Ind. Eng. Chem. Res. 1990, 29, 1503-1509
1503
Liquid- and Solid-Phase Mixing in a Sectionalized Bubble Column Slurry Reactor Ashok S. Khare, Sanjeev V. Dharwadkar, Jyeshtharaj B. Joshi,* and Man Mohan Sharma Department of Chemical Technology, University of Bombay, Matunga, Bombay 400 019, India
Liquid-phase and solid-phase mixing times were measured in a 0.4-m-i.d. sectionalized bubble column employing radial baffles. The superficial gas velocity, average particle size, and solid loading were varied over a wide range. Radioactive mTc (technetium-99 metastable, as an aqueous solution of sodium pertechnate) and lg8Au (as chloroauric acid) were used as the liquid- and solid-phase tracers, respectively. The results obtained on the optimum dimensions and configuration of radial baffles closely conform to those suggested in the literature. Bubble columns are widely used in industry because of their simple construction, ease of operation, and flexibility with respect to liquid-phase residence time. However, bubble columns suffer from the drawback of severe liquidand solid-phase backmixing. The high degree of backmixing is basically because of intense liquid circulation. Therefore, for reducing the liquid- and solid-phase backmixing, the overall liquid circulation needs to be arrested. This can be conveniently done by providing radial baffles in the column (Figure 1). Joshi and Sharma (1979) have suggested an optimum design of radial baffles. They recommended that the baffle spacing should be 0.81 times the column diameter and the central hole diameter should be 0.71 times the column diameter. The reduction in solid- and liquid-phase backmixing is beneficial in a variety of situations. Field and Davidson (1980) have measured liquid-phase dispersion coefficient (DL)in a 3.2-m-i.d. and 18.9-m-longcolumn. The value of the liquid-phase Peclet number was found to be 2.6, and for many other column configurations, it can be shown that the Peclet number lies in the range 0.2-3.0. These values of the Peclet number are relatively very low, and an increase in Peclet number by a factor of 3-4 will increase the throughput of the column by a large factor. The benefit associated with the reduction in backmixing can be explained in an alternative way. In the column under reference, the liquid-phase residence time was 430 s. The liquid-phase mixing time can be estimated by using the following equation (Deckwer et al., 1973; Blenke, 1985; Murakami et al., 1982): aHD2 ,9=(1)
DL
Equation 1 was obtained from the dispersed plug flow model. The constant “a” depends upon the extent mixing time and it equals 0.5 for 95% degree of mixing. The value of DL was found to be 0.5 m2/s by Field and Davidson (1980), and the value of the mixing time (0) works out to be 357 s. It can be seen that the values of residence time and mixing time are comparable. Van de Vusse (1962) has shown that, for a near plug-flow behavior, the value of mixing time should be much larger than the residence time. It will be shown later that the liquid-phase mixing time can be increased by a factor of 3-4 by sectionalization and the criterion given by van de Vusse can be satisfied. The reduction in liquid-phase backmixing in bubble columns has far-reaching advantages as compared with the obvious advantage in single-phase reactors. In bubble columns, substantial variation in the total pressure occurs
* Author to whom
correspondence should be addressed.
along the height due to the reduction in the static head. As a result, the partial pressure of solute gas continuously decreases along the height because of the reduction in total pressure in addition to the decrease due to the adsorption. By contrast, the dissolved solute concentration in the liquid phase is practically uniform throughout because of the intense backmixing. The marked decrease in the gas-phase partial pressure and the uniform concentration in the liquid phase may result in a situation where absorption occurs in the bottom region and desorption occurs in the top region. This results into an underutilization of column volume. Parulekar et al. (1989) have shown that the underutilization can be eliminated by decreasing the liquidphase backmixing by a factor of 3-4. This can be conveniently achieved in a sectionalized bubble column. Further, the sectionalization increases the gas-liquid mass-transfer coefficient by 20-40% (Patil et al., 1984). It also decreases the gas-phase backmixing and becomes particularly useful in large columns. There are several examples of industrial importance that can benefit from the reduction in solid- and liquid-phase backmixing (Doraiswamy and Sharma, 1984; Shah, 1978; Joshi et al., 1988). The well-known example of the Solvay tower in the manufacture of sodaash may be cited where sectionalized bubble columns are used. For hydrometallurgical operations, the extent of backmixing in the solid phase, for a high degree of leaching of the valuable component, is clearly important. In view of the substantial advantages offered by the sectionalized bubble columns, it was thought to be desirable to undertake a systematic study of the effect of baffle design on the extent of backmixing. It was also thought to be desirable to arrive at an optimum design and compare it with the theoretical recommendations of Joshi and Sharma (1979). In the present paper the values of mixing time have been measured for the liquid and solid phases. Conical baffles (Figure 2) have been used in place of flat baffles (Figure 1); conical baffles should be particularly well suited for three-phase reactors because some solid particles may settle on the flat baffles.
Experimental Section Experiments were performed in a 0.4-m-i.d. Perspex column having a total height of 3.0 m. The solid phase consisted of nonsphericalaluminum oxide (A1203) particles ranging from 12 to 250 pm in size and having a density of 4000 kg m-3. The liquid phase was water, and compressed air was the gas phase. The superficial gas velocity (VG) was studied in the range from 0.07 to 0.366 m s-l. The sparger consisted of a sieve plate, made from 1Bmm-thick Perspex plate and having 2-mm diameter holes, 5684 in
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1504 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990
IS
ROTAMETER
7
BLOWER
8
INJECTION PORT
L
387 10.
GAS
, ,
Figure 1. Sectionalized bubble column with radial baffles,
number, drilled on a triangular pitch. In order to prevent the weeping of fine solid particles, a wire gauze was placed below the sieve plate. Wire gauze was made of stainless steel, of 150 mesh and 45 gauge. The wire diameter was 71 pm with an aperture of 100 pm. The air permeability of the wire gauze was 2.2 m3/s/m2 a t 10 mm of water column. The column was operated in a semibatch manner, and the clear height-to-diameter ratio ( H J T ) was four in all experiments. The solid loading was varied from 4 to 20 (percent by weight). Figure 2A shows the schematic diagram of experimental setup. Figure 2B shows the geometry of the radial baffle. Radial baffles, made from Perspex and having an initial dimension of 387 mm 0.d. and 120 mm i.d. and having a cone angle of 45O, were employed. In subsequent experiments, the inner diameter of the baffles was varied from 120 to 320 mm so that the d,/T ratio covered was in the range 0.3-1.0. The radial baffles were supported on four Perspex plates, each 10 mm X 50 mm and 1500 mm long and having 10-mm-diameter holes drilled on it, a t an interval of 25 mm. Baffles spacing was varied from 0.2 to 0.4 m. The fractional gas holdup (cG) was measured by noting the clear liquid height and the dispersed height. The liquid-phase and solid-phase mixing times were measured by employing the radioactive tracer technique. Technetium-99 metastable (%TC), as sodium pertechnate salt, was used as the liquid-phase tracer. Sodium pertechnate was extracted (milked) from the aqueous solution of sodium molybdate (g4Mo)by using methyl ethyl ketone as an organic phase. -Tc in the form of sodium pertechnate has a more convenient half-life (tl,* = 6 h) than 99Mo( t l l z
SOLID TRACER ADDITION
~
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8 8 THK $USSETS
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MY
(8) Figure 2. (A) Experimental setup. (B)Sectionalized view of radial baffle.
Ind. Eng. Chem. Res., Vol. 29, No. 7 , 1990 1505
CHART S P E E D
1-1
M I X I N G TIME
=
=
4 . 1 7 mm / s
126/4*17
P O I N T OF T R A C E R INJECTION D I S T A N C E , mm
Figure 3. Typical response curve for mixing time measurement.
= 66.7 h). A dilute aqueous solution of sodium pertechnate 99mTcwas then used as the liquid-phase tracer. 99mT~ is primarily a y-ray emitting source of convenient energy 0.14 MeV. Aluminum oxide particles of various sizes labeled with radioactive gold '%Au (in the form of chloroauric acid) were used as the solid-phase tracer. lg8Auis also primarily a y-ray emitting source having a half-life of 66.7 h and an energy of 0.4 MeV. The tracer was directly introduced from the top of the column, with the help of a beaker and a pair of tongs. y-Rays emitted from the tracer source in the system were counted by using sodium iodide (thallium impurity) scintillation detector. The detector was shielded against any background activity by using lead bricks, and a single-point detection technique was employed. The counting apparatus consisted essentially of a "Modular bin type of y-ray spectrometer". Several methods have been employed by many workers for the determination of mixing time in multiphase reactors. Hackl and Wurian (1979) have briefly described these methods. Various physical methods include those of conductivity, pH, thermal, optical, and density measurements. A probe or a senser, which is necessarily within the system, is a prerequisite for such systems. This disturbs the hydrodynamic behavior and is likely to affect the mixing process. Also, the presence of gas bubbles makes the conductivity measurements difficult. With radioactive tracers (y-ray emitting), these difficulties are eliminated, since the detector is placed outside the system. Liquid tracer was introduced through the injection ports, which were provided at 1.0 and 1.4 m from the bottom of the column. The solid tracer (labeled spherical glass beads) was directly introduced from the top of the column with the help of a beaker and tongs. It was observed that the position of the detector had no effect on the values of liquid- and solid-phase mixing times, for the same extent of homogeneity. Only the nature'of the transient variation of concentration was found to depend on the location. Also the amount of pulse was found to have no effect on the values of mixing time. The tracer particles were identical with the solid phase under investigation. In fact, a small amount of the same glass particles was labeled with radioactive gold to act as a tracer. A typical response curve is shown in Figure 3. It can be seen from Figure 3 that the count rate (response) practically attains a constant value after a lapse of some time. A horizontal line was drawn through this constant value. The point a t which the response curve meets the constant value was selected for the estimation of mixing time. In Figure 3, this point is shown by A,
which is 126 mm away from the point of injection. Since the chart speed was 4.17 mm/s, the value of the mixing time works out to be 30.3 s. It is useful to know the extent of homogeneity at the measured value of the mixing time. By use of the dispersed plug flow model described by Murakami et al. (1982), the extent of mixing was found to be more than 99%.
Results and Discussion Joshi and Sharma (1979) and Joshi (1980) have analyzed the liquid-phase flow pattern in bubble columns by using the multiple cell circulation model. A typical flow pattern is shown in Figure 4A. It can be seen that the liquid flows upward in the central region and downward near the column wall. These internal circulation flows are of very high order of magnitude as compared with typical values of superficial gas velocities encountered in practice. Further, this intense liquid circulation is responsible for the liquid-phase backmixing. Therefore, the extent of liquid-phase backmixing can be reduced by arresting the liquid downflow near the wall as shown in Figure 4. The flow arresters (radial baffles) now decide the height of the individual circulation cells. As the spacing between two neighboring baffles is reduced, the height of the circulation cell decreases. However, at a certain critical baffle spacing, the flow structure changes and it takes the form as shown in Figure 4B. This change occurs because the liquid circulation adjusts itself to result into minimum vorticity (Joshi and Sharma, 1979). The changed flow pattern introduces a marked change as far as liquid-phase backmixing is concerned. Figure 4B shows that, in addition to the liquid downflow near the column wall, the liquid also flows in the downward direction in the central region. Under these conditions, the radial baffles cease to be effective. This means that the baffle spacing should not be reduced below a certain critical value. Joshi and Sharma (1979) have recommended the spacing to be 0.81 times the column diameter. This recommendation was based on the theoretical analysis of the flow pattern. In order to support such a recommendation, it was thought to be desirable to investigate the effect to baffle spacing on the liquid-phase and solid-phase mixing times. Experiments were performed with 98-pm alumina particles and at two levels of superficial gas velocities. The results are shown in Figure 5. It can be seen that the liquid-phase and solid-phase mixing times show maximum values at a baffle spacing of 0.75 times the column diameter. It can be seen that the experimental observation is fairly close to the theoretical prediction. It may be noted from Figures 5C and 6C that the superficial gas velocity does not affect the solid-phase mixing time. This observation has been explained in detail by Khare et al. (1989). The effect of the central hole diameter was studied in the range 120-320 mm so that the d,/T ratio was covered in the range 0.3-1. Figure 6A,B shows the effect of the d,lT ratio on liquid-phase mixing in the presence and absence of a solid phase. Figure 6C shows the effect on solid-phase mixing. In all the cases, the optimum d,/T ratio was 0.7. In some experimental sets (not shown), the maximum was observed at a d,/T ratio of 0.6. The decrease of do/ T from l to 0.7 increasingly prevents the liquid downflow near the wall and results into an increase in the mixing time. A further decrease in d,/T was found to result into a decrease in the mixing time. This is probably because the large conical baffles disturb the circulation cell structure and results in multiple cells, as shown in Figure 4B.
1506 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990
A El SYMBOL
l120 3 I
v,, mi'
a
i
70SYSTEM: AIR-WATER,
60
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,Hc/T=4,Ldo/Tlr0.7
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Figure 4. Schematic diagram of multiple circulation cells in the axial direction with (A) one donut cell in the radial direction and (B) two donut cells in the radial direction.
The effect of solid loading and particle size was studied in the range 0-20% (w/w) and 12-250 j.tm, respectively. The presence of solid particles is known to affect the hydrodynamics depending upon the particle size and solid
I
0.3 B A F F L E SPACING,HI
0.4 Lml
C
Figure 5. Effect of baffle spacing on the liquid-phase mixing time for the (A) air-water system, (B)air-water-98-pm AlzO, particle system, and (C) solid-phase mixing time for the air-water-98-pm AI,O, particle system.
loading. Pandit and Joshi (1984,1986)have discussed this aspect in detail. When the particle size is less than about 100 p m and the solid loading is less than about 0.6-1%
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1507 SYSTEM
:AIR-WATER
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, H,/T
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C
Figure 6. Effect of the ratio of the baffle central hole diameter to the column diameter on the (A) liquid-phase mixing time for the air-water system, (B)liquid-phase mixing time for the air-water98-pm A1203particle system, and (C) solid-phase mixing time for the air-water-98-pm A1,03 particle system.
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I
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s, % I w ! / w l
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Figure 7. Effect of solid loading on the (A) liquid-phasemixing time for the air-water-26-pm A1203particle system and (B)solid-phase mixing time for the air-water-26-pm A1,0, particle system.
(v/v), the bubble size is smaller in the presence of particles as compared to that in the absence. This region of particle size and loading may be called region A. Region B covers the particle size range 0-100 pm (for loadings greater than about 0.6-170 (v/v) and 0-1000 pm for all loadings). In this region, the bubble size monotonically increases with an increase in the particle size as well as an increase in the solid loading. In region C (looo-SOOOpm and all loadings), the bubble size decreases with an increase in d, because of the breaking action of the particles. Above 6000 pm (region D), the bubble size remains constant irrespective of the particle size and loading. In the present work, some representative particle sizes and loadings in regions A and B were covered. In region A, bubble sizes are smaller, whereas in region B bubble sizes are larger as compared to those observed in the absence of solid phase. The smaller bubble sizes have relatively lower rise velocities and result in higher gas holdup. The increased holdup dissipates more energy a t the gasliquid interface and results in lower values of liquid circulation velocity and in turn higher values of mixing time. Thus, in region A the values of the mixing time initially increase with the particle size and then attain a maximum. Similarly, the mixing time also increases with the solid loading up to 1%(v/v) or 4 % (w/w) in the case of alumina particles (Figure 7). In region B (Figure a), however, the mixing time decreases with an increase in the particle size
1508 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990
7' I
- 0.31
AVERAGE PARTICLE SIZE , d p l
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(81
Figure. 8. Effect of the average particle size on the (A) liquid-phase and (B)solid-phase mixing times for the air-water system.
OS
OSR __
-_-____ __-----e -
4-----------A-
0.4
0.1
BAFFLE SPACING, 0.1 H, I 0.115 ml
0.150
Figure 9. Effect of baffle spacing on fractional gas holdup for airwater and air-water-98-pm A1,03 particles systems.
and solid loading. From the foregoing discussion it is clear that the regime classification in three-phase reactors remains unaffected in the presence of baffles. The effects of central hole diameter and baffle spacing on fractional gas holdup are shown in Figures 9 and 10, respectively. It can be seen that the variations in the holdup are nominal. Correlations and Scale-up It was thought to be desirable to correlate the mixing time data. The effect of the central hole diameter on the liquid-phase mixing time was correlated by the following equation with a standard deviation of 8%:
_e -- 3.59(T - do) + 0*079 - 0.72 OB
T - do
for d o / T < 0.8 (2)
HB
(3)
The effects of the central hole diameter and baffle spacing on the solid-phase mixing time were correlated by the following equation: -=
____ *___-
dB
4.39(T - do) + 0*755 - 0.785 T - do
d o / T < 0.8,
SD = 5% (4) OS
-= OSB
1.34T 0.324HB + -- 3.89 HB
SD = 5%
(5)
Similar to the correlation given by eq 2, the effects of VG,d,, and solid loading on 8sB get correlated by eqs 4 and 5 through their effects on Os. The mathematical model of Joshi and Sharma (1979) recommends the optimum hole diameter and the baffle spacing in a constant proportion of the column diameter. These recommendations have been confirmed experimentally with a 0.4-m-i.d. column. Though it is desirable to find the optimum baffle design for one or two large columns, it is suggested a t this stage that the results obtained in this work should be useful for scale-up.
Conclusions (i) In the present work, an attempt has been made to maximize the values of mixing time by manipulating the baffle design. It was observed that the maximum mixing time is obtained at a d o l T ratio of 0.7 and baffle spacing of 0.75 times the column diameter. Good agreement was found between the predicted and experimental values of optimum baffle spacing and the optimum diameter of the central hole. It is suggested that the optimum spacing be in the range 0.75-0.81 times the column diameter and the optimum hole diameter be in the range 0.6-0.7 times the column diameter.
Ind. Eng. Chem. Res. 1990,29, 1509-1516
(ii) The effects of particle size and solid loading in baffled columns on liquid- and solid-phase mixing times were found to be analogous to those observed in unbaffled columns. Acknowledgment The present work was supported by a grant from the Board of Research in Nuclear Sciences, Department of Atomic Energy, Government of India (Project 35/4/86-G). Nomenclature a = constant in eq 1 A = distance between column axis and the point of maximum vorticity, m B = point of maximum vorticity do = diameter of the central hole, m d, = particle diameter, pm DL= liquid-phase dispersion coefficient, m2 s-l HB = baffle spacing, m H, = clear liquid height, m HD = height of dispersion, m T = column diameter, m VG= superficial gas velocity, m s-l Greek L e t t e r s CG = fractional gas holdup t S = fractional solid holdup
8 = liquid-phase mixing time for unbaffled bubble column, S
8s = liquid-phase mixing time in the presence of baffles, s Os = solid-phase mixing time for unbaffled bubble column, S
8 s = ~ solid-phase mixing time in the presence of baffles, s
Literature Cited Blenke, H. In Biotechnology; Brauer, H., Ed.; VCH Weinhein, 1985; VOl. 11.
1509
Deckwer, W. D.; Graeser, V.; Serplemen, Y.; Langemann, H. Zones of Different Mixing in the Liquid Phase of Bubble Columns. Chem. Eng. Sci. 1973,28, 1223-1225. Doraiswamy, L. K.; Sharma, M. M. Heterogeneous ReactiomAnalysis, Examples and Reactor Design; vol. 11, Wiley-Interscience: New York, 1984; Vol. 11. Field, R. W.; Davidson, J. F. Axial Dispersion in Bubble Columns. Trans. Inst. Chem. Eng. 1980,58, 228-236. Hackl. A,: Wurian. H. Determination of Mixing Time. Ger. Chem. Eng. 1979,2, 103-107. Joshi, J. B. Axial Mixing in Multiphase Contactors-A Unified Correlation. Trans. Inst. Chem. Ena. 1980.58, 115-165. Joshi, J. B.; Sharma, M. M. Some Design Features of Radial Baffles in Sectionalized Bubble Columns. Can. J. Chem. Eng. 1979,57, 375-377. Joshi, J. B.; Shertukde, P. V.; Godbole, S. P. Modelling of Three Phase Sparged Catalytic Reactors. Reu. Chem. Eng. 1988, 6, 72-156. Khare, A. S.; Dharwadkar, S. V.; Joshi, J. B. Solid Phase Mixing in Three Phase Sparged Reactor. J. Chem. Eng. J p n . 1989, 22, 125-130. Murakami, Y .; Hiranono, T.; Ono, S.; Nishijima, T. Mixing Properties in Loop Reactor. J. Chem. Eng. J p n . 1982, 15, 121-125. Pandit, A. B.; Joshi, J. B. There Phase Sparged Reactors Some Design Aspects. Reu. Chem. Eng. 1984,2, 1-84. Pandit, A. B.; Joshi, J. B. Mass and Heat Transfer Characteristics of Three Phase Sparged Reactors. Chem. Eng. Res. Des. 1986,64, 125-157. Parulekar, S. J.; Shertukde, P. V.; Joshi, J. B. Underutilization of Bubble Column Reactors Due to Desorption. Chem. Eng. Sci. 1989, 44, 543-558. Patil, V. K.; Joshi, J. B.; Sharma, M. M. Sectionalized Bubble Column; Gas-hold-up and Wall Side Solid-Liquid Mass Transfer Coefficient. Can. J. Chem. Eng. 1984, 62, 228-232. Shah, Y. T. Gas Liquid-Solid Reactor Design; McGraw-Hill: New York, 1978. Van de Vusse, J. G. A New Model for the Stirred Tank Reactor. Chem. Eng. Sci. 1962, 17, 507-521. I
Received for review April 27, 1989 Revised manuscript received January 17, 1990 Accepted January 25, 1990
Law of Corresponding States of Uniunivalent Molten Salt Mixtures. 1. Mixing Rule of Pair Potential Parameters Yutaka Tada,* S e t s u r o Hiraoka, and Tomokazu U e m u r a Department of Applied Chemistry, Nagoya Institute of Technology, Nagoya 466, J a p a n
Makoto Harada Institute of Atomic Energy, Kyoto University, Uji, Kyoto 611, J a p a n
A mixing rule for the pair potential parameters of molten alkali halide mixtures was obtained. The pair potential between the ions was simplified to soft-sphere and effective Coulomb potentials. The characteristic potential parameters of the mixtures were selected such that the Helmholtz energy of the mixture was equal to that of a hypothetical reference system. Molar volume and surface tension of the mixtures were correlated in a corresponding states correlation using the characteristic parameters. I t was also discussed how the mixing volume and surface tension were described by using the characteristic parameters. 1. Introduction
A law of corresponding states is one of useful methods for predicting physical properties of molten salt mixtures. The characteristic parameters that are used to reduce the temperature, distance between two ions, volume, and other physical properties should be determined theoretically. The pair potential of molten salt is expressed by the sum of Coulomb, core-repulsion, dipole-dipole (dispersion), induced-dipole-ion, and dipole-quadrupole interactions. O ~ S S - ~ S901 S ~2629-1509$02.50/0 /
It is important in a law of corresponding states how the pair potential is simplified and what are chosen as the characteristic parameters. Reiss et al. (1961) simplified the pair potential to the sum of Coulomb interaction and hard-sphere repulsion, which is the same for unlike-charged ions and for likecharged ions based on the assumption that the short-range repulsion between like ions contributes little to the configuration integral. They examined the corresponding 1990 American Chemical Society
