4876
Ind. Eng. Chem. Res. 2004, 43, 4876-4882
Calcium Bisulfite Oxidation in the Flue Gas Desulfurization Process Catalyzed by Iron and Manganese Ions D. Karatza,† M. Prisciandaro,‡ A. Lancia,*,† and D. Musmarra§ Dipartimento di Ingegneria Chimica, Universita` di Napoli “Federico II”, Piazzale Tecchio 80, 80125 Napoli, Italy, Dipartimento di Chimica, Ingegneria Chimica e Materiali, Universita` di L’Aquila, Monteluco di Roio, 67040 L’Aquila, Italy, and Dipartimento di Ingegneria Civile, Seconda Universita` degli Studi di Napoli, Real Casa dell’Annunziata, Via Roma 29, 81031 Aversa (CE), Italy
Among different flue gas desulfurization processes for control of sulfur dioxide emissions from combustion of fossil fuels, wet limestone scrubbing is the most widely used. Forced oxidation in the scrubber loop substantially improves the dewatering properties of the sludge, leading to the formation of gypsum (CaSO4‚2H2O). In view of this, the present paper reports the experimental study of calcium bisulfite oxidation in the presence of catalysts (ferrous and manganese ions) both separately and simultaneously added in the reaction vessel. A laboratory-scale apparatus was used; the experiments were performed at a fixed oxygen partial pressure (21.3 kPa) and at a temperature of 45 °C. In particular, the effect of the simultaneous addition of both catalysts has been studied. The analysis of the experimental results, carried out by using the theory of mass transfer with chemical reaction, indicated that the slow reaction regime has been explored and the transition from the kinetic to the diffusional subregime identified. Experimental results, as compared with those obtained in the presence of the single catalytic species (Mn2+ alone and Fe2+ alone) allowed one to observe the synergistic effect that the two catalysts added simultaneously have on the oxidation reaction. Introduction Wet limestone scrubbing is the most common flue gas desulfurization (FGD) process (or limestone/gypsum process) for control of sulfur dioxide emissions from combustion of fossil fuels because it gives excellent results for SO2 removal; moreover, it is simpler with respect to other processes, such as the dual alkali process, which requires a double step not needed in the limestone process, thus resulting in the process being noncompetitive. Calcium bisulfite oxidation is considered to be an important issue in limestone/gypsum processes because forced oxidation in the scrubber loop improves the dewatering properties of the sludge, leading to the formation of gypsum (CaSO4‚2H2O), a byproduct with a low adverse impact on the environment in comparison with the solid mixture of CaSO3‚1/2H2O and CaSO4 usually produced.1 The calcium bisulfite oxidation reaction has been extensively studied, both in the absence2,3 and in the presence4,5 of catalysts; a number of researchers devoted their studies to comprehension of the oxidation reaction path,4,6 in particular when the occurrence of a chemical reaction is accompanied by the diffusion of oxygen in the liquid phase, which causes complex interactions that are rather difficult to enlighten.7 This circumstance is encountered when the oxidation reaction takes place in the so-called heterogeneous conditions, achieved by contacting a sulfurous solution with an oxygen-containing gas phase, that is, the operating condition in FGD processes. On the other hand, the study of sulfite * To whom correspondence should be addressed. Tel.: +39 81 7682243. Fax: +39 81 2391800. E-mail:
[email protected]. † Universita` di Napoli “Federico II”. ‡ Universita` di L’Aquila. § Seconda Universita` degli Studi di Napoli.
oxidation in homogeneous conditions (by contacting a sulfite solution with an oxygen-saturated solution) led to relatively consistent results: in a previous work, Lancia et al.1 showed how the following equation appears to be the most appropriate to describe the kinetics of the oxidation reaction for a pH range of 7.5-9 in homogeneous conditions:
r ) kcM1/2cS(IV)3/2
(1)
where r is the reaction rate expressed as moles of SO42produced per unit time and volume, k is the kinetic constant, cM is the catalyst concentration, and cS(IV) is the total sulfite concentration. A partial agreement, between results reported in the literature, exists only on the value of the kinetic constant at 25 °C, which ranges between 2 × 106 and 36 × 106 m3/mol, while the activation energy ranges from 50 to 150 kJ/mol. Equation 1 can be interpreted by assuming that the reaction takes place via a free-radical mechanism, with a chain initiated by the catalyst autoxidation or by the action of UV light.8,9 On the other hand, in both homogeneous and heterogeneous oxidation, the reaction is highly sensitive to operative conditions, such as the liquidphase composition (sulfite concentration, dissolved oxygen, and pH) and the presence, even in traces, of catalysts (Co2+, Cu2+, Mn2+, and Fe2+) and inhibitors (alcohols, phenols, and hydroquinone). The previous experimental study1 of the bisulfite oxidation reaction in heterogeneous conditions has given the kinetic equation for calcium bisulfite oxidation that follows, which is of zero order in oxygen and three halves in HSO3- ions:
r ) kucHSO3-3/2
10.1021/ie030836l CCC: $27.50 © 2004 American Chemical Society Published on Web 07/02/2004
(2)
Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4877
Figure 1. Experimental apparatus.
where ku is the uncatalyzed kinetic constant and cHSO3the bisulfite ion concentration, with ku ) 1.19 × 10-4 m3/2/mol1/2‚s at T ) 45 °C. Afterward, the reaction was carried out in the presence of a catalyst, in a laboratory-scale well-mixed reactor, where the gas phase was a mixture of oxygen and nitrogen, while the liquid phase was obtained by mixing two aqueous solutions, one obtained by dissolving Ca(OH)2 into a SO2 solution and the other containing manganese sulfate.10 The results have been interpreted following the approach indicated by Astarita et al.;11 that is, with increasing catalyst concentration, three different reaction regimes were identified, namely, the slow kinetic, the slow diffusional, and eventually the fast reaction regime, together with the transition from one regime to another. In particular, a parallel reaction mechanism was developed, according to which the overall reaction rate can be calculated as the sum of the uncatalyzed and catalyzed reaction rates, with the last being of first order in manganese ion, as expressed by the following equation:
r ) kucHSO3-3/2 + kccMn2+
(3)
where kc is the catalyzed kinetic constant and cMn2+ the bisulfite ion concentration, with kc ) 0.193 s-1 at T ) 45 °C. The purpose of the present paper is to study the oxidation reaction in the presence of a different catalyst, namely, the ferrous ion added as FeSO4, and in the simultaneous presence of both catalysts (Fe2+ and Mn2+) to verify the occurrence of interfering effects. As a matter of fact, the catalytic synergism of two or more metal ion catalysts toward sulfite oxidation is a wellestablished topic in the literature,12-14 and catalysis by Fe and Mn ions is particularly interesting because these impurities are already present in scrubbers for FGD processes.15 Materials and Methods A sketch of the laboratory-scale apparatus is reported in Figure 1. The apparatus consists of a thermostated
stirred reactor with lines for continuous feeding and discharging of both gas and liquid phases. The reactor is a Pyrex 0.088-m-i.d. cylinder with a hemispherical bottom, two vertical baffles, and a liquid overflow, allowing a liquid head of about 100 mm. A two-flat-blade axial stirrer, located about 70 mm below the liquid overflow, was used to provide thorough mixing in the liquid phase, with a stirrer speed variable in the range of 0-13.3 s -1. The vessel is jacketed, and the temperature was set in all experiments at 45 °C. The gas phase was a mixture of oxygen and nitrogen, with oxygen concentrations of 21%; it was taken from cylinders and bubbled in the reactor through a glass tube submerged about 80 mm below the liquid free surface. The volumetric flow rate of the gas fed to the reactor, measured by a rotameter (ASA), was kept constant at 1.39 × 10-4 m3/s. Such a gas flow rate, in conjunction with the stirrer speed of 6.7 s-1, gave a liquid holdup of 4.2 × 10-4 m3. Concerning the liquid solution, particular attention was paid to its preparation, carefully setting up two distinct feed solutions, to avoid the reaction initiation by catalyst in the tank itself. Thus, one tank was filled with a clear solution prepared by dissolving analytical-grade calcium hydroxide in analytical-grade sulfur dioxide in solution and by diluting with bidistilled water. A second tank was instead filled with a solution of the catalyst (FeSO4‚7H2O) in bidistilled water or with a mixture of the two catalysts (FeSO4‚7H2O and MnSO4). Referring concentrations to the reactor volume, the Ca2+ concentration ranged from 0.5 to 30 mol/m3, while the total S(IV) concentration ranged from 0.6 to 64 mol/m3, with a pH in the range of 2.0-4.0. The concentration of ferrous sulfate was varied in the range of 1 × 10-3-1 × 10-1 mol/m3, while the concentration of manganese sulfate was varied in the range of 3.3 × 10-3-1.6 × 10-2 mol/m3. The total liquid flow rate was kept constant at the value 9.53 × 10-7 m3/s, corresponding to a mean residence time in the reactor τ of about 440 s. At the beginning of each experiment, as soon as the liquid in the reactor reached the overflow, agitation was started and the gas stream was introduced. It was assumed that steady state was reached after a time
4878 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 Table 1. Experimental Results for T ) 45 °C, pO2 ) 21.3 kPa, and cFe2+ ) 1 × 10-3, 3 × 10-3, 5 × 10-3, and 1 × 10-2 mol/m3 no.
S(IV)in (mol/m3)
S(IV)out (mol/m3)
S(VI)in (mol/m3)
S(VI)out (mol/m3)
Ca2+ (mol/m3)
Fe2+ (mol/m3)
r × 10-3 (mol/m3‚s)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
6.20 20.50 5.10 2.40 1.60 41.10 5.40 1.00 3.30 2.60 14.00 0.60 30.12 31.50 34.00 5.80 3.00 0.80 3.40 20.80 30.80 42.83 7.40 3.30 14.50 13.89 28.10 49.50 64.00 5.50 42.80
4.44 11.50 2.07 1.45 1.27 30.60 3.12 0.32 1.76 1.05 6.20 0.67 16.50 23.30 24.50 1.87 0.92 0.20 1.57 11.25 20.30 28.36 2.10 0.27 5.94 10.80 19.87 28.50 38.41 1.40 35.00
0.98 2.60 0.97 0.78 0.35 3.02 1.06 0.54 0.98 0.10 1.33 0.76 1.17 2.72 1.22 0.34 0.78 0.55 1.19 1.71 1.46 1.21 0.50 0.41 1.10 1.41 2.12 1.89 3.14 0.69 3.26
1.48 4.70 1.23 1.14 0.60 11.74 2.08 1.28 1.82 1.88 2.88 1.51 4.81 7.53 9.73 2.13 2.21 1.52 2.71 4.66 6.44 8.31 3.59 2.65 5.02 5.66 8.28 10.80 12.31 3.49 12.37
2.00 × 100 6.90 × 100 1.80 × 100 6.00 × 10-1 5.00 × 10-1 1.96 × 101 2.60 × 100 5.00 × 10-1 2.00 × 100 1.50 × 100 5.80 × 100 1.00 × 100 1.07 × 101 1.45 × 101 1.90 × 101 2.00 × 100 1.30 × 100 5.00 × 10-1 2.00 × 100 7.90 × 100 1.40 × 101 1.87 × 101 2.90 × 100 1.60 × 100 5.60 × 100 8.10 × 100 1.27 × 101 1.82 × 101 2.36 × 101 2.40 × 100 2.72 × 101
0.001 0.001 0.001 0.001 0.001 0.001 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010
0.81 4.36 0.49 0.72 0.52 18.45 2.02 1.45 1.61 1.71 3.03 1.52 7.36 10.16 17.98 3.61 2.79 1.91 3.03 5.95 10.29 14.10 6.24 4.46 7.81 8.76 12.74 17.76 18.27 5.59 19.25
Table 2. Experimental Results for T ) 45 °C and pO2 ) 21.3 kPa no.
S(IV)in (mol/m3)
S(IV)out (mol/m3)
S(VI)in (mol/m3)
S(VI)out (mol/m3)
Ca2+ (mol/m3)
Fe2+ (mol/m3)
r × 10-3 (mol/m3‚s)
30 19 7 3 32 33 34
5.50 3.40 5.40 5.10 16.00 8.70 16.80
1.40 1.57 3.12 2.07 2.49 0.72 1.17
0.69 1.19 1.06 0.97 1.29 0.59 1.99
3.50 2.71 2.09 1.23 10.45 6.84 10.84
2.40 2.00 2.60 1.80 7.70 4.00 8.20
0.010 0.005 0.003 0.001 0.030 0.020 0.100
5.59 3.03 2.02 0.49 19.36 13.37 18.70
longer than 6τ had elapsed. The oxidation rate at steady state was evaluated by measuring in the inlet and in the outlet liquid streams the total sulfate concentration; specifically, the total sulfate concentration was measured by means of a turbidimeter (Hach DR/2010) at 450 nm wavelengths. Furthermore, in both streams the concentrations of the total sulfite and Ca2+ ions were measured. The total sulfite concentration was measured by iodometric titration using starch as an indicator, while the Ca2+ ion concentration was measured by ethylenediaminetetraacetic acid titration using murexide as an indicator. Results and Discussion To determine the effect of some process parameters on the oxidation reaction, particularly of the catalyst concentration, three sets of experiments have been performed, with a fixed pO2 equal to 21.3 kPa because a previous experimentation using manganese as the catalyst showed that pO2 variations were not influent.7 The first set includes experimental runs carried out by varying the bisulfite concentration in the range of 1 × 10-1 < cHSO3- < 4 × 101 mol/m3, at four Fe2+ levels, namely, cFe2+ ) 1 × 10-3, 3 × 10-3, 5 × 10-3, and 1 × 10-2 mol/m3. The second experimental set concerns runs carried out for various Fe2+ concentrations in the range
of 1 × 10-3-1 × 10-1 mol/m3 and with cHSO3- in the range of 0.5-3 mol/m3. The third set includes four series of experiments carried out at a fixed Mn2+/Fe2+ concentration ratio equal to 4.1, by varying the relative manganese and ferrous ion concentrations; in particular, cMn2+ has been varied in the range of 0.00328-0.00615 mol/m3, while cFe2+ ranged from 0.0015 to 0.008 mol/ m3. Raw experimental data are reported in Tables 1-6. First of all, the composition of the liquid phase outflowing from the reactor has to be speciated in order to individuate a kinetic equation on the basis of the experimental measurements. With this aim, the equilibrium equations for the following reactions were used (see the Appendix): for which the values of the thermo-
SO2(aq) + H2O ) H+ + HSO3-
(4)
HSO3- ) H+ + SO32-
(5)
HSO4- ) H+ + SO42-
(6)
H2O ) H+ + OH-
(7)
dynamic equilibrium constants were calculated using data reported by Goldberg and Parker16 (reactions 4 and
Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4879 Table 3. Experimental Results for T ) 45 °C, pO2 ) 21.3 kPa, cFe2+ ) 4 × 10-3, and cMn2+ ) 1.64 × 10-2 no.
S(IV)in (mol/m3)
S(IV)out (mol/m3)
S(VI)in (mol/m3)
S(VI)out (mol/m3)
Ca2+ (mol/m3)
Fe2+ (mol/m3)
Mn2+ (mol/m3)
r × 10-3 (mol/m3‚s)
35 36 37 38 39 40 41 42 43 44
22.60 10.50 2.50 30.40 45.80 16.00 79.60 5.00 7.80 63.00
12.70 4.10 0.14 18.70 29.50 6.96 52.00 0.40 2.00 24.37
1.03 0.99 0.73 1.41 1.16 1.10 3.59 0.77 0.75 3.58
5.51 4.25 3.57 6.78 9.80 4.58 13.68 4.34 4.46 10.49
9.80 5.40 1.30 13.60 19.90 5.20 29.00 4.80 2.60 13.60
0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004
0.0164 0.0164 0.0164 0.0164 0.0164 0.0164 0.0164 0.0164 0.0164 0.0164
9.37 6.89 5.99 11.21 18.25 7.36 17.90 6.02 6.25 15.10
Table 4. Experimental Results for T ) 45 °C, pO2 ) 21.3 kPa, cFe2+ ) 8 × 10-3, and cMn2+ ) 3.28 × 10-3 no.
S(IV)in (mol/m3)
S(IV)out (mol/m3)
S(VI)in (mol/m3)
S(VI)out (mol/m3)
Ca2+ (mol/m3)
Fe2+ (mol/m3)
Mn2+ (mol/m3)
r × 10-3 (mol/m3‚s)
45 46 47 48 49 50 51 52
6.75 15.75 2.80 8.62 5.50 42.30 5.80 58.33
0.71 4.62 2.00 0.70 0.40 23.21 0.20 27.17
1.14 1.82 1.41 2.95 1.47 2.10 0.86 5.35
6.30 8.59 6.47 8.54 6.94 8.70 4.15 17.34
2.00 6.60 1.20 4.60 2.60 20.10 2.40 23.60
0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008
0.003 28 0.003 28 0.003 28 0.003 28 0.003 28 0.003 28 0.003 28 0.003 28
10.90 13.80 15.20 11.80 10.30 18.90 8.55 19.40
Table 5. Experimental Results for T ) 45 °C, pO2 ) 21.3 kPa, cFe2+ ) 2 × 10-3, and cMn2+ ) 8.2 × 10-3 no.
S(IV)in (mol/m3)
S(IV)out (mol/m3)
S(VI)in (mol/m3)
S(VI)out (mol/m3)
Ca2+ (mol/m3)
Fe2+ (mol/m3)
Mn2+ (mol/m3)
r × 10-3 (mol/m3‚s)
53 54 55 56 57 58 59
0.38 0.29 18.40 30.90 12.40 54.60 45.30
2.62 2.01 12.07 19.62 8.10 33.37 29.20
3.60 2.50 0.65 1.02 1.08 1.67 0.98
2.32 0.45 4.23 6.36 3.87 10.29 5.43
2.90 1.60 8.20 13.50 5.40 20.40 18.70
0.002 0.002 0.002 0.002 0.002 0.002 0.002
0.0082 0.0082 0.0082 0.0082 0.0082 0.0082 0.0082
4.74 3.58 7.57 10.70 5.88 19.50 18.20
Table 6. Experimental Results for T ) 45 °C, pO2 ) 21.3 kPa, cFe2+ ) 1.5 × 10-3, and cMn2+ ) 6.15 × 10-3 no.
S(IV)in (mol/m3)
S(IV)out (mol/m3)
S(VI)in (mol/m3)
S(VI)out (mol/m3)
Ca2+ (mol/m3)
Fe2+ (mol/m3)
Mn2+ (mol/m3)
r × 10-3 (mol/m3‚s)
60 61 62 63 64 65 66 67
6.00 3.80 2.20 1.80 5.00 19.20 42.90 61.00
3.05 1.80 0.60 1.00 2.80 10.42 21.92 33.80
0.84 0.17 0.26 0.36 0.40 1.18 2.46 1.85
3.05 1.80 1.74 1.72 1.75 3.32 7.31 10.50
2.70 1.30 1.10 1.00 2.00 6.10 17.00 20.20
0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015
0.006 15 0.006 15 0.006 15 0.006 15 0.006 15 0.006 15 0.006 15 0.006 15
3.15 1.70 2.72 2.90 2.89 4.52 10.23 18.30
5) and by Brewer17 (reactions 6 and 7). Together with the equilibrium equations relative to reactions 4-7, the stoichiometric equations for the total sulfite and sulfate concentrations and the electroneutrality equation were considered:
cSO2(aq) + cHSO3- + cSO32- ) cS(IV)
(8)
cHSO4- + cSO42- ) cS(IV)
(9)
∑I zIcI ) 0
(10)
where zI is the electric charge of the Ith species, with I ) Ca2+, H+, HSO3-, SO32-, HSO4-, SO42-, OH-, and M2+. In Figure 2, the behavior of the oxidation rate vs the bisulfite ion concentration is reported for each Fe2+ concentration level; evidently, the oxidation rate increases while the catalyst concentration increases in the range explored. Moreover, it can be seen that the oxidation rate grows while cHSO3- increases until it
Figure 2. Reaction rate as a function of cHSO3- for four levels of cFe2+: O, cFe2+ ) 0.010 mol/m3; 0, cFe2+ ) 0.005 mol/m3; 4, cFe2+ ) 0.003 mol/m3; ], cFe2+ ) 0.001 mol/m3.
reaches a plateau, where r becomes almost independent of it. To compare uncatalyzed and catalyzed experimental data, the kinetic equation previously found (eq 2) has been reported in the plot as a continuous line. The
4880 Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004
Figure 3. Reaction rate as a function of the catalyst species concentration: 4, Fe2+ concentration.
catalytic effect of Fe2+ ions appears to be particularly evident at low bisulfite concentrations; precisely, when cHSO3- < 7 mol/m3, the difference between catalyzed and uncatalyzed oxidation rates is more than 20% for all ferrous concentrations, while for higher cHSO3-, the difference between the catalyzed and uncatalyzed reaction rates becomes less marked. Eventually, as the bisulfite concentration continues to grow, the oxidation rate coincides with the uncatalyzed reaction rate, reaching the plateau individuated by the diffusional subregime, with the value of such a limit depending on the oxygen partial pressure in the gas phase. Figure 3 reports the behavior of the oxidation rate vs ferrous ion concentration. It can be noted that the oxidation rate increases with increasing cFe2+, until the upper limit of the diffusional ceiling is reached. The results obtained have been analyzed following the approach of Astarita and co-workers.11,18 Actually, concerning the ferrous ion catalyzed oxidation reaction (see Figures 2 and 3), for a low bisulfite concentration, the absorption rate, which is the same as the reaction rate in the slow kinetic reaction regime, is almost constant; then it grows until it reaches the transition toward the slow diffusional reaction regime, where it becomes once more almost constant. For the left part of the plot, the reaction rate is highly sensitive to the catalyst concentration, and it is suitably expressed, as it was for the manganese catalysis, by a parallel reaction mechanism analogous to that of eq 3. Considering the uncatalyzed contribution (eq 2), together with a ferrous-catalyzed contribution, the overall kinetic equation for ferrous-catalyzed bisulfite oxidation is
r ) ru + rc ) kucHSO3-3/2 + kccFe2+
(11)
where kc is the constant of the catalyzed reaction, equal to 0.548 s-1. The proposed reaction mechanism derives from testing of various kinetic models, among which this in-parallel model gives the best fit of the experimental data. Equation 11 is reported as a continuous line in Figures 2 and 3, showing that a quite good agreement with the experimental data in the kinetic subregime exists. Moreover, Figure 3 shows as a comparison the parallel behavior of the oxidation rate vs the manganese ion concentration (eq 3). A comparison with the oxidation rate catalyzed by manganese,7 as for the kinetic
Figure 4. Reaction rate as a function of cHSO3- for cMn2+/cFe2+ ) 4.1: 4, cMn2+ ) 0.003 28 mol/m3 and cFe2+ ) 0.008 mol/m3; O, cMn2+ ) 0.0164 mol/m3 and cFe2+ ) 0.004 mol/m3; 0, cMn2+ ) 0.0082 mol/ m3 and cFe2+ ) 0.002 mol/m3; ], cMn2+ ) 0.006 15 mol/m3 and cFe2+ ) 0.0015 mol/m3.
subregime, shows that the contribution to the overall reaction expression given by the catalyzed reaction has the same feature; specifically, the catalyzed reaction rate has the same first-order dependence on the catalytic species (Mn2+ and Fe2+), with a different value of the catalyzed kinetic constant kc. Figure 3 evidences clearly how the ferrous ion is a more effective catalyst than the manganese ions. Figure 4 shows the behavior of the oxidation rate as a function of the bisulfite concentration for a fixed Mn2+/ Fe2+ ratio, equal to 4.1, obtained by varying the relative manganese and ferrous ion concentrations. It can be observed that the highest oxidation rate is reached at higher concentration levels adopted for the two catalysts (e.g., cFe2+ ) 0.008 mol/m3 and cMn2+ ) 0.00328). For experimental results obtained in the presence of both catalysts, it is important to say that the catalyst concentration levels have been chosen in order to work in the slow kinetic subregime. Once again the kinetic equation has been devised by considering a parallel reaction mechanism in which the total reaction rate is the sum of the uncatalyzed and of the two catalyzed, by manganese and ferrous ions, reaction rates. The overall kinetic equation is thus
r ) ru + rc1 + rc2 ) kucHSO3-3/2 + kc1cMn2+ + kc2cFe2+ (12) where ku is the kinetic constant of eq 2, kc1 is the rate constant of eq 3, and kc2 is the kinetic constant of eq 11. Equation 12 has been reported as a continuous line in Figure 4, but as can be noted, model curves lay slightly below the associated experimental points. This circumstance is clearer from Figure 5, in which the reaction rate, calculated from eq 12, is reported as a function of the experimental reaction rate. It is very clear that the actual rate of bisulfite oxidation catalyzed by a mixture of Mn2+ and Fe2+ is higher than that obtained by summation of the rates for single catalysts as in eq 12. This occurrence has been explained by considering the synergistic effect of the catalyst simultaneously added. For data in the diffusional subregime, a different approach is to be used to interpret them; as suggested by Danckwerts,19 in this subregime the overall rate becomes independent of the liquid-phase composition, and it is only controlled by the rate of diffusive oxygen absorption. Therefore, the overall rate of the process (R),
Ind. Eng. Chem. Res., Vol. 43, No. 16, 2004 4881
where RI is the stoichiometric coefficient of the Ith species and is assumed to be positive for the reactants and negative for the products. The equilibrium condition for reaction A1 is
K)
∏I aI-R
(A2)
I
where aI is the activity of the Ith species. The activity aI is related to the molar concentration by
a I ) cI γ I
Figure 5. Calculated vs experimental reaction rates: 4, cMn2+ ) 0.003 28 mol/m3 and cFe2+ ) 0.008 mol/m3; O, cMn2+ ) 0.0164 mol/ m3 and cFe2+ ) 0.004 mol/m3; 0, cMn2+ ) 0.0082 mol/m3 and cFe2+ ) 0.002 mol/m3; ], cMn2+ ) 0.006 15 mol/m3 and cFe2+ ) 0.0015 mol/ m3.
relative to the diffusional subregime in Figure 2 can be described by means of the following equation:18 i R ) 2kL°acO 2
log γI ) -0.509zI2
The oxidation reaction of bisulfite in the presence of catalysts, i.e., ferrous ions and a mixture of ferrous and manganese ions, has been experimentally studied. The reaction takes place in the slow kinetic regime, and the transition from the slow kinetic subregime to the slow diffusional subregime has been described, with the individuation of the diffusional plateau. A kinetic equation has been devised, with a parallel reaction mechanism, for which the overall reaction rate is the sum of the catalyzed and uncatalyzed reaction rates. The comparison between the present experimental data and those previously obtained by using manganese ions as a catalytic species has shown that Fe2+ is a more effective catalyst than Mn2+ and that Fe2+ and Mn2+ simultaneously added show a synergistic effect; that is, the actual rate of bisulfite oxidation catalyzed by the catalytic mixture is higher than that obtained by summing the rates for single catalysts. Appendix The chemical reactions taken into account can be written in the following general form:
(A1)
(
)
xFI - 0.2FI 1 + axFI
(A4)
where FI is the ionic strength, which can be evaluated by means of the following equation:
FI )
Conclusions
∑I RII ) 0
where γI is the activity coefficient. Values of the activity coefficients for cations and anions can be calculated by means of the extension of the Debye-Hu¨ckel equation, proposed by Davies:21
(13)
where kL°a is the product between the liquid-side masstransfer coefficient and the specific gas-liquid contact i is the interfacial oxygen concentration, area and cO 2 which can be evaluated by means of Henry’s law. Using data relative to the right side of Figure 2 and the value of 1.02 × 105 m3‚Pa/mol for Henry’s constant for O2 at 45 °C,20 it is possible to estimate the value of kL°a that is equal to 4.63 × 10-2 s-1. With this value of kL°a so calculated, the straight horizontal lines reported in Figures 2 and 3 were achieved.
(A3)
1
N
cIzI2 ∑ 2I)1
(A5)
Nomenclature a ) specific interfacial area, m-1 aI ) activity of the Ith species, mol/m3 cI ) concentration of the Ith species, mol/m3 i cO ) oxygen interfacial concentration, mol/m3 2 FI ) ionic strength, mol/m3 k ) kinetic constant, m3/mol‚s kc ) kinetic constant for the “catalyzed” reaction, s-1 ku ) kinetic constant for the “uncatalyzed” reaction, s-1 kL° ) liquid-side mass-transfer coefficient, m/s K ) equilibrium constant p ) pressure, Pa r ) reaction rate, mol/m3‚s R ) overall oxidation rate, mol/m3‚s T ) temperature, °C zI ) electric charge Greek Letters RI ) stoichiometric coefficient of the Ith species γI ) activity coefficient of the Ith species τ ) liquid residence time, s
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Received for review November 12, 2003 Revised manuscript received March 22, 2004 Accepted March 23, 2004 IE030836L
