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GENERAL RESEARCH Critical Impeller Speed (NSG) for Solid Suspension in Sparged Stirred Vessels Fitted with Helical Coils Bhaurao P. Nikhade, Jacob A. Moulijn,† and Vishwas G. Pangarkar* Chemical Engineering Division, Institute of Chemical Technology (formerly UDCT), Mumbai University, Matunga, Mumbai 400019, India
An attempt has been made to investigate the effect of the presence of a helical coil, used in specific cases to increase the heat-transfer rate, on the critical impeller speed (NSG) for a solid suspension in a sparged stirred tank reactor. It has been observed that the coil disturbs the flow pattern generated by the impeller, consequently affecting the critical impeller speed. The critical impeller speed increases with an increase in the superficial gas velocity (investigated in the range of 0.52-9.74 mm s-1). For the small-size solids (50 kJ mol-1), e.g., in hydrogenation of nitro to amino compounds, the jacket may not be sufficient, particularly for largediameter stirred tanks, because the jacket area/unit volume ∝ 1/T. The external heat-transfer loop offers * To whom correspondence should be addressed. Tel.: +9122-2414 5616. Fax: +91-22-2414 5614. E-mail:
[email protected] or
[email protected]. † Present address: Reactor and Catalysis Engineering Group, Delft ChemTech, Julianalaan 136, 2628 BL Delft, The Netherlands.
flexibility but incurs a high power expenditure. The internal coil option is apparently more cost-effective because of the advantages of accommodating a large heat-transfer area within a small space, a high heattransfer coefficient, and substantially lower costs.5 However, it is possible that the coils may seriously affect the hydrodynamics of the stirred tank and may even result in settling of solids if operated at the impeller speed for a just suspension calculated on the basis of data without the presence of the coils. Moreover, the coils can cause localized regions of poor mixing.6,7 Very few papers are available in the literature that deal with the location of the helical coil in the stirred tank. Nunhez and McGreavy4 and Street and McGreavy8 have indicated in their work that no coils should be placed at the impeller blade height because fluid circulation is restricted and the overall heat transfer is poor, even though there is an excellent local heat transfer in the impeller region. This is due to the fact that the sweeping flow at the impeller region is at a high speed and it loses considerable momentum when it encounters the coils placed between the impeller blades and the wall of the vessel. If no coils are present, momentum is lost only at the walls, and as a result, fluid circulation away from the impeller is greater and the overall heat transfer is improved. Mass transfer at the interface between suspended particles and liquid is one of the most important factors in chemical and biochemical processes. Therefore, many correlations for the critical impeller speed for a just suspension of solids in solid-liquid systems have been reported in the literature.9-12 Similarly, considerable information is also available on the critical speed for a suspension in three-phase, gas-liquid-solid systems.2,3,13-15 However, there is no universally agreed upon correlation for NSG, primarily because there is no fundamental understanding of the flow fields in such vessels. These correlations are, therefore, useful only when geometric and process similarity exists. No infor-
10.1021/ie0500974 CCC: $30.25 © 2005 American Chemical Society Published on Web 05/11/2005
Ind. Eng. Chem. Res., Vol. 44, No. 12, 2005 4401 Table 1. Details of the Impellers no. of impeller blades DT PTD PTU
6 6 6
D (m) 0.19 0.19 0.19
vertical horizontal blade height blade length angle of (cm) (cm) pitch (deg) 3.7 5.5 5.5
4.5 7.0 7.0
45 45
Table 2. Details of the Coils coil 1 coil 2 coil 3
no. of turns
pitch (m)
surface area (m2)
5 8 12
0.095 0.059 0.0396
0.3535 0.6990 0.9600
mation is available in the literature on the suspension of solids and the corresponding power consumption at the critical impeller speed in the presence of coils. The subject is of considerable practical importance because at a just complete suspension speed satisfactory massand heat-transfer rates can be observed at low power consumption.16 In the present work, the minimum impeller speed for a just suspension of solid particles NSG and the corresponding power consumption have been experimentally measured in a 0.57-m-diameter sparged stirred tank for a variety of impellers and coil configurations with varying solid loading (0.5-2 wt %) and superficial gas velocity (0.52-9.74 mm s-1). The critical impeller speed for a just suspension of solid particles (NSG) was defined as the speed at which no solid particle remains stationary on the tank base for longer than 1 s. This was the criterion proposed by Zweitering9 in his pioneering work in this field. “Just suspension” is the most commonly encountered level of liquid agitation and is of practical significance because it often represents an economic optimum. Higher levels of agitation do not lead to significantly enhanced rate processes, while lower levels of agitation lead to the formation of permanent deposits of solids on the tank base, which, in turn, can lead to lower process rates and/or the formation of undesired byproducts.17 2. Experimental Section The experiments were performed in a cylindrical tank of 0.57-m diameter fitted with four standard baffles of width equal to 1/10 of the tank diameter and depth equal to the full vessel height. Three types of impellers, namely, a six-bladed disk turbine (6DT) and six-bladed pitched turbine downflow (6PTD) and six-bladed pitched turbine upflow (6PTU), both having an angle of pitch of 45°, were used. The details of the impellers used are given in Table 1. The diameters of all of the impellers and the clearance of the impellers from the tank bottom were equal to 1/3 of the tank diameter. Air and water were used as the gas and liquid phases. The air was introduced through a ring sparger of 0.185-m diameter and having 26 orifices of 4-mm diameter. Air for sparging was derived from an oil-free compressor. The flow rate was controlled and measured using a precalibrated rotameter. The superficial gas velocity range used was 0.52-9.74 mm s-1. The sparger was located at 0.1 m from the tank bottom. Three different helical coils of different numbers of turns were used, the details of which are given in Table 2. The outside diameter of the coil tubing was 0.19 m, the diameter of the helix was 0.35 m, and the overall height of the coil was 0.48 m. The coils were positioned such that the bottommost
turn was located midway between the impeller and the sparger (0.145 m from the bottom of the tank). The solids used were spherical glass beads (density ) 2500 kg m-3) of 50-, 80-, and 125-µm size. The solid loading was varied in the range of 0.5-2 wt %, which is representative of industrial catalytic reactions in stirred vessels. A 2-hp dc motor with an infinitely variable speed controller was used to rotate a centrally mounted shaft, to which the impeller was fitted. Figure 1 shows the schematic diagram of the experimental setup. The rotational speed of the impeller was measured by a digital tachometer provided with a light sensor, accurate within (1 rpm. The impeller power input was determined by measuring the torque exerted by fluid on the frictionless torque table. The torque table was restrained from rotating, and the force was measured by connecting it to a cantilever-type load cell. Multiplication of this force by the radius of the torque table gives the torque acting on the table. Power drawn by the impeller was calculated by P ) 2πNτ. The reproducibility of the NSG measurements by visual observation was typically within (3% of the impeller speed. 3. Results and Discussion The critical impeller speed for the solid suspension was measured for both solid-liquid and gas-liquidsolid systems. Measurements of the critical speed were made by visually observing the solid suspension by placing a mirror below the tank base, which was well illuminated to enable visual inspection of the tank bottom. Each run began at a low agitation speed, and the speed was gradually raised in small increments until the critical impeller speed (NSG) is reached. At constant superficial gas velocity (VG) and solid loading, when the impeller speed is gradually increased, more and more particles get suspended. The position of the suspension of the last group of particles depends on the impeller design. As the impeller speed increased, the amount of solids present on the tank bottom gradually decreased. When the critical impeller speed is reached, all of the particles vigorously move on the tank bottom before getting suspended. In reality, the Zweitering9 criterion is a subjective measure and few particles or groups of particles remained on the tank bottom, in the gap between baffles and tank corners, or at places where the liquid flow could not reach the tank bottom because of the coil. However, this fraction of solids was negligible in terms of a complete off-bottom suspension. 3.1. Effect of the Superficial Gas Velocity (VG). The superficial gas velocity was varied between 0 (solid-liquid) to 9.74 mm s-1. The effect of the superficial gas velocity on the critical impeller speed is shown in Figure 2 for PTD for coil 3 and for a configuration without a coil for comparison. Figure 3 shows the power required for a solid suspension for coil 3 at 2% solid loading. The critical impeller speed increases with the superficial gas velocity, with the extent of increase being different for different impellers and coils. This is obvious because the presence of gas causes a reduction in the power consumption and a reduction in the pumping capacity. To compensate for this reduction in the power consumption with increasing gas velocity, a net increase in the power input from the impeller is required. In other words, the impeller speed has to be increased to suspend the solids. The increase in NSG for PTD in the presence of gas is highest, followed by DT and PTU. This is because, in
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Figure 1. Experimental setup: (1) tank; (2) baffle; (3) impeller; (4) helical coil; (5) sparger; (6) torque table; (7) weights and pan; (8) dc motor; (9) control panel to convert ac to dc.
Figure 2. Effect of the superficial gas velocity (VG) on the critical impeller speed (NSG) for the PTD.
the case of PTD, the flow generated by the impeller is directly opposite to the flow of gas, while for PTU, the flow of gas aids the flow generated by the impeller, and hence there is a smaller increase in NSG in the presence of gas for PTU. However, the PTD impeller is most effective for a solid suspension for any gas velocity and for any coil in terms of lower overall impeller speed and power required, as can be seen from Figures 2 and 3. The DT and PTU impellers require about 3 times more power than PTD at the same solid loading and superficial gas velocity. For example, at 2% solid loading and VG ) 3.59 mm s-1, DT requires 0.89 kW m-3 and PTU requires 1.282 392 kW m-3, whereas PTD requires 0.36 kW m-3 at NSG. The low energy requirement of the PTD impeller can be attributed to the relatively short distance that the fluid has to travel before hitting particles
Figure 3. Effect of the superficial gas velocity (VG) on the power required (kW m-3) at 2% solid loading for coil 3.
on the base.13 In the case of DT and PTU, in addition to the greater distance that the fluid has to travel before hitting the solids, more power is also dissipated at the coil surface. 3.2. Effect of the Solid Loading (X). For all of the impellers and coils, the solid loading was varied between 0.5 and 2 wt %. Figure 2 shows the effect of the solid loading on the critical impeller speed for PTD for coil 3. It is observed that the solid loading has a very small effect on the critical suspension speed for all of the coils used. Similar observations have been made by Rewatkar et al.2 The values of NSG increased slightly with an increase in the solid loading. This can be related to the reduction in the liquid flow, which is probably due to turbulence dampening, with an increase in the solid
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Figure 4. Effect of the solid size on NSG at 2% solid loading in the presence of coil 3. DT: ([) 50 µm; (9) 80 µm; (2) 125 µm. PTD: (]) 50 µm; (0) 80 µm; (4) 125 µm. PTU: (+) 50 µm; (*) 80 µm; (-) 125 µm.
Figure 5. Power required over the absence of coil for the three coils versus the superficial gas velocity at 2% solid loading.
loading. For PTD, the increase in NSG with the solid loading is less compared to that of PTU and DT. 3.3. Effect of the Solid Size. The effect of the solid size was studied by conducting the experiments in the presence of coil 3. Three solid sizes, viz., 50, 80, and 125 µm, and a density of 2500 kg m-3 were used. Figure 4 shows the variation of NSG with the solid size for the three impellers at 2% solid loading. NSG increases with the solid size for all of the impellers. The larger particles, which have higher settling velocities, require higher lifting forces. The PTU impeller requires the highest NSG for all of the particle sizes. 3.4. Effect of the Coil Geometry and Type of Impeller. For any impeller, the critical impeller speed for a just complete suspension of solids is higher in the presence of coils than in their absence, implying that the flow pattern generated by the impeller is disturbed by the coil. The extent of increase depends on the type of impeller and superficial gas velocity. Figure 5 shows the excess power per unit volume, ∆(P/V), required over that in the absence of coil for the three coils versus the superficial gas velocity at 2% solid loading. The power required at NSG increases with VG. Figure 5 shows that the extra power required varies from coil to coil and
from impeller to impeller. Another observation that can be made is that the critical impeller speeds and power for coils 1 and 2 are not significantly different (marginally higher for coil 2), while for coil 3, they are significantly higher. This behavior can be attributed to the gap between the turns or, in other words, the pitch of the coil. The lower the pitch of the coil, the more the hindrance caused to the flow pattern developed by the impeller. The effect of the type of impeller can be understood by considering the flow patterns generated by the impellers. The flow patterns generated by these impellers in the absence of the coil can be found in the literature.18 There is almost no effect of the coil for the PTD impeller because the coil does not interfere with the flow generated by the impeller. The mean flow and its consequent turbulence travel the least hindering path and directly impinge on the tank bottom, lifting the solid particles. However, the flow is disturbed once it reaches the top and changes its direction, but by then, the job of a solid suspension is already accomplished. The disk turbine is a radial flow impeller, and it generates a circulatory pattern in a baffled cylindrical tank. The high-speed radial jet generated entrains surrounding fluid, and it first strikes the coil at places where the coil turn is directly in front of the impeller. Because of the helical nature of the coil, some part passes through the gap between the turns and is divided into two streams at the tank wall, of which the lower part is available for a solid suspension. In the case of PTU, the flow upon reaching the top first strikes the coil at some places. The part passing through the gap between the turns then strikes the tank wall, changes its direction, and travels all along the wall surface to the bottom, where it is available for a solid suspension. Thus, for both DT and PTU, a very lean flow reaches the tank base, where it would sweep the particles at the center region. Again, it is more difficult to lift the particles from the center than to drive them toward the corners, from where they are picked up. Therefore, for any coil, the PTU impeller requires the highest impeller speed for a solid suspension, followed by DT and PTD. 4. Correlations A number of reliable correlations are available in the literature to predict the critical impeller speed (NSG) as a function of basic system variables. Some of the correlations also give the extent of increase in NSG in the presence of gas over its absence. In view of the fact that NSG can be predicted reliably, it was thought that correlations of the type ∆NSG ) NSGcoil - NSGwithout coil quantifying the effect of the coil would be more appropriate. To account for the presence of the coil, the outside surface area (S) of the coils was used. This choice is based on the fact that the disturbance caused by the coil in the natural flow pattern is directly related to its surface area. Thus, the data were regressed to yield the following correlations:
∆NSG ) 1119VG0.27dP0.55X0.03S0.3 0.01
∆NSG ) 601VG
dP
0.09
∆NSG ) 13.86VG
0.59
X
0.11
dP
PTD
SD ) 5%
DT
SD ) 10%
PTU
SD ) 13%
0.25 0.61
S
X
0.11 0.70
S
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speeds and, hence, lower power input within the range of experimental conditions studied. The data reported would be useful for situations in which an existing agitated reactor is to be retrofitted with an additional cooling surface in the form of helical internal coils. Notations
Figure 6. Parity plot for the PTD impeller. Table 3. Comparison of ∆NSG and ∆(P/V) at NSG for Various Impellersa PTD DT PTU a
m2.
∆NSG (s-1)
∆(P/V) (kW m-3)
1.36 2 2.93
0.36 0.89 1.28
VG ) 3.594 × 10-3 m s-1; dP ) 50 µm; X ) 2 wt %; S ) 0.96
where ∆NSG is in s-1, VG in m s-1, dP in m, and S in m2 and NSGcoil ) critical impeller speed in the presence of the coil and NSGwithout coil ) critical impeller speed in the absence of the coil. Figure 6 shows a comparison of the experimental and predicted values of NSG for the PTD impeller. It can be seen that there is very good agreement between the experimental and predicted values of NSG. The indices on S for DT and PTU are comparable and higher than that for PTD, indicating that the flow pattern is disturbed more for DT and PTU. The effect of VG on ∆NSG for PTD is highest, followed by PTU and DT, which is in accordance with their flow patterns. Table 3 shows values of ∆NSG and ∆(P/V) for one set of variables common to all of the impellers. It is clear that PTU requires the highest ∆NSG in the presence of the coil. The extent of increase in the power input at NSG, ∆(PG/V), is also tabulated for the same set of variables in Table 3. It is clear from these values and also Figure 5 that PTD requires the least increase in the power input in the presence of the coil. Hence, it can be concluded that PTD is the most energy-efficient impeller when helical coils are used. 5. Conclusion The critical impeller speeds for a just complete suspension for various impellers in the presence and absence of gas and internal coils have been measured. The critical impeller speeds in the presence of gas/coils are always higher than those in their absence. There was only a slight increase in NSG with the particle size and the solid loading in the range investigated. The pitched turbine impeller (PTD) emerged as the most efficient impeller for a solid suspension in terms of lower
D ) impeller diameter dP ) particle diameter C ) clearance of the impeller from the tank bottom NS ) critical impeller speed for a complete suspension of the particles NSG ) critical impeller speed for a complete suspension of the particles in the presence of sparged gas P ) power (W m-3) VG ) superficial gas velocity S ) surface area of the coil (m2) T ) tank diameter (m) X ) solid loading (%) τ ) torque ∆NSG ) difference in the critical impeller speed in the presence and absence of coil (s-1)
Literature Cited (1) Fishwick, R. P.; Winterbottom, J. M.; Stitt, E. H. Effect of gassing rate on solid-liquid mass transfer coefficients and particle slip velocities in stirred tank reactors. Chem. Eng. Sci. 2003, 58, 1087. (2) Rewatkar, V. B.; Raghava Rao, K. S. M. S.; Joshi, J. B. Critical impeller speed for solid suspension in mechanically agitated three phase reactors. 1. Experimental part. Ind. Eng. Chem. Res. 1991, 30 (8), 1770. (3) Rewatkar, V. B.; Raghava Rao, K. S. M. S.; Joshi, J. B. Critical impeller speed for solid suspension in mechanically agitated three phase reactors. 2. Mathematical model. Ind. Eng. Chem. Res. 1991, 30 (8), 1784. (4) Nunhez, J. R.; McGreavy, C. A. A comparison of the heat transfer in helical coils and jacketed stirred tank reactors. 10th International Heat Transfer Conference, Brighton, England, Aug 1995; Institution of Chemical Engineers: Rugby, U.K., 1995; pp 345-350. (5) Ali, S. Pressure drop correlations for flow through regular helical coil tubes. Fluid Dyn. Res. 2001, 28, 295. (6) Mohan, P.; Emery, A. N.; Al-Hassan, T. Review: Heat Transfer to Newtonian Fluids in Mechanically Agitated Vessels. Exp. Therm. Fluid Sci. 1992, 5, 861. (7) Brain, T. J. S.; Man, K. L. Heat transfer in stirred tank bioreactors. Chem. Eng. Prog. 1989, July, 76-80. (8) Street, D. A.; McGreavy, C. A. A model of the heat transfer in internally cooled reaction vessels. In Heat Exchange Engineering; Foumery, E. A., Heggs, P. J., Eds.; Ellis Horwood Ltd.: Chichester, U.K., 1991; Vol. 2, pp 279-302. (9) Zweitering, T. N. Suspending solid particles in liquid by agitators. Chem. Eng. Sci. 1958, 8, 244. (10) Baldi, G.; Conti, R.; Alaria, E. Complete suspension of particles in mechanically agitated vessels. Chem. Eng. Sci. 1978, 33, 21. (11) Barresi, A.; Baldi, G. Solid dispersion in an agitated vessel. Chem. Eng. Sci. 1987, 42 (12), 2949. (12) Upadhyay, S.; Rai, B. N.; Kumar, V.; Shah, Y. T. Particle suspension and liquid-solid mass transfer in mechanically agitated vessel. Rev. Chem. Eng. 1994, 10 (1), 4. (13) Raghava Rao, K. S. M. S.; Rewatkar, V. B.; Joshi, J. B. Critical impeller speed for solid suspension in mechanically agitated solid-liquid contactors. AIChE J. 1988, 34, 1332. (14) Kato, Y.; Hiraoka, S.; Tada, Y.; Suzuki, J.; Hirose, K.; Lee, Y.; Koh, S. Solid-liquid mass transfer in gas-liquid-solid agitated system. J. Chem. Eng. Jpn. 2001, 34 (12), 1532. (15) Neale, J. W.; Pinches, A. Determination of gas-liquid mass-transfer and solids-suspension parameters in mechanically-
Ind. Eng. Chem. Res., Vol. 44, No. 12, 2005 4405 agitated three-phase slurry reactors. Miner. Eng. 1994, 7 (2/3), 389. (16) Pangarkar, V. G.; Yawalkar, A. A.; Sharma, M. M.; Beenackers, A. A. C. M. Particle-liquid mass transfer coefficient in two/three-phase stirred tank reactors. Ind. Eng. Chem. Res. 2002, 41 (17), 4141. (17) Myres, K. J.; Corpstein, R. R.; Bakker, A.; Fasano, J. Solid suspension agitator design with pitched blade and high efficiency impellers. AIChE Symp. Ser. 1994, 90, 186.
(18) Gray, J. B. Flow patterns, fluid velocities and mixing in agitated vessels. In Mixing: Theory and Practice; Uhl, V. W., Gray, J. B., Eds.; Academic Press Inc.: New York, 1967; Vol. I.
Received for review January 24, 2005 Revised manuscript received April 6, 2005 Accepted April 13, 2005 IE0500974
