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Ind. Eng. Chem. Res. 2008, 47, 4270–4277
GENERAL RESEARCH Temperature Effects on Gas Dispersion and Solid Suspension in a Three-Phase Stirred Reactor Yuyun Bao,† Lei Chen,† Zhengming Gao,*,† Xinnian Zhang,† John M. Smith,‡ and Norman F. Kirkby‡ School of Chemical Engineering, Beijing UniVersity of Chemical Technology, Beijing 100029, China, and Fluids and Systems Research Centre, School of Engineering (J2), UniVersity of Surrey, Guildford GU2 7XH, United Kingdom
Temperature effects on gas dispersion and solid suspension have been investigated in a fully baffled, dishedbase stirred tank of 0.48 m diameter holding 0.145 m3 of liquid stirred by a triple-impeller combination. The impeller combination consisted of a half-elliptical disk turbine below two up-pumping wide-blade hydrofoils (WHU). This configuration is efficient for both gas dispersion and solid suspension. Power consumption, gas holdup, and the critical off-bottom just-suspension agitation speed have been measured at solid concentrations up to 21 vol % at six different temperatures ranging from 24 to 95 °C in increments of about 14 °C. The results confirm significant effects of temperature on the hydrodynamic characteristics. The relative power demand increases somewhat at increased temperature, although this effect is less when more solids are present. Gas holdup decreases significantly at higher temperatures, again an effect that is reduced at higher solid concentrations. The critical impeller speed for off-bottom just suspension (NJSG) increases with increasing gas rates over the whole temperature range of this work, though the effect of the gas rate on NJSG is less at higher temperatures. The effects of the temperature on power consumption, gas holdup, and NJSG have been quantified in a series of correlations that are relevant for the design and operation of hot-sparged three-phase reactors. 1. Introduction Three-phase, gas–liquid–solid, stirred reactors are widely applied in many industrial multiphase processes, including polymerization, halogenation, minerals processing, fermentation, and sewage treatment. In an aerated system at ambient (“cold”) temperature, such as in fermentation and water treatment, the vapor pressure can be assumed to be insignificant in relation to the operating pressure. Extensive studies of cold-sparged threephase systems, involving settling particles, have been reported during the last 30 years.1–7 However, many of the processes named above are exothermic and “hot”, operating at higher temperatures, when the assumption of negligible vapor pressure is likely to be invalid. During the past decade, studies of hot gas–liquid systems have shown that hot-sparged conditions differ significantly from those in cold gassed systems.8–15 The agitator power draw is somewhat greater at higher temperatures, although bulk and micromixing times are essentially unaltered while retained gas fractions are substantially reduced. The temperature dependence of the void fraction retained in a sparged reactor was measured by Smith et al.10 The reduction in the gas holdup over the range from 290 to 367 K could be correlated with the absolute temperature to the power -3.2. However, studies of the possible influence of suspended solids on these temperature effects have not previously been reported. In our previous work with aqueous aerated suspensions,15 the gas dispersion and solid suspension performances have been reported for both cold and hot (at the specific temperature of 81 °C) conditions. The reactor used had a composite agitator * To whom correspondence should be addressed. Tel: +86-10-64418267. Fax: +86-10-6444-9862. E-mail:
[email protected]. † Beijing University of Chemical Technology. ‡ University of Surrey.
with a concave (half-elliptical) blade disk turbine (HEDT) below two up-pumping wide-blade hydrofoils (WHU), shown in Figures 1 and 2, respectively, as recommended for these duties.5 Because the presence of solids, and their concentration, together with the system temperature, has a significant influence on the gas retention, the results of the work will be of particular industrial significance. The present work with an agitated tank stirred by a threeimpeller agitator focuses on the effects of the temperature and solid concentration on the power consumption, gas holdup, and suspension. Suspensions of up to 21 vol % of settling particles were used at six different temperatures between 24 and 95 °C (297 and 368 K). Correlations of power consumption, gas holdup, and the critical off-bottom suspension speed have been developed that describe the quantitative effects of the temperature and solid concentration and which will provide some guidance for industrial design. 2. Experimental Section 2.1. Experimental System. All of the experiments reported here were carried out with the same equipment as that used in our previous work.15 The fully baffled, stainless steel, dishedbottom cylindrical tank has an internal diameter of 0.48 m and a filled aspect ratio of H/T ) 1.8, as sketched in Figure 3. The volume of the liquid or liquid–solid slurry is about 0.145 m3. There are four vertical electrical heaters of 3 kW and a 0.16m-diameter ring sparger mounted 0.33 T above the tank base. Water vapor in the off-gas is condensed and returned. A previously published work5 in a cold-gassed three-phase stirred tank has recommended a compound agitator for both gas dispersion and solid suspension. Two types of impellers are involved in this configuration, all of which were in this case
10.1021/ie701726e CCC: $40.75 2008 American Chemical Society Published on Web 05/29/2008
Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4271 Table 1. Saturation Percentage of Bubbles under Deferent “Equilibrium Temperature” T*/°C
Figure 1. HEDT impeller.
Figure 2. WH impeller.
Figure 3. Scheme of the experimental arrangement.
0.4 T (0.19 m) diameter. Two up-pumping (WHU) wide-blade hydrofoils (WH; Figure 2) are mounted above a gas-dispersing disk turbine with concave half-elliptical blades (HEDT; Figure 1), which was itself 1.0 D above the base of the tank. The ungassed power number of the combination, NP, is about 4.20.5 Deionized water, purified air, and cleaned glass beads of average diameter 90 µm and a density of 2500 kg · m-3 were used in all of the experiments. The volumetric solid concentrations (volume of solid per volume of suspension) were 3, 6, 9, 15, and 21%. The total gas rates, including the vaporized water, ranged from 0.0014 to 0.011 m3 · s-1 (the corresponding superficial velocities were from 0.0078 to 0.063 m · s-1). Impeller rotational speeds ranged from 3.5 to 9 s-1, producing fully turbulent conditions in the reactor. The power consumption was calculated from the torque and rotational speed of the shaft measured with a torque transmitter and a portable tachometer. The gas holdup was calculated from changes in the liquid level measured by a calibrated radar probe
Qg/m3 · h-1
Qg+v/m3 · h-1
saturation/%
15 30 9.5 25 6.5 17 1.6 3.5
17.6 35.8 15.7 41.2 15.6 40.7 15.2 33.3
95.5 104.2 94.8 102.6 95.2 99.3 98.8 99.7
40.0 40.0 68.0 68.0 81.0 81.0 96.0 96.0
(Krohne Reflex-Radar BM100A, Duisburg, Germany). The previous paper has the details of the calculation of gas holdup.14,15 The critical just-suspension impeller speed was again determined visually by observation through the base of the tank. Following the Zwietering (1958) criterion for the just-suspended condition for settling particles, the critical speed, NJS, could consistently be judged within an accuracy of about 5% in experiments by a given person. The critical agitation speed in a three-phase system is identified as NJSG. The agitator speeds were above the just-suspension speed during all of the measurements of gas holdup. 2.2. Saturation Percentage of Air in the Hot-Sparged System. Our previous paper14,15 dealing with a hot-sparged system calculated the volumetric gas rate on the assumption that sparged gas is immediately effectively saturated with vapor at the reactor temperature. The liquid temperature established in the reactor is a consequence of the balance between the supplied heat (from reaction or, in the present case, electrical heating) and the latent heat required to evaporate the water vapor. In order to confirm the validity of this assumption of almost complete saturation, a series of extended runs have been carried out at various temperatures (controlled within 0.2 °C) and gas rates. In runs of at least 30 min, but much longer in the case of lower reactor temperatures, no condensate was returned to the reactor and the mass of water calculated from accurate measurements of the liquid level using the radar-based surface level probe. The mass of water lost from the reactor combined with knowledge of the (water-free) inlet gas rate allowed calculation of the percentage of full saturation reached in the off-gas. The results of these balances are given in Table 1 and clearly support the assumption of virtually complete saturation. Those results that show a recovery of over 100% can be ascribed to water droplet carryover from the reactor at high gas rates. A straightforward material balance shows that the augmented gas-phase-sparged volume rate, including both gas and vapor, Qg+v, is given by eq 1, Qg+v )
[
]
QgP0 T/ + 273.15 QgP0 TK ) P0 - Pv T0 + 273.15 P0 - Pv TK0
(1)
where T* is the various hot-sparged “equilibrium temperatures” ranging in this paper from 24 to 95 °C. T0 is the temperature of the gas at the inlet in centigrade; TK and TK0 are “equilibrium temperatures” and the inlet gas temperature in Kelvin, respectively. Qg is the inlet gas flow rate. P0 is the ambient pressure. Pv is the saturated vapor pressure at T* calculated by the Antoine equation,16 and Qg+v is the total flow rate of the saturated gas. Throughout this paper, all of the hot-sparged system data and gas flow numbers are calculated and compared on this basis. This includes those at the ambient temperature of 24 °C when the very small contribution of the vapor pressure was also taken into account.
4272 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008
3. Results and Discussion 3.1. Gassed Power Demand. 3.1.1. Effect of Temperature on the Relative Power Demand (RPD) at Various Solid Concentrations. Our previous papers have reported that the RPD, the ratio of gassed to ungassed power, at the higher temperature of 81 °C is higher than that at ambient temperature for suspensions of both settling and buoyant particles.14,15 The effects of the temperature on the RPD at different solid concentrations are shown in Figure 4a-c. It is clear that when no particles were present, the higher the temperature, the greater the RPD. However, the effect of the temperature on the RPD is less at higher solid concentrations, until, with the highest concentration of 21 vol %, the RPD is almost independent of the temperature. As discussed in our previous papers, around ambient temperature, the RPD is almost independent of the solid concentration.15 However, at 81 °C the RPD decreased slightly with increasing solid concentration. Our experiments found that the difference between RPDs at ambient temperature and 81 °C was about 17% in a gas–liquid system, but this fell to about 5% with 21 vol % solids present. Gassed power consumption is affected by both the cavities behind each impeller blade and the average density of threephase systems. As discussed in our previous paper,15 the larger bubbles present at high operating temperature might be more likely to escape from the free surface, and this will probably reduce the size of the blade cavities. Moreover, the rapid release of bubbles from a hot system will lead to a reduction in the retained gas and so to a higher mean liquid density. A reduction in the cavity size and a higher mean density will both increase the RPD. In order to quantify the effect of the temperature on the gassed power draw, the absolute temperature, TK in Kelvin, has been added to the correlation for gassed power number Npg (eq 2). NPg ) aFlgbFrcTKd
(2)
Because of the apparently differing effects of the temperature on the gassed power draw at various solid concentrations seen in Figure 4, the data for different Cv are correlated separately. Over the range of solid concentrations studied, the exponents b and c on the gas flow and Froude numbers in eq 2 changed by only 5 or 10% of their original values of -0.13 and -0.11, so these have been retained for the preferred format of eq 3. NPg ) a′Flg-0.13Fr-0.11TKd′
(3)
The factor a′ and exponent d′ on the absolute (Kelvin) temperature for different solid concentrations are given in Table 2. With an increase in Cv, d′ decreases significantly, reflecting the reduced effect of the temperature on gassed power numbers. It should be noted that application of the equations in Table 2 should be limited to the range of gas flow numbers from 0.02 to 0.27 and Froude numbers from 0.69 to 1.56. Figure 5 shows examples of four relationships between the experimental gassed power numbers NPg and the relevant groups Flg-0.13Fr-0.11TKd′ at different solid concentrations. Four straight lines of slope 0.095, 0.161, 0.238, and 0.963 correspond to solid volume percent concentrations of 0%, 3%, 9%, and 21%. The experimental data are consistent with the form of eq 3. There are more than 300 experimental points for each solid concentration. It should be noted that the exponent d′ for TK, which is shown in the same figure, is different for each solid concentration. The factor a′ and exponent d′ are related with the solid concentrations, which could be regressed as the exponential growth and the linear function of the solid concentrations, Cv, respectively,
Figure 4. Influence of the temperature on the RPD (N ) 6 s-1): (a) Cv ) 0%; (b) Cv ) 9%; (c) Cv ) 21%.
and lead to the equation NPg ) [0.0942 exp(Cv/ 0.088)]Flg-0.13Fr-0.11TK0.567–1.953Cv with a reasonably high correlation coefficient R2 of 0.975. 3.1.2. Effect of the Solid Concentration on the RPD at Different Temperatures. The influence of the volumetric solid concentration, Cv, on the RPD for three different temperatures at a given agitator speed of 8 s-1 is shown in Figure 6. The results are consistent with our earlier observation15 that varia-
Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4273 Table 2. Regression Results of NP According to Equation 3
Table 3. Regression Results of Npg as in Equation 5
Cv/%
a′
d′
R2
T*/°C
k′
e′
R2
0 3 6 9 15 21
0.095 0.161 0.150 0.238 0.503 0.963
0.566 0.474 0.488 0.408 0.280 0.169
0.971 0.970 0.965 0.974 0.969 0.966
24 40 54 68 81 95
2.394 2.443 2.523 2.587 2.637 2.705
0.277 0.172 0.0089 -0.051 -0.102 -0.180
0.966 0.981 0.984 0.977 0.967 0.908
Since the effects of the solid concentrations on the gassed power draw are different at high or low temperatures, the data were correlated separately for the different temperatures. The exponents b and c for the flow number and Froude number in eq 4 changed by about only (10% of their values of -0.13 and -0.11 for the different temperatures. It is sufficiently accurate to use these values as fixed exponents, as shown in eq 5. NPg ) k′Flg-0.13Fr-0.11(1 + Cv)
e′
Figure 5. Comparison of the gassed power number correlations and the experimental data for different solid concentrations.
(5)
The factor k′ and exponent e′ on the solid concentration terms at different temperatures are given in Table 3. These equations should only be used for the same range of gas flow numbers and Froude numbers as those for Table 2. With an increase in the temperature, the factor k′ increases by about 10% while the exponent e′ decreases from +0.277 to -0.18, passing close to zero at 54 °C. This means that at ambient temperature gassed power numbers increase with increased solid concentration. At higher temperatures, this rise becomes less until, at about 54 °C, NPg becomes independent of Cv. At still higher temperatures, the gassed power draw decreases as the solid concentration is increased. This can also be seen in Figure 6. Figure 7 shows selected relationships between the experimental data NPg and the relevant groups Flg-0.13Fr-0.11(1 + Cv)e′ at low, medium, and high temperatures, respectively. With different values of the exponent e′ for 24, 54, and 95 °C, three straight lines with the slightly different slopes of 2.4, 2.5, and 2.7 show reasonable agreement between correlation (5) and the experimental data. It is also very clear that the gassed power numbers increase with increasing temperature. 3.2. Gas Holdup. 3.2.1. Effect of the Temperature on the Gas Holdup for Different Solid Concentrations. The gas holdup and its distribution, which have a close relationship with the gas-phase residence time, are very important parameters for the design and scale-up of gas–liquid stirred-tank reactors. The effects of the temperature on the gas holdup for six different temperatures are shown in parts a-c of Figure 8 for
Figure 6. Influence of Cv on the RPD (N ) 8 s-1).
tions in the solid concentration at low temperature give little change in the RPD, only slightly increasing at high concentrations. The RPD values in the suspensions are only slightly different from those without solids, although the cold RPD does increase a little at the greatest Cv of 21 vol % that we have studied. At the highest temperatures, the RPD is slightly lower with higher solid concentrations. The balance between the opposing changes with concentration at high and low temperatures reduces the effect of the temperature on the gassed power draw in highconcentration suspensions. The effect of the solid concentration on the RPD in cold- or hot-sparged systems will be discussed, together with that on the gas holdup, in section 3.2.2. The effect of solid concentrations on the gassed power draw for different temperatures can be described by an equation of the form NPg ) kFlgbFrc(1 + Cv)e
(4)
Figure 7. Comparison of the gassed power number correlations and the experimental data for different temperatures.
4274 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 Table 4. Regression Results of the Gas Holdup as in Equation 7 Cv/%
R′
m′
R2
0 3 6 9 15 21
3.345 × 108 7.773 × 107 3.314 × 107 5.11 × 106 4.506 × 105 7.935 × 103
-3.465 -3.214 -3.072 -2.754 -2.345 -1.656
0.987 0.989 0.990 0.988 0.988 0.991
to avoid flooding of the lowest impeller and to suspend all of the settling particles. It should be noted that the total energy contribution to mixing the liquid phase considered and discussed in this section includes both the agitator shaft power and the potential energy of the liquid displaced by the sparged gas. The detailed calculation of the total power input has been reported in our previous paper.14 With the same power input and total gas flow rate, including the contribution of the evaporation from the liquid phase, the gas holdup decreases with increasing temperature. Without solids, the gas holdup in cold conditions is over twice that at the highest temperature. Similarly to the influence of the temperature on the gassed power draw, the gas holdup difference between various temperatures was reduced, to a factor of about 1.4 when a high concentration of solids was present, e.g., 21 vol %. The effect of the temperature on the gas holdup apparently depends on the solid concentration. The results for gas holdup were regressed to produce correlations in the form of eq 6 with TK as the absolute temperature in Kelvin. ε ) RPTmβVsγTKm
(6)
The exponents for the total specific power input and the gas rate were consistently about 0.16-0.17 and 0.54-0.55, respectively, so that the correlations for the gas holdup as a function of the solid concentrations used the specific exponents 0.16 and 0.55 for PTm and VS (eq 7). ε ) R′PTm0.16Vs0.55TKm′
Figure 8. Influence of the temperature on the gas holdup: (a) Cv ) 0% (VS ) 0.024 m · s-1); (b) Cv ) 9% (VS ) 0.024 m · s-1); (c) Cv ) 21% (VS ) 0.024 m · s-1).
solid volume fractions of 0%, 9%, and 21%, respectively. In all of these experiments, the agitator speed was sufficient both
(7)
The results are shown in Table 4. All of the exponents for TK at different solid concentrations are negative. This reflects the tendency for the gas holdup to decrease at increased temperature in both two- and three-phase systems. However, the absolute value of the power m′ for the absolute temperature was reduced from 3.46 to 1.66, while Cv increased from 0 to 21 vol %, reflecting the lower gas holdup at higher solid concentrations, as shown in Figure 8a-c. Figure 9 shows the reasonable agreement between the experimental data and the correlations at three different temperatures. The only literature relating to the quantitative effect of the temperature on the gas holdup in two-phase systems has been reported by Smith et al.,10 who correlated their data with ε ) 69 × 106PTm0.20Vs0.55TK-3.2, where TK was the absolute temperature in Kelvin. Their stirredtank and impeller configurations were similar to but not exactly the same as those used in this work. For the purposes of comparison, Smith et al.’s equation was used as a basis to regress all of the two-phase data generated in our work, yielding the very similar correlation ε ) 70.1 × 106PTm0.20Vs0.55TK-3.2 with a reasonably high correlation coefficient R2 of 0.984. 3.2.2. Effect of the Solid Concentration on the Gas Holdup at Different Temperatures. Figure 10 shows the different effects of the solid concentration on the gas holdup at different temperatures. In cold-gassed conditions, the gas holdup decreases considerably in the presence of solids, as is seen in the results for 24 °C. This reduction is smaller at higher
Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4275
Figure 9. Comparison of the gas holdup correlations and the experimental data for different solid concentrations.
Figure 11. Comparison of the gas holdup correlations and the experimental data for different temperatures.
might cause the collision and coalescence of bubbles to dominate the breakup when more solids are introduced in the systems. The resulting higher mean density and reduced blade cavity size will cause the RPD to be greater in cold conditions. Consequently, as more particles are suspended in the tank, the higher rise velocity of the resulting larger bubbles will itself lead to a reduced gas holdup. For each temperature, the influence of solid concentrations on the gas holdup has been correlated in the form of eq 8 using the given exponents on the total specific power and superficial gas rate. The regression results are shown in Table 5. n′
ε ) λ′PTm0.16Vs0.55(1 + Cv)
Figure 10. Influence of Cv on the gas holdup under different temperatures. Table 5. Regression Results of Gas Holdup as in Equation 8 T*/°C
λ′
n′
R2
24 40 54 68 81 95
0.890 0.792 0.681 0.571 0.478 0.402
-1.777 -1.514 -0.998 -0.497 -0.022 0.141
0.990 0.992 0.994 0.994 0.990 0.993
temperature until at about 81 °C the gas holdup becomes independent of the solid concentration. At the highest temperature used in this work of 95 °C, the gas holdup increases further when more solids are present. The changing effect of the solid concentration at different temperatures can be interpreted in terms of the bubble size and the influence of Cv on it. Bubbles are larger in hot-sparged systems than when the system is cold because of the lower liquid viscosity in a hot system, and surface tension, which helps to stabilize the bubble, is also lower at higher temperature. As a result, in comparison with cold conditions, bubbles in a hot system are more easily broken by the settling particles. Moreover, because the particles occupy part of the bulk liquid volume, they will enhance the probability of bubble collision and coalescence. The competing results of breakup and coalescence of bubbles may lead to a relatively larger stable bubble size in hot systems. When the temperature is low, the smaller bubble size and higher interfacial tension
(8)
The exponent n′ on the solid concentration term changed from –1.77 to 0.141 between the temperatures of 24 and 95 °C, respectively, reflecting the opposite effects of the solid concentration on the gas holdup at ambient temperature and in nearboiling conditions. The factor λ′ is smaller at higher temperature, indicating the lower gas holdup in a hot system. Figure 11 compares the experimental results with the correlations of Table 5 and shows a good agreement between the experiment and correlation and reflects the lower gas holdup in high-temperature conditions. The comparison between Figures 7 and 11 leads to the conclusion that stirred tanks working at higher temperatures will have lower gas holdup and higher gassed power numbers than those operating at ambient temperatures. It should again be noted that all equations and all regression results presented in Tables 2–5 are restricted to the temperature range from 24 to 95 °C with HEDT + 2WHU impellers used in the specific system and conditions as described in section 2.1. 3.3. Solid Suspension in Sparged Systems. 3.3.1. Effect of the Solid Concentration at Different Temperatures. Because of the quantity of vapor evolved at high temperatures, it is very difficult to observe off-bottom suspension visually from the base of a tank at 95 °C. For that reason, observations of the minimum suspension conditions have been limited to the range from 24 to 81 °C. Figure 12 shows the similar, but small, effect of the solid concentration on the minimum gassed suspension speed at different temperatures. In each case, following an initial increase in the minimum suspension speed, this passes through a maximum at concentrations on the order of 10-15 vol %, before decreasing slightly. Even in the early stages, the dependence on the concentration is less than the 0.1 exponent in the Zwietering equation, which is widely accepted as providing a
4276 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008
Figure 12. Influence of Cv on NJS at different temperatures.
Figure 14. Relationship between ∆NJSG and Vs at different temperatures.
linearly with the superficial gas velocity, although the effect of this on the critical suspension speed at higher temperatures is reduced to about half of that at ambient temperature. Because the influence of Vs on NJSG is strongly affected by the temperature, taking all data solid concentrations ranging from 3% to 21% and temperatures between 24 and 81 °C, eq 9 correlates the influence of Vs on ∆NJS at different temperatures. ∆NJSG ) 5.24 × 107Vs0.65TK-2.68 R2 ) 0.984
(9)
4. Conclusions
Figure 13. Influence of gas rates on NJSG at different temperatures
useful basis for calculations of ungassed suspension conditions at low (less than ∼5 mass %) solid concentrations. The different exponents in this work can be partly attributed to the different structures of the bottom, including the presence of the additional four cylindrical electrical heaters, the ring sparger, and the different shapes of the vessel bottom, which is a dished base with a flat glass window with a diameter of 0.12 m located in the center of the bottom. Figure 12 shows the effect of the temperature and Cv on NJS in ungassed solid–liquid two-phase systems. With an increase in the temperature, NJS increases steadily. However, the relationship between NJSG and the temperature in three-phase systems is also influenced by the gas flow rate. This is discussed below. 3.3.2. Effect of the Superficial Gas Velocity at Different Temperatures. In Figure 13, which gives results for a 3 vol % suspension, it can be seen that the introduction of gas leads to an increase in the minimum suspension speed. However, the influence of the superficial gas velocity, Vs, on NJSG is less at higher temperatures. It can also be seen in Figure 13 that when Vs is 0.032 m · s-1, NJSG is almost independent of the temperature. As yet more gas is introduced into the system, NJSG is higher at lower temperature, which is the opposite to the behavior in ungassed systems seen in Figure 12. ∆NJS is defined as the difference between NJSG and NJS at a given solid concentration. Figure 14 shows that ∆NJS increases
The effects of the temperature on the gassed power draw, gas holdup, and solid suspension in the presence of different concentrations of settling glass beads have been measured in a baffled sparged vessel. (1) The absolute value of the RPD increases significantly with increased temperature, although this effect is reduced as more solids are added to the system. At low temperatures, the RPD increases a little as the solid concentration is increased. At temperatures above 54 °C, the RPD falls at high particle concentrations, with this trend increasing further at higher temperatures. These observations can be explained in terms of the different effects of the volumetric concentration of settling particles, Cv, on the RPD at different temperatures. (2) The gas holdup decreases significantly with increasing, near-ambient, temperatures. This reduction in the gas retention with rising temperature is less at higher solid concentrations. As the volume fraction of solids is increased from 3% to 21%, at ambient temperature the gas holdup falls significantly, although the trend stops at about 81 °C, above which temperature the gas retention increases with the concentration of the suspension. (3) The critical impeller speed required for off-bottom just suspension (NJSG) increases with increasing gas rates for all temperatures studied in this work. However, at the higher temperatures, the effect of the gas rates on NJSG is less. The difference between NJSG and NJS, ∆NJS, increases linearly with the gas rate but with a decreasing slope of the line of ∆NJS against the total gas flow rate at higher temperatures. (4) Temperature effects on the power consumption, gas holdup, and NJSG have been quantitatively described in this paper as a series of correlations. These can provide useful guidance for the design and operation of hot-sparged multiphase reactors.
Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4277
Acknowledgment The authors sincerely acknowledge financial support from the National Nature Science Foundation of China (No. 20576009) and, in part, by the National Basic Research Program of China (973 Program, No. 2007CB714300). Appendix Nomenclature Cv ) volumetric solid concentration, m3 · (m3 suspension)-1 D ) diameter of impeller, m Flg ) gas flow number; Flg ) Qg/ND3 for a cold-sparged system and Qg+v/ND3 for a hot-sparged system Fr ) Froude number; Fr ) N2D/g H ) height of the liquid in the tank (general), m H0 ) height of the liquid without gas input, m HG ) height of the liquid during dispersion, m NP ) power number; NP ) P/FLN3D5 NPg ) aerated power number NJS ) just-suspension agitation speed in the solid–liquid system, s-1 NJSG ) just-suspension agitation speed in the gas–solid–liquid system, s-1 PTm ) mean total specific energy dissipation rate, W · kg-1 Qg ) inlet gas flow rate, m3 · s-1 Qg+v ) total gas flow rate including both air and vapor, m3 · s-1 R2 ) correlation coefficient T ) diameter of the tank, m T0 ) ambient temperature of the air, °C T* ) equilibrium temperature in a hot-sparged system, °C TK ) absolute temperature in a sparged system, K V ) volume of the liquid in the tank, m3 Vs ) superficial gas velocity, m · s-1 ε ) gas holdup AbbreViations HEDT ) half-elliptical hollow-blade disk turbine WHU ) wide-blade, up-pumping hydrofoil
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ReceiVed for reView December 19, 2007 ReVised manuscript receiVed February 28, 2008 Accepted March 13, 2008 IE701726E
