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Ind. Eng. Chem. Res. 2002, 41, 120-127
Ozone Transfer into Water in a Gas-Inducing Reactor Yung-Chien Hsu,*,† Tse-Yu Chen,† Jyh-Herng Chen,‡ and Chao-Wen Lay† Department of Chemical Engineering, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 106, Taiwan, and Department of Material and Mineral Resources Engineering, National Taipei University of Technology, 1 Chung-Hsiao E. Road, Section 3, Taipei, Taiwan
In this study, ozone gas mass transfer into water using a new gas-inducing reactor was investigated. The effects of various operation parameters upon the ozone volumetric mass-transfer coefficient (kL,O3a) were determined, including agitation speed, working liquid level, temperature, and superficial gas velocity in a semibatch system. Experimental results show that the ozone volumetric mass-transfer coefficient increases with increasing agitation speed, temperature, and superficial gas velocity. As the agitation speed increases, the effect on volumetric mass-transfer coefficient (kL,O3a) decreases at higher agitation speed and superficial gas velocity. For this new gas-inducing reactor, a higher ozone volumetric mass-transfer coefficient can be obtained at lower working liquid level. The kL,O3a obtained in this study ranged from 0.6 to 1.2 min-1 and was close to the literature results. In addition, the correlation for the ozone volumetric masstransfer coefficient at pH 7 was obtained. Introduction Many chemical industries discharge wastewater containing refractory compounds that have low biodegradability and are difficult to treat using conventional methods. For example, the wastewater from the textile industry contains large amounts of dye, mordant, sizing agents, and dyeing aids.1 The wastewater from the petrochemical industry might also contain refractory phenolic compounds.2 Ozonation was proposed for the treatment of dye and textile wastewater3-5 and phenolic wastewater.6-8 Although excellent results were obtained with the ozonation treatment, the high production cost of ozone and low ozone solubility in water have limited ozone treatment applications.9,10 These limitations can be alleviated by improving the ozone utilization rate in aqueous solutions. Consequently, the development of a gas-liquid reactor with a high ozone utilization rate is needed. In a conventional gas-liquid reactor, the agitation interaction between the turbines and baffles results in high power consumption. In addition, the short residence time for the gas in the liquid phase results in a low gas utilization rate. These problems are frequently solved using an accessory compressor and external gas circulating facilities, which increase the investment and operation costs.11-14 To improve the drawbacks of conventional agitation tanks, Rielly et al. and Saravanan et al. developed hallow shaft-type and standpipe-type gas-inducing reactors.11,15 Although the additional gas circulation facilities are not needed for both the hollow shaft and standpipe types of gas-inducing reactors, the configurations of both reactors are complex and their agitation power consumption is still high. Consequently, a series of studies for reactor development were conducted in our laboratory. * To whom correspondence should be addressed. Phone: +886-2-27376616. Fax: +886-2-27376644. E-mail: hsu@ ch.ntust.edu.tw. † National Taiwan University of Science and Technology. ‡ National Taipei University of Technology.
Hsu and Chang and Hsu et al. developed gas-inducing reactors with long and short baffles.16,17 Hsu and Huang further developed a new gas-inducing reactor that has two in-series 45° pitched-blade turbines enclosed in a draft tube.18,19 The required agitation power consumption of this reactor is low because there is no baffle on the inside wall of the tank. This reactor can increase the gas residence time in the liquid phase and the gas utilization rate without any accessory equipment. Hsu and Huang determined the proper geometrical factors and the ozone volumetric mass-transfer coefficients.20 Hsu et al. also studied the onset speed, power consumption, gas holdup, and bubble dimensions in this new gasinducing reactor.21 Hsu et al. employed this new gasinducing reactor to ozonate eight kinds of dye solutions.22 Their results indicated that, regardless of the input dye concentration and the pH value, the ozone utilization rates were all greater than 90% when the ADMI color elimination value reached 90%. Similar results were obtained for treating phenolic wastewater with ozone.23 It is concluded that ozonation of many organic compounds in this new gas-inducing reactor can be effectively conducted with a high ozone utilization rate with a lower required power consumption. A scale-up study was also investigated for commercial applications with this new gas-liquid reactor.24 To make the application of this new gas-inducing reactor more convenient and practical, a continuous process gas-inducing reactor was also studied.25 The effects of various operation parameters on the ozone volumetric mass-transfer coefficient (kL,O3a) were studied, including agitation speed, working liquid level, temperature, and superficial gas velocity in a semibatch system. In our previous research, the ozone volumetric mass-transfer coefficient under acid conditions (pH 2) was studied.20 In practical applications, ozonation is normally conducted at pH 7.0 or higher because of the formation of hydroxyl free radicals, which have a higher oxidation potential than ozone molecules.26 To compare this with the literature, a systematic investigation of
10.1021/ie0101341 CCC: $22.00 © 2002 American Chemical Society Published on Web 12/08/2001
Ind. Eng. Chem. Res., Vol. 41, No. 1, 2002 121
the effects of various operation parameters on the ozone volumetric mass-transfer coefficient was carried out at pH 7. Theory Kinetic of Ozone Self-Decomposition. Weiss proposed the ozone self-decomposition mechanism in water.27
Initiation: ki
O3 + H2O 98 2HO• + O2 k′i
O3 + OH- 98 •O2- + HO2•
k1
k2
O3 + HO2• 98 2O2 + HO ‚
(2)
(3) (4)
Termination: k3
2HO2• 98 O2 + H2O2
(5)
According to this reaction mechanism, Sotelo et al. deduced that the ozone self-decomposition reaction rate in water could be expressed as28
d[O3] ) kA[O3] + k3[OH-]0.5[O3]1.5 rO3 ) dt
d[O3] ) kA[O3] dt
[O3]e [O3]
) kAt
(7)
(8)
where [O3]e is the equilibrium ozone concentration. When ln([O3]e/[O3]) is plotted versus time t, kA can be obtained from the slope. The rate constant, kB, can be determined as follows. At pH 7, the stock solution was buffered, the hydroxide ion concentration is a known value, and kA is determined from eq 8. Equation 9 can be obtained by integrating eq 6, where kT ) kB[OH-]0.5. When exp(kAt/
(
) ( )
kT kT k At 1 1 )+ + exp 0.5 0.5 k k 2 [O3] [O3]0 A A
decomposition rate in water. When eqs 6 and 10 are combined, eq 11 can be obtained. At equilibrium, d[O3]/
d[O3] ) kL,O3a([O3]* - [O3]) - kA[O3] dt kB[OH-]0.5[O3]1.5 (11) dt is equal to zero and [O3] becomes the equilibrium ozone concentration [O3]e. Therefore, the saturated ozone concentration in water, [O3]*, can be expressed by eq 12. When eq 12 is substituted into eq 11, eq 13
[O3]* ) [O3]e +
(6)
an initial ozone concentration equal to the equilibrium ozone concentration, [O3]e, the ozone self-decomposition rate can be obtained by integrating eq 7 to yield eq 8
ln
(10)
kA[O3]e + kΒ[OH-]0.5[O3]e1.5 kL,O3a
(12)
can be obtained where ZO3 ) kL,O3a([O3]e - [O3]). The
where kA ) 2ki and kB ) 2k2(k′i/k3)0.5. The rate constant, kA, can be determined as follows. For pH < 3, the hydroxide ion has no effect on the selfdecomposition rate;28 therefore, eq 6 can be reduced to eq 7. If the solution was equilibrated with ozone to have
r O3 ) -
d[O3] ) kL,O3a([O3]* - [O3]) - rO3 dt
(1)
Propagation: O3 + HO• 98 O2 + HO2•
If kA and kB are obtained at different temperatures, the activation energies, EA and EB, for kA and kB can be derived from the Arrhenius plots. Ozone Volumetric Mass-Transfer Coefficient. The two-film theory was used for modeling the ozone mass transfer. The gas and liquid phases are mixed well, and the gas phase undergoes negligible ozone depletion. Because the system is operated at a steady state, the ozone material balance can be performed using eq 10,9 where rO3 represents the ozone self-
(9)
2) is plotted versus 1/[O3]0.5, kB can be obtained from the slope.
ZO3 )
d[O3] + kA([O3] - [O3]e) + dt kB[OH-]0.5([O3]1.5 - [O3]e1.5) (13)
term d[O3]/dt can be determined from the ozone concentration data measured at different times t. Therefore, when the values of kA, kB, and [O3]e are known, ZO3 can be calculated from eq 13. When ZO3 is plotted against ([O3]e - [O3]), the ozone volumetric mass-transfer (i.e., the slope kL,O3a) coefficient can be obtained. Experimental Section Determination of the Ozone Concentration in Water. The ozone concentration in water was determined with indigo reagent, which was prepared using the method of Bader and Hoigne´.29 All of the chemicals were analytical grade. A buffer solution mixture (KH2PO4/NaH2PO4 and KH2PO4/NaOH) was used to adjust both the ionic strength (0.01 M) and the pH of the solutions. The ionic strength was kept constant to eliminate its possible affects on ozone self-decomposition.30 Indigo stock solution was prepared by adding 822 mg of potassium indigo trisulfonate (C16H7N2O11S3K3; Acros Organics Co., Geel, Belgium) into 1 mL of concentrated phosphoric acid and a suitable amount of distilled water to make up 1 L of solution. Indigo reagent was prepared by mixing indigo stock solution (100 mL), sodium dihydrogen phosphate (NaH2PO4; 10 g), and concentrated phosphoric acid (7 mL). A known quantity of sample was added into a 20 mL tube containing 5 mL of indigo reagent. The change in absorbency at 600 nm for the indigo reagent was determined using an UV/
122
Ind. Eng. Chem. Res., Vol. 41, No. 1, 2002 Table 1. Major Geometric Dimensions of This Gas-Inducing Reactor item inner diameter of the reactor, Dt diameter of the impeller, Di kind of impeller number of impellers number of impeller blades width of blade, W distance between two impellers, Ci clearance of the lower impeller, C clearance of the draft tube draft tube length, HL draft tube inner diameter, Dd
Figure 1. Schemes of a new gas-inducing reactor and the impeller.
geometric design 0.29 m 0.102 m 45° downward pitched-blade turbine 2 6 0.0128 m 0.102 m 0.131 m 0.131 m 0.204 m 0.133 m
ozone self-decomposition rate was determined by measuring the concentration of the dissolved ozone using a liquid ozone UV photometry analyzer (Erwin Sander Co., Eltze, Germany). The indigo method was used to determine the ozone concentration in aqueous solution. The operation parameter effect on the ozone mass-transfer rate was conducted at different agitation speeds (600-1300 rpm), superficial gas velocities (9.16-13.32 m/h), temperatures (17-30 °C), and working liquid levels (1.5-2.0Dt). The ozone volumetric mass-transfer coefficients were determined using the experimental data. Results and Discussion
Figure 2. Experimental setup.
visible spectrophotometer. The ozone concentration in the aqueous solution was determined using the calibration curve. Procedure. Figures 1 and 2 show the scheme of this gas-inducing reactor and the experimental setup for this study, respectively. The important dimensions of this gas-inducing reactor are listed in Table 1. Air was fed to an ozone generator (Trailigaz model LABO 76) to produce ozone gas. The gas flow rate was regulated using a rotameter. The ozone gas concentration was controlled using the electric current of the ozone generator. For the ozone self-decomposition experiment, the pH of aqueous solution was adjusted using a buffer solution. The temperature varied from 18 to 30 °C. Stock buffered water (38.3 L) was ozonated with ozone gas (10 mg/NL) until the buffered water was saturated with ozone. The
1. Ozone Self-Decomposition Rate Constants. To determine the volumetric mass-transfer coefficient, kL,O3a, the ozone self-decomposition rate constants should first be determined. The ozone self-decomposition reaction experiments were carried out at pH 2.6 ( 0.1 and 7.0 ( 0.1. The temperature was varied from 18 to 30 °C. For pH < 3, the hydroxide ion has no effect on the decomposition rate;28 therefore, from eq 8, the ozone self-decomposition rate constant, kA, at different temperatures can be obtained by plotting ln([O3]e/[O3]) versus time. The experimental result at pH 2.6 ( 0.1 is shown in Figure 3. The results fit eq 8 well. The selfdecomposition rate constant, kA, increases with increasing temperature. This coincides with the Arrhenius equation. To investigate the effect of hydroxide ions on ozone self-decomposition, kB was determined at pH 7. For known kA and pH value, kB can be obtained by plotting [O3]-0.5 against exp[kA(t/2)], according to eq 9. The result is shown in Figure 4. The experiment data also fit eq 9 well. From Figure 4, kB also increases as the temperature increases. The values for kA and kB in this study and those reported in other literature are summarized in Table 2. According to Table 2, there are some differences between this result and those reported in the literature. This may be because the ion strength and the buffer solution were different for each experiment. Nevertheless, the order of magnitude is the same. The influences of temperature on the self-decomposition rate constants, kA and kB, were derived from the Arrhenius plots to yield
kA ) 3.77 × 108 exp(-7025/T)
(14)
kB ) 3.77 × 1024 exp(-14340/T)
(15)
and
Ind. Eng. Chem. Res., Vol. 41, No. 1, 2002 123 Table 2. Values of kA and kB in This Study and Those Reported in Other Literature worker Sotelo et
al.28
this study
kA (min-1)
kB (min-1‚M-1)
operation condition
0.0127-0.025
4334-17204
0.0123-0.0321
3556-25036
pH: 2.5, 5, 7, 8, 9 temp (oC): 10, 20, 30, 40 N: 100 rpm ion strength: 0.15 M buffer type: KH2PO4, Na2HPO4 pH: 2.6, 7.0 temp (oC): 18, 20, 25, 28, 30 N: 0 rpm ion strength: 0.01 M buffer type: KH2PO4/H3PO4, KH2PO4/NaOH
Figure 4. Ozone self-decomposition rate constant (kB) at different temperatures. Figure 3. Ozone self-decomposition rate constant (kA) at different temperatures.
The activation energy for kA, 58.4 kJ/mol, is very close to the values obtained in other works (Table 3). 2. Ozone Volumetric Mass-Transfer Coefficient. The effects of various parameters on the mass transfer were investigated, including agitation speed, working liquid level, temperature, and superficial gas velocity in a semibatch system. (1) Effect of the Agitation Speed. The effect of the agitation speed on the dissolved ozone concentration in water is shown in Figure 5. From this figure, the equilibrium ozone concentration in water increases with increasing agitation speed. This is due to the unique advantage of this new gas-inducing reactor, in which the higher the agitation speed, the higher the pumping pressure. Therefore, the gas-phase pressure at the ozone gas-liquid interface increases with increasing agitation speed. Figure 6 shows the relationship between ZO3 and ([O3]e - [O3]). The ozone volumetric mass-transfer coefficient can be determined from the slope. It was found that the ozone volumetric mass-transfer coefficient increases with increasing agitation speed. Several reasons account for this phenomenon. As the agitation speed increases, a large amount of smaller bubbles are formed and a higher mixing extent can also be obtained.31-33 The ozone volumetric mass-transfer coefficient, therefore, can be significantly raised. In addition, the liquid film thins as the agitation speed
Table 3. Activation Energy (EA) Compared with the Reported Values in the Literature
pH
temp (°C)
0.5-3 7.5-10.5 0-2 8 0.5-10 2.5-9 2.6, 7.0
0-27 1.2-19.8 5-40 10-20 3.5-60 10-40 18-30
reaction order with respect to activation hydroxide energy, EA ozone ion (kJ/mol) 1 1 1 or 2 1 1 1 and 1.5 1 and 1.5
0.5 0.75 0.12 0.5 0.5
58.6 111.8 59.0 70.5 46.4 41.23 58.4
ref 39 40 41 42 43 28 present work
increases. The ozone volumetric mass-transfer coefficient, therefore, increases. However, as the agitation speed increases, the effect on the volumetric masstransfer coefficient decreases at higher agitation speed (>1000 rpm). This can be attributed to the gas holdup reaching a maximum value as well as the extent of mixing. This result agrees with Sotelo et al. and Lee and Forster.9,34 (2) Effect of the Working Liquid Level. The working liquid levels for conventional gas-liquid agitators should be maintained from 1.0 to 1.2Dt for agitators with a single impeller35 and 2.0Dt for dual impellers. This new gas-inducing reactor can operate with good mixing and gas induction at working liquid levels as high as 2.0Dt. Above all, the power consumption of this
124
Ind. Eng. Chem. Res., Vol. 41, No. 1, 2002 Table 4. Effects of Temperature, Superficial Gas Velocity, and Working Liquid Level on the Ozone Volumetric Mass-Transfer Coefficient
Figure 5. Effect of agitation speed on the dissolved ozone concentration in water.
N (min-1)
temp (°C)
UG (m/h)
CO3,i (mg/NL)
Hs/Dt
kLa (min-1)
900 900 900 900 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
17 20 25 30 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25
9.16 9.16 9.16 9.16 9.99 9.99 9.99 9.99 10.82 10.82 10.82 10.82 13.32 13.32 13.32 13.32 9.16 9.99 10.82 13.32 9.16 9.99 10.82 13.32
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
2.0 2.0 2.0 2.0 2.0 1.8 1.7 1.5 2.0 1.8 1.7 1.5 2.0 1.8 1.7 1.5 2.0 2.0 2.0 2.0 1.8 1.8 1.8 1.8
0.672 0.701 0.741 0.762 0.866 0.880 0.883 0.911 0.892 0.939 0.952 0.943 1.024 1.061 1.072 1.064 0.794 0.866 0.892 1.024 0.815 0.880 0.939 1.061
Figure 7. Effect of temperature on the dissolved ozone concentration in water.
Figure 6. Relationship between ZO3 and ([O3]e - [O3]) at different agitation speeds.
new gas-inducing reactor is much lower than that of a conventional gas-liquid reactor.21 This is because there is no baffle on the inside wall of the tank, and a draft tube equipped to improve the axial flow is present.18 Consequently, the mass-transfer experiments were carried out at the working liquid levels of 1.5-2.0Dt. Table 4 shows the ozone volumetric mass-transfer coefficients at different superficial gas velocities and working liquid levels. The general trend is that the lower the working liquid level, the higher the ozone volumetric mass-transfer coefficient. This is because the gas holdup is larger at the lower working liquid level
(Hs/Dt ) 1.5), providing the same agitation speed and superficial gas velocity. However, it should be noted here that, upon further lowering of the working liquid level, the ozone volumetric mass-transfer coefficient decreases because much of the inlet ozone gas escapes along the agitation shaft. (3) Effect of Temperature. The influence of temperature on the gas-liquid mass transfer is very significant.36 The effect of temperature on the dissolved ozone concentration in water is shown in Figure 7. From this figure, the higher the temperature, the lower the ozone concentration equilibrium in water. It is sufficient to understand that the Henry’s constant for ozone is larger at higher temperatures. The ozone volumetric mass-transfer coefficients at different temperatures are listed in Table 4. From Table 4, it is evident that the
Ind. Eng. Chem. Res., Vol. 41, No. 1, 2002 125 Table 5. Correlations of kLa in Various Types of Gas-Inducing Reactorsa impeller type pipe with orifice Wemco Denver hollow pipe downward pitch blade a
geometry Dt ) 0.41-1 m Di ) 0.2-0.5 m Dt ) 0.3 m Di ) 0.05 m Dt ) 0.1-0.38 m Di ) 0.07-0.115 m Dt ) 0.45 m Di ) 0.154 m Dt ) 0.29 m Di ) 0.102 m
correlation equation
ref 44
kLa (s-1) ) 3.26 × 10-3(P1/V)0.55Vg0.25, Vg > 0.005
45
kLa (s-1) ) 0.0159(Pg/V)0.86
46
kLa (s-1) ) 0.0195(Pg/V)0.5
47
kLa (s-1) ) 0.01(P1/V)0.475Vg0.4
present work
kLa ) 0.228(Pg/V)0.148UG0.731(Hs/Dt)
P1/V: W/m3. Vg: m/s.
Figure 8. Comparison of the observed and calculated kL,O3a at various operation conditions.
ozone volumetric mass-transfer coefficient increases with increasing temperature. This is because the diffusivity of ozone in water increases as the temperature increases. Therefore, the ozone diffusion in water was enhanced and the ozone volumetric mass-transfer coefficient increased via higher temperatures.37 (4) Effect of the Superficial Gas Velocity. Table 4 also lists the ozone volumetric mass-transfer coefficients for different superficial gas velocities at the same agitation speed. kL,O3a increases with increasing superficial gas velocity regardless of the working liquid level (Hs/Dt ) 1.8 and 2.0). This is because at a 1000 rpm agitation speed the superficial gas velocity will further increase the gas liquid mixing and gas holdup. However, as the superficial gas velocity increases, the effect on the ozone volumetric mass-transfer coefficient decreases. Nishikawa et al. studied the oxygen volumetric mass transfer in an aerated mixing vessel.38 They indicated that, at high agitation speed, the influence of the superficial gas velocity on kL,O3a decreases. These results coincided with this investigation. 3. Correlation of Mass-Transfer Coefficient. To predict the ozone volumetric mass-transfer coefficients at various operating conditions for the new gas-inducing reactor, the correlation of the ozone volumetric masstransfer coefficient with various parameters (agitation speed, superficial gas velocity, and working liquid level)
Figure 9. Comparison of kL,O3a in this work with that in the literature.
was obtained by linear regression.
kL,O3a ) 0.228
() Pg V
0.148
UG0.731
() Hs Dt
-0.07
(16)
The values of Pg/V at various operating conditions can be calculated from eqs 17 and 18. The deviations for eqs
() ()
Hs Pg ) 0.323NFr0.197NQG-0.202 P Dt Np ) 0.107NFr-0.592
Hs Dt
-0.254
(17)
0.987
(18)
17 and 18 are (9% and (4%, respectively. The comparison of the observed volumetric mass-transfer coefficient results with the calculated results at various operating conditions is shown in Figure 8. The deviation is only (5%. This correlation can accurately predict the ozone volumetric mass-transfer coefficients at pH 7 and various operating conditions in this investigation for the new gas-inducing reactor. Table 5 shows the correlations of the volumetric masstransfer coefficient for various types of gas-inducing reactors. However, the volumetric mass-transfer coef-
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Ind. Eng. Chem. Res., Vol. 41, No. 1, 2002
ficient correlations in the literature are for oxygen. Therefore, the two-film theory was used to correct the oxygen volumetric mass-transfer coefficients for the differences in diffusivity, assuming that the influence of temperature on the gas-liquid specific surface area can be ignored, i.e., kL,O3a/kL,O2a ) DL,O3/DL,O2. At 25 °C, the diffusivity of oxygen is 2.41 × 10-9 m2/s48 and the diffusivity of ozone calculated by Matrozov (1976) is 1.42 × 10-9 m2/s.49 Based on the same specific power consumption and superficial gas velocity of 9.99 m/h, Figure 9 shows the comparison of the volumetric masstransfer coefficient in this study with that found in the literature. A comparison of the calculated ozone volumetric mass-transfer coefficients using the correlations at the same specific power consumption and superficial gas velocity (9.99 m/h) in this work with that in the other gas-inducing reactors is drawn in Figure 9. These results show that the ozone volumetric mass-transfer coefficient of the new gas-inducing reactor is higher than those of other types of gas-inducing reactors. Conclusion Based on the ozone self-decomposition kinetic mechanism, this study investigated the ozone mass-transfer behavior in a new gas-inducing reactor. The experimental results show that an increase in the agitation speed increases the equilibrium ozone concentration in the water as well as the volumetric mass-transfer coefficient. The ozone volumetric mass-transfer coefficient also increases with increasing superficial gas velocity. In general, a lower working level has a better ozone volumetric mass-transfer coefficient because of the higher gas holdup. However, further lowering the working liquid level has an inverse influence. The higher the temperature, the higher the mass-transfer rate and the lower the equilibrium ozone concentration in the water. A correlation between kL,O3a and the operation parameters was obtained. The deviation in the calculated and observed values was less than (5%. A comparison with other literature results showed that the new gasinducing reactor has a higher volumetric mass-transfer coefficient. Notation a ) specific surface area, m-1 ADMI ) color value developed by American Dye Manufacturers Institute C ) clearance of the lower impeller, m Ci ) space between the upper and lower impellers, m CO3,i ) inlet ozone concentration, mg‚L-1 DL,O3 ) diffusivity of ozone in water, m2‚s-1 DL,O2 ) diffusivity of oxygen in water, m2‚s-1 Dd ) inner diameter of the draft tube, m Di ) impeller diameter, m Dt ) inner diameter of the reactor, m EA ) activiation energy of kA, J‚mol-1 EB ) activiation energy of kB, J‚mol-1 Qg ) gas flow rate, NL‚s-1 Hd ) dynamic working liquid level, m HL ) length of the draft tube, m Hs ) static working liquid level, m k1 ) reaction rate constant in eq 3, min-1‚M-1 k2 ) reaction rate constant in eq 4,min-1‚M-1 k3 ) reaction rate constant in eq 5, min-1‚M-1 kA ) ozone self-decomposition rate constant at pH 2.6, min-1
KAo ) frequency factor of kA, min-1 kB ) ozone self-decomposition rate constant at pH 7, min-1‚M-1 KBo ) frequency factor of kB, min-1 ki ) reaction rate constant in eq 1, min-1 k′i ) reaction rate constant in eq 2, min-1‚M-1 kL,O3a ) ozone volumetric mass-transfer coefficient in water, min-1 kL,O2a ) oxygen volumetric mass-transfer coefficient in water, min-1 kT ) kB[OH-]0.5, min-1‚M-0.5 N ) agitation speed, min-1 NFr ) Froude number ) N2Di/g NQG ) gas flow number ) Qg/NDi3 Np ) power number ) P/FN3 Di5 Ns ) agitation speed, s-1 [O3] ) ozone concentration in water, mol‚L-1 [O3]e ) equilibrium ozone concentration in water, mol‚L-1 [O3]0 ) initial ozone concentration in water, mol‚L-1 [O3]* ) calculation by the partial pressure of ozone in the gas phase with Henry’s law, mol‚L-1 [OH-] ) concentration of hydroxide ions, mol‚L-1 P ) power consumption at no gas input condition, kW Pg ) power consumption at gas input condition, kW rO3 ) ozone self-decomposition rate, mol‚L-1‚s-1 t ) time, min T ) temperature, K UG ) superficial gas velocity, m‚h-1 V ) working liquid volume, m3 Vg ) superficial gas velocity, m‚s-1 W ) width of the blade, m ZO3 ) d[O3]/dt + kA([O3]e - [O3]) + kB[OH-]0.5([O3]e1.5 [O3]1.5), mol‚L-1‚min-1
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Received for review February 13, 2001 Revised manuscript received October 11, 2001 Accepted October 15, 2001 IE0101341
