Hydrodynamics in a Horizontal Stirred Tank Reactor - Industrial

Ind. Eng. Chem. Res. 2001, 40, 785-794

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Hydrodynamics in a Horizontal Stirred Tank Reactor Gert-Jan S. van der Gulik,* Johan G. Wijers, and Jos T. F. Keurentjes Process Development Group, Eindhoven University of Technology, Department of Chemical Engineering and Chemistry, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

In this study, the hydrodynamics in a horizontal stirred tank reactor is investigated. This type of reactor is used in industry for fast polycondensation processes. Overall circulation, poorly mixed zones and macro-mixing times are determined in scale models under turbulent (Re > 105) and laminar (Re < 300) conditions using planar laser induced fluorescence. For both sets of conditions, the observed overall circulation is complex and changes when the length-to-diameter ratio is varied. Under laminar conditions, the flow appears to be chaotic. The poorly mixed zones change in location, number, and life span for different length-to-diameter ratios. Dimensionless macro-mixing times under turbulent conditions are correlated with parameter variations and show nonlinear relationships with fill ratio, length-to-diameter ratio, and Reynolds number. Under laminar conditions, macro-mixing times could not be determined unambiguously, but they are only 2.5 times larger than those found under turbulent conditions. Introduction The design of a reactor for fast polycondensations is a major challenge for chemical engineers, as often several conflicting needs have to be fulfilled. Generally, two types of agitation are needed as the flow regime changes from turbulent to laminar, because of a tremendous increase in viscosity. In both regimes, the mixing has to be sufficient as it has a large influence on the final product quality.1,2 This influence can easily be understood by considering the production process of Twaron, an aromatic polyamide produced via the polycondensation reaction of a diamide with a diacyl chloride.3,4 The fast propagation step is given as reaction 1

Theoretically, a small excess of the diamide determines the degree of polymerization. When the relative excess equals 1/n, the average chain will contain n + 1 units. In practice, the degree of polymerization is controlled by adding water that can terminate a reactive acyl chloride group via the slow reaction 2

Water is added at the start of the process because, at the end of the process, the viscosity is too high to mix water sufficiently to molecular scale. The initial presence of water complicates the process, as water is able to terminate chains too early when mixing is insufficient, leading to short chains and a broad molecular weight distribution (MWD). * Author to whom correspondence should be addressed. E-mail address: [email protected].

Table 1. Order of Magnitude of Reaction Time for Reactions 1 and 25 viscosity (Pa s)

reaction time for propagation (s)

reaction time for termination (s)

10-3 10

10-4 10

102 102

In Table 1, the orders of magnitude of the reaction half-life times for both reactions are given for low and high viscosity levels. Going from low to high viscosity, the propagation rate slows by 5 orders of magnitude, while the termination rate remains unchanged. The propagation reaction is slowed for two reasons. First, RNH3 + Cl- groups are formed, which are less reactive than NH2 groups.3 Second, the reactive end groups are more sterically hindered upon an increase in molecular weight. The chain stopper (water) will not be hindered as much, because it is a relatively small molecule. In production, the reactor is filled with the diamide component (containing the required amount of water), to which the diacyl component is added semi-batchwise. To allow for an exact stoichiometric ratio of the two monomers, only one single injection point is used. This implies that good overall circulation is needed to allow the acyl molecules to react with all the amide-containing molecules throughout the reactor before termination occurs. This implies that a fundamental insight into the hydrodynamic behavior of this type of reactors is mandatory to guarantee constant product quality upon scale-up and to allow for quality improvements in existing equipment. The polymerization described above is performed in a horizontal stirred tank reactor of the Drais type.4 This multifunctional reactor, as depicted in Figures 1 and 2, can be used for powder mixing, turbulent fluid mixing, and kneading at high viscosities with an energy dissipation up to 200 W/kg. Literature on the hydrodynamics in horizontal mixing vessels is very limited compared to the literature on vertical vessels. There is some literature on turbulent mixing, but literature on laminar mixing is absent. Ando et al.6 studied power consumption and flow behavior under turbulent conditions in an

10.1021/ie000054h CCC: $20.00 © 2001 American Chemical Society Published on Web 01/12/2001

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Ind. Eng. Chem. Res., Vol. 40, No. 3, 2001

Figure 1. Drais reactor, given in front, top, and side views with clearance length L, diameter D, blade angles R and β, blade width w, blade height h, and a hatch. The arrows point out the direction of rotation during operation.

unbaffled horizontal vessel with Rushton turbine impellers with Di/D ) 0.9. They distinguish two flow states A and B. State A is obtained at a relatively low stirrer speed. The liquid is then pushed up by the impellers and sprayed, leading to the formation of fine liquid droplets and fine air bubbles. State B, the so-called hollow state, is obtained at a higher stirrer speed, providing a ring of fluid. As their research mainly focused on applications to gas-liquid absorption, mainly state A in baffled vessels was investigated.7-10 This is due to a larger gas-liquid interface in the A state compared to state B. Ando et al.11 also studied turbulent mixing in an idealized horizontal vessel with baffles and multiple impellers. Macro-mixing times were measured, and a model was proposed for predicting them. It was established that the dimensionless macro-mixing time Nt is proportional to L/D. The information available in the literature on turbulent mixing in horizontal stirred tank reactors is not directly applicable to polycondensations in the Drais reactor for two reasons. First, the impeller geometry is completely different. Second, the fluid in the polycondensation process is in the hollow state (or the B state according to Ando6) because of a high stirrer speed. Therefore, we conducted an experimental study on the hydrodynamics in this type of reactor. For this purpose, mixing patterns, the life span of poorly mixed zones, and the macro-mixing times have been established experimentally. This is done for turbulent as well as laminar conditions and for different reactor fill ratios. Subsequently, scaling rules will be defined based on these macro-mixing times. Experimental Section The reactor used in this study was a horizontal stirred tank of the Drais type (Turbulent Schnellmischer, Drais Ltd, Mannheim, Germany), as depicted in Figures 1 and 2. Typical for the unbaffled cylindrical reactor is its

horizontal position and the heavily designed impeller. This impeller can provide a high mixing power, needed to achieve sufficient mixing under highly viscous conditions. The reactor is characterized by length L and diameter D. Typical for the reactor is the clearance C, the distance between the blades and the reactor wall. For a small clearance, the blades perform a scraping action that keeps the reactor walls free of polymer material and also provides good heat exchange with the cooled walls. The blades have a pumping action toward the reactor center, providing an easy way to empty the reactor through the opened hatch. To determine macro-mixing times and the life span of poorly mixed zones, planar laser induced fluorescence (PLIF) was used. With PLIF, it is possible to make a digital film of the mixing of a tracer in a twodimensional plane in which the poorly mixed zones can easily be located. In contrast with methods used in other studies,2-6,12-16 PLIF is unobtrusive, has a small measurement volume, and is flexible in changing the monitoring point, as only the position of the laser sheet has to be changed. PLIF experiments were performed in three small-scale models of the Drais reactor. These reactors, as depicted in Figures 1 and 2, were all 0.18 m in diameter but differed in length, being 0.20, 0.27, and 0.36 m, providing L/D ratios of 1.1, 1.5, and 2.0, respectively. From this point on, these scale-models are referred to as reactor-11, reactor-15, and reactor-20, respectively. The blade width w was equal to 0.1 m, the clearance was 0.003 m, the blade height h was equal to 0.015 m, and the shaft had a diameter of 0.03 m. The blades were evenly distributed over the shaft for each reactor. The mutual angles of the blades were 180, 120, and 135° for reactor-11, reactor-15, and reactor-20, respectively. These angles correspond to industrial configurations and proved to provide the most stable fluid ring in partially filled reactors. The side walls, the shaft, and the impeller blades were made of stainless steel, and the cylindrical wall of glass. Under turbulent conditions, tap water was used as the reactor content for the three fill ratios 40, 60, and 100%. The rotational speed varied between 3.8 and 11.6 Hz, resulting in turbulent flow with Reynolds numbers ranging from 123 000 to 375 000, as defined by FNDi2/µ. When the reactor was partially filled, the rotational speeds always resulted in the hollow state or the B state according to Ando.6 For laminar conditions, glycerin (Heybroek, Amsterdam; purity >99.9%) was used at Reynolds numbers ranging from 90 to 270. Glycerin limits the use of PLIF to the examination of completely filled reactors because air bubbles lead to an untransparent fluid in partially filled reactors. Figure 3 shows the experimental arrangement for the PLIF experiments, which is comparable to the setup used by Schoenmakers et al.17 The laser beam was generated by a 2-W Ar/Kr laser (model Stabilite 2017005, Spectra Physics) and had a wavelength of 488 nm. The beam was converted to a laser sheet with a thickness of 0.5 mm by a cylindrical lens (Dantec 9080XO.21). The position of the laser sheet in the vessel geometry was always parallel to the shaft. Therefore, the observed mixing process was always the mixing in the axial and radial directions. This is secondary mixing, superimposed on the mixing in the tangential direction. Disodium fluorescein (C20H10O5Na2) was used as the fluorescent dye (Merck, Darmstadt; purity >98 wt %). This dye emits light with an intensity depending on the

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Figure 2. Stirrer geometries for reactor-15 (top) and reactor-20 (bottom). The white blades transport fluid to the right during rotation, the black stirrers transport fluid to the left. Thus, both have a pumping action toward the center of the reactor. The blades are evenly distributed over the shaft and are not drawn in perspective.

from 0 to 255, providing a resolution of 256 values. For complete mixing, a gray scale of around 150 was obtained. In the range from 0 to 255, the gray scale corresponds linearly with concentration. In Figure 3, the evaluated region is depicted as a dotted rectangle. This region was always set to the left part of the reactor. It was sufficient to monitor mixing in one half of the reactor because we observed that mixing was symmetrical with respect to the reactor center. The number of recorded images per second ranged between 30 and 120 and depended on the impeller speed and the expected mixing time. The number of pixels per image in the axial direction, i.e., from injection point to sidewall, ranged from 90 to 150 for reactor-11 and reactor-20, respectively. In the radial direction, i.e., from shaft to cylindrical wall, the number was 68 for every image. This results in a spatial resolution of about 1 × 1 × 0.5 mm per pixel. Figure 3. Sketch of the experimental setup.

power of the laser light, the concentration, and the pH of the solvent. The power of the laser light was kept constant at 0.4 W. During every experiment, the final dye concentration was around 10-7 M. Therefore, the amount of injected solution, with dye concentration of 2 × 10-3 M, varied between 0.3 and 0.5 mL, depending on the reactor volume and fill ratio. The pH of both the injected solution and the reactor content was kept constant at a value of 10, as the intensity of the emitted light is independent of the pH at pH > 8. A high-speed camera (JAI CV-M30), connected to a PC, with an EISA compliant frame grabber (Magic) recorded the light that was emitted by the fluorescein molecules in the laser light plane. The commercial software package DMA-MAGIC was used for data acquisition. The value of the recorded gray scales ranged

Results and Discussion This section starts with a brief description of the mixing pattern and the establishment of poorly mixed zones or islands, as observed in the PLIF images. Then, the technique for measuring concentrations and mixing times is shown. Finally, the mixing times are correlated with process parameters in order to formulate empirical correlations for scale-up. Mixing Patterns and Chaotic Mixing. The mixing of the injected dye in the axial and radial directions in reactor-11 is shown in Figures 4 and 5 for turbulent and laminar conditions, respectively. Although not the same, these mixing patterns show a resemblance. In Figures 4b and 5a, it can be seen that the dye is mainly transported in the axial direction as it flows from the central injection point toward the sidewall. Figures 4d and 5b show that the dye is subsequently transported in the radial direction along the sidewall, followed by

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Figure 4. Mixing pattern in water in reactor-11 at N ) 6 Hz.

Figure 5. Mixing pattern in glycerin in reactor-11 at N ) 8 Hz.

transport to the bulk along the shaft in the axial direction. The overall circulation in Figures 4 and 5 is therefore turning counterclockwise. This is the opposite of what was expected, based on the center-oriented pumping action of the stirrer blades. Figures 6 and 7 show how the dye is mixed in reactor20. The PLIF images show that two regions are present

that differ in overall circulation: one at the left-hand side of the PLIF image and one at the right-hand side. The circulation at the left-hand side is counterclockwise and thus shows resemblance with the circulation in reactor-11. The circulation at the right-hand side is clockwise. This circulation is visible in Panels a and b of Figure 7 in which the injected dye is transported first


Figure 6. Mixing pattern in water in reactor-20 at N ) 6 Hz.

Figure 7. Mixing pattern in glycerin in reactor-20 at N ) 6 Hz.

in the radial direction toward the shaft and subsequently in the axial direction along the shaft. By way of illustration, the generalized overall circulation in the radial and axial directions is depicted in Figure 8 for reactor-11, reactor-15, and reactor-20. The flow in Figures 5 and 7 can be considered as a three-dimensional discontinuous periodic flow in which the impeller blades provide the discontinuous movement with a period equal to 1/N. This allows a comparison with the two-dimensional flow in a cavity studied by Leong and Ottino.18,19 Clearly, the laminar flow has a chaotic nature as it is capable of stretching and folding a region of fluid and returning itsstretched and foldeds to its initial location after one period, i.e., one impeller revolution. Furthermore, the formed striations are reoriented when the impeller blades cross them. This

event is visible in Figure 5d, in which the vertical impeller arm, as present in the right-hand side of the laser sheet, plows through the horizontal striations. These reorientations further enhance chaotic mixing. A quantitative indication for chaotic behavior is the Liapunov exponent σ in the formula PE ) PE0 exp(σt).18,19 This formula represents the stretching rate of the flow as it describes the perimeter of intermaterial area between the dye and the clear fluid as a function of time. A positive exponent σ implies exponential generation of an intermaterial interface and, hence, implies chaotic flow. The inset in Figure 9 gives the perimeter as a function of time for reactor-20 at N ) 11 Hz. The initial exponential increase yields the Liapunov exponent by a fit procedure for which all of the perimeter values after the maximum has been reached are

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Figure 8. Observed overall circulation in reactor-11, reactor-15, and reactor-20.

ignored. The perimeter decreases after the maximum has been reached because the striations are lost when they become smaller than the pixel size. For all experiments under laminar conditions, the Liapunov exponent is given in Figure 9 as a function of impeller speed. The positive exponents increase linearly with impeller speed and appear to be independent of L/D. This indicates that chaotic mixing in all three reactors occurs in a similar fashion. Poorly Mixed Zones and Islands. Under turbulent conditions, poorly mixed zones are visible in Figures 4 and 6 as the areas in the reactors that remain dark the longest. These areas are visible in Figures 4e and 6e (reactor-11 and reactor-20) near the shaft between the two outer impellers blade (the same holds for reactor-

15, although not shown here). Apparently, under turbulent conditions, the location does not depend on L/D. Nevertheless, the poorly mixed zones are not very stagnant, as they disappear within seconds through turbulent dispersion. Under laminar conditions, the islands (as a poorly mixed zone is usually referred to at laminar conditions) in reactor-15 and reactor-11 (Figure 5e) are located below the injection point. These islands are unstable and consequently disappear within seconds (compare, e.g., panels e and f of Figure 5). This observation leads to the conclusion that reactor-11 and reactor-15 are globally chaotic. Leong and Ottino18 indicate that the existence of multiple folds along the island boundary is indicative for the instability of islands. The presence of a “rough” island boundary in Figure 5e can be regarded as an indication for this. In reactor-20 (Figure 7e and f) four islands are visible throughout the reactor. These islands are very stable in the range of impeller frequencies applied. This leads to the conclusion that reactor-20 is not globally chaotic. The four islands, in fact, form four segregated torii, fluid elements that have often been observed in mixing vessels.20-24 These fluid elements act as barriers to mixing and are therefore highly undesirable in the polycondensation process as their existence allows for early termination, hence leading to an undesired broad MWD. Probably, the segregated torii can be terminated by changing the mutual angle between the blades or by periodically changing the impeller speed.18,25,28 Macro-Mixing Times under Turbulent Conditions. For turbulent conditions, mixing is quantified by determining macro-mixing times from response curves. These curves are created by plotting gray scales at a certain position in the PLIF images against the elapsed time. The chosen position is located as depicted in Figure 3 by an “x” and is exactly two pixels from the sidewall and two pixels from the cylindrical wall. This

Figure 9. Liapunov exponents σ as a function of impeller frequency N. The inset provides the perimeter as a function of time for reactor20 at 11 Hz. The line in the inset represents the fit PE ) PE0 exp(σt).


Figure 10. Normalized gray scale, plotted versus time, in reactor-11 at 6 Hz with a fill ratio of 40%. The dots represent the raw data, and the line represents the data after Fourier transformation. The frequency plot from the Fourier transformation is depicted in the inset.

position is selected to be representative for the mixing in the whole reactor as it is covered with fluid at every fill ratio. An example of a response curve is depicted in Figure 10 for the mixing in reactor-11, 40% filled with water. The dots represent the raw data after normalization on the final gray scale. The maximum in the gray scale is often obtained because of the appearance of the blades and air bubbles in the measurement point as a consequence of the presence of 60% air in the reactor. Because the stirrer had a constant speed, the disturbance of the blades could be removed by using fast Fourier transformation filtering (FFT filtering) from the commercial software package Tablecurve by Jandel Scientific. A standard 40% smoothing level is used to zero 80% of the higher frequency components and all stirrer-related frequencies, resulting in the line in Figure 10. The accompanying frequency plot is also given in Figure 10 and is discussed in the Appendix. Figure 11 shows normalized response curves after FFT filtering at 6 Hz in all three reactors that are completely filled. The profiles for reactor-11 and reactor15 exceed unity, meaning that the dye is preferentially transported in the axial direction, toward the position where the gray scales are recorded. For reactor-20, the profile gradually rises to unity, without exceeding this limit. From Figure 11, it is concluded that when L/D is increased, it will take longer to mix the dye to the final concentration. Macro-mixing times are determined from the response curves after FFT filtering, as in Figure 11. As a representative value, the time that the normalized concentration differed by less than 10% from the final concentration was chosen. In Figure 12, these mixing

Figure 11. Normalized gray scale plotted versus time at 6 Hz in reactor-11, reactor-15 and reactor-20 at a fill ratio of 100%.

times, hereafter referred to as t10, are represented as a function of the stirrer speed. The mixing times decrease with increasing impeller speed, whereas the macromixing times increase with increasing L/D. This is due to the fact that the distance between the injection point and the measuring position is larger with higher L/D. A fill ratio of 60% results in shorter mixing times than those for 100 or 40%. Mixing at a fill ratio of 60% can be shorter than mixing at 100%, because the slowest mixed zone near the shaft is absent at 60%. The difference from the mixing times at 40% can be a result of a lower overall circulation at 40%. From this result, it is suggested that, for good circulation, a minimum amount of fluid is needed. These results also reveal that the mixing time is not linearly dependent on the fill ratio.

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Figure 12. Mixing time versus impeller frequency for the three reactors at three different fill ratios for turbulent conditions.

It is supposed that the macro-mixing time will depend on the process and reactor variables as follows:

tm ) tm(F, µ, N, D, g, geometrical dimensions of the system) (3) Then, using dimensional analysis, the functional relationship can be arranged as

Ntm )

(

tm

)

FND2 N2D , , geometrical dimensions as ratios µ g (4)

which applies to mixing vessels in general. The polycondensation process is operated in the hollow state in which the Froude number N2D/g is irrelevant. This leaves L/D as the only relevant geometrical dimension. When the obtained mixing times are correlated with the parameters varied by applying the relevant dimensionless numbers as given in eq 4, the following empirical correlation holds for D ) 0.18 m:

(DL)

Nt10 ) 16f(x)Re0.11

1.21

(5)

with

f(x) ) 0.22 + (x - 0.70)2

(6)

A power series was chosen to describe the dependence of the mixing time on the fill ratio. The dimensionless mixing time Nt10 increases with the Reynolds number, although the contribution is less than 15%. The influence is small, as the mixing is turbulent over the entire range of applied impeller speeds. However, the positive power indicates that an increase in impeller frequency results in an increase in dimensionless mixing time. This suggests that mixing is less efficient at high stirrer

speeds as the fluid tends to more solid-body rotation. The power of 1.2 in L/D indicates that the mixing mechanism is a combination of convection and dispersion, as 1 would indicate full convective flow and 2 full dispersive flow. As mentioned in the Introduction, Ando et al.6 studied mixing in horizontal vessels with baffles in order to prevent the tendency to solid-body rotation. Their dimensionless mixing time correlated with L/D, indicating a larger convective contribution due to the baffles. Mixing in the reactor investigated here is more dispersive because of the absence of baffles, resulting in a dependency of (L/D)1.2 and, therefore, larger mixing times. Applying baffles can decrease mixing times under turbulent conditions. For high viscosity levels, however, baffles are not required, as viscous shear will damp out behind these baffles. Macro-Mixing Times for Laminar Conditions. Using the same black-box approach as used for turbulent conditions, macro-mixing times could be determined for laminar conditions. In the range of the parameters varied and with D ) 0.18 m, the empirical correlation Nt10 ) 60(L/D) can be obtained. This result is in good agreement with the correlations provided by Hoogendoorn and Hartog20 and Novak and Rieger26 for helical ribbon impellers in vertical vessels. According to this equation, mixing under laminar conditions is only 2.5 times slower than that under turbulent conditions. However, establishing the mixing time in this manner is of course troublesome as the segregated torii in reactor-20 do not disappear within the determined macro-mixing times. A second method for quantifying mixing times is setting the macro-mixing time equal to the life span of the islands in reactor-11 and reactor-15. In the polycondensation process it is important to minimize this life span as the presence of islands implies a concentration ratio deviating from unity. This deviation results in an increased possibility of early termination, thereby


Under laminar conditions, the flow patterns found indicate that the mixing is chaotic. Reactor-11 and reactor-15 are globally chaotic, whereas reactor-20 appears to have elements of order. This behavior shows that mixing in the Drais reactor is complex and complicates effective scale-up. The location, number, and life span of the islands, as well as the overall flow pattern in the Drais reactor, change when L/D is enlarged. Macro-mixing times could not be determined unambiguously, as the islands do not disappear within the measurement time. However, the macro-mixing time seems to be only 2.5 times larger than it is under turbulent conditions. Nomenclature Figure 13. Life span of islands versus impeller frequency in reactor-11 and reactor-15 for laminar conditions.

leading to an undesired broad MWD. In Figure 13, the life spans are plotted against impeller frequency. From Figure 13, it follows that the life span decreases with increasing impeller speed. It also follows that, at low impeller frequency, the life span in reactor-15 is larger than that in reactor-11, whereas the two are comparable at high frequencies. Mixing at Intermediate Viscosities. In this study, we use only water and glycerin, both with Newtonian behavior. For the polycondensation process, one can imagine that viscosity and rheologic behavior will change continuously, and mixing behavior will go through a wide range of scenarios. Leong and Ottino19 investigated chaotic mixing in viscoelastic two-dimensional flows for various viscosities. Upon an increase in viscosity, islands grow, and chaotic regions shrink. From this observation, it appears plausible to conclude that, between our extreme cases (water and glycerin), nothing dramatic will occur. However, additional experiments by Leong and Ottino in which the shear rate was increased show that, in viscoelastic fluids, the number of islands increases, whereas in Newtonian fluids, this number is constant. Translating this observation to our practical situation indicates that, at higher impeller speeds (higher shear rate), more islands are formed. These observations show that studying hydrodynamics in the Drais reactor with viscoelastic fluids is mandatory for obtaining a complete picture of the mixing process. Conclusions This study provides information about flow patterns, the presence of poorly mixed zones, and macro-mixing times in three industrial configurations of the Drais reactor. Under turbulent conditions, the flow pattern shows flow circulation that is opposite to the pumping action of the impeller blades. The location of poorly mixed zones is the same in all three reactors. The dimensionless macro-mixing time Nt10 is correlated with L/D, the stirrer frequency N, and the fill ratio x. The obtained empirical correlation shows the following three relationships: Nt10 is at a minimum value at fill ratios around 60%. Nt10 increases more than linearly with increasing L/D ratio. The incorporated Reynolds number has a positive power, indicating that mixing at high stirrer speeds becomes less efficient.

Symbols C ) clearance, m Di ) impeller diameter, m D ) vessel diameter, m g ) gravitational constant, m/s2 h ) blade height, m L ) vessel length, m N ) number of revolutions, Hz PE ) perimeter, m PE0 ) perimeter at t ) 0, m Re ) Reynolds number t ) time, s tm ) mixing time, s t10 ) time at which dye concentration only differs 10% from final concentration, s V ) reactor volume, m3 w ) blade width, m x ) fill ratio R ) angle between impeller blade and shaft, degrees β ) angle between impeller blades in the tangential direction, degrees µ ) dynamic viscosity, kg m-1 s-1 F ) liquid density, kg/m3 σ ) Liapunov exponent, s-1

Appendix In this appendix, some remarks are made on the frequency plot in Figure 10. The plot shows spikes at frequencies that are characteristic for raw data like the impeller speed, i.e., 6 Hz and accompanying higher frequencies such as 12, 18, and 24 Hz. The peak at around 3.5 Hz originates from differences in dye concentration in the tangential direction and is responsible for the large fluctuations in the response curve. In the response curve of reactor-11 in Figure 11, the fluctuations reappear with a time period of 1/3.5 s, the so-called circulation time tc.37 As 10 periods can be distinguished, one can estimate a mixing time in the tangential direction of 3 s. Because the macro-mixing time t10 for this experiment was found to be 4.0 s, distributive mixing in the tangential direction is faster than in the axial and radial directions. The mixing in the tangential direction was also faster than that in the axial and radial directions in reactor15 and reactor-20 because no large fluctuations were observed in the accompanying response curves in Figure 11. In these reactors, the dye is homogeneously distributed in the tangential direction before it reaches the position where gray scales are read. It is suggested that the clockwise circulation in the larger reactors, as depicted in Figure 8, enhances the tangential mixing.

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Figure 14. Ratio of fluid velocity to stirrer speed in reactor-11.

According to the frequency plot in Figure 10, the concentration in the tangential direction in reactor-11 fluctuates with a specific frequency. However, this frequency is not constant throughout the reactor. Figure 14 shows the ratio of the frequency and impeller frequency in one-fourth of reactor-11. The figure shows that, near the wall, the fluid is retained more than in the bulk as the ratio is smaller. The largest ratio is 0.9, positioned between the two impeller blades. The fluid in that area rotates almost as a solid body and will therefore not be well-mixed, as is confirmed by the presence of the poorly mixed zone in Figure 4e at the same position. Acknowledgment Thanks are due to Hanny van Amerongen-van Enschot and Eric Rossou for their experimental work. Frank Jeurissen and Jan Surquin of Akzo Nobel Central Research are thanked for valuable discussions and financial support. Literature Cited (1) Thoenes, D. Chemical Reactor Development; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994. (2) Manaresi, P.; Munari, A. Factors affecting rate of polymerization. Compr. Polym. Sci., Step Polym. 1989, 5, 35. (3) Gaymans, R. J.; Sikkema, D. J. Aliphatic polyamides. Compr. Polym. Sci., Step Polym. 1989, 5, 357. (4) Vollbracht, L. Compr. Polym. Sci., Step Polym. 1989, 5, 374. (5) Jeurissen, F. T. H.; Surquin, J. Private communication. Borkent, G.; Tijssen, P. A. T.; Roos, J. P.; Van Aartsen, J. J. Kinetics of the reactions of aromatic amines and acid chlorides in hexamethylphosphoric triamide. Recl. Trav. Chim. Pays-Bas 1976, 95, 84. (6) Ando, K.; Hara, H.; Endoh, K. Flow behavior and power consumption in horizontal stirred vessels. Int. J. Chem. Eng. 1971, 11, 735.

(7) Ando, K.; Hara, H.; Endoh, K. On mixing time in horizontal stirred vessel. Kagaku Kogaku 1971, 35, 806. (8) Ando, K.; Fukuda, T.; Endoh, K. On mixing characteristics of horizontal stirred vessel with baffle plates. Kagaku Kogaku 1974, 38, 460. (9) Ando, K.; Shirahige, M.; Fukuda, T.; Endoh, K. Effects of perforated partition plate on mixing characteristics of horizontal stirred vessel. AIChE J. 1981, 27 (4), 599. (10) Fukuda, T.; Idogawa, K.; Ikeda, K.; Ando, K.; Endoh, K. Volumetric Gas-phase mass transfer coefficient in baffled horizontal stirred vessel. J. Chem. Eng. Jpn. 1990, 13 (4), 298. (11) Ando, K.; Obata, E.; Ikeda, K.; Fukuda, T. Mixing time of liquid in horizontal stirred vessels with multiple impellers. Can. J. Chem. Eng. 1990, 68, 278. (12) Perona, J. J.; Hylton, T. D.; Youngblood, E. L.; Cummins, R. L. Jet mixing of liquids in long horizontal cylindrical tanks. Ind. Eng. Chem. Res. 1998, 37, 1478. (13) Mayr, B.; Nagy, E.; Horvat, P.; Moser, A. Scale-up on basis of structured mixing models: A new concept. Biotechnol. Bioeng. 1994, 43, 195. (14) Kersting, Ch.; Pru¨ss, J.; Warnecke, H. J. Residence time distribution of a screw-loop reactor: experiments and modelling. Chem. Eng. Sci. 1995, 50, 299. (15) Moo-young, M.; Tichar, K.; Takahashi, A. L. The blending efficiencies of some impellers in batch mixing. AIChE J. 1972, 18, 178. (16) 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. (17) Schoenmakers, J. H. A.; Wijers, J. G.; Thoenes, D. Determination of feed stream mixing rates in agitated vessels. Proc. 8th Eur. Mix. Conf. (Paris): Re´ cents Prog. Ge´ nie Proce´ de´ s 1997, 11 (52), 185. (18) Leong, C. W.; Ottino, J. M. Increase in regularity by polymer addition during chaotic mixing in two-dimensional flows. Phys. Rev. Lett. 1990, 64(8), 874. (19) Ottino, J. M. Unity and diversity in mixing: Stretching, diffusion, breakup and aggregation in chaotic flows. Phys. Fluids A 1991, 3 (5), 1417. (20) Hoogendoorn, C. J.; den Hartog, A. P. Model studies on mixers in the viscous flow region. Chem. Eng. Sci. 1967, 22, 1689. (21) Dong, L.; Johanson, S. T.; Engh, T. H. Flow induced by an impeller in an unbaffled tank. Chem. Eng. Sci. 1994, 42, 549. (22) Lamberto, D. J.; Muzzio, F. J.; Swanson, P. D.; Tonkovich, A.l. Using time-dependent RPM to enhance mixing in stirred vessels. Chem. Eng. Sci. 1996, 51 (5), 733. (23) Lamberto, D. J.; Alvarez, M. M.; Muzzio, F. J. Experimental and computational investigation of the laminar flow structure in a stirred tank. Chem. Eng. Sci. 1999, 54, 919. (24) Nomura, T.; Uchida, T.; Takahashi, K. Enhancement of mixing by unsteady agitation of an impeller in an agitated vessel. J. Chem. Eng. Jpn. 1997, 30 (5), 875. (25) Harvey III, A. D.; Wood, S. P.; Leng, D. E. Experimental and computational study of multiple impeller flows. Chem. Eng. Sci. 1997, 52 (9), 1479. (26) Nova´k, V.; Rieger, F. Homogenization efficiency of helical ribbon and anchor agitators. Chem. Eng. J. 1975, 9, 63. (27) Holmes, D. B.; Voncken, R. M.; Dekker: J. A. Fluid flow in turbine-stirred, baffled tanks. I. Circulation time. Chem. Eng. Sci. B 1964, 19, 201. (28) Unger, D. R.; Muzzio, F. J. Laser-induced fluorescence technique for the quantification of mixing in impinging jets. AIChE J. 1999, 45 (12), 2477.

Received for review January 13, 2000 Revised manuscript received October 2, 2000 Accepted October 20, 2000 IE000054H

Hydrodynamics in a Horizontal Stirred Tank Reactor - Industrial

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