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Liquid-Phase Mixing Times in Sparged and Boiling Agitated Reactors with High Gas Loading Donglin Zhao, Zhengming Gao, Hans Mu 1 ller-Steinhagen,† and John M. Smith* School of Engineering, Department of Chemical & Process Engineering, University of Surrey, Guildford GU2 7XH, U.K.
This work reports the effects of the presence of a gas or vapor phase on mechanically agitated liquid mixing. A conductivity technique was used to follow the assimilation of tracer added at the liquid surface of cool aerated, hot sparged, and unsparged boiling liquid. The 75-L-capacity baffled vessel had a single, centrally mounted, Chemineer CD-6 hollow blade impeller. Sparging increases the rate of mixing at a given shaft power, especially at high gas flow rates. Inconsistencies in the literature on the effect of aeration on the mixing time are satisfactorily resolved if the potential energy input from gas sparging is considered. When this is done, hot and cold sparged and unsparged mixing times are comparable, provided that the contribution of the volume of any vapor generated is included. Mixing of surface added tracer into boiling liquid is considerably faster at a given impeller power than in any of the other conditions. This is probably a result of the additional disturbance at the liquid surface produced by vapor evolution causing a rapid initial distribution of tracer. Introduction Industrial stirred-tank reactors frequently involve boiling liquid or hot sparged (when gas is sparged into nearly boiling liquid) conditions. Exothermic processes, and others where the operating temperature is raised in order to accelerate reaction kinetics, may require the maintenance of dispersions of large volumes of vapor or gas in the liquid phase. Smith and Gao1 have shown that the hydrodynamics of such systems, in which the vapor pressure of the liquid is a significant fraction of the operating pressure, are radically different from those in the “cool” ambient environment that has been used in most research. It may be unwise to design reactors for boiling and hot sparged systems on the basis of data obtained in cool systems. Inefficient mixing is one of the major causes of difficulty in the scale-up of chemical and biochemical processes. A rapid distribution of reagents is often decisive for the success of a process. The batch liquid mixing time provides a useful characterizing parameter, and extensive data obtained in single-phase systems are available for these conditions. There is, however, much less information about the mixing of the liquid phase in sparged systems. Nienow2 has pointed out that no consistent conclusions can be drawn about the influence of the gas phase on mixing times. Cronin et al.3 argued that mixing times in aerated conditions are, in general, longer than those in unaerated conditions with the same specific power input (based on the total fluid mass in the reactor). Paca et al.4 stated that the mixing time depends on the aeration rate, fluid rheology, mixing intensity, and system geometry, with increased aeration decreasing the mixing time under certain conditions. Bryant and Sadeghzadeh5 reported that mixing in the * To whom correspondence should be addressed. E-mail:
[email protected]. Fax: +44 1483 876581. † Present address: Institute for Thermodynamics and Thermal Engineering, University of Stuttgart, Plaffenwaldring 6, D-70550 Stuttgart, Germany.
liquid phase was more or less independent of the gas flow rate. Smith and Ruh6 have also commented that there is some evidence that mixing in an unsparged boiling system appears to be faster than that in otherwise similar sparged conditions. All of these conclusions have been based on work at low gas flow rates. As far as we are aware there is no published literature on the influence of large volumes of gas or vapor on liquid phase mixing times in sparged and boiling stirred-tank reactors. The present work compares mixing times in aerated and boiling systems and seeks to explain the inconsistencies in the literature. Equipment and Experimental Method Equipment. The experiments have been carried out in an insulated fully baffled vessel of 0.45 m diameter and 0.50 m height (Figure 1). The glass body of the tank has a flat stainless steel top, just clear of the free liquid surface, and a dished base in which three 2.7-kW immersion heaters are mounted. The reactor volume is 75 L, a scale commensurate with many pilot-plant installations. Because our purpose is primarily to compare the performance under differing physical conditions, we have chosen to work with a standardized geometry and procedure. A Chemineer CD-6 hollow blade impeller of 176 mm diameter at an ungassed submergence of 250 mm has been used for all of the work reported here. This impeller has a turbulent ungassed power number, as measured in the present equipment, of 2.6. The vapor generated in the tank was condensed in a coil heat exchanger and returned to the vessel. The shaft power was measured with a Vibrometer TE 106/M4 torque measuring system. Air is introduced through a perforated ring sparger after passing through a calibrated rotameter. For safety reasons, the shaft was lightly constrained by a loose poly(tetrafluoroethylene) (PTFE) sleeve acting as a bottom bearing which did not exert any measurable torque. Experimental Method. The conventional 95% mixing time (i.e., the time required for the response at a
10.1021/ie000445w CCC: $20.00 © 2001 American Chemical Society Published on Web 02/16/2001
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Figure 2. Probe responses for unsparged mixing (upper at boiling; lower at low temperature).
Figure 1. Experimental rig.
defined point to remain within (5% of the total change following a pulse injection) was determined from changes in conductivity following the introduction of a small quantity of phosphoric acid. Problems associated with bubbles interfering with the point conductivity detector probe were circumvented in a way similar to that used by Otomo et al.,7 by arranging that the electrode was surrounded by a mesh. In our case the cage had large openings at the top to allow the occasional trapped bubble to escape. This design virtually eliminated any disturbance to the signal. A standard 20 mL solution of dilute phosphoric acid was added automatically, in less than 0.5 s, to the free surface of the liquid. While it would have been preferable to add the tracer at the impeller discharge, we felt unable to achieve rapid enough addition of the relatively large volume of liquid while avoiding significant kinetic energy input or eliminating diffusion problems in a submerged dip tube. The detector was at a fixed position near the bottom of the tank, as shown in Figure 1. Although the use of a single detector is not as satisfactory as taking a mean from simultaneous measurements from multiple probes with separate conductivity meters would be, the detector location used is considered to be satisfactorily representative. The output from the conductivity meter was filtered, amplified, and converted to digital format for storage and subsequent analysis. By injection of consistent volumes of increasing concentration, the technique allowed up to eight successive measurements of mixing time without the need to change the liquid in the mixing vessel. Typical actual output signal curves (with arbitrary conductivity units) for the four characteristic conditions are shown in Figures 2 and 3. The traces reflect the low noise level in the signals. The rapid initial distribution when boiling (Figure 2) is reflected in the
Figure 3. Probe responses for sparged liquid mixing (upper at ambient temperature; lower hot sparged).
increased damping of the signal achieving the +5% criterion as it returns from the initial peak, in contrast to the low-temperature signal which overshoots before satisfying the -5% criterion. All of the mixing times used in the analysis were averaged from at least three sets of measurements. The experimental data were very reliable and consistent, with individual values always within 10% of the mean. Results and Discussion Ungassed Conditions. Ruszkowski8 and Grenville et al.9 have proposed the following correlation for liquid mixing time θM in a single-phase tank reactor with a liquid height equal to the vessel diameter T agitated by a single impeller of diameter D and power number Po mounted about one-third height off the bottom when driven at N rps:
NθM ) 5.3Po-1/3(D/T)-2
(1)
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Figure 4. Dependence of unsparged liquid mixing time on the impeller power input. Equation 2 from Grenville et al.9
This can also be expressed as
θM ) 5.9T2/3S-1/3(D/T)-1/3
(2)
in which S is the specific power input, W kg-1, based on the shaft power and the total mass of liquid in the reactor. These equations predict that when the impeller diameter and reactor geometry are fixed, the liquid mixing time is directly determined by the average energy dissipation rate. Nienow2 developed a theory based on the decay of concentration gradients under the influence of large scales of turbulence to explain the success of these correlations which have been found to be valid for single-phase mixing with a wide range of axial and radial flow impellers. Figure 4 shows the mixing times measured in cold ungassed conditions in the present equipment related to the mean shaft power input. The times are significantly longer than those predicted by the correlation of eq 2, though they reflect the same -1/3 exponent dependence on the specific power input. The differences probably arise from our impeller being at midheight in the tanksbecause of an elongated bottom shaft housings and the different location at which we added the tracer. Grenville et al. followed the preferred industrial practice, introducing the tracer at a point near the impeller discharge. In our case time is needed for the tracer to be carried down from the free surface before it reaches a similar location. Modified equations based on the present results with free surface addition are -1/3
NθM ) 7.9Po
(D/T)
-2
(1a)
Figure 5. Mixing time dependence on the shaft power input at various temperatures and flow rates.
The potential energy (PE) gained by the liquid due to gas sparging per unit time is given by
PE ) FLQGgHs
where FL is the liquid density at the operating temperature, kg m-3; QG is the gas flow rate (NTP), m3 s-1; g is the acceleration due to gravity, m s-2; and HS the submergence of the sparger below the liquid free surface, m. The total power contributing to the liquid phase mixing can be expressed as
PT ) PS + PE
θM ) 8.9T2/3S-1/3(D/T)-1/3
(2a)
Aerated Conditions. (a) Cool Sparged Systems. Most of the energy input in gassed agitation comes from either the agitator shaft power or the potential energy of the liquid displaced by the sparged gas. Although the kinetic energy associated with the gas may be considerable at high gas flow rates, Middleton et al.10 showed that it does not contribute significantly to the mixing of the liquid phase. There may, however, be a small contribution from the motion of liquid near the bubble surfaces as they rise and expand.
(4)
The mean shaft power dissipation in the liquid in the reactor, W kg-1, is
S ) PS/FLV
(5)
so that the mean total energy dissipation rate, based on the mass of liquid in the reactor, is
T )
and
(3)
PT PS + PE ) FLV FL V
(6)
The power draw by the agitator will usually decrease under gassed conditions as a result of the development of gas cavities behind the impeller blades, but this is compensated to some extent by energy transfer from the gas phase. The influence of gas sparging on the liquid mixing performance may be positive, neutral, or negative, depending on the tradeoff between these two power inputs. This may explain the different conclusions of the various authors on the effect of sparging on the liquid mixing time. Figure 5 includes the mixing times measured under cold ungassed and cool gassed conditions as a function
Ind. Eng. Chem. Res., Vol. 40, No. 6, 2001 1485 Table 1. Power Input conditions N ) 180 rpm, QG ) 155 L min-1 N ) 210 rpm, QG ) 280 L min-1 N ) 240 rpm, QG ) 356 L min-1
Table 2. Combined Gas and Vapor Flow Rates in Hot Sparged Water
shaft power (W)
potential energy input (W)
total (W)
N (rpm)
QG (L min-1)
T (°C)
Q (kW)
QGV (L min-1)
10.84
10.24
21.08
15.89
18.43
34.32
210 240 300
10 50 100
98.8 94.37 89.16
8.1 8.1 8.1
320 340 375
22.63
23.52
46.15
of mean dissipation rates based on the transmitted shaft power. Discussion of the hot sparged data also shown will follow later. With equal impeller power input, the sparged liquid mixing times are less than those in ungassed conditions, and they decrease further with increasing gassing rate, provided that the impeller is not flooded. The hollow blade impeller used in this work (Chemineer CD-6) has a relatively flat power draw curve when aerated. With this impeller the shaft power drop is much less than the additional potential energy contributed by the sparged gas. Table 1 gives some experimental data on the contributions from these two sources to the mechanical energy input in the present equipment. At high gas flow rates the potential energy transfer exceeds that from the agitator shaft. The increased dissipation rate that results reduces the mixing time. Nienow2 suggested that eqs 1 and 2 may be used to predict aerated mixing times if the ungassed power number, Po, and the shaft power dissipation, S, are substituted by the corresponding gassed values, provided the impeller is not flooded. This conclusion is only valid at low gas flow rates when the contribution of the potential energy to the liquid mixing is negligible. This observation is consistent with the results of Cronin et al.,3 who found that at higher gas flow rates the inverse proportionality between the mixing time and impeller speed no longer holds precisely and that the mixing time cannot be correlated satisfactorily with the shaft power alone. The results obtained under cool gassed conditions which are included in Figure 5 show that the mixing time correlates reasonably well against the total specific dissipation rate. In general, the mixing times decrease with the energy dissipation rate to an exponent of -1/3 in accordance with eq 2. The sparged mixing time is about 10% faster than that in ungassed conditions, a difference that is unlikely to be of significance in process applications. One would expect that a consistent mixing time behavior will depend on the maintenance of the overall flow pattern in the vessel. In view of this the deviation from the -1/3 slope of the data at high gas flow rates and specific power should perhaps not be regarded as surprising, though as pointed put below incorporation of a changed slope into correlating equations would not be straightforward. (b) Hot Sparged Systems. (1) Gas-Phase Volume. When an inert gas is passed into a boiling liquid, there is a change in the thermodynamic equilibrium. Because the bubbles must contain at least some inert gas, the partial vapor pressure of the condensable components is less than the total pressure at which the liquid was previously boiling. The liquid is, therefore, initially superheated relative to the mixed gas phase. There will be an immediate increase in the evaporation rate so that latent heat can remove the excess energy. The liquid temperature will fall until the energy supply and
removal rates are in balance. When there are constant net heat input and gas throughput rates, Smith and Millington11 pointed out that a steady equilibrium temperature, which is independent of the impeller speed, will be established. Even a simplified analysis shows that only a fraction of a second is required for a fresh bubble to approach saturation with vapor from the surrounding liquid. This simplifies the analysis because a constant vapor pressure can be assumed for a given gas rate, and this allows reasonable estimates to be made of the combined gas and vapor flow (QGV) loading the impeller. QGV is given by
p0 QGV ) QG p0 - pV
(7)
where QG is the sparged gas volume flow rate corrected to the liquid temperature T, p0 the ambient pressure, and pV the liquid vapor pressure at T. The contribution of vapor to the total gas volume can be significant, especially when the gas sparging rate is low and there is a significant heat supply. Because of the low specific heat of the gas phase, the temperature of the inlet gas is only of secondary significance. Table 2 illustrates some typical data. This table also illustrates the dominant effect of heat availability on the sparged volume. Essentially, all of the present data were obtained with 8-kW electrical heat input. Even large variations in the sparged air rate produce only small differences in the total gas-phase throughput. (2) Potential Energy Input. If we may assume that the saturation of the sparged gas is virtually instantaneous, the power associated with the potential energy input of a hot sparged system can be calculated using QGV instead of QG in eq 3.
PE ) FTQGVgHS
(8)
This energy input is subsequently transferred to the liquid phase as the gas rises. (3) Mixing Time. Examination of the hot sparged mixing time data included in Figures 5 and 6 shows immediately that when the total (gas and vapor) sparged flows are similar, the hot and cold sparged mixing times are comparable. Furthermore, in both sparged and unsparged cases, the liquid mixing time correlates reasonably well with the total energy dissipation rate. At the highest gas volume, and associated dissipation, rates, the hot sparged data show an increase in the negative slope of the data in Figure 6 similar to that for the cold sparged results. If our assumption that the gas phase is saturated virtually from the moment of injection into the liquid were seriously in error, we would be overestimating the energy input at a given speed and the data points would have been displaced toward longer mixing times. It might be considered desirable to provide correlating equations based on the data in Figure 6. The use of the -1/3 exponent has a sound basis in the relationship between flow and kinetic energy. If all of the nonboiling
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Figure 6. Mixing times on the basis of shaft plus buoyancy power input.
data are to be fitted by a simple equation, then
θΜ ) 6.8T-1/3
(3)
is reasonably satisfactory. This can be expressed in dimensionally consistent terms as
θΜ ) 5.9T2/3T-1/3(D/T)-1/3
(2b)
A better overall agreement appears to be achieved by
θM ) 6.1T-0.45
(4)
which is the dashed line in the figure. Unfortunately, with an exponent of -0.45 on the dissipation, it is impossible to produce a dimensionally consistent correlating equation which only involves D and T in addition. Boiling Conditions. Impellers operating in boiling liquids develop vapor cavities of a form similar to those observed in cold gas-liquid dispersion. The pattern of power demand is, however, different and is uniquely related to an agitation cavitation number, defined by Smith and Katsenavakis12 as twice the submergence of the impeller times the gravitational acceleration divided by the square of the impeller tip speed. It has been suggested by the Fluid Mixing Processes Subject Group of IChemE that this cavitation number should be called the Smith number, Sm, and this convention will be followed here. Because we are here concerned only with the relationship between the power input and mixing time, the precise form of the relative power demand curve is only of passing interest, but for the record, a cavitating CD-6 impeller in boiling liquid obeys
RPD ) 0.5Sm0.25
(9)
As is very evident in Figures 5 and 6, when the liquid phase is boiling, the mixing time with a given shaft power input is reduced to about 60% of that in the other
conditions, including sparged systems with similar gasphase loadings. The gas-phase distribution in a boiling system is very different from that under cool or hot sparged conditions. In a sparged reactor, gas bubbles are distributed throughout much of the liquid, and they remain of relatively constant size in response to modest pressure fluctuations. In true boiling conditions vapor bubbles only appear near the free surface of the liquid, even when the vapor generation rate is high (∼360 L min-1). Small changes in the local pressure or temperature will lead to any bubbles released from hot surfaces or formed in regions of low pressure behind impeller blades to condense or collapse almost instantaneously. This is very different from the incondensable bubbles in sparged systems. In the search for reasons for the accelerated mixing in a boiling liquid, conditions near the immersion heaters must also be considered. The rapid collapse of bubbles released from the superheated surface of a heater can generate localized turbulence which would help liquid mixing, though preliminary experiments with heated liquid, simmering as it approaches the boiling point, suggest that this mechanism is not important enough to explain the differences. It is much more difficult to quantify the contribution of additional energy in boiling liquids than for sparged conditions because vapor evolution is limited to the top few centimeters of the liquid and the potential energy contribution will consequently be small. Bubble evolution near a boiling free surface is more violent, however, with rapid expansion, and this may transfer a great deal of kinetic energy to the liquid. A cursory examination of Figure 6, which successfully brings the other data together, implies that in these experiments on the order of 4 times as much of the mechanical energy contributing to the mixing is being received from these rapidly expanding bubbles than is being supplied to the liquid by the impeller. It is significant that this extra energy transfer occurs in the liquid near the free surface, where it is very effective in promoting the initial distribution of the tracer added at the surface. To put this into perspective, in our hot experiments the agitator shaft power was between 15 and 60 W in comparison with the 8 kW of electrical heating. Utilization of These Results for Process Design and Scale-Up The limited experimental program has provided information on the rate of homogenization of the liquid phase during two-phase agitation. The difference between the single phase mixing times reported here, which have provided the basis for the influence of the gas phase to be assessed, and the accepted correlation of Grenville et al.9 underlines the relevance of vessel geometry and the importance of the location of reagent addition. There are two ways that these results may be used for process design or scale-up. In the first instance, with equipment of this geometry and mode of use, surface addition to a reactor of aspect ratio unity with a single radial flow agitator at half-depth can be designed on the basis of eqs 1a and 2a using both shaft and buoyancy energy in assessing the total power input. In boiling systems, when addition is through a dip tube, correlations (1a) and (2a) should again be used because there will be no contribution to faster mixing from the boiling
Ind. Eng. Chem. Res., Vol. 40, No. 6, 2001 1487
action at the liquid surface. For boiling without sparging or inert gas generation, when surface addition is used in a vessel of H ) T, the bulk mixing time is approximately halved. For H ) T reactors with lower mounted impellers and submerged injection, the batch mixing times can be predicted on the basis of the Grenville et al.9 equations (1) and (2), provided that both the buoyancy terms and the gassed power levels are used in the calculations. It must be pointed out that in taller vessels with multiple impeller agitators the void distribution is significantly changed. In such vessels mixing times are generally longer and very dependent on the impeller configuration. At this stage no conclusions on the effect of the presence of gas or vapor can, or should, be drawn. Conclusions In this work, mixing times following addition at the free surface have been measured using a conductivity technique. The following conclusions are drawn from the results with ungassed, cool gassed, hot sparged, and boiling systems in a standard H ) T vessel with a single radial impeller: 1. The mixing times in cool or hot sparged systems can be correlated on the basis of the specific energy dissipation rate in the liquid phase, provided that this includes the contribution to the potential energy from the injected volume of gas. 2. When material is added at the liquid surface, eqs 1a and 2a predict ungassed or sparged bulk mixing times satisfactorily for a radial impeller mounted approximately at half-depth in a tank filled to a depth about equal to its diameter. 3. The contradictions in the literature concerning the effects of aeration on mixing times in agitated vessels can be resolved by considering both the reduced aerated power draw of most impellers and the positive potential energy contribution from the gas. 4. Sparging gas into nearly boiling liquid greatly increases the gas-phase volume. When the total gasphase (gas and vapor) flow rates are similar in hot and cold conditions, hot sparged mixing times differ little from those in cold sparged conditions if the potential energy associated with both the vapor and the sparged gas is included. 5. Mixing in an unsparged boiling system is faster than what would be expected on the basis of the shaft power input, with much shorter mixing times than those for sparged systems with similar gas-phase loadings. This probably reflects the kinetic energy transmitted to the water during vapor generation near the free surface. 6. Significantly different gas-phase distribution in tall vessels with multiple impeller agitators in tall vessels is likely to change the liquid mixing performance. Notation A ) total area of all sparger holes, m2 D ) impeller diameter, m g ) acceleration due to gravity, m s-2 H ) total liquid depth in the vessel, m HS ) distance from the sparger to the free liquid surface, m
N ) impeller rotation speed, rps PS ) shaft power input, W PT ) total power input, W p0 ) barometric pressure, Pa p1 ) pressure at the gas sparger, Pa Q0 ) gas flow rate at barometric pressure, m3 s-1 Q1 ) gas flow rate at p1, m3 s-1 S ) impeller submergence in ungassed liquid, m Sm ) agitation cavitation (Smith) number [)2Sg/vt2] T ) vessel diameter, m V ) liquid volume in the vessel, m3 vt ) impeller tip speed [)πDN], m s-1 Greek Letters S ) mean specific shaft energy dissipation rate, W kg-1 T ) mean total specific energy dissipation rate, W kg-1 FL ) liquid density at operating temperature, kg m-3 θM ) mixing time, s
Literature Cited (1) Smith, J. M.; Gao, Z. Vertical Void Distribution in GasLiquid Reactors. Proceedings of the 3rd International Symposium on Mixing in Industrial Processes, Osaka, Japan, 1999; Society of Chemical Engineers: Japan, 1999; pp 189-196. (2) Nienow, A. W. On impeller circulation and mixing effectiveness in the turbulent flow regime. Chem. Eng. Sci. 1997, 52, 25572565. (3) Cronin, D. G.; Nienow, A. W.; Moody, G. W. An experimental study of mixing in a proto-fermenter agitated by dual Rushton turbines. Trans. Inst. Chem. Eng., Part C (Food & Bioprod. Proc.) 1994, 72, 35-40. (4) Paca, J.; Ettler, P.; Gregr, V. Hydrodynamic behaviour and oxygen transfer rate in a pilot plant fermenter. J. Appl. Chem. Biotechnol. 1976, 26, 309. (5) Bryant, J.; Sadeghzadeh, S. Circulation rates in stirred and aerated tanks. Proceedings of the 3rd European Conference on Mixing, York, 1979; BHRA: 1979; pp 325-336. (6) Smith, J. M.; Ruh, C. The design and operation of vapour generating gas-liquid reactors. Proceedings of CHEMECA 98 (Australian Institute of Chemical Engineers, unpaginated CDROM), 1998. (7) Otomo, N.; Nienow, A. W.; Bujalski, W. Mixing time measurements for an aerated single and dual impeller stirred vessel. The 1993 IChemE Research Event, Birmingham, U.K., 1993; Institution of Chemical Engineers: Rugby, U.K., 1993; pp 669-671. (8) Ruszkowski, S. A rational method for measuring blending performance and comparison of different impeller types. Proceedings of the 8th European Mixing Conference, Cambridge, U.K.; Institution of Chemical Engineers: Rugby, U.K., 1994; pp 283291. (9) Grenville, R.; Ruszkowski, S.; Garred, E. Blending of miscible liquids in the turbulent and transitional regimes. NAMF Conference, “Mixing XV”, Banff, Canada, 1995. (10) Middleton, J. C.; Cooke, M.; Litherland, L. The role of kinetic energy in gas-liquid dispersion: do we need an agitator? Proceedings of the 8th European Mixing Conference, Cambridge, U.K.; Institution of Chemical Engineers: Rugby, U.K., 1994; pp595-602. (11) Smith, J. M.; Millington, C. A. Boil-off and power demand in gas-liquid reactors. Trans. Inst. Chem. Eng., Part A (Chem. Eng. Res. Des.) 1996, 74, 424-430. (12) Smith, J. M.; Katsanevakis, A. Impeller Power Demand in Mechanically Agitated Boiling Systems. Trans. Inst. Chem. Eng., Part A (Chem. Eng. Res. Des.) 1993, 71, 145-152 and 466.
Received for review May 2, 2000 Revised manuscript received December 12, 2000 Accepted January 4, 2001 IE000445W
