.K.
A first-order decay of a diazonium salt, rate constant ∼ 10-3 s-1, and a parallel, very fast, secondorder coupling with the addition of pyrazolone, i.e., A f S and A + B f R, have been used to study macromixing in a stirred semibatch reactor. The experiments undertaken include two types of impeller, two liquid heights, two feed positions, three feed rates, and three semitechnical scales of vessel from 0.3-0.6 m diameter. At high impeller speeds, all conditions give similar yields of around 90%. At lower speeds, typical of those found on the industrial scale, the yield fell as low as 65%. However, feeding into the impeller zone compared to the surface and using a larger 60° pitch blade impeller rather than a standard Rushton turbine increased yields at similar values of power/volume to about 85%. Yields under geometrically similar conditions at each scale were the same when operating at constant agitator speed. Such results fit in well with the concept that the same scale-up rule applies to macromixing as that for equal mixing times. It also matches the scale-up rule implied by the “network-of-zones” model developed by Mann and co-workers, though the absolute values of yield predicted differ widely from those obtained experimentally at low speeds and with surface addition. The results also show that improving bulk blending is a good strategy for increasing yields. The performance of a 60-ton industrial-scale reactor used to produce reactive dyes was significantly enhanced following this work by changing a feed point from the surface to the impeller region. Introduction
Scheme 1. Reaction Kinetics and Chemistry
Much work has been conducted concerning the impact of micromixing on fast reactions (Bourne, 1992; Villermaux, 1983). Less has been done for relatively slower reactions where macromixing is important, i.e., where the gross mixing time in a stirred vessel is of the same order as the characteristic time of the chemical reaction (Bourne, 1992). Such reactions produce special problems for scale-up because under all realistic operating conditions, mixing time increases (Nienow, 1974). However, chemical reactions which have been specially selected for studying macromixing are very limited. A particularly simple reaction scheme conceptually is a first-order decay accompanied by a second-order couk1
k2
pling, i.e., A f S and A + B f R. B is added to A, but while B is being mixed in, A is decaying. The slower the rate of mixing, the more A decomposes and the less R is formed. The relative yields of R and S thus serve as a measure of imperfect macromixing. Such a scheme has been briefly reported previously (Nienow et al., 1992). In that paper, the results for one set of experimental conditions were used in an example of the application of the “network of zones” model of macromixing developed extensively by Mann and co-workers since the early 1980s (e.g. Mann and El-Hamouz, 1991). Here, the main experimental results are presented and the experimental protocol too is provided in more detail. The results are then discussed with respect to agitation conditions, feed point, and scale-up/scale-down implications. Experimental Method and Data Treatment A diazonium salt (A) (diazotized 2-chloro-4-nitroaniline) decays, and pyrazolone (B) (1-(4-(sulfophenyl)3-carboxypyrazol-5-one) is added. R, the product, is a dyestuff. The decomposition of A is independent of the †
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mixing conditions, though the rate of both reactions is very sensitive to pH and temperature. The decomposition reaction therefore serves as an internal clock producing S, the unwanted product at a rate which can be finely tuned to match the agitation conditions of interest. The precise chemistry is given in Scheme 1. The rate of decay was chosen to ensure that emulating mixing conditions on the large scale would show different results. In particular, the large-scale operation of interest consisted of a 60-ton reactor agitated at 12 or 25 rpm. A decay rate constant of ∼10-3 s-1 was found to be satisfactory and also to be slow enough to allow the precise rate to be established during each experiment by taking samples. The pH and temperature needed were 6.3 and 40 °C, respectively. The secondorder time constant was too fast to measure at these conditions but was ∼7000 M-1 s-1 at a pH ) 3.5 and 25 °C as measured in a stop-flow device. Experiments were mainly conducted in a 0.3-mdiameter vessel (T) with a liquid height (H) equal to T. Four 0.1T strip baffles were used with a standard Rushton turbine, diameter D ) 1/3T with a clearance off the base C ) 1/3T. The power number for the impeller was 4.8 as measured by an air-bearing dynamometer (Nienow and Miles, 1969). Experiments were © 1997 American Chemical Society
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Figure 1. Plot of ln(CA/CAi) against time, t (s), used to evaluate the decomposition rate constant, k1.
Figure 2. Experimental apparatus and summary of operating conditions.
also conducted at the 0.45-m and 0.61-m scales with the Rushton turbine under geometrically similar conditions (with power measured by strain gauge/telemetry (Kuboi et al., 1983)) and in the 0.30-m tank at H/T )1.35. In addition, a few experiments were undertaken in the 0.30-m-diameter vessel at H/T ) 1.35 using a 60° pitch, six-bladed turbine (D/T ) 0.54) of projected blade height to diameter ratio 0.2 and of power number 4.5. The results were compared with those for the Rushton turbine. In this case, six special baffles, triangular in plan view with an apex height equal to 0.1T, were used, as this geometry mimicked closely the commercial-scale reactor which had a diameter of 4 m. In a typical experiment, warm distilled water at 39 °C was added to give 90% of the working volume. The agitator speed was set, and then monosodium phosphate at ∼0.5 M was added as a buffer followed by 50% sodium hydroxide solution to give a pH of 6.25. To this was added the diazonium salt (which was prepared in-house and stored at a pH of 1-2 for not more than 5 days in a refrigerator) to give a concentration of ∼8 × 10-5 M (CAi). Final adjustments were then made to the level, the temperature (40 °C) and pH (6.3) and agitator speed. The precise initial diazo concentration and that of five, 20-mL samples were obtained by quenching with a solution of pyrazolone and monosodium phosphate buffer and analyzing off-line using a Cecil CE515/Pye Unicam SP8 400 double-beam UV spectrophotometer at 430-nm wavelength and a 10-mm cell path length. A typical example of a decay is shown in Figure 1, which enabled k1 to be calculated. The average value of k1 ) 1.26 × 10-3 s-1 (with a standard deviation of (7%) and this value enabled the time to be estimated at which the diazo (A) concentration (CAO) was ∼6 × 10-5 M. This fall from ∼8 × 10-5 to ∼6 × 10-5 M ensured that the decomposition products did not react with the pyrazolone coupler (also prepared in-house) which was added at this time.
Sufficient coupler at a concentration of 7.4 × 10-2 M was then added to give an excess mean concentration of ∼1.1CAO based on the quantity added being dispersed in the total volume of liquid. The addition was done using a peristaltic pump through a glass pipe, generally for 60 s either onto the top surface or into the impeller zone. The vessel arrangement is shown in Figure 2. At the end of the run, three samples were used to determine the concentration, CR, of the product R, again spectrophotometrically. Occasionally, a 15-s feed time or other feed positions were used, and this change is noted when applicable. Two yields were calculated, the “observed yield” and the “theoretical yield”. The former was the amount of product formed, CR, compared to that which could have been formed if all of the CAO, the concentration of diazonium salt at the start of addition of the coupler, were converted into product, i.e., CR/CAO. The latter was calculated, allowing for (i) the amount of decay of A during the addition time and (ii) the rate of coupling assuming perfect mixing, as the amount of B added to the vessel increases from zero to CBO (=1.1CAO) at the end of the addition time. Thus, the theoretical yield was independent of agitation conditions, but it was affected by the addition time. Observed/theoretical yield values from repeat experiments conducted from time to time were within (2%. Further details are given elsewhere (Drain, 1987). In order to recognize this as a macromixing problem, Table 1 compares the order of magnitude of the characteristic times for the different possible mixing processes in the 0.30-m-diameter tank and those of the chemical reactions. Results and Discussion Effect of Agitation Speed. In general, the agitation speed did not greatly affect the observed yield for agitator speeds above about 100 rpm regardless of
2986 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 Table 1. Comparison of Time Scales at 120 rpm (Drain, 1987) (Except as Noted) tank mixing time, TMa circulation time, TC diffusional half-life time, T1/2Dmb first-order dec half-life time, T1/2R ()ln 2/k1) second-order coupling half-life time, T1/2R ()1/k2CAO) based on CBO ∼ CAO = 6 × 10-5 M based on CBf = 7.4 × 10-2 M k1 ) 1.25 × 10-3 s-1 (pH 6.25, 40 °C) k2 ) 7000 M-1 s-1 (pH 3.5, 25 °C , stopped-flow technique)
15.4 s (at 12 rpm ) 154 s) 3.8 s 0.079 s 578.0 s 2.56 s 1.3 × 10-3 s
a Ruszkowski, 1994. b Assuming T 2 1/2Dm ) 0.15(0.2λK) /Dm where λK ) (ν3/jT)0.25 ) 90 µm at 120 rpm (Bourne, 1992), Dm ) 6 × 10-10 m2/s, and ν ) 10-6 m2/s.
Figure 4. Effect of scale on yield with a surface addition time of 60 s at H/T ) 1 using the Rushton turbine.
Figure 5. Flows for the i, j zone in the network-of-zones model.
Figure 3. Effect of agitator speed on yield in the 0.30-m vessel at H/T ) 1 using the Rushton turbine with a 60-s addition time: (a, top) to the surface; (b, bottom) into the impeller zone.
impeller type, H/T ratio, addition time or point, or scale of operation (see Figures 3, 4, and 6-9). Observed yields were always above ∼90%. Using the extensive work of Mann and co-workers on network-of-zones modeling, such high yields were predicted for the set of experiments conducted with the Rushton turbine with 15-s addition times (Nienow et al., 1992). However, at low speeds of the order of those used at the industrial scale, the yield dropped significantly, especially for surface addition. For the latter addition mode, the drop was much more than predicted by the network-of-zones model; i.e., at 12 rpm, the experimental value was approximately 70% (Figure 9a) while the predicted value was still 88.9% (Nienow et al., 1992). Effect of Feed Position. Figure 3 shows the observed and theoretical yields for surface addition (Figure 3a) and impeller addition (Figure 3b) as a function of agitator speed with an addition time of 60 s at H/T ) 1. For the surface addition (Figure 3a), the yield falls to around 70% for addition onto the surface (as had been used at the industrial scale) at the lowest speed of 12 rpm, which also matched the industrial conditions. Some additions were made just below the surface to eliminate any possibility that the surface itself offered a resistance. However, the data for these
conditions follow closely the same trend. Figure 3b for impeller addition has slightly higher yields over the whole speed range and much less of a fall at the lowest speed. Effect of Scale. Figure 4 shows the results for the three scales of operation with addition onto the top surface. It can be seen that the data are well correlated by agitation speed on each scale with a large drop in yield occurring at the lowest speeds. Such a correlation might be expected where macromixing dominates (Nienow, 1974) since mixing time is constant on different scales at constant agitator speed. A similar result was predicted by Goldstein (1973). Details of the network-of-zones model have been given many times elsewhere (for example, Wang, 1991; Mann and El-Hamouz, 1991), so only a very brief outline is included here in order to indicate its scale-up implications. The flows for the i, j zone are shown in Figure 5. The unsteady-state material balance for each individual zone is then
Vij
dCIi,j ) dt q[CIi-1,j - (1 + 2β)CIi,j + β(CIi,j-1 + Cli,j+1)] ( rIi,j
This equation is applied independently of the scale of operation, and for a Rushton turbine, β ) 10 in the impeller zone and is 0.2 elsewhere, the values being estimated from work using acid/alkali tracers, e.g., Wang (1991). The main flow between zones q ) Q/n where Q ) KND3 (with K assumed equal to 2.75 (Mann and El-Hamouz, 1991)) and n is the number of zones (also independent of scale) so that Vi,j ) V/n. The
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 2987
Figure 6. Effect of addition position on yield: addition time, 60 s; H/T ) 1, Rushton turbine.
overall yield requires the yield for each zone to be determined and then summed over all zones. The precise solution clearly depends on the kinetics (and the assumptions made for K, β, and the number of zones). However, for a particular set of assumptions and kinetic parameters, the solution is only dependent on the ratio q/Vi,j. For geometrically similar systems of different scale,
q/Vij ∝
ND3 ND3 ∝ 3 ∝N V D
Therefore, the network-of-zones model predicts for semibatch reactions that an equal yield is obtained on scale-up if constant agitator speed is maintained. It is also interesting to note that Paul (1988) used the Bourne reactions (Bourne, 1992) to study the impact of mixing on yield. These very fast competing consecutive reactions are typically used to study micromixing, but this requires low feed rates of reactants. At sufficiently low feed rates, equal local energy dissipation rates give equal yields. However, if higher feed rates are used, both meso- and macromixing effects can become dominant (Bourne, 1992). Paul (1988) did not report feed rates, but he showed equal yields in both 100- and 1000gal geometrically similar, glass-lined reactors agitated by retreat-blade impellers at speeds from 90 to 150 rpm, giving yields increasing from ∼90 to ∼95% over this speed range. Figure 6 compares both addition modes at the 0.30and 0.45-m scales. This figure supports the two previous findings, namely, that impeller addition is more effective and that constant agitator speed gives equivalent results on different scales. Effect of Liquid Height. Figure 7 compares the yields at H/T ) 1.35 for surface addition (Figure 7a) and impeller addition (Figure 7b). The reduction in yield now occurs at a higher speed (∼100 rpm) for surface addition (Figure 7a) compared to H/T ) 1 (Figure 3a). Cooke et al. (1988) showed that with increasing H/T above 1, the mixing time increased very rapidly, proportional to (H/D)2.43. Addition to the impeller region only produces a small reduction in yield, however (compare Figures 7b and 3b). Both results suggest that H/T > 1 combined with surface addition should, if possible, be avoided. The reason that high H/T levels and surface addition give such poor results is the very low energy dissipation rates and liquid velocities (CAO, see Figure 1) CAO ) concentration of A at the time at which coupler addition begins CB ) concentration of B CR ) concentration of R CBf ) concentration of B in feed C ) impeller clearance Dm ) molecular diffusivity D ) impeller diameter H ) liquid depth i ) zone column position (radial) j ) zone row position (axial) k ) reaction rate constant K ) total internal flow coefficient N ) stirrer rotation speed n ) network size Q ) total internal cirulatory flow in the vessel q ) circulation loop flow qf ) feed rate rI ) reaction rate for I T ) vessel diameter t ) time ta ) time at which addition of coupler begins tf ) feed time V ) fluid volume Vi,j ) volume of the i,j zone Greek Symbols β ) lateral exchange flow coefficient jT ) mean energy dissipation rate λK ) Kolmogoroff length scale ν ) kinematic viscosity
Literature Cited Bourne, J. R. Mixing in Single Phase Chemical Reactors. In Mixing in the Process Industries, 2nd ed.; Harnby, N., Edwards, M. F., Nienow, A. W., Eds.; Butterworth: Heineman, 1992; Chapter 10, pp 184-199. Cooke, M.; Middleton, J. C.; Bush, J. Mixing and Mass Transfer in Filamentous Fermentations. In Proc. 2nd Int. Conf. on Bioreactor Fluid Dynamics, Cambridge, U.K.; King, R., Ed.; Elsevier Science: Amsterdam, 1988; pp 37-64. Drain, S. M. The Development of a Competing Reaction Scheme and Its Application to the Study of Mixing in Stirred Tanks. Ph.D. Thesis, The University of Birmingham, Birmingham, U.K., 1987. Geisler, R.; Krebs, R; Forschner, P. Local Turbulent Shear Stress in Stirred Vessels and Its Significance for Different Mixing Tasks. Proc. 8th Euro. Mixing Conf., Cambridge, U.K.; Institution of Chemical Engineers; Rugby, U.K., 1994; pp 241-251. Goldstein, A. M. The Application of Simulation Vessel Flow Studies to an Industrial Chemical Reactor Mixing Problem. Chem. Eng. Sci. 1973, 28, 1021-1029.
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 2989 Kuboi, R.; Nienow, A. W.; Allsford, K. A Multipurpose Stirred Tank Facility for Flow Visualisation and Dual Impeller Power Measurement. Chem. Eng. Commun. 1983, 22, 29-39. Mann, R.; El-Hamouz, A. Effect of Macromixing on a Competitive/ Consecutive Reaction in a Stirred Semi-Batch Reactor: Paul’s Iodination Experiments Interpreted by Networks-of-Zones. Proc. 7th Europ. Conf. Mixing, Brugge, Belgium; KVIV: Brussels, 1991; pp 1-10. Nienow, A. W. Constant Turnover-time as a Scale-up Criterion for Agitated Tanks. Chem. Eng. Sci. 1974, 29, 1043-1044. Nienow, A. W. On Impeller Circulation and Mixing Effectiveness in the Turbulent Flow Regime. Chem. Eng. Sci. 1997, in press. Nienow, A. W.; Miles, D. A Dynamometer for the Accurate Measurement of Mixing Torque. J. Sci. Inst., 1969, 2, (Series 2), 994-995. Nienow, A. W.; Drain, S. M.; Boyes, A. P.; Mann, R.; El-Hamouz, A. M.; Carpenter, K. J. A New Pair of Reactions to Characterize Imperfect Macro-Mixing and Partial Segregation in a Stirred Semi-Batch Reactor. Chem. Eng. Sci. 1992, 47, 2825-2830. Paul, E. Design of Reaction Systems for Speciality Organic Chemicals. Chem. Eng. Sci. 1988, 43, 1773-1782.
Ruszkowski, S. A Rational Method for Measuring Blending Performance and Comparison of Different Impeller Types. Proc. 8th Euro. Mixing Conf., Cambridge, U.K.; Institution of Chemical Engineers: Rugby, U.K., 1994; pp 283-291. Villermaux, J. In Chemical Reaction EngineeringsPlenary Lectures; Wei, J., Georgakis, C., Eds.; ACS Symposium Series No. 226; American Chemical Society: Washington, DC, 1983; pp 135-186. Wang, Y. Effect of Mixing on Complex Reactions in a Stirred SemiBatch Reactor. Ph.D. Thesis, UMIST, U.K., 1991.
Received for review October 4, 1996 Revised manuscript received December 24, 1996 Accepted January 18, 1997X IE960618A
X Abstract published in Advance ACS Abstracts, June 15, 1997.
