Znd. Eng. Chem. Res. 1995,34, 2258-2271
2258
Oxidation of Sulfur Dioxide in Aqueous Suspensions of Activated Carbon V. M. H. Govindarao* and E(. V. Gopalakrishna Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012, India
Sulfur dioxide in aqueous solutions a t low pH levels exists both in molecular SOz(aq) and in hydrolyzed ionic form HSOa-. Experiments indicate that only HS03- is the reacting species in the oxidation catalyzed by activated carbon, while SOz(aq) deactivates by competing with HS03for the active sites of the catalyst particles. A mechanism is proposed and a rate model is developed that also accounts for the effect of sulfuric acid (product of the oxidation) on the solubility of sulfur dioxide. It predicts first order in HS03-, half order in dissolved oxygen, and a linear deactivation effect of SOz(aq), which are confirmed by experimental data. The deactivation reaches a constant level corresponding to saturation of the active sites by SOAaq). Activation energy for the oxidation is 93.55 kJ mol-l and for deactivation is 21.4 kJ mol-l.
Introduction Sulfur dioxide emissions, particularly from fossil-fuelfired power plants, can be effectively controlled by oxidation in aqueous phase. The oxidation produces sulfuric acid which when recovered, being an important industrial chemical, might make the desulfurization process for pollution control even profitable. Activated carbon is reported to be an important catalyst for the aqueous phase oxidation (Hartman and Coughlin, 1972; Seaburn and Engel, 1973; Komiyama and Smith, 1975a, 1975b; Brodzinsky et al., 1980; Pavko et al., 1981; Recasens et al., 1984; Ahn et al., 1985;Goto and Kojima, 1985; Amadeo et al., 1989; Fu et al., 1989; Lu et al., 1990). These reports have described rate models by considering that dissolved molecular sulfur dioxide (SOz(aq))gets oxidized. However, in these oxidation systems the pH is always below 4 and it is k n o w n that in such systems SO2 in aqueous solutions exists in both molecular form SOz(aq) and ionic form HS03-, and that the presence of sulfuric acid in the solution has a significant effect on the dissolution (Johnstone and Leppla, 1934; Hartman and Coughlin, 1972; Barrie, 1978; Beilke and Gravenhorst, 1978; Hunger et al., 1990; Govindarao and Gopalakrishna, 1993). As will be seen later, experiments in the present work clearly indicate that the only possible reactant for the aqueous phase oxidation is HS03- and SOz(aq) is not only a nonreactant but has deactivating effect on the catalytic oxidation. The purpose of the present work is t o develop and experimentally evaluate a rate model for the activated carbon catalyzed aqueous phase oxidation of sulfur dioxide based on a proposed mechanism. The model also takes into account the effect of sulfuric acid (produced in the reaction) on the solubility of SOz. Investigations are carried out at low partial pressures of SO:!, so that the data and the rate model are of direct relevance t o desulfurization of flue gases.
Experimental Section Apparatus. The experimental setup and the materials used in the oxidation experiments are same as those reported in Govindarao and Gopalakrishna (1993). Additional provisions are made to provide for supply of air. The air is metered (and mixed with inlet nitrogen, if so desired) before bubbling through the reactor. The ~~
* Author to whom correspondence should be addressed.
activated carbon catalyst particles are obtained from Ws. E. Merck (India) Ltd. These particles are sieved to get three mean sizes, namely, 49, 90, and 250 pm. Mainly particles of 250 pm mean size are employed in the present investigations. Particles of the other two sizes are used for evaluating the effects of internal diffusion. The methods of sampling and analysis and the experimental procedure are modified as explained below to suit the present reaction experiments. Sampling and Analysis. Air (or its mixture with nitrogen) is combined with SO:! and bubbled through the reactor. Flow rates of air and sulfur dioxide are measured separately through suitably calibrated orificetype flowmeters. The gases are mixed in predetermined proportions to get desired concentrations of oxygen and sulfur dioxide in the inlet gas. Liquid samples are analyzed for both total dissolved S(IV)(consisting of SOz(aq) and HSOa-) and total S(VI) (consisting of HzSO4 and S 0 2 - ) by the following two-step procedure. First, the concentration of the total S(IV)in a portion of the sample is measured by iodimetry as described in Govindarao and Gopalakrishna (1993). The other portion of the sample is treated with a k n o w n volume of H z 0 ~solution (2% w/v), whereby all the S(IV)in the sample gets converted to S(VI). The total quantity of S(VI)in the treated sample is then estimated by means of a suitably calibrated conductivity analyzer. The product S(VI) formed during the reaction is then obtained from the difference between the observed total S(VI)and the total S(IV). The difference between the concentrations of total S(IV) and SO:!(aq) (computed from C,so$T/H) gives the concentration of HS03- in the liquid phase. It may be noted that in the above analytical procedure the oxidizing agents used (namely, iodine and hydrogen peroxide) are 2-equiv type. Such agents almost invariably give sulfate as the only product, and any dithionate formed is negligible (Jolly, 1989). The estimation methods (carried out with all necessary precautions) are therefore considered to give accurate results. This has been verified by using synthetic samples of sodium sulfite and sulfurous acid. Procedure. Before starting an experiment, the pores of the catalyst particles are first completely filled with water by boiling the catalyst particles in a k n o w n quantity of water for about 1 h. The water along with the catalyst particles is then cooled to the required temperature and transferred to the reactor. In all the
0888-5885/95/2634-2258$09.QQIQ 0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2259 experiments total gas flow rate and agitator speed are set at 0.102 m3/h and 200 rpm, respectively (selected well above the values beyond which these variables do not affect the observed data). The mixture of gases after it attains constant concentration in the inlet is let into the reactor; the reaction is considered to have started a t this point of time. All the experiments are carried out with 1.5 x m3 of liquid and 4.0 x kg of 250 pm size activated carbon particles. The progress of the reaction is monitored by estimating, a t regular intervals of about 10 min, the concentration of SO2 in the exit gas and simultaneously the concentrations of total S(IV) and total S(VI)in the liquid phase. The gas phase concentration is estimated as described in Govindarao and Gopalakrishna (1993) and the liquid phase concentrations are estimated as discussed above. The experiments are carried out well beyond the point at which the exit gas concentration has attained a steady value; this usually takes about 2-4 h.
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80
120
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Time, min
Preliminary Experiments Preliminary experiments under homogeneous conditions (that is, without carbon particles, but with oxygen and sulfur dioxide in the inlet gas) have shown that the oxidation reaction, if any, is negligible. Similarly, experiments with catalyst particles but without oxygen in the inlet gas have also shown no reaction. Material balance calculations on sulfur dioxide in all the catalyzed oxidation reaction experiments have indicated that the total S(IV)and S(VI)contents of the liquid phase account for more than 99% of the SO2 transferred from the gas phase. This not only ensures the reliability of the experiments but shows that adsorption of the species SOz(aq), HS03-, so42-,and/or H2SO4 on the catalyst particles is not strong.
Reacting Species Govindarao and Gopalakrishna (1993) have shown that, a t concentrations of sulfuric acid above 0.37 kmol m-3, sulfur dioxide exists in the solution mainly in the molecular form, SOz(aq); HS03- is negligible. An kmol m-3 experiment is conducted at Cgozi= 8.4 x (air), T = 303 K, and with a solution of sulfuric acid of concentration 0.88 kmol m-3 as the reaction mixture, so that only SOz(aq)is present in the mixture throughout the experiment. Figure 1 shows the results presented as transient profiles of concentration of SO2 in the exit gas and of total S(IV)and total S(VI) in the liquid phase. Also included in the figure are data from experiments conducted under similar conditions but with no oxygen in the inlet gas. The results indicate that the concentration profiles are the same in both experiments (with and without oxygen in the inlet gas) and that the concentration of total S(VI) remains constant at the initial value throughout the experiment. This clearly indicates that there is no oxidation reaction during the experiments and hence that SOa(aq) is not a reacting species. As will be seen later, in all the oxidation experiments in the present work sulfuric acid has formed throughout, and its concentration is always below the above limiting value. Therefore, HSO3- is obviously the main reacting species. One could also expect, as is found in the present work, that the molecular form of dissolved SO2 competes with HSO3for the catalyst sites, thus leading t o a deactivating effect of the SOdaq) on the reaction.
Figure 1. Transient profiles with Cs(w) = 0.88 kmol m-3, T = 303 K, Cgsoll= 6.117 x kmol m-3.
Mechanism and Rate Model At the low pH levels that exist in aqueous phase oxidation systems, the components present in the solution are SOz(aq), HS03-, so42-,and H2S04. There is no S0s2- present at all. Therefore, reaction mechanisms based on s0s2- such as the ones proposed by Fu et al. (1989) are not applicable. Most of the investigations reported in the literature on the mechanism of the aqueous phase oxidation of sulfur dioxide are related to homogeneous catalytic reactions with catalysts such as Cu2+,Mn2+,Co2+etc. (for example, Hegg and Hobbs, 1978;Altwicker, 1979; Pasiuk-Bronikowska and Ziajka, 1989). These mechanisms are usually based on freeradical chain reactions involving the formation of radicals such as so$- and SO5'-. Again, such mechanisms are not applicable in the present system since S032- is not present. Hartman and Coughlin (1972), Komiyama and Smith (1975a), Pavko et al. (1981), Recasens et al. (1984),Ahn et al. (19851, Goto and Kojima (1985) and Amadeo et al. (1989), who have studied the aqueous phase oxidation with activated carbon as catalyst, have expressed the rate by an empirical power-law model in C S O ~ ( ~ ~ ) based on the overall reaction
+
+
S02(aq) (1/2)02(1) H20
- H2S0,(1)
(1)
Seaburn and Engel (1973) have suggested a HougenWatson type model based on the surface reaction between adsorbed sulfur dioxide and dissolved oxygen as the rate-controlling step. However, the discussion under the preliminary experiments in the present work have clearly indicated the complete absence of any oxidation of SOz(aq) under the conditions of interest. Therefore, models such as the above ones based on the reaction of SOz(aq) are also not tenable. On dissolution in water, sulfur dioxide exists in molecular form (SOa(aq))and ionic form (HS03-1. These two components are adsorbed on active sites of the catalyst particles. The adsorbed HS03- gets oxidized
2260 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995
by dissolved oxygen to form Sod2- which further reacts with H+ to give sulfuric acid. Thus, the proposed reaction mechanism involves the following elementary steps: S02(g)= S02(aq)
+ H 2 0 = H+ + HS03S02(aq)+ w =+ o*SO,(aq)
SO,(aq)
a t t = 0,
(2) (3)
(4)
Cgso,= 0 and C,,,, = 0
(14)
1 41 = vg Vl(b3
(15)
where
+
2%
+
-.H++ SO:- + w
w*HS03- (1/2)02
42 = -
(16)
a1 + a2 43 = -
(17)
a3
(6)
a3
where w = an active site on the carbon, w*SOz(aq)= chemisorbed SOz(aq), and weHSO3- = chemisorbed HS03-. The rate of change in the concentration of each of the species can be obtained by writing its mass balance. By assuming steady-state approximation for the chemisorbed intermediates and then eliminating the terms corresponding to the concentration of the intermediates from the mass balance equations, we get for the rate of formation of the total S(VI)
RTM,
a, = H
a4=1where
k,, = krC1n02
(9)
The kinetic rate model, eq 8, shows that the order is 1 in HS03- and 1/2 in dissolved oxygen. The term [ l ~ C S O , (indicates ~ ~ ) ] the deactivating effect of the concentration of SOdaq) due t o its chemisorption on the active sites of the catalyst, thereby reducing the number of active sites available for HS03-, the main reactant. That HSO3- is the reactant and SOdaq) has a deactivating effect are the two main features of the proposed rate mechanism and model. When the external and internal mass transfer effects become insignificant (as is found in the present work), writing the mass balance for SO2 in the reactor, and combining with eq 8 for the kinetics of the reaction and with the following solubility equation (eq 10 of Govindarao and Gopalakrishna (1993); rewritten in the present notation),
where
we get
a52 %+a:
(21)
(22)
(23) In this rate model kr and a are the two unknown parameters. They are estimated from the experimental data by using Marquardt's nonlinear parameter estimation procedure wherein the solution of the nonlinear differential eq 13 is obtained by fourth-order RungeKutta method.
Results and Discussion Experiments are conducted a t various levels of the operating variables in the range inlet concentration of sulfur dioxide 7.86 x to 115.2 x kmol mW3, inlet concentration of oxygen 2.0 x 10-3 to 8.4 x 10-3 kmol m-3, and temperature 303 to 353 K. Figures 2-10 give the observed transient profiles in concentration of SO2 in the exit gas phase, and of HS03- and total S(VI) in the liquid phase. The Appendix contains an analysis which shows that the effects of external and internal mass transfer are negligible. Therefore, the rate model described by eq 13 can be directly applied t o the data. In all the experiments the transient profiles of concentration of SO2 in the gas phase (and hence CSO,(aq) in the liquid phase) show a gradual rise in the initial stage and then a fairly constant value. The steady value
Ind. Eng. Chem. Res., Vol. 34,No. 7,1995 2261
,
is due to the following reasons. As the concentration of the product S(VI)in the liquid phase increases, the solubility of SO2 decreases (Hartman and Coughlin, 10.0 1972; Govindarao and Gopalakrishna, 1993), and therefore the concentration of S(IV)decreases. As discussed 8.0 under Mechanism and Rate Model, HSO3- is the main reactant in the oxidation, while SOz(aq)is a nonreacting species. Hence, the concentration of HS03- falls as the 6.0 reaction proceeds even as Cgso2remains steady. We call this region beyond which the gas phase concentration 4.0 of SO2 attains a constant value, but the concentrations of total S ( N )and total S(VI)in the liquid phase are still varying, the pseudo-steady-state region. Since the 2.0 concentration of the product S(VI) increases as the reaction proceeds, it may be expected (though not 0.0 observed in the present experiments) that, at suf0 40 80 120 160 200 240 280 320 360 ficiently large values of this concentration, Cgsozbegins Time, min to gradually increase and attain a value equal to Cgsozi. At this point there will be no HS03- in the liquid phase (because of high values of CSCVI,) and hence no further oxidation, thus leading to a constant value of Csp,q,. The concentration profiles of HS03- and S(VI)also indicate that in the pseudo-steady-stateregion the reaction rate decreases with time. Therefore, the analysis of the + 2b x 2c * 8.96 2a oxidation experiments adopted by earlier workers (Hartman and Coughlin, 1972; Komiyama and Smith, 1975a; * 3b 0 3c @ 3a 13.5 Pavko et al., 1981; Recasens et al., 1984; Ahn et al., 1985; Goto and Kojima, 1985;Amadeo et al., 1989),who Figure 2. Transient profiles in aqueous phase oxidation of sulfur considered constant rate based on the steady-statevalue dioxide a t T = 303 K,Cp,i = 8.4 x kmol m-3, and at different of Cgsoz,does not appear tenable. inlet concentrations of SOz; curves represent solution of eq 13. The transient data on the concentration of total S(VI) are used to estimate the kinetic parameters k, and a. is always less than the concentration in the inlet, thus The estimation leads not only to the values of the two showing that reaction continues beyond this point also. However, in this region, the concentration of S(W) in parameters but also to the predictions of prpfiles of the the liquid phase continues to increase and that of HS03concentration of sulfur dioxide in the gas phase and of (and therefore, of total S(IV))falls. The fall in CHSO~- HS03- in the liquid phase. As will be seen later, the 12.0
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333
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2c
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*
2262 Ind. Eng.Chem. Res., Vol. 34, No. 7, 1995 25.0
Pseudo-steady state Considerations
20.0
For a given experiment, after Cgsoz (and therefore Csoz(aq))attains a steady value, eq 8 becomes
Fl
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n
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.--
(24)
0
where
-
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P
and
=
ar0u- aCSOz(aq))
a,, = arcoz
0
112
0
40
80
120 160 200 240 280 320 360
Time, min cnso-
24.60
Figure 4. Transient profiles in aqueous phase oxidation of sulfur kmol m-3, and at different dioxide at T = 303 K, Cp0,i = 8.4 x inlet concentrations of S02; curves la-c represent solution of eq 13 and curves 2a-c represent solution of eq 32.
closeness of these predicted profiles to the experimental data is used in judging the adequacy of the rate model and the estimated parameters. The algorithm requires initial guesses for the two parameters k r and a. These are obtained from the pseudo-steady-state considerations discussed in the next section.
24.0
48.0
I
t
E 32.0
L5 2.0
E:
**
40.0
(26)
The overbar on the parameters and variables in the above equations (and others to follow)indicates that the particular parameter or variable is evaluated for (or corresponds to) the data in the pseudo-steady-state region. Figure 11 gives plots of observed rate versus &so3in the pseudo-steady-state region for different levels of Cgsozi at Cazi = 8.4 x kmol m-3 and T = 353 K. The rates are estimated from Cs(v11versus time data in this region (see Figures 3,5,8,and 10). The plots show that the linear dependence of the rate on concentration of HS03- predicted by eq 24 is valid. The curves for Cgsozi I61.1 x m-3 (curves 3, 4,and 5 in Figure 11)have the same slope; indeed, the three lines form an extension of each other, thus showing that the apparent rate constant in these experiments is independent of CflOzi (and therefore Csoz(aq)), unlike at lower levels of C@ozi. This behavior is analyzed later. Similar observations are made from the data from experiments at other temperatures and other levels of CaZialso (the plots are not reported here).
56.0
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r' I
0
40
I BO
I
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1 1 I I I 1 1 I [ I I 110.0 120 160 200 240 280 320 360
Time
10.0
mir,
353
Figure 6. Transient profiles in aqueous phase oxidation of sulfur dioxide at C&oli = 24.60 x and at different temperatures; curves represent solution of eq 32.
kmol m-3, Cp0*i= 8.4 x
kmol m-3,
Ind. Eng. Chem. Res., Vol. 34,No. 7, 1995 2263 70.0
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Time, min
2.0
la
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lb
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4.0
2a
+
2b
x
2c
*
6.0
Figure 6, Transien profiles in aqueous phase oxidation of sulfur dioxide at T = 303 K,C@o,i = 61.17 x inlet concentrations of 0 2 ; curves represent solution of eq 32. 70.0 60.0 50.0 40.0
30.0 20.0 10.0
0.0
0
40
80
120 160 200 240 280 320 360
Time, min
1
42.78 61.17
1
303 318
1 1 1 1 1 1 I la
0
lb
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2a
+
Zb
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2c
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I I I I I I I I Figure 7. Transient profiles in aqueous phase oxidation of sulfur kmol m-3 and at different inlet dioxide at Cflzi = 8.4 x concentrations of SO2 and temperatures;curves represent solution of eq 32.
The values of the apparent rate constant &,a estimated by least squares fit of the experimental data on the rate in pseudo-steady-state region from all the experiments at different levels of temperature, Cgsozi, and C@zi are
..mol m-3, and at different
listed in Table 1. Figures 12,13, and 14 show plots of against Csoz{aq)for the three temperatures 303,333, and 353 K,respectively, and a t C@zi = 8.4 x kmol m-3. The plots indicate that the rate constant falls linearly at low values of CSOz(aq) and attains a constant value as CSOz(aq) increases beyond a limiting value, thus leading t o a simple two-line type representation as shown in these figures. Since the values of CSOz(aq) used in the plots are from separate experiments, we may consider that the effect shown in the plots correspond in general to values of Csoz(aq),both under pseudosteady-state and dynamic conditions. That the conclusions drawn under pseudo-steady-state apply t o the transient region also is shown a t a latter point. This observed strong linear deactivating effect of CSOz(aq) at low values on the rate constant agrees with the predictions of the proposed model. The nonreactant molecular SOz(aq)gets adsorbed on the active carbon, thereby reducing the number of the active sites available for the reacting species HS03-. The observed decrease in the rate constant with CSOz(aq) cannot be explained by simply considering the effect of sulfuric acid on the solubility of S02. The model, anyway, already takes this into account, as expressed by eq 11. Apparently, the active carbon becomes saturated with and hence SOn(aq) beyond a certain value of Csoz(aq), there is no further effect of CSOz(aq) after this value; this corresponds to the horizontal part of the curves in Figures 12-14. At or beyond the saturation concentrait may be considered that catalyst sites tion Cgo occupiediy SOz(aq)are a constant fraction 8 of the total
2264 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 70.0 60.0
,I
- 7.5
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x,
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80
120 160 200 240 280 320 360
Time, min
Figure 8. Transient profiles in aqueous phase oxidation of sulfur dioxide at Cflo,i = 61.17 and at different temperatures; curves represent solution of eq 32.
sites, which is independent of SOdaq). For this condition the mechanism eqs 2-7 lead to R*A
= kr#cHS03-
(27)
= k:aCHS03-
(28)
where
By comparison with eq 8, we have
x
kmol m-3, C@*i= 8.4 x loT3kmol m-3,
p
eq 25. At each of the three temperatures is estimated (by using eq 34)from the apparent rate constant of the horizontal part of the curve in Figures 12-14 (data reported i? column 7 of Table 2) and the corresponding estimate kro. The estimates are listed in _columns3-5 of Table 2. The three quantities Cgo2bq)., kro, and a depend strongly on temperature while is independent and equal to 0.27. The value of j3 calculated from B and by eq 33 for each of the temperatures is also found to be very close to 0.27, thus confirming the constancy of the deactivation effect in the saturation region. The effect of temperature on ti is shown in Figure 16. The data show an Arrhenius equation-type dependency of ti on temperature. The activation energy is estimated after considering the data in the transient region also, as will be discussed later. From eqs 26 and 33, we note that Aro and are boJh independent of CSOz(ae Therefore, their product, k:, is also in.ependent_of CSOz(aq), thus leading to the same curves a t high levels of Cgsozi slope of RAversus (261.17 x kmol m-3) and for a given temperature, as seen from curves 3-5 in Figure 11. Figure 17 shows the plot of kro versus Cozon log-log coordinates at 303 K. The least squares estimate of the slope of the line is 0.49, which is very close to 0.5, the value predicted by eq 26. The line in Figure 17 is indeed the one drawn with the slope of 0.5, and is seen to represent the experimental data very well. For the experiment at 318 K conducted a t a single value of Cgsozi, namely, 61.17 x kmol m-3, curve 2a of Figure 7 show? that Cgso, is 57.5 x kmol m-3. The corresponding CSoz(aq) is 9.28 x kmol m-3. This value is considerably higher than Cgo,(aq)at even 303 K, and therefore, the pseudo-steady-state reson of the experiment at 316 K should be in the horizontal portion of the kra versus C S O ~ (plot. ~ ( L )Therefore, eqs 33 and 34 apply. The values of C&,zO,(aqj and a t 318 K are read
B
The intersection of the horizontal line _and the linear line (in Figures 12-14) gives the limit Cgoz(aq) (for the given temperature). The limiting values are listed in column 2 of Table 2. -Figure 15 gives a plot of the effect of temperature on C~oo2(a4j. The data show a linear dependency of the limiting value on temperature. The intercept and slope of the nonhorizontal lines in Figures 12-14 are estimated by linear least squares method, and kro and B are estimated from them by using
Ind. Eng. Chem. Res., Vol. 34, No. 7,1995 2266 120.0
,
,
c)
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Time, min C,SO,~Xlo6 Temperature
I
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C,S, Cnso; Cs(vr) curve symbol curve symbol curve symbol
kmol m-3
K
82.73
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2a
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Figure 10. Transient profiles in aqueous phase oxidation of sulfur dioxide at T = 353 K, C,,, = 8.4 x kmol m-3, and at different inlet concentrations of SOz; curves represent solution of eq 32.
from- the graphs in Figures 15 and 16, respectively, to get Cgo,(a = 5.57 x kmol m-3 and a = 130.56 m3 kmol-'. &om these tw_o values, and using eq 33, we get a value of 0.272 for /?,which is remarkably close to the value of 0.27 found for the experiments at the other three temperatures (see column 5 of Table 2). This
For the experiments at low Cgsozi (at different temperatures and different inlet oxygen concentrations) it i_s found that C S O ~at( ~any ~ ) time is always less than C30,(a at the corresponding temperature. It is assume2 that this limiting value for pseudo-steady-state region holds good in the transient region also. For each experiment the rate constant k, and the deactivation constant a in the rate model (eq 13) are estimated from CS(VI)versus time data by the algorithm discussed earlier using the above determined values for the initial guesses. Table 3 lists the estimated values for the different sets of experiments. The curves in Figures 2, 3, and 5 and curves la-c in Figure 4 represent the predictions of the rate model with these estimates. As seen from the figure, the agreement with the experimental data for the entire range of variables studied is excellent. A
2266 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 4.0
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0
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50.0 60'o
40.0
c
Figure 11. Observed rate versus concentration of HSOa- in the pseudo-steady-state region at T = 353, Cf12i = 8.4 x kmol m-3, and at different levels of inlet concentration of sulfur dioxide. Table 1. Apparent Rate Constant in the Pseudo-SteadystateRegion at Different Temperatures and Different Concentrations of Sulfur Dioxide and Oxygen in the Inlet Gas
lo5
303 303 303 303 303 303 303 303 303 303 303 318 333 333 333 333 333 353 353 353 353 353
7.86 8.96 13.56 17.88 24.60 42.78 61.17 61.17 61.17 61.17 82.73 61.17 8.96 24.60 61.17 90.20 115.20 8.96 24.60 61.17 90.20 115.20
15.0
20.0
2!
.o
xl 03, kmol m-3
cflzix 103 (kmol m-3) 8.4 8.4 8.4 8.4 8.4 8.4 2.0 4.0 6.0 8.4 8.4 8.4 8.4 8.4 8.4 8.4 8.4 8.4 8.4 8.4 8.4 8.4
h -
m
t
(kmol m-3)
10.0
Figure 12. Effect of concentration of dissolved molecular sulfur dioxide on apparent rate constant in the pseudo-steady-state kmol m-3. region at T = 303 K and Cgozi = 8.4 x
I
Cgs02i x
Csol(,)
-
(K)
5.0
kmol m-'
ijziiii
temp
1 ~
E,,
104 (S-1)
2.59 2.40 2.36 2.16 0.98 0.94 0.46 0.58 0.72 0.95 0.97 4.47 46.83 33.70 14.17 14.20 14.18 541.48 375.00 144.23 144.20 144.21
particular point t o be noted is that the algorithm estimates the kinetic parameters using only C m )versus time data from the experiments and predicts the Cgso2 and CHSO~profiles. The close agreement between the model predictions and the experimental data corre-
-
0 30.0 7
X
-
0
I3 ' 20.0 -
-
j l
0.0 0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8
3
Figure 13. Effect of concentration of dissolved molecular sulfur dioxide on apparent rate constant in the pseudo-steady-state kmol m-3. region at T = 333 K and CflZ, = 8.4 x
sponding t o these two profiles particularly signifies the adequacy of the proposed rate model (and, therefore, the mechanism) and the accuracy of the estimated parameters. A comparison of the estimated values of k , and a (columns 4 and 5 of Table 3) with those estimated from the data of the corresponding pseudo-steady-state region (columns 6 and 4 of Table 2) shows close agreement between the two values. It may therefore be concluded that the deactivation effects of CSOz(aq) discussed above in connection with the pseudo-steady-state region also hold good in the transient region. The data of Table 3 indicate that the estimated values of a are independent of Cgso2i and Co2and depend only on temperature. For the experiments with high Cgso2ithe observed data indicate that Cso2(aq)at any time (except perhaps a t the very start) is always greater than CgOz(aq) for the corresponding temperature (listed in column 2 of Table
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2267 600
I
500
-
1
:
loo0
-
c
1-
400 -
0
E
-
Y
300 -
100
200
-
0 ; 0.0
1
1
1
1
1.0
1
2.0
I
,
3.0
1 1
10
1
4.0
1
I
I
I
I
2.75
2.50
5.0
I/T
3. '0
x103, K-'
1
8.0
I
3.25
Figure 16. Effect of temperature on ti in the pseudo-steady-state region.
Figure 14. Effect of concentration of dissolved molecular sulfur dioxide on apparent rate constant in the pseudo-steady-state kmol m-3. region at T = 353 K and Cf12i = 8.4 x 10.0
I
I
3.00
-
6.0 -
4.0
Line is with slope = 0.5
-
2.0
10-a
2.5
2.9
3.3
3.7
T xlO-*,
4.1
/
I 4
I
s
1
I I
7
1 1
1 1
I '
I
I
I
3
4
10
4.5
Co, , kmol m-3
K
Figure 17. Rate constant ,A, versus concentration of dissolved kmol m4. oxygen at T = 303 K and C,so,i = 61.17 x
Figure 15. Effect of temperature on limiting value of concentration of SOz(aq) in the pseudo-steady-stateregion.
Co,but with low CgsOzi (therefore low CS02(aq)) hold good for high levels of Cgsozi also. Therefore, using these values of kro and the estimated ki, vlues, p for high Cgso2iexperiments are calculated from eq 30 and are also included in Table 3. The data indicate that p is independent of temperature and C&ozi. It is the same as that estimated for the data of the pseudo-steady-state region. The observed value of 0.27 for /3 is thus valid for the entire range of the variables investigated. The value also suggests that if the deactivation due to SOz(aq) is not taken into account (at high Cgso2i),the measured rate constant would be about 4 times lower than the true intrinsic value.
2). It is therefore expected that the rate data from these experiments may be better represented by eq 27. Values of k:, are estimated for all these experimental data and are listed in Table 3. A comparison of the value of k:, (column 6 of Table 3) with that estimated from the data in pseudo-steady-state region (column 7 of Table 2) a t each of the temperatures shows close agreement. Since Kro, as seen from eq 9, depends upon temperature and concentration of the dissolved oxygen and is independent of C S O ~ (the , ~ )values , of k r o computed for a given temperature from the estimated value of k, and
Table 2. Parameters Estimated from Data in Pseudo-Steadystate Region at Different TemDeratures ~
temp
C/TO,(~ 103
(K)
(kmo? m-3) 7.44 3.75 2.25
303 333 353
R,
x
104
(8-1)
3.22 53.07 565.65
a (m3kmol-') 98.10 194.60 324.43
B 0.27 0.27 0.27
R,
102 ((m3km01)1/2s-l) 2.06 38.97 434.08 x
k;,
x 104
(s-1)
0.87 14.33 152.72
2268 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 Table 3. Estimated Values of Intrinsic Rate Constant k, (or kiJ and Deactivation Constant a (or/?) at Different TemDeratures and Different Concentrations of Sulfur Dioxide and Oxygen in the Inlet Gas temp CBsoplx lo5 Cgop,x lo3 It, x lo2 a k:, x IO4 C ~ (aO x IO3 (K) (kmol m-3) (kmol m-3) ((m3kmol)1'2s-l) (m3kmol-I) (s-1) B (k&o\ m-3) curves/Figure 7.44 lad2 98.00 303 7.86 8.4 2.05 7.44 2a-cf2 2.06 98.10 8.4 303 8.96 7.45 3a-c/2 97.92 2.06 8.4 303 13.56 la-cI4 7.45 2.05 97.90 8.4 303 17.88 2a-c/4 0.87 0.27 8.4 303 24.60 0.27 la-c/7 0.87 8.4 303 42.78 0.27 la-cf6 0.87 2.0 303 61.17 2a-cf6 0.87 0.27 4.0 303 61.17 0.27 3a-c/6 0.88 6.0 303 61.17 4a-c/6 0.87 0.27 8.4 303 61.17 0.27 la-cf9 0.88 8.4 303 82.73 2a-cI7 5.57 4.13 0.27 11.30 130.89 8.4 318 61.17 3.76 la-c/3 194.14 38.75 8.4 333 8.96 3.75 la-c/5 38.97 194.50 8.4 333 24.60 la-c/8 14.32 0.27 8.4 333 61.17 14.31 0.27 2a-cf9 8.4 333 90.20 14.32 0.27 3a-cf9 8.4 333 115.20 2.25 2a-c/3 434.17 324.43 8.4 353 8.96 324.21 2.25 2a-c/5 434.20 8.4 353 24.60 2a-cf8 152.60 0.27 8.4 353 61.17 0.27 1a -c/lO 152.75 8.4 353 90.20 2a-cf10 152.55 0.27 8.4 353 115.20 ~~~
~
~~
Since both a and are indepenLmt of Cgsozi, us..ig values of a estimated from experiments a t lower levels of Cgsoziat a given temperature and the above calculated values of p, Cgo2(aq)is calculated from eq 31. The values are listed in column 8 of Table 3. A comparison of these values with the values estimated from pseudosteady-state data at the corresponding temperature (column 2 of Table 2) shows that they agree closely with each other, thus confirming the validity of_the assumpt o the tion about the applicability of the limit C,2jo'0,(aq) transient data. The constancy of the limiting value (CgO,(aq)) and also the closeness with which the experimental data is predicted by eq 32 (as seen from the curves 2a-c in Figure 4 and all the curves in Figures 7-10) demonstrate that the rates at high levels of CSOz(aq) are independent of this concentration and thus also confirm the validity of the saturation limit for the deactivation. Using p = 0.27 for the experiment at 318 K, and the estimated value of Kia, the rate constant 12, at this temperature is obtained. Similarly, using C,2jop(aq) at 318 K from Figure 15, the value of a a t 318 K is also obtained. These are also included in Table 3. The predictions of the model are compared with the experimental data at this temperature in curves 2a-c in Figure 7. A close agreement is seen here also. The observed independence of the rates on CSOdaq) at fairly high concentrations of sulfur dioxide in the gas phase reported by Seaburn and Engel (19731, Komiyama and Smith (1975a,b), Pavko et al. (19811, Recasens et al. (1984), Ahn et al. (1985), Amadeo et al. (19891, and Fu et al. (1989) can perhaps be as well explained by the rate model proposed here, where SOn(aq) is not a reactant at all but competes for the active sites on the catalyst. Thus, the rate model given by eqs 13 and 32 along with the estimated parameters is found to be adequate to represent the aqueous phase oxidation of sulfur dioxide with active carbon as catalyst in the range of the variables studied. The kinetics of the oxidation in the transient as well as pseudo-steady-state regions are characterized by half order in oxygen, first order in HS03-, and linear or constant deactivating effects of the concentration of SOz(aq).
10
r
I
m
2=
1
Y
\
n
E
Y '
' O - 4
lo-'
I
I
2.50
1
I
2.75
I
I
I
3.00
3.25
1 /T x i 03,
\
I
3 0
K-'
Figure 18. Effect of temperature on intrinsic rate constant.
Activation Energies Table 3 gives the estimated values of the constants kr and a a t different temperatures. Plots of K r versus 1/T and a versus 1/T on semilog coordinates are shown in Figures 18 and 19, respectively. The plots show a linear trend, thus suggesting Arrhenius equation-type dependency on the temperature. These can be expressed as (with least squares estimates of the constants)
K , = 2.19
x
a = 4.54 x
1014exp
25T74)
io5 exp(- -
(36)
The activation energies estimated from the slopes of the plots are
E, = 93.55 k J mol-'
E, = 21.4 k J mol-'
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2269 u5 = defined by
1000
eq 22
= defined by eq 23 U b = gas-liquid interfacial areas, m-l up= particle external surface area per unit weight, m2kg-l a6
n
E
100
10
1
I
1
2.50
I
2.75
I/T
I
I
3.00
I
3.25
I
3.50
x103, K-'
Figure 19. Effect of temperature on deactivation constant, a. The low value of the activation energy for the deactivation suggests a weak dependency of the deactivation on temperature. This may be expected since, as discussed earlier, the adsorption of the SOz(aq)in the liquid phase on carbon is not strong. The estimated value of E, is relatively high compared to the values reported in the literature (Brodzinsky et al., 1980;Pavko et al., 1981; Recasens et al., 1984)which fall in the range 10-50 kJ mol-l. It should be noted, however, that the reported values are estimated from models which do not (i) take the deactivation effect of SOa(aq) into consideration, (ii) account for the effects of sulfuric acid and temperature on the solubility, and (iii) consider the oxidation of HS03-.
Con,clusions Oxidation of sulfur dioxide in suspensions of activated carbon in water is analyzed rigorously and evaluated experimentally. The observed data show that the external and internal mass transfer effects are not significant and, therefore, the overall rates are kinetically controlled. A mechanism is proposed and a rate model is derived from it based on chemisorption of SOdaq) and HS03on the active carbon and the reaction of the chemisorbed HSO3- with dissolved oxygen. The model with the estimated parameters predicts the experimental data very closely. The oxidation is thus observed t o be first order in HS03- and half order in dissolved oxygen. Concentration of SOz(aq)has a deactivating effect which is linear at lower levels of the concentration and attains a limiting value as the concentration increases. The limiting value is about 0.27 and is found t o be independent of temperature. The nonreactant SOz(aq)competes with HS03- for chemisorption on the active sites of the carbon particles thus leading to deactivation. The activation energy for the reaction is 93.55 k J mol-I and for the deactivation is 21.4 kJ mol-I.
C6.j = concentration of 0 2 in inlet gas, kmol m-3 Cgsoz= concentration of SO2 in exit gas, kmol m-3 Cgsozi= concentration of SO2 in inlet gas, kmol m-3 = concentration of HS03-, kmol m-3 CO, = concentration of dissolved 02,kmol m4 Cs(w)= concentration of S(IV)in bulk liquid, kmol m-3 Cgirv)= equilibrium concentration of S(IV) at gas-liquid interface, kmol m-3 Cs(m)= concentration of S(VI) in bulk liquid, kmol m-3 CSO~(,~) = concentration of SOz(aq),kmol m-3 CgoO,(aq) = limiting concentration of SOz(aq),kmol m-3 db = mean bubble diameter, m d, = diameter of particles, m dT = diameter of reactor, m D = diffisivity of SO2 in gas phase, m2 s-l D, = diffusion coefficient of sulfur dioxide in aqueous systems, m2 s-l E, = activation energy for reaction, kJ mol-' E , = activation energy for deactivation, kJ mol-' g = gravitational constant, m s-2 g, = conversion factor, kg m N-' s - ~ H = Henry's law constant, Pa (mole fraction)-1 K;' = equilibrium constant of hydrolysis of SOz(aq),kmol m-3 K2= equilibrium constant of dissociation of H2S04, kmo12 m-6 kab = backward rate constant of reaction eq 4 kaf = forward rate constant of reaction eq 4 k , = gas-side mass transfer coefficient, m s-l kL = liquid-side mass transfer coefficient, m s-l &, = intrinsic rate constant (m3/km01)1/2s-1 k,, = apparent rate constant, evaluated in pseudo-steadystate region, s-l ki, = apparent rate constant, defined by eq 30 k , = defined by eq 9 k , = liquid-solid mass transfer coefficient, m s-1 Mt = total molarity, kmol m-3 N = stirrer speed, s-l N g = rate of mass transfer in gas phase, kmol m-3 s-l Ng-l = rate of mass transfer across gas-liquid interface, kmol m-3 s-1 N I -= ~ rate of mass transfer across liquid-solid interface, kmol m-3 s-1 PG = power delivered by impeller with gas flow, N m s-l PsoZ= partial pressure of SO2 in bulk gas, Pa Pgoz = equilibrium partial pressure of SO2 at interface, Pa Q = volumetric flow rate of gas, m3 s-1 R = gas constant, 8314.73 m3 Pa kmol-I K-' RA = rate of reaction, kmol m-3 s-l RZ = rate of reaction in saturation region, kmol m-3 s-1 us = superficial gas velocity, m s-1 V, = volume of gas in reactor, m3 VI = volume of liquid in reactor, m3 t = time, s T = temperature, K w = concentration of particles in reactor, kg m-3 W = defined by eq 12 Greek Letters a = deactivation constant, defined by eq 10, m3 kmol-I ,8 = deactivation constant in saturation range E,
Nomenclature a1 = defined by a2 = defined by a3 = defined by a4 = defined by
eq 18 eq 19 eq 20 eq 21
= fractional gas holdup
8 = fraction of active sites occupied by SOdaq) p, = viscosity of gas, kg m-l s-l p1 = viscosity of liquid, kg m-l s-l Q, = density of gas, kg m-3 81 = density of liquid, kg m-3 ~7= surface tension, N
2270 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 = defined by eq 15 42 = defined by eq 16 4 3 = defined by eq 17 w = active site
(42) The mass transfer coefficient KL is estimated from the correlation of Calderbank and Moo-Young (1961):
Appendix
k External Mass Transfer. The significance or otherwise of mass transfer effects is verified by comparing the maximum value of the observed rate with the rates of mass transfer in the gas phase and across the gas-liquid and liquid-solid interfaces, if each of these steps were to control the overall absorption completely. For a typical experiment at T = 303 K, Cgsozi = 7.86 x kmol m-3, and Cflzi = 8.4 x kmol m-3, the observed rate, say at 45 min, is 3.2 x kmol m-3 s-l (calculated from the data of curve IC of Figure 2). Diffusion in Gas Phase. The transfer rate within the gas phase is given by (37) If the rate of absorption of sulfur dioxide were completely controlled by diffusion within the gas phase, then Pgo would approach zero. f i e gas-side mass transfer coefficient, k,, is estimated from the equation (Schaftlein and Russel, 1968) kg = ( h J d b ) " 2
(38)
The diffisivity D of sulfur dioxide in gas phase is calculated from the Wilke-Lee correlation (Treybal, 1982) as 1.84 x m2 s-l. The superficial gas velocity is 5.97 x m s-l. Fractional gas holdup 6, is measured to be 3.0 x by observing the increase in the height of the liquid column in the reactor when gas is bubbled through. The mean bubble diameter d b is estimated to be 1.89 x m by using the following correlation (Treybal, 1982):
where PGis estimated to be 1.06 x N m s-l as per the method suggested by Treybal (1982). For these values, kg from eq 38 is 2.41 x m s-l. The gasliquid interfacial area per unit volume of the dispersion is given by ab
= 66ddb
(40)
and for the experimental conditions under consideration is equal t o 95.24 m-l. Then, the rate of diffusion within the gas phase is obtained from eq 37 as 1.15 x kmol m-3 s-l. This is about 350 times higher than the observed rate, and hence, the effect of diffision within the gas phase may be neglected. Mass Transfer across the Gas-Liquid Interface. The rate of mass transfer across gas-liquid interface is given by Ng-l
= kL'b(c&IV)
- cS(IV))
(41)
where C&IV,is the equilibrium concentration at the interface. If the rate given by eq 41 were to completely control the overall rate, then CSCIV, would approach zero and eq 41 becomes
For the typical experiment under consideration, kmol m-3. The diffusion coefficient of sulfur dioxide Da in aqueous systems at 303 K is 2.0 x m2 s-l (Hikita et al., 1978). The liquidside mass transfer coefficient is thus estimated from eq 43 to be 4.12 x m s-l. The rate of mass transfer across the gas-liquid interface is now calculated from eq 42 as 1.28 x kmol m-3 s-l. The calculated rate is thus about 400 times greater than the observed rate. This value is large enough for the effects of gas-liquid mass transfer to be neglected even if some of the parameters used in the calculations are somewhat in error. Mass Transfer across the Liquid-Solid Interface. The mass transfer rate across the liquid-solid interface, if this step were to control the overall rate, is given by
CziIV)= 2.25 x
Nl-s
= ksapwCS(Iv)
(44)
where the largest value of the gradient across the interface is considered. The coefficient k, is estimated to be 1.4 x m s-l for the conditions of the experiment by using the following correlation proposed by Boon-Long et al. (1978). -0.011
The particle external surface area per unit weight a,, is given by 6/(dgp)and is equal to 30 m2 kg-' for the 250 pm carbon particles used. The catalyst loading w used is 2.67 kg m-3. The estimated value of is therefore 3.65 x kmol m-3 s-l. This is about 114 times greater than the observed rate. Therefore, effects of transfer across the liquid-solid interface are also negligible. Thus, the effects of all the three external mass transfer processes may be considered negligible. A similar conclusion is drawn for all the experiments a t the other conditions of interest in the present work. B. Internal Diffusion. Experiments are conducted with two other mean sizes of the carbon particles, namely, 49 and 90 pm, a t the typical operating conditions T = 303 K, CgS0,i = 7.86 x kmol m-3, and CNzi = 8.4 x kmol m-3. These results along with those for 250 pm size particles (at the same conditions of operation and replotted from curves la-c of Figure 2) are shown in Figure 20. The data indicate that a 5-fold change in the particle size does not have any significant effect on the transient profiles, thus showing that internal diffision effects are likely to be insignificant. In all further experiments particles of mean size 250 pm are used. The profiles of the normalized concentration of total S(IV),oxygen, and total S(VI)in the pores at different
Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2271 *)
E
0
10.0
C L Y
-
1
L 10.0
7
6.0
mo
8.0
c)
0 X
6.0
z
h
0"
7
X
4.0
4.0
0"
6 2.0
2.0
0.0
0.0
0
40
EO
120
160 200 240 280
320 360
Time, min
Figure 20. Transient profiles in aqueous phase oxidation of sulfur kmol m-3, C&,i = 8.4 dioxide at T = 303 K, C,so,i = 7.86 x x kmol m+, and with different sizes of carbon particles; curves represent solution of eq 13.
times, if the effects of intraparticle diffusion of each of these species and product were dominant, are estimated by solving the appropriate equations for pore diffusion (Gopalakrishna, 1994). The data on the effective diffusivity of each of the species used in the estimation are obtained from Komiyama and Smith (197513): for S(IV),6.76 x m2 s-l (the value reported for SOz(aq) is assumed to hold good for total S(IV));for oxygen, 5.35 x m2 s-l; and for S(VI)(assumed to be same as that of HzSOd, 3.2 x m2 s-l. The results (not presented here, but available in Gopalakrishna (1994)) indicate that the concentration of each of the three species in the pores reaches a uniform value in the pore within about 112 min, while the reaction times of interest in the present experiments are well above 100 min. This indicates very high pore rates of diffusion for all the species of interest. Therefore, the effects of internal diffusion are neglected in the present investigations.
Literature Cited Ahn, B. J.; McCoy, B. J.; Smith, J. M. Separation of Adsorption and Surface Reaction Rates: Dynamic Studies in a Catalytic Slurry Reactor. AZChE J . 1985,31, 541-550. Altwicker, E. R. Oxidatiodnhibition of Sulfite Ion in Aqueous Solution. AIChE Symp. Ser. 1979, 75, (No. 188), 145-150. Amadeo, N. E.; Laborde, M. A.; Lemcoff, N. 0. Oxidation of Sulfur Dioxide in a Slurry Reactor. Chem. Eng. J . 1989, 41, 1-8. Barrie, L. A. A n Improved Model of Reversible SO2-Washout by Rain. Atmos. Environ. 1978, 12, 407-412. Beilke, S.; Gravenhorst, G. Heterogeneous SO2-Oxidation in the Droplet Phase. Atmos. Environ. 1978, 12, 231-239.
Boon-Long, S.; Laguerie, C.; Couderc, J. P. Mass-Transfer from Vessels. Chem. Eng. Suspended Solids to a Liquid in Agitated Sci.-1978,33, 813. Brodzinsky, R.; Chang, S. G.; Markowitz, S. S.; Novakov, T. Kinetics and Mechanism for the Catalvtic Oxidation of Sulfur Dioxide on Carbon in Aqueous Suspensions. J . Phvs. Chem. 1980,84,3354-3358. Calderbank. P. H.: Moo-Young. M. B. The Continuous Phase Heat and Mass Transfer Propezes of Dispersions. Chem. Eng. Sci. 1961,16,39-54. Fu, C. C.; McCoy, B. J.; Smith, J. M. Slurry Reactor Studies of Homogeneous and Heterogeneous Reactions. AZChE J . 1989. 35, 255-266. Gopalakrishna, K. V. Aqueous Phase Oxidation of Sulfur Dioxide in Stirred Slurry Reactors, Ph.D Thesis, Indian Institute of Science, Bangalore, 1994. Goto, S.; Kojima, Y. Oxidation of Sulfur Dioxide in Different Types ofThree Phase Reactors. Chem. Eng. Commun. 1985,34,213224. Govindarao, V. M. H.; Gopalakrishna, K. V. Solubility of Sulfur Dioxide at Low Partial Pressures in Dilute Sulfuric Acid Solutions. Znd. Eng. Chem. Res. 1993,32, 2111-2117. Hartman, M.; Coughlin, R. W. Oxidation of SO2 in a Trickle-Bed Reactor Packed with Carbon. Chem. Eng. Sci. 1972,27,867880. Hegg, D. A.; Hobbs, P. V. Oxidation of Sulfur Dioxide in Aqueous Systems with Particular Reference to the Atmosphere. Atmos. Environ. 1978, 12, 241-253. Hikita, H.; Asai, S.; Nose, H. Absorption of Sulfur Dioxide into Water. AZChE J . 1978,24, 147-149. Hunger, T.; Lapicque, F.; Storck, A. Thermodynamic Equilibrium of Diluted SO2 Absorption into NaS04 or H2S04 Electrolyte Solutions. J . Chem. Eng. Data 1990,35, 453-463. Johnstone, H. F.; Leppla, P. W. The Solubility of Sulfur Dioxide at Low Partial Pressures. The Ionization Constant and Heat of Ionization of Sulfurous Acid. J . Am. Chem. SOC.1934, 56, 2233-2238. Jolly, W. L. Modern Inorganic Chemistry, Intl. ed., 3rd printing; McGraw-Hill Book Co.: Singapore, 1989. Komiyama, H.; Smith, J. M. Sulfur Dioxide Oxidation in Slurries of Activated Carbon. Part I-Kinetics, AZChE J . 1975a, 21, 664-670. Komiyama, H.; Smith, J. M. Sulfur Dioxide Oxidation in Slurries of Activated Carbon. Part 11-Mass Transfer Studies. AZChE J . 1975b, 21,670-676. Lu, G. Q.; Gray, P. G.; Do, D. D. A Study of H2S04 Formation in the Process of Simultaneous Sorption of S02,02 and H2O onto a Single Carbon Particle. Chem. Eng. Commun. 1990,96, 1530. Pasiuk-Bronikowska, W.; Ziajka, J. Kinetics of Aqueous SO2 Oxidation at Different Rate Controlling Steps. Chem. Eng. Sci. 1989,44,915-920. Pavko, A.; Misic, D. M.; Levec, J. Kinetics in Three-phase Reactors. Chem. Eng. J . 1981,21, 149-154. Recasens, F.; Smith, J. M.; McCoy, B. J. Temperature Effects on Separate Values of Adsorption and Surface Reaction Rates by Dynamic Studies. Chem. Eng. Sci. 1984,39, 1469-1479. Schaftlein, R. W.; Russel, T. W. F. Gas-Liquid Tank Reactor Design via Simple Mass Transfer Models and Judicious Assessment of Model Parameters. Znd. Eng. Chem. 1968, 60, 12-27. Seaburn, J. T.; Engel, A. J. Sorption of Sulfur Dioxide by Suspension ofActivated Carbon in Water. AZChE J . 1973,134, 71-75. Treybal, R. E. Mass-Transfer Operations, 3rd ed.; McGraw-Hill Inc.: New York, 1982. Received for review November 21, 1994 Revised manuscript received March 7, 1995 Accepted April 10, 1995@
-
-
IE940692Y Abstract published in Advance ACS Abstracts, May 15, 1995. @
