Article pubs.acs.org/IECR
Kinetics and Mechanism of Sulfite Oxidation in the MagnesiumBased Wet Flue Gas Desulfurization Process Zhigang Shen,† Shaopeng Guo,† Wanzhong Kang,†,‡ Kun Zeng,† Ming Yin,† Jingyu Tian,† and Jun Lu*,† †
College of Resource and Environmental Engineering, East China University of Science and Technology, Shanghai 200237, China SINOPEC Ningbo Engineering Co., Ltd., Ningbo 315103, China
‡
ABSTRACT: The kinetics of sulfite oxidation in the magnesium-based wet flue gas desulfurization (FGD) process were investigated in a stirred bubbling reactor by varying the concentrations of MgSO3 and MgSO4, pH, air flow and temperature. The reaction was found to be 0.88 order with respect to magnesium sulfite and the oxidation could reach the maximum rate when the pH value was close to 6.5. The mechanism of the oxidation was discussed, and it was concluded that the oxidation is controlled by diffusion of oxygen. These results would be useful for the design or process optimization of the magnesium-based wet FGD system.
1. INTRODUCTION Flue gases are sometimes scrubbed with magnesium hydroxide slurry to reduce their sulfur oxide content.1−5 In China, the magnesium-based wet FGD process has been increasingly used on the industrial boiler in recent years because of its low investment, compact flow sheet, less land occupied, high efficiency, reliable operation, rare fouling, and low price of the magnesium-based absorbent.6−8 Magnesium sulfite with a relatively low dissolution rate is obtained as a byproduct from the magnesium-based wet FGD process, and it can be easily oxidized to high-solubility magnesium sulfate which is used as a fertilizer.6 Thus, the recycling absorbing slurry could reach a higher concentration during the oxidation of magnesium sulfite, and the enrichment of the absorbent could promote the desulfurization process. Meanwhile, the magnesium sulfate would be efficiently crystallized and separated from the enriched excess slurry. However, the oxidation of magnesium sulfite in aqueous solution while important for many industrial applications has not been the subject of many studies. Compared to magnesium sulfite, oxidation of other kinds of sulfite has been extensively studied. These studies have included the effects of such variables as sulfite concentration, oxygen mass transfer, pH, and temperature. Barron and O’Hern studied the oxidation of sodium sulfite and found that the reaction was 3.5 orders with respect to sulfite.9 Sawicki and Barron found that the oxidation reaction of sodium sulfite was 2.0 order with respect to oxygen.10 Long et al. studied the catalyzed oxidation of concentrated ammonium and found that the reaction order with respect to oxygen is 1.2 and sulfite is zero.11 Zhou et al. studied the oxidation of ammonium sulfite and found a critical sulfite concentration, below which the reaction order with respect to sulfite is 0.2, while above which the order turns to −1.0.12 Jia et al. found the reaction to be −0.5 order with respect to sulfite, and the bisulphate could be oxidized easier than sulfite.13 Zhang and Millero found that the reaction of sulfite was 2.0 order with respect to S(IV) in seawater.14 Zuo studied the Fe-catalyzed oxidation of aqueous sulfite in atmospheric water. The results showed that both sunlight and UV−visible light could enhance the rate of © 2012 American Chemical Society
oxidation and the oxidation was 1.0 order with respect to sulfite ion concentration. The presence of organic complex ligands, such as oxalate, can completely inhibit the Fe-catalyzed oxidation of sulfite in the dark.15−18 Some of the results relevant to calcium sulfite oxidation in FGD conditions are reported in Table 1. 19−27 The table shows that the interpretation of the experimental results is somewhat contradictory. Probably, this is due to the interactions between the reaction steps on the one side and the diffusive transport of reactants, inhibitors, or catalysts on the other side.28 In FGD plants, since calcium sulfite solubility is quite low, the concentrations involved in the reaction are lower than those taken into account by the researchers who worked with other kinds of sulfite, which caused the different results under saturated and unsaturated conditions of CaSO3. Though the oxidation of sulfite has been studied by several researchers and has resulted in different conclusions, it should be noted that most of these previous studies significantly differ from those encountered in magnesium-based wet FGD plants and the detailed information on kinetics of the oxidation of magnesium sulfite and the parameters of industrial importance is thin in the literature. Therefore, it can be concluded that more data and a closer study on the mechanism is necessary. The present work was undertaken to make a systematic study of the magnesium sulfite oxidation relevant to magnesiumbased wet FGD plants.
2. EXPERIMENTAL SECTION The oxidation of magnesium sulfite was carried out in a stirred bubbling reactor (Figure 1). The stirred bubbling reactor used was a glass cylindrical vessel, 6.5 cm in internal diameter and 9.5 cm in height. Before performing the experiment, 150 mL of high purity water was added into the stirred bubbling reactor which was installed in a magnetic stirring constant-temperature Received: Revised: Accepted: Published: 4192
October 20, 2011 February 28, 2012 February 29, 2012 February 29, 2012 dx.doi.org/10.1021/ie300163v | Ind. Eng. Chem. Res. 2012, 51, 4192−4198
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The intrinsic reaction of sulfite was carried in an intermittent reactor (Figure 2). First, a known quantity of high-purity water
Table 1. Literature Results for the Calcium Sulfite Oxidation Kinetics in FGD Conditions reaction order
refs
status
19
saturated CaSO3, uncatalyzed saturated CaSO3, MgCl2 saturated CaSO3, peracetic acid saturated CaSO3, MnSO4 saturated CaSO3, MnSO4 unsaturated CaSO3, uncatalyzed unsaturated CaSO3, uncatalyzed unsaturated CaSO3, MnSO4 unsaturated CaSO3, MnSO4 unsaturated CaSO3, MnSO4 unsaturated CaSO3, Fe2+ unsaturated CaSO3, ethanol
20 20 21 19 22 23 24 25 21 26 27
sulfite
dissolved O2
0
partial pressure of O2
catalyst/ inhibitor
1.0
0
0
0
0.5
0
1.0
0.5
1.0
1.0
0
1.5
0
1.5
0
Figure 2. Experimental apparatus of intrinsic reaction (1) quantitative liquid filling injector, (2) dissolved oxygen meter, (3) magnetic stirring constant-temperature water bath, (4) intermittent reactor, (5) rubber stopper, (6) magnetic stirrer, (7) thermocouple.
was added into the intermittent reactor which was installed in a magnetic stirring constant-temperature bath. The stirrer started at a predetermined speed, and a dissolved oxygen probe was fixed in the solution. A certain quantity of sodium sulfite solution was then added into the reactor to a total volume of 1.0 L and the reaction started at the same time. The time was noted, and the concentration of dissolved oxygen was recorded during the reaction process. The concentration of sulfate could be calculated using the following formula:
1.5
1.5
0.5
0.75
1.0
1.0
0
1.0
2.0
0.5 −0.5
SO32 − + 1/2O2 → SO4 2 −
The software Origin was used for regressive analysis of the experimental data. All the chemicals used were of analytical grade because even a minute quantity of impurity, especially metal ions, will affect the oxidation rate of sulfite solution. Magnesium sulfite used in the experiments was laboratorymade from MgCl2 and Na2SO3. Mixing the MgCl2 solution and the Na2SO3 solution, magnesium sulfite will separate out as the sediment because its solubility is quite low. In order to avoid the influence by other salts, the product was washed by highpurity water five times to remove the soluble ions and then filtered and dried. A small amount of MgSO3 was oxidized to MgSO4 in the process of filtration and drying, which caused the product with purity above 80% of magnesium sulfite and the residual component was magnesium sulfate. As the magnesium sulfite is easily oxidized, the contents of magnesium sulfite and magnesium sulfate were measured before experiments and the dosages were determined from the measurement results.
Figure 1. Experimental apparatus of magnesium sulfite oxidation (1) air compressor, (2) air flow meter, (3) pH meter, (4) magnetic stirring constant-temperature water bath, (5) stirred bubbling reactor, (6) magnetic stirrer, (7) aeration header, (8) thermocouple.
bath. The stirrer started at a predetermined speed. A certain amount of magnesium sulfite and magnesium sulfate were then added into the stirred bubbling reactor. The time was noted and the air was injected into the solution in a steady manner. Hydrochloric acid and ammonia were used to adjust the pH. The reaction ceased at the scheduled time and the product, including magnesium sulfite and magnesium sulfate, was acidified by hydrochloric acid to remove aqueous-phase S(IV). The concentration of sulfate was then measured by means of ion chromatography, which was determined according to the standard curve of sulfate. The observed oxidation rate was calculated using the following formula: r = dC SO 2 −/dt 4
(2)
3. RESULTS AND DISCUSSION 3.1. Results of Magnesium Sulfite Oxidation. 3.1.1. Magnesium Sulfite Concentration. Figure 3 shows that the oxidation rate of sulfite increases as the magnesium sulfite concentration increases. The oxidation rate of sulfite is found to be 0.88 order with respect to magnesium sulfite. Zhao et al. found the reaction to be 1.0 order with respect to the sodium sulfite when controlled by the intrinsic reaction and which turned to be zero order when controlled by the gas−liquid mass transfer.29 Zhou et al. found a critical ammonium sulfite concentration, below which the reaction order with respect to sulfite is 0.2, while above which the order turns to −1.0.12 However, Jia et al. found the reaction to be −0.5 order with respect to ammonium sulfite.13 Different kinds of sulfite have different characters and reaction conditions, such as solubility, catalysts or inhibitors, range of sulfite concentration, pH, and ionic strength, which may lead to different results. Wang et al.
(1)
The given points in the figures representing the data are from a single series of experiments, and each point was repeated five times. The relative deviations within the series is less than 5% for magnesium sulfite concentration, 2% for magnesium sulfate concentration, 4% for pH value, 5% for air flow, and 3% for temperature. 4193
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the reaction. While the latter thesis on this kind of reaction has not been confirmed, further investigation is needed. 3.1.3. pH Value. Figure 5 shows that the oxidation rate of sulfite increased slowly with pH from 4.5 to 5.5 and increased
Figure 3. Effect of sulfite concentration on the oxidation rate (CMgSO4 = 0.1 mol/L; pH = 6.0; Q = 40 L/h; T = 303.15 K).
found that the uncatalyzed oxidation of saturated magnesium sulfite is zero order with respect to sulfite because the dissolved magnesium sulfite under different dosages are the same.30 The magnesium sulfite in this work was under unsaturated conditions, though the dissolved magnesium sulfite under different dosages was completely different. However, only less than 8.0% of magnesium sulfite had been oxidized after the reaction, which means that magnesium sulfite was far from excessive. Therefore, the changing of the oxidation rate in this section is corresponding to magnesium sulfite concentration and its reaction order. Since the magnesium sulfite solubility is much lower than most other kinds of sulfite, the oxidation of it is similar to that of calcium sulfite. 3.1.2. Magnesium Sulfate Concentration. The relation of sulfite oxidation rate and magnesium sulfate concentration in this work is shown in Figure 4. It is obvious that the oxidation
Figure 5. Effect of pH on the oxidation rate (CMgSO3 = 0.1 mol/L; CMgSO4 = 0.1 mol/L; Q = 40 L/h; T = 303.15 K).
quickly with pH from 5.5 to 6.5, while the oxidation rate began to decrease rapidly with pH above 6.5. This tendency is similar to that reported by Zhang and Millero on sulfite in seawater and by Gürkan et al. on ammonium sulfite.14,34 However, Zhou et al. and Jia et al. found that the oxidation rate of ammonium sulfite decreases with the increase of pH.12,13 These results were supported by the theory that the sulfite oxidation mechanism depends on the bisulfite concentration and the ratio of bisulfite concentration to sulfite concentration decreases with the pH increases.13,35 Figure 6 shows the
Figure 6. Distribution of bisulfite and sulfite with pH (25 °C, [SO3]total = 0.1 mol/L). Figure 4. Effect of sulfate concentration on the oxidation rate (CMgSO3 = 0.1 mol/L; pH = 6.0; Q = 40 L/h; T = 303.15 K).
distribution of bisulfite and sulfite with pH.36 On the other hand, some investigators found that the oxidation effect of oxygen significantly reduced under low pH.37 It is difficult to explain the phenomenon on a specific theory and the characteristics of oxidation kinetics of different sulfites with pH are obviously different. Thus, the changes of the reaction with different pH can be considered due to the interaction of different impact factors. Under lower pH, the bisulfite concentration was maintained at a high level while the effect of oxygen was greatly reduced, resulting in a lower oxidation rate. When pH value raised, the effect of oxygen increased while the bisulfite concentration declined rapidly, causing the corresponding reduction of the oxidation rate.
rate slowly decreases as the magnesium sulfate concentration increases, which is relatively flat to most reports.12,13 While the magnesium sulfate concentration raised to 3.0 mol/L, the oxidation rate of sulfite was reduced by about 35% compared to the low magnesium sulfate concentration, which certified that too high concentration of sulfate will inhibit the oxidation of sulfite. One reason that sulfate ion hampers the oxidation may be due to the decrease of the solubility of oxygen in solution and the diffusion coefficient changes.31−33 Another reason maybe due to the excess sulfate as the product simply inhibited 4194
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3.1.4. Air Flow. Figure 7 shows that the oxidation rate of sulfite increased quickly with the air flow raised to 60 L/h,
Figure 8. Effect of temperature on the oxidation rate (CMgSO3 = 0.1 mol/L; CMgSO4 = 0.1 mol/L; pH = 6.0; Q = 40 L/h).
of sulfite in the solution, and diffusion of oxygen from air bubbles into the solution. 3.2.1. Dissolution of Magnesium Sulfite. The dissolution is important for flue gas desulfurization in wet scrubbers and spray dryer reactors, and it is controlled by pH.41 The ionization equilibriums of sulfurous acid are36
Figure 7. Effect of air flow on the oxidation rate (CMgSO3 = 0.1 mol/L; CMgSO4 = 0.1 mol/L; pH = 6.0; T = 303.15 K).
above which it increased slowly. While the dissolved oxygen concentration in the solution was close to zero, it means that the oxygen transferred from air bubbles to the solution was all reacted. The material balance for a liquid volume V in the reactor is38 NO2aV = rV
H2SO3 ↔ H+ + HSO3−
(6)
H2SO3− ↔ H+ + SO32 −
(3)
The distribution coefficient of SO32‑ is δ0 =
(4)
The solution composition and the oxygen content in the air will not change under different air flow, and the diffusion rate of oxygen can be regarded as a constant. Thus, the oxidation rate changes consistently with the interfacial area per unit volume of liquid. When the air flow was below 60 L/h, the bubbled air dispersed uniformly, resulting in a quiet bubbling area and had little stirring effect on the reaction solution. The gas−liquid contact area increased as the air flow increased. When the air flow increased up to 60 L/h, some air froth collided and agglomerated, resulting in a turbulent bubbling area and little change of gas−liquid contact area.13,39 The results on the effects of air flow by different investigators are similar. 3.1.5. Temperature. Figure 8 shows that the oxidation rate of sulfite increases slowly as the temperature increases. According to the Arrhenius formula: ln k = ln k 0 −
Ea 1 R T
Ka2 = 1.0 × 10−7 (25°C) (7)
where NO2 is the diffusion rate of oxygen, a is the interfacial area per unit volume of liquid, and r is the reaction rate. Equation 3 can be simplified as r =NO2a
Ka1 = 1.5 × 10−2 (25°C)
[SO32 −] Ka1Ka2 = +2 [SO3]total [H ] + Ka1[H+] + Ka1Ka2
(8)
The conditional solubility product of MgSO3 is K sp,MgSO ′ = [Mg 2 +][SO3]total =
K sp,MgSO
3
3
−3
δ0
(9)
where Ksp,MgSO3 = 3.0 × 10 (18−25 °C). Considering the common ion effect, [Mg2+] in eq 9 is the total concentration of Mg2+ from MgSO3 and MgSO4. The solubility of MgSO3 under 18−25 °C was calculated as 0.14 mol/L when pH was 6.0 and MgSO4 concentration was 0.1 mol/L, which was approaching the experiment results. If the reaction rate was controlled by dissolution of magnesium sulfite, most dissolved magnesium sulfite should be oxidized. In fact, only less than 8.0% of magnesium sulfite has be oxidized, which showed that the dissolution of magnesium sulfite is not the controlling step. 3.2.2. Intrinsic Reaction. According to the research by Wang et al., the intrinsic kinetics of sulfite oxidation includes two steps, a rapid reaction in the rich oxygen zone and a slow reaction in the poor oxygen zone.43 As the oxidation of magnesium sulfite was investigated under low dissolved oxygen, the results of the intrinsic reaction in the poor oxygen zone was shown in Figure 9, which shows that the reaction rate increases as the sodium sulfite concentration increases and it is found to be 2.0 order with respect to the sodium sulfite concentration. Furthermore, the dissolved oxygen concentration decreased linearly with reaction time under a large excess of sodium sulfite, indicating that the reaction was zero order with respect to dissolved oxygen concentration.
(5)
where k is the reaction rate constant which quantifies the speed of a chemical reaction and depends on temperature, and the apparent activation energy for the oxidation was calculated to be 2.02 kJ/mol, which is lower than the previously reported activation energy for the oxidation of other kinds of sulfite.11−14,39,40 3.2. Mechanism of Magnesium Sulfite Oxidation. According to the oxidation process of calcium sulfite,39 that of magnesium sulfite may include three steps: dissolution of magnesium sulfite particles into solution, an intrinsic reaction 4195
42
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solubility of oxygen H is 5.8 × 10−4 mol/(L atm).38 The equilibrium concentration of oxygen at the interface CO2*, neglecting the gas-phase resistance, is (0.21 atm)H = 1.22 × 10−4 mol/L.38 According to section 3.2.2, the reaction rate constant k is 4.55 × 10−2 L/(mol s). The reaction order of oxygen m is zero and that of sulfite n is 2.0. The Hatta number was calculated to be 1.2, which is slightly higher than 1.0; meanwhile, the reaction finished within the liquid film. Thus, the reaction can be considered as a fast chemical reaction.38 The mass transfer rate of oxygen is controlled by the liquid film mass transfer process, and the diffusion rate of oxygen is obtained according to the double film theory: NO2 = KL′(CO2* − CO2) Figure 9. Effect of sulfite concentration on the intrinsic reaction rate (T = 293.15 K).
where KL′ can be simplified when the chemical reaction was rapid:44
On the basis of the experimental results above, the intrinsic reaction rate can be expressed as
(
⎡ 2 KL′ = ⎢ D k(C *)m − 1 C SO 2 − 3 ⎣ m + 1 O2 O2
(
2
)
r = k C SO 2 − 3
(12)
n ⎤1/2
) ⎥⎦
(13)
The concentration of dissolved oxygen in the solution was close to zero and the diffusion rate of oxygen can be written as
(10)
The effect of temperature on the intrinsic reaction rate is shown in Figure 10. The apparent activation energy was calculated to be 99.70 kJ/mol with a frequency factor of 6.84 × 1015 L/(mol s).
n ⎤1/2 ⎡ 2 m − 1 D k(C *) C SO 2 − ⎥ ·CO2* NO2 = ⎢ 3 ⎣ m + 1 O2 O2 ⎦
(
)
2
(
) ]1/2
= [2DO2kCO2* C SO 2 − 3
(14)
According to eq 4, the oxidation rate can be written as
(
2
) ]1/2 a
r = NO2a = [2DO2kCO2* C SO 2 − 3
(15) 2
where the interfacial area a ranged from 500 to 1800 m /m3 in this experiment. According to eq 15, the oxidation rate was 0.5 order with respect to CO2* and 1.0 order with respect to CSO32−. Wang et al.30 found that the oxidation of magnesium sulfite was 0.47 order with respect to the partial pressure of O2, and the reaction in this work was found to be 0.88 order with respect to magnesium sulfite. These experimental results were generally consistent with eq 15. On the basis of the discussion above, it can be considered that the diffusion of oxygen is the controlling step of the oxidation of magnesium sulfite. 3.3. Discussion. According to the experimental results, the dissolved magnesium sulfite concentration, pH value, and air flow are the most sensitive operating parameters on the reaction rate, which will cause a significant change in the reaction rate. In order to improve the oxidation rate, the magnesium sulfite concentration should be raised to the saturated condition, the pH value should be controlled at about 6.5, and the efficient aerators should be used. The apparent activation energy of the intrinsic reaction is 99.7 kJ/mol, and that of the heterogeneous reaction is only 2.02 kJ/mol, which means that the temperature has much less effect on the latter. For the heterogeneous reaction, it is indicated that the intrinsic reaction is one step of the oxidation process of magnesium sulfite, and the diffusion of oxygen is the controlling step. At a higher temperature, the intrinsic reaction rate will raise while the solubility of oxygen in the solution will reduce, which causes a minor change in the total reaction rate. As the temperature has little effect on the reaction and the waste heat of the flue gas can increase the slurry temperature, it does not
Figure 10. Effect of temperature on the intrinsic reaction rate (CSO32− = 6 mmol/L).
The intrinsic reaction rate of sulfite can be calculated by eq 10. If intrinsic reaction were the controlling step, the reaction rate should be 3.1 × 10−4 mol/(L s) when the concentration of dissolved sulfite is 0.1 mol/L at 303.15 K. Figure 4 shows that the oxidation rate is much lower than the calculated intrinsic reaction rate and confirmed that the intrinsic reaction is not the controlling step either. 3.2.3. Diffusion of Oxygen. The Hatta number is always used to determine a reaction to be a fast chemical reaction or not, which can be written as44
Ha =
⎡ 2 D k(C *)m − 1 C SO 2 − ⎢ 3 ⎣ m + 1 O2 O2
(
KL0
n ⎤1/2
) ⎥⎦
(11)
At 30 °C, 1 atm, and 0.1 mol/L sulfite concentration, the physical mass transfer coefficient KL0 is 1.13 × 10−4 m/s, the diffusion coefficient of oxygen DO2 is 2.6 × 10−9 m2/s, and the 4196
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Ha = Hatta number, dimensionless Ka1 = equilibrium constant of the first step Ka2 = equilibrium constant of the second step KL0 = physical mass transfer coefficient, m/s KL′ = liquid-phase mass transfer coefficient, m/s k = the reaction rate constant k0 = frequency factor m = reaction order of oxygen NO2 = diffusion rate of oxygen, mol/(m2 s) n = reaction order of sulfite Q = air flow, L/h R = gas contant, 8.3145 J/(mol K) r = the reaction rate, mol/(L s) T = temperature, K t = reaction time, s V = volume of liquid, L
need additional heating for the reaction. Though the oxidation rate was slightly affected by the sulfate concentration, it will be inhibited to a considerably low value if the solution includes too many sulfates. Thus, the oxidation product, magnesium sulfate, should be removed by crystallization techniques when it is accumulated to a certain extent.
4. CONCLUSION In the literature of chemical engineering, the oxidation of other kinds of sulfite in wet FGD process has been extensively studied. However, the oxidation of magnesium sulfite only gained very little attention, though the magnesium-based wet FGD process has been increasingly used on the industrial boiler in recent years. In this paper, the oxidation of magnesium sulfite relevant to magnesium-based wet FGD plants, including the kinetics of sulfite oxidation under related operating parameters and the mechanism of the oxidation, has been systematically studied. Using the stirred bubbling reactor, the kinetics of magnesium sulfite oxidation was studied by varying MgSO3 concentration, MgSO4 concentration, pH, air flow, and temperature. The reaction was found to be 0.88 order with respect to sulfite, and the apparent activation energy for the oxidation was calculated to be 2.02 kJ/mol. The oxidation rate can be speeded up by increasing the dissolved magnesium sulfite concentration, raising the air flow and maintaining the pH value at 6.5, while the sulfate concentration and the temperature will slightly affect the oxidation rate. These results provide the basis for operation optimization in the oxidation process of magnesiumbased wet flue gas desulfurization. The mechanism of the oxidation of magnesium sulfite was discussed, which involved dissolution of magnesium sulfite, intrinsic reaction, and diffusion of oxygen. It was concluded that the oxidation was controlled by diffusion of oxygen. This finding will be beneficial for designing the oxidation process during the magnesium-based wet flue gas desulfurization.
■
Greek Symbols
δ0 distribution coefficient of sulfite ions
■
REFERENCES
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AUTHOR INFORMATION
Corresponding Author
*Phone: +86-21-64252058. Fax: +86-21-64252737. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS The present work was supported by the project cooperating with SINOPEC Ningbo Research Institute of Technology and the Shanghai Leading Academic Discipline Project (Grant No. B506).
■
NOTATION a = the interfacial area per unit volume of liquid, m2/m3 CMgSO3 = concentration of magnesium sulfite, mol/L CMgSO4 = concentration of magnesium sulfate, mol/L CO2* = equilibrium concentration of oxygen at the interface, mol/L CO2 = concentration of oxygen in the solution, mol/L CSO32− = concentration of sulfite, mol/L CSO42− = concentration of sulfate, mol/L DO2 = diffusion coefficient of oxygen in the solution, m2/s Ea = apparent activation energy, kJ/mol H = solubility of oxygen in the solution, mol/(L atm) 4197
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dx.doi.org/10.1021/ie300163v | Ind. Eng. Chem. Res. 2012, 51, 4192−4198
