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Sep 18, 2014 - Sourab Sinha , Abhijeet Raj , Ahmed S. Al Shoaibi , and Suk Ho Chung ... Baron Rubahamya , K. Suresh Kumar Reddy , A. Prabhu , Ahmed Al...
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Toluene Destruction in the Claus Process by Sulfur Dioxide: A Reaction Kinetics Study Sourab Sinha,† Abhijeet Raj,*,† Ahmed S. AlShoaibi,† Saeed M. Alhassan,†,‡ and Suk Ho Chung§ †

Department of Chemical Engineering and ‡Gas Processing and Materials Science Research Centre, The Petroleum Institute, Abu Dhabi, UAE § Clean Combustion Research Centre, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia S Supporting Information *

ABSTRACT: The presence of aromatics such as benzene, toluene, and xylene (BTX) as contaminants in the H2S gas stream entering Claus sulfur recovery units has a detrimental effect on catalytic reactors, where BTX forms soot particles and clogs and deactivates the catalysts. BTX oxidation, before they enter catalyst beds, can solve this problem. A theoretical investigation is presented on toluene oxidation by SO2. Density functional theory is used to study toluene radical (benzyl, o-methylphenyl, mmethylphenyl, and p-methylphenyl)−SO2 interactions. The mechanism begins with SO2 addition on the radical through one of the O atoms rather than the S atom. This exothermic reaction involves energy barriers of 4.8−6.1 kJ/mol for different toluene radicals. Thereafter, O−S bond scission takes place to release SO. The reaction rate constants are evaluated to facilitate process simulations. Among four toluene radicals, the resonantly stabilized benzyl radical exhibited lowest SO2 addition rate. A remarkable similarity between toluene oxidation by O2 and by SO2 is observed. BTX requires temperatures above 1050 °C for oxidation.11 The temperature in the Claus furnace is well above this value, but, with the given process conditions of the Claus furnace, H2S oxidation by O2 is preferred over BTX oxidation due to their low concentrations; thus, some of the BTX is able to enter the catalytic units. Ibrahim et al.12 studied the effect of the presence of toluene in the H2S gas stream and observed an increase in the concentration of H2, which was directly proportional to toluene concentration. The H2 molecule thus formed had a tendency to inhibit the oxidation of H2S. The formation of pollutants such CO and COS was also observed. Clearly, the presence of BTX in the feed gas to the Claus process is not desired. Several solutions have been proposed in the literature to remove or destroy BTX before the gas stream carrying them enters the catalytic units, as mentioned below. The increase in the temperature in the Claus furnace may help in oxidizing BTX.5,9,10,13 For this, three methods have been suggested: (a) enriching air with oxygen, (b) co-firing natural gas with feed, and (c) preheating the feed gas. Method (a) does not raise the furnace temperature high enough for complete BTX oxidation when H2S concentration in feed is low. Moreover, enriching air with oxygen is an expensive process. Method (b) requires burning natural gas along with acid gases in a furnace of high volume for BTX destruction and, thus, has high capital cost. Method (c) is able to raise the furnace temperature since the adiabatic flame temperature increases with feed preheating, but it is not high enough to completely destroy BTX, especially when the feed is lean in H2S.

1. INTRODUCTION The Claus process is widely used in oil and gas industries to recover sulfur from H2S, an acid gas present in appreciable amounts in natural gas and in byproduct gas streams.1−3 It has two major sections: (a) Claus furnace, where noncatalytic partial oxidation of H2S in air through the reaction, H2S + 1.5O2 → SO2 + H2O, takes place. Some sulfur is also produced in this section. (b) Catalytic units, where the uncombusted H2S and SO2 present in the exhaust gas from the furnace (after heat recovery) undergo catalytic reaction (2H2S + SO2 → 3S + 2H2O) to form sulfur.4 This process is responsible for the production of 90−95% of elemental sulfur worldwide. During the separation of H2S from raw natural gas streams in amine sweetening units, several contaminants from the raw gases such as benzene, toluene, xylenes (collectively known as BTX), heavy hydrocarbons, NH3, CO2, N2, CS2, and COS accompany the H2S gas stream. These contaminants hamper the efficiency and increase the operational cost of the Claus process5 by deactivating catalysts, reducing sulfur quality, triggering the formation of toxic compounds such as H2SO4, CO, COS, and CS2,6 and corroding the downstream equipment. Out of these, BTX leads to the loss of catalytic activity through the formation of sulfur hydrocarbons (similar to soot particles). These hydrocarbons clog the catalyst pores, increase the pressure drop through the reactor beds, and lead to the production of offspec black sulfur.7,8 Due to these reasons, BTX has been a major concern for sulfur recovery unit (SRU) operators and an ongoing area for research. Crevier et al.9 observed that, among BTX, while benzene is relatively benign, toluene and xylenes proficiently deactivate Claus catalysts within hours of operation. In a study on the destruction of hydrocarbons in a Claus furnace, Klint10 reported that BTX is more difficult to destroy than the aliphatic hydrocarbons that get easily oxidized at the furnace temperature. © 2014 American Chemical Society

Received: Revised: Accepted: Published: 16293

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Our present investigation focuses on the development of reaction mechanisms for H atom abstraction from toluene to form benzyl, o-methylphenyl, m-methylphenyl, and p-methylphenyl radicals and the oxidation by SO2 of these radicals. The energetics and the molecular parameters for the species involved in their reactions have been determined through quantum chemical calculations. The rates of the elementary reactions have been evaluated using transition state theory. The possible reaction pathways leading to the formation of some chemical species such as CO, SO, OH, CHO, HCHO, and CO2 have been identified.

The adsorption of BTX using activated carbon beds is a promising solution,9 but in the presence of moisture in the gas stream, the adsorbed BTX on carbon beds is replaced with water. To avoid this problem, feed preheating is required. In general, four to five beds of activated carbon in series are required for effective removal of BTX. To regenerate the beds, steam is used to desorb BTX. This is followed by drying of beds. As evident, the high-energy usage makes this solution expensive. With the brief description of some existing solutions for BTX removal presented above, it is clear that they either require huge capital costs or involve high-energy consumption, but they still do not provide complete removal of BTX. Moreover, all of the BTX removal techniques have concentrated on the pretreatment of feed or on the destruction of BTX in the Claus furnace. However, the presence of BTX in the acid gas stream does not have a detrimental effect on the efficiency of the Claus furnace. The effect is primarily seen in the catalytic section of the Claus process, as explained before. The residence time of the gas-phase species in the Claus furnace is usually about 0.5−0.6 s, and the residence time required for the destruction of BTX in the furnace is about 1 s (note that the time required for BTX destruction is dependent on the feed composition and temperature that affects the maximum flame temperature in the furnace).13 Thus, it is possible to get rid of them by increasing the residence time of the gaseous mixture in the high-temperature environment. This problem could be solved by increasing the Claus furnace size to provide sufficient time for BTX oxidation or by installing an adiabatic BTX destruction unit between the Claus furnace and the catalytic units, where BTX can be oxidized under required process conditions (if the gas industries with existing SRUs prefer to install an additional process equipment instead of replacing the existing Claus furnace). Since SO2 is already present in the hot exhaust gas from the furnace in high concentration, it is possible to oxidize BTX by SO2 if favorable process conditions such as temperature and residence time are maintained in the furnace or the BTX destruction unit. Though this solution involves capital cost to increase furnace size or for the BTX destruction unit, no significant additional operating and maintenance costs will be required, which the other solutions require through the use of pure oxygen, adsorbents, or natural gas. The high SO 2 concentration already present in the anoxic region makes it highly likely that BTX will be effectively oxidized. An experimental study was conducted by Levy et al.,14 where the oxidation of benzene by SO2 was carried out in sealed Pyrex bulbs at temperatures in the range of 400−540 °C. The reaction between them was shown to take place at temperatures above 540 °C. Since the exhaust gas from the Claus furnace is well above this temperature, the reactions between SO2 and BTX can take place. The high-temperature studies of SO2 addition to hydrocarbon flames15−18 also suggest that SO2 reduces the concentrations of aromatic hydrocarbons and soot through their oxidation. In refs 19 and 20, low-temperature oxidation of toluene by SO2 was studied, where toluene was observed to be readily oxidized and involved an activation energy of about 200 kJ/mol. In order to determine, through simulations, the optimum operating conditions under which BTX could be oxidized by SO2, a detailed reaction mechanism is required. In ref 21, the oxidation of benzene by SO2 was studied. However, detailed studies on the oxidation by SO2 of toluene and xylenes are not present in the literature.

2. COMPUTATIONAL DETAILS The ground state molecular structures of the stable chemical species as well as the transition states were found using density functional theory (DFT) with Becke’s three-parameter exchange and the Lee, Yang, and Parr correlation (B3LYP) functional with the 6-311++G(d,p) basis set. For large molecules such as aromatic hydrocarbons, DFT is considered to be a standard choice, as it is computationally less expensive than higher levels of theory and has already been validated and used for aromatic hydrocarbons in previous studies.22−32 The molecular structures were optimized with different spin multiplicities to identify the multiplicity with a minimum energy, reasonable geometry, and low-spin contamination. All of the calculations were performed using Gaussian 09 software.33 Spin contamination in open-shell systems can significantly affect the energy, geometry, and calculated spin density of the molecules.34 The expectation value of the spin operator S2̂ , ⟨S2⟩, gives a measure of the amount of spin contamination introduced by a given level of theory. By observing ⟨S2⟩ for a number of stable species and transition states, it is shown in previous studies24,35 and in this work that DFT introduces a negligible amount of spin contamination. The values of ⟨S2⟩ for all of the chemical species and transition states involved in the proposed processes are presented in the Supporting Information. The rate constants for the reactions involved in the proposed processes were evaluated using transition state theory. The partition functions for the transition states and reactants were calculated at a range of temperatures (300−3000 K) using the vibrational frequencies, moments of inertia, mass, and electronic multiplicity, all of which are given by the quantum calculations. Further details are provided in ref 21. A linear least-squares fitting algorithm was used to fit the modified Arrhenius expression (k = ATne(−E/RT)) to the data points of the rate constants in order to obtain the kinetic parameters of the frequency factor A, the temperature exponent n, and the activation energy E. To assess the role of quantum tunneling, in the literature, there are four efficient methods to evaluate the tunneling correction factor (or transmission constant): Wigner correction, Eckart correction, zero-curvature tunneling correction, and small curvature tunneling correction. At temperatures greater than 500 K, the correction factors from all of the methods converge to similar values.36,37 In this paper, the Wigner method was employed to obtain the tunneling correction factors for all of the elementary reactions.21 3. RESULTS AND DISCUSSION In the high-temperature environment of the Claus furnace, H atom removal from toluene to form a radical species (benzyl, omethylphenyl, m-methylphenyl, and p-methylphenyl), as shown below, can take place through H abstraction by gas-phase radical 16294

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+G(d,p). Moreover, the activation energies for the formation of benzyl, o-methylphenyl, m-methylphenyl, and p-methylphenyl were found to be 5.2, 12.6, 15.5, and 13.9 kJ/mol, respectively, using CBS-QBS and 2.5, 9.9, 12.8, and 11.2 kJ/mol, respectively, using experimental and computational estimates on H abstraction.41 These match very well with the values of 5.6, 9.4, 10.2, and 11.3 kJ/mol, respectively, obtained in this work for the four radicals. Figure 3 presents the potential energy diagrams for H abstraction from toluene by the HS radical. All of the reactions are endothermic. The transition states were not found for these reactions. Except for benzyl formation, the reaction energies were found to be very high (101−104.4 kJ/mol), indicating that H abstraction by HS is less likely to form methylphenyl radicals than by H and OH. The rest of this study focuses on the reaction mechanisms for the oxidation of benzyl and methylphenyl radicals by SO2. To facilitate the description of the reaction mechanisms in this paper, two terms have been used. (a) Pathways: They describe the reactions of the major species formed from the addition of SO2 on benzyl and methylphenyl radicals. (b) Routes: They describe the different reaction channels for the decomposition of intermediate species in a pathway. In an experimental study on toluene oxidation by SO2,19 an activation energy of about 200 kJ/ mol was determined. In this paper, all the routes with overall activation energies near 200 kJ/mol will be highlighted as the highly probable routes. 3.1. Benzyl−SO2 Reactions. Figure 4 presents the pathways for the oxidation of the benzyl radical by SO2. Their reaction begins with the attack of the O atom of SO2 on the free radical site of benzyl due to higher electronegativity of O atoms than the S atom. This addition reaction results in a chemical species, CS1. For CS1 decomposition, two possible pathways have been studied in this work. Pathway 1 involves the elimination of SO, while Pathway 2 involves the attack of a nearby C atom by the dangling O atom in CS1. The reaction energetics of the two pathways are provided in sections 3.1.1 and 3.1.2. The intermediate species formed in the mechanisms have some common sulfur- and oxygen-containing functional groups on them, which are shown in Figure 5. 3.1.1. Pathway 1. Figure 6 presents the potential energy diagram for pathway 1 with the energies of the chemical species and the transition states relative to the total energy of the reactants, benzyl and SO2. The benzyl−SO2 addition reaction requires a small activation energy barrier of 5.4 kJ/mol to be overcome to form CS1. In this exothermic reaction, an energy of 76.4 kJ/mol is released. Though there is no detailed experimental study on the reaction energetics for the addition of SO2 on benzyl, there are two studies on the reactions of SO2 with methyl (CH3)42 and ethyl (C2H5) radicals.43 For CH3 + SO2 → CH3SO2, we found activation energies of 6.3 kJ/mol for the forward reaction and 93.7 kJ/mol for the backward reaction, while for C2H5 + SO2 → C2H5SO2, activation energies of 12.9 kJ/ mol for the forward reaction and 83.3 kJ/mol for the backward reaction were found. In this work, for SO2 addition on the CH2 radical in benzyl, the forward and reverse energy barriers were calculated as 5.4 and 81.8 kJ/mol, respectively. While these values for benzyl may not be compared directly with the energies associated with CH3 and C2H5 due to the difference in their molecular structures, the similarities in the activation energies for their forward and reverse reactions are noteworthy. After SO2 addition to benzyl, the SO molecule from CS1 is eliminated barrierlessly to form CS2, where a reaction energy of

species such as H, OH, and HS that are present in the Claus furnace in appreciable concentrations.

Figures 1−3 provide the energy diagrams for the abstraction of the H atom from toluene to form these radical species. In Figure 1, the reaction involving the formation of a resonantly stabilized benzyl radical through H abstraction by the H atom was exothermic with an activation energy of 13.8 kJ/mol, while in the cases of methylphenyl radicals, the reactions were endothermic with comparable activation energies between 50.1 and 51.6 kJ/ mol. In our previous work,21 an activation energy of 50.9 kJ/mol was found for benzene + H → phenyl + H2, which is very similar to the activation energies for the formation of methylphenyl radicals. The lower potential energy barrier for benzyl formation than that for the other radicals is a consequence of a weaker methyl C−H bond (with bond dissociation energy of 375.7 kJ/ mol) than a phenyl C−H bond (with bond dissociation energy of 472.4 kJ/mol).38 In a high-temperature experimental study on the rate constant for H abstraction from toluene to form a benzyl radical,39 an activation energy of 15.4 kJ/mol was found, which is close to the computed activation energy of 13.8 kJ/mol for this reaction. In ref 40, from the experimental rate constants for H abstraction from toluene to form methylphenyl radicals, an activation energy of 54 kJ/mol was found, which is very similar to the computed values (50.1−51.6 kJ/mol). In Figure 2, all the H abstraction reactions from toluene by OH were found to be exothermic. The formation of a benzyl radical was barrierless with B3LYP/6-311++G(d,p), while a small barrier of 5.6 kJ/mol was found with M06-2X/6-311++G(d,p). For the formation of methylphenyl radicals, activation energies between 9.4 and 11.3 kJ/mol and reaction energies between 17.6 and 21.1 were obtained, which are very close to the activation energy of 11.4 kJ/mol and the reaction energy of 18.9 kJ/mol for benzene + OH → phenyl + H2O. The H abstraction reactions from toluene by OH were also studied41 using the CBS-QB3 level of theory. The reaction energies for the formation of benzyl, o-methylphenyl, m-methylphenyl, and p-methylphenyl radicals were found to be 119.1, 20.2, 20.4, and 15.5 kJ/mol, respectively, which are very close to the energies of 117, 21.1, 19.9, and 17.6 kJ/mol, respectively, found in this work with B3LYP/6-311+ 16295

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Figure 1. Potential energy diagrams at 0 K for H abstraction from toluene by a H atom to form benzyl and methylphenyl radicals.

+192.7 kJ/mol is involved. For further reactions, the species CS2 can follow four different routes (Routes a−d), which are shown in Figures 6−8 and discussed below. Route a. This route, shown in Figure 6, involves an attack on the C atom at the ortho-position by an O radical in CS2 to form a fused four-membered ring with an ether group in CS3 after crossing an energy barrier of 136.1 kJ/mol. The dissociation of a C−O bond in CS3 gives CS4. The very low potential energy barrier of 4.1 kJ/mol for the forward reaction for CS4 to form a bicyclic species (CS5) indicates that CS4 is a short-lived species. In CS5, the cleavage of the bond connecting the carbon atoms at ortho- and meta-positions forms a seven-membered ring in CS6 after crossing an energy barrier of 59.9 kJ/mol. This species can then undergo molecular rearrangement to form a fused fivemembered ring with a methylene group and a four-membered ring with an O atom in CS7. This step requires overcoming a high energy barrier of 185.0 kJ/mol. The intermediate species, CS7, then rearranges itself to form a stable species, CS8, containing an aldehyde (CHO) group with the release of 126.8 kJ/mol of reaction energy. Thereafter, from CS8, CHO is eliminated to

form CS9 (5-methylenecyclopenta-1,3-diene) after overcoming an energy barrier of 116.2 kJ/mol. An alternate route for CS4 is shown in the same figure by dotted lines where an activation energy of 81.7 kJ/mol is involved to form CS10, from where CHO is removed to form CS9. As shown in Figure 7, CS3 can also undergo H-migration from the ortho-position to the carbon atom carrying the methylene group, but this requires a high activation energy barrier of 222.3 kJ/mol to be overcome to form CS11. This is followed by the breakage of a C−C bond to fuse phenyl and oxetane rings to form CS12. This reaction requires an activation energy of 189.2 kJ/ mol. The species CS12 is highly unstable, and it undergoes barrierless C−O bond fission to form CS13. The α-carbon of the carbonyl group forms a bond with the methylene group to obtain CS14 by overcoming an energy barrier of 118.2 kJ/mol. Thereafter, the loss of a CO molecule from CS14 takes place to form cyclohexa-1,3-diene (CS15). For CO desorption in this step, only a small activation energy of 9.5 kJ/mol is required. Route b. This route for CS2 decomposition is shown by the dashed lines in Figure 8 and involves an ipso attack by the 16296

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Figure 2. Potential energy diagrams at 0 K for H abstraction from toluene by OH to form benzyl and methylphenyl radicals.

opening in CS20 through C−O bond scission to form a chainlike molecule, CS21. After overcoming an energy barrier of 96.2 kJ/mol, CS21 forms CS10 with a five-membered ring along with methylene and CHO groups. The CHO group is then eliminated to form CS9. Route c. The dotted lines in Figure 8 present this route, which involves the formation of the phenyl radical (CS18) in a single step from CS2 through the elimination of HCHO. This reaction requires an energy barrier of 99.5 kJ/mol to be overcome. Route d. Shown by thin solid lines in Figure 8, this route involves the migration of a H atom from the methylene group to the carbon atom at the ipso-position, which requires an activation energy of 85.7 kJ/mol to form CS22. Thereafter, the elimination of CHO takes place after overcoming an energy barrier of 55.5 kJ/mol to form benzene (CS23) as one of the end products. Further oxidation of benzene by SO2 can take place through the pathways detailed in our previous work.21

dangling O atom in CS2 to form an epoxide group in CS16. This reaction requires an activation energy of 55.2 kJ/mol. The backward activation energy for this reaction is, however, very low (0.8 kJ/mol), which indicates that the reaction would mainly occur at high temperatures. The breakage of the C−C bond of the epoxide ring in CS16 forms a very stable species, CS17, from where a HCHO group is eliminated to form a phenyl radical (CS18). The loss of HCHO from CS17 is a highly endothermic reaction involving an activation energy of 138.8 kJ/mol and a reaction energy of 102.3 kJ/mol. Further oxidation of the phenyl radical can take place through the pathways detailed on our previous work.21 The species CS16 can also undergo bond rearrangement to form CS19, as shown by dash-dotted lines in Figure 8, but this involves a high energy barrier of 219 kJ/mol. The resultant molecule, CS19, is very unstable, and it gets converted to CS20 having a seven-membered ring. The next step involves ring 16297

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Figure 3. Potential energy diagrams at 0 K for H abstraction from toluene by HS to form benzyl and methylphenyl radicals.

Route e. Shown by thick solid lines in Figure 8, this route involves the loss of a H atom from the CH2O chain to form benzaldehyde (CS24). This reaction requires a high activation energy of 95.4 kJ/mol. Further reactions of CS24, involving the loss of CHO, were already studied in ref 44. Out of the five routes discussed above for CS2, Routes b−e involve overall activation energies of 204.3 kJ/mol (corresponding to TS18), 202.2 kJ/mol (corresponding to TS25), 215.8 kJ/ mol (corresponding to TS24), and 211.7 kJ/mol (corresponding to TS27), respectively, which are close to the experimentally observed overall activation energy of 200 kJ/mol for toluene oxidation by SO2. 3.1.2. Pathway 2. Figure 9 shows the potential energy diagram for an alternate pathway for CS1. The addition of the terminal O atom to the α-carbon of CS1 leads to the formation of a fused bicyclic ring in CS25. However, this reaction is highly endothermic, which requires an energy barrier of 190.1 kJ/mol to be overcome, and has a reaction energy of 177.7 kJ/mol. The breakage of one of the O−S bond leads to the formation of a

three-membered C−C−O ring and an O−S chain in CS26. This is followed by desorption of the SO molecule to form CS16. Further reactions for CS15 are already discussed in the previous section. 3.2. o-Methylphenyl−SO2 Reactions. Figure 10 presents the reaction mechanism for the oxidation by SO2 of the omethylphenyl radical. To begin with, SO2 is added to the radical site through one of the O atoms due to the reason mentioned previously to form CS27. Three pathways have been studied in this work for this species. Pathway 1 involves the elimination of the SO group, that is, CS27 → CS28; Pathway 2 involves the migration of the SO group to the meta-position, that is, CS27 → CS40; and Pathway 3 involves the addition of the terminal O atom to the meta-position, that is, CS27 → CS46. The energetics involved in these pathways and the routes comprising them are detailed in sections 3.2.1−3.2.3. 3.2.1. Pathway 1. Figure 11 presents the potential energy diagram for Pathway 1. For the addition of SO2 on the radical site of o-methylphenyl, a small activation energy barrier of 4.8 kJ/mol 16298

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Figure 4. Reaction mechanism for the oxidation of benzyl radical (C6H5CH2•) by SO2. The numbers given below the chemical species will be used for their identification in the paper.

mol for C6H5• + SO2 → C6H5SO2.21 Thereafter, the elimination of the SO group from CS27 leads to the formation of CS28, which lies 87.7 kJ/mol above CS27. The chemical species, CS28, can follow five different routes for its decomposition, as shown in Figures 10 and 11 and discussed below as Routes a−e. Route a. Figure 11 presents this route, where a H atom from the methyl group in CS28 migrates to the O radical to form CS29 having a methylene and a hydroxyl group. This requires an activation energy of 156.4 kJ/mol to be overcome. The

is required, which is lower than the activation energy involved for SO2 addition to the benzyl radical. Moreover, this addition reaction is highly exothermic with a reaction energy of 181.6 kJ/ mol and results in the formation of a stable species, CS27. This indicates that SO2 addition to the radical site at the orthoposition is preferred over the resonantly stabilized benzyl radical possibly due to high electron density at the ortho-position imposed by the electron-donating methyl group. Note that its reaction energy is very close to the reaction energy of −182.0 kJ/ 16299

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requires an activation energy of 86.5 kJ/mol. The species, CS37, then rearranges itself to form CS33, whose further reaction is discussed above. Route d. The dash-dotted lines in Figure 12 represent this route. Similar to Route c, this route also begins with the formation of a seven-membered ring in CS38 that lies 294.6 kJ/mol above CS28. However, the backward activation energy barrier for this reaction is only 0.3 kJ/mol, which makes this route less likely to proceed in the forward direction at low temperatures. The molecular rearrangement of CS38 requires overcoming an energy barrier of 53.5 kJ/mol to form CS34, a species that is also present in Route b. Route e. This route, represented by dotted lines, involves the highest activation energy of 395.9 kJ/mol among all five routes for CS28. It forms a closed-shell species, 2H-benzo[b]oxete (CS39), resulting from the attack of the O radical of CS28 on the methyl group with simultaneous elimination of a H atom. Due to a very high activation energy barrier involved in this pathway, the product CS39 is least likely to form, and therefore, its further reactions have not been studied. 3.2.2. Pathway 2. Figure 13 presents an alternate pathway for CS27, which involves SO migration from the OSO chain to the meta-position. This migration requires overcoming an energy barrier of 199.6 kJ/mol to form CS40. The species, CS40, can follow two routes. The first route involves the elimination of SO to form CS28. A small activation energy of 44.9 kJ/mol is required for this reaction. The further reaction of CS28 has already been studied above. The second route involves the intramolecular rearrangement of CS40 to form a sevenmembered heterocyclic ring in CS41. This rearrangement requires a very high activation energy of 203.1 kJ/mol, thus making this route less favorable than the previous one. As shown in Figure 13, in subsequent steps, CO and SO are eliminated to form CS35. 3.2.3. Pathway 3. Figure 14 presents the energy diagram for a third pathway for CS27 involving the addition of the terminal O atom to the meta-position (with respect to methyl group) to form CS46, a fused bicyclic metastable structure. The activation energy required for this reaction is 202.7 kJ/mol. This species can readily undergo the dissociation of the S−O bond to form CS47, which requires an activation energy of only 0.9 kJ/mol. The further reactions for CS47 involve (a) the elimination of the SO

Figure 5. Some oxygen- and sulfur-containing functional groups formed during the progress of the reaction between benzyl/methylphenyl radicals and SO2.

methylene group then attacks the carbon atom carrying the OH group to form a bicyclic structure in CS30. A comparatively high activation energy of 265.5 kJ/mol is involved in this reaction. Thereafter, the elimination of the OH group gives 1Hcyclopropabenzene (CS31). Route b. This route, represented by solid lines in Figure 12, involves the conversion of a six-membered ring in CS28 to a fivemembered and a three-membered ring in CS32. This requires crossing an activation energy barrier of 224.7 kJ/mol. The species CS32, thus formed, is highly unstable, and it can barrierlessly form CS33 and CS34 through the breakage of the threemembered ring, with CS33 being more stable than CS34 by 14.1 kJ/mol. This is followed by the loss of CO from CS33 and CS34 after overcoming energy barriers of 25.3 and 10.2 kJ/mol, respectively, to form CS35. There are no experimental data on the kinetics for this reaction involving the loss of CO through the conversion of a six-membered ring in methylphenoxy (CS28) to methylcyclopentadienyl radical (CS35). However, there are experimental studies on the conversion of phenoxy (C6H5O) to the CO and cyclopentadienyl (C5H5) radical through this route,45,46 where an activation energy of 184−200 kJ/mol was reported. This value is in close agreement with the overall activation energy of 224.7 kJ/mol for CS28 → CS25 + CO. Route c. This route, represented by dashed lines in Figure 12, involves the formation of a seven-membered ring in CS36 from CS28 through the attack by the O radical on carbon at the ipsoposition after crossing an energy barrier of 288.2 kJ/mol. The breakage of a C−O bond in CS36 forms CS37, which is more stable than the former molecule, but this bond scission reaction

Figure 6. Pathway 1. Potential energy diagram at 0 K showing the formation of 5- methylenecyclopenta-1,3-diene, CS9, as the end product during benzyl oxidation by SO2. 16300

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Figure 7. Potential energy diagram at 0 K showing the formation of CS14 from CS3 during the oxidation of the benzyl radical by SO2.

Figure 8. Potential energy diagram at 0 K showing the formation of benzene and phenyl as end products during the oxidation of the benzyl radical by SO2.

place at high temperatures. The species, CS48, thus formed, is of high interest, as it also forms during the oxidation of toluene by O2.38 Therefore, further reactions for this molecule have been studied in detail. Four possible routes have been identified, as shown in Figures 14−17 and discussed below. Route a. This route for CS48 decomposition is shown in Figure 14. The O radical at the meta-position in CS48 attacks the C atom at the para-position to form an epoxide group in CS49. This reaction is exothermic with a reaction energy of 52.9 kJ/mol and activation energy of 8.3 kJ/mol. Thereafter, the cleavage of a C−C bond forms CS50 with a seven-membered ring. This species can undergo molecular rearrangement to form a bicyclic molecule, CS51. Upon the cleavage of a C−C bond in it, CS52 is formed after overcoming an energy barrier of 51.9 kJ/mol. This is followed by the elimination of CO to form CS53 as one of the end products. Route b. Figure 15 presents the energy diagram for an alternate route for CS48 involving the breakage of a C−C bond to form a chain-like molecule, CS54 with O atoms at the two ends. A small activation energy of 11.1 kJ/mol is required to form CS54 that has higher stability than CS48. A rearrangement in CS54 gives CS55 having a five-membered ring with methyl and CHO groups. The elimination of CHO from CS55 forms CS56. Route c. This route, shown in Figure 16, involves the formation of CO2 during the decomposition of CS48. The first step involves the formation of a seven-membered ring with an

Figure 9. Pathway 2. Potential energy diagram at 0 K for CS1 decomposition during the oxidation of the benzyl radical by SO2.

molecule to form CS28 (studied above) after crossing a small activation energy barrier of 29.7 kJ/mol and (b) the loss of the S atom from CS47 to form CS48. The elimination of the S atom from CS47 is a barrierless, endothermic reaction involving a reaction energy of 241 kJ/mol, which indicates that it would take 16301

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Figure 10. Reaction mechanism for the oxidation of the o-methylphenyl radical by SO2. The numbers given below the chemical species will be used for their identification in the paper.

oxypinyloxy group in CS57 after overcoming an energy barrier of 45.8 kJ/mol. The species CS57 then rearranges itself to form a bicyclic molecule, CS58. This species eventually releases CO2, where an overall activation energy of 42.2 kJ/mol is required. Route d. As shown in Figure 17, this route involves the attack by an O radical on the carbon atom at the ipso-position to form a bridged structure in CS60. This species is highly unstable, and a C−C bond in it breaks barrierlessly to form CS61. The CO molecule then desorbs from CS61 to form CS62 after crossing a small energy barrier of 5.8 kJ/mol with the release of 63.2 kJ/mol of reaction energy. For o-methylphenyl oxidation, several routes were found with the overall activation energy of about 200 kJ/mol or less, as observed in experiment. For example, Route b of Pathway 1 and Pathway 2 and Routes b and c of Pathway 3 involved overall

activation energies of 130.3 kJ/mol (corresponding to TS36), 130.3 kJ/mol (corresponding to TS36 involved in the decomposition of CS28 that was also formed in Pathway 2), 207.6 kJ/mol (corresponding to TS66), and 205.3 kJ/mol (corresponding to CS56), respectively. These reaction channels are the highly probable ones through which o-methylphenyl radicals can be oxidized. 3.3. SO2 Addition to m- and p-Methylphenyl Radicals. Figure 18 shows the energy diagrams for the addition of SO2 to m-methylphenyl and p-methylphenyl radicals. The activation energies required for these addition reactions are about 6 kJ/mol, which are slightly higher than the activation energies for SO2 addition to benzyl and to o-methylphenyl radicals, as evaluated above, but are very close to activation energy of 6.4 kJ/mol for SO2 addition to the phenyl radical.21 Moreover, the energy 16302

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fashion as toluene oxidation by O2, the two cases may be compared. During toluene oxidation, cresols and benzyl alcohol are commonly observed.44,47 In the mechanism for toluene oxidation by SO2, their radicals are present (CS2, CS28, CS64, and CS66), and their further reactions have been studied. Other species such as benzaldehyde (C6H5CHO) and C5 (cyclopentadienyls) species and small products such as CO, CO2, and CH2O are also present in toluene flames,44 which can be found in different pathways proposed in this work. 3.5. Reaction Rate Constants. Table S1 in the Supporting Information provides the high-pressure limit rate constants for the elementary reactions involved in the H abstraction from toluene and in the oxidation of benzyl and methylphenyl radicals by SO2, as discussed in the previous sections. For some barrierless reactions (CS1 → CS2 + SO, CS27 → CS28 + SO, CS63 → CS64 + SO, and CS65 → CS66 + SO), variational transition state theory was used to calculate their rate constants by determining their potential energy surfaces through partial geometry optimizations at different O−S bond lengths. The method is described in our previous work.21 Figure S1 in the Supporting Information provides some validation cases for the rate constants where the experimentally observed rate constants for some of the reactions involved in the mechanism proposed above have been compared to their calculated values at different temperatures, and a good match has been reported. The experimental data in the literature were available only for a few aromatic reactions relevant to this study and over narrow temperature ranges. Figure 19 presents the rate constants for SO2 addition on benzyl, methylphenyl, and phenyl radicals and O2 addition on benzyl and o-methylphenyl radicals. The rate constants for SO2 addition to methylphenyl radicals were similar to each other as well as to the rate constant for SO2 addition to the phenyl radical evaluated in ref 21. On the other hand, the rate for SO2 addition to the benzyl radical was significantly lower than those for methylphenyl radicals even though the activation energies for SO2 addition on all the radicals of toluene were very close to each other (within 1.3 kJ/mol). This is possibly a result of the high stability of the benzyl radical, where the free electron is delocalized and is not completely available for reactions. The same trend can be seen during the oxidation by the O2 of benzyl and o-methylphenyl radicals, where a difference of more than an order of magnitude in their rate constants was observed. The rate

Figure 11. Pathway 1. Potential energy diagram at 0 K showing the formation of 1H-cyclopropabenzene (CS31) during the oxidation of the o-methylphenyl radical by SO2.

released when SO2 is added to the m-methylphenyl radical to form CS65 is 182.4 kJ/mol and is 183.8 kJ/mol when it is added to the p-methylphenyl radical to form CS67. These energies are comparable to the reaction energy of 182 kJ/mol for SO2 addition to the phenyl radical.21 After the addition reactions, CS63 and CS65 undergo barrierless O−S bond scission to form CS64 and CS66, respectively. The reaction energies of 94.7 and 89.7 kJ/mol for the formation of CS64 and CS66, respectively, are also close to the reaction energy of 97 kJ/mol for the O−S bond scission reaction during phenyl radical oxidation by SO2. Further reactions for CS64 and CS66 are expected to be similar to the reactions for C6H5O (owing to large separation between the O radical and the CH3 group), which have already been studied.21 Therefore, their further reactions are not shown here. 3.4. Intermediate and Product Species. The oxidation pathways for benzyl and methylphenyl radicals by SO2, as discussed above, involved several intermediate and product species. A way to validate the mechanism could be to ensure that the species found in experiments during toluene oxidation are also present in the mechanism. While there is no detailed study on species identification during toluene oxidation by SO2, there are several studies in the literature reporting the intermediate species formed during toluene oxidation by O2. Since toluene oxidation by SO2 after SO desorption proceeds in a similar

Figure 12. Potential energy diagram at 0 K showing different routes for the decomposition of CS28 during the oxidation of the o-methylphenyl radical by SO2. 16303

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Figure 13. Pathway 2. Potential energy diagram showing the formation of CS35 as the reaction progresses from CS27 → CS40 during the oxidation of the o-methylphenyl radical by SO2.

Figure 14. Pathway 3. Potential energy diagram for the formation of the 3-methyl-2H-pyran radical (CS53) during the oxidation of the o-methylphenyl radical by SO2.

Figure 16. Potential energy diagram at 0 K showing the formation of the 3-methylcyclopent-1-ene radical (CS35) from CS48 during the oxidation of the o-methylphenyl radical by SO2.

Figure 15. Potential energy diagram for the formation of 2methylcyclopenta-2,4-dienone (CS56) from CS48 during the oxidation of the o-methylphenyl radical by SO2.

constants for the addition of O2 on benzyl and o-methylphenyl radicals to form benzylperoxy and o-methylphenylperoxy radicals 16304

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Figure 19. Rate constants for the addition of SO2 on benzyl, methylphenyl, and phenyl radicals and for the addition of O2 on benzyl and o-methylphenyl to form benzylperoxy and o-methylphenylperoxy radicals, respectively.

Figure 17. Potential energy diagram at 0 K showing the formation of the 6-methyl-2H-pyran radical (CS62) from CS48 during the oxidation of the o-methylphenyl by SO2.

were obtained from refs 48 and 38, respectively. The rates for O2 addition to m- and p-methylphenyl radicals were not found in the literature. The rates for the additions of SO2 and O2 on the omethylphenyl radical can also be compared in this figure. The difference between the two rate constants diminishes with increasing temperature. It may appear that SO2 addition on CS1 is only competitive at temperatures above 1000 K where both the rates are within an order of a magnitude. However, given that SO2 is present in a high concentration in the anoxic region of the Claus furnace with sufficiently high temperature, the reactions between SO2 and toluene may be possible. This needs to be verified in the future by carrying out flame simulations. Figure 20 provides the comparison between the rate constants for the alternate pathways for CS1 and CS27. It is clear that, for these species, the reactions involving CO−SO bond scission are most likely to take place. This was also observed during the oxidation by SO2 of benzene in a previous study.21 Figure 21 provides the rate constants for the elimination of SO through the breakage of the CO−SO bond in the species CS1, CS27, CS63, CS65, and C6H5SO2 (formed from SO2 addition to benzyl, methylphenyl, and phenyl radicals) and the rate constants for the reverse reactions for CS1, CS27, CS63, and CS65 (leading to SO2 desorption). The rate constants for the elimination of SO from CS27, CS63, CS65, and C6H5SO2 were found to be very close to each other with differences within an order of magnitude. Moreover, the reverse reactions for CS27, CS63, and CS65 were found to be slower than the forward reactions at all temperatures studied in this work. However, for CS1, the SO elimination rate was very low compared to the other species in this figure. Also, the rate constant for the reverse reaction (CS1 → benzyl + SO2) was much higher than the forward one. At high temperatures, toluene oxidation by O2 can proceed through O−O bond scission in methylphenylperoxy radicals,36 while during its oxidation by SO2, CO−SO bond scission takes place. Figure 21 provides a comparison between the rate constants for these bond scission reactions in o-methylphenylperoxy (C7H7O2) and CS27. Clearly, the dangling OSO chain can break more easily than the O−O bond. This behavior can be attributed to the high electronegativity of the two O atoms

Figure 18. Potential energy diagrams at 0 K for the oxidation by SO2 of m- and p-methylphenyl radicals.

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Moreover, along with BTX and SO2, other gas-phase species present in the exhaust gas from the Claus furnace such as H2O, O2, N2, CO2, and sulfur may affect BTX−SO2 interactions and should be investigated.

4. CONCLUSION The reaction mechanisms for H atom abstraction from toluene to form benzyl and methylphenyl radicals and for the oxidation of these radicals by SO2 using the B3LYP/6-311++G(d,p) level of theory were presented to investigate the possibility of the destruction of toluene by SO2 at high temperatures. The addition of SO2 on these radicals was found to be highly exothermic with a reaction energy of 76.4 kJ/mol for benzyl and between 181.6 and 183.8 for methylphenyl radicals, and it required very small activation energy barriers between 4.8 and 6.1 kJ/mol to be overcome. This indicates that their interaction is energetically favored. From the rate constant profiles for this addition reaction, we conclude that SO2 addition is more favorable on the methylphenyl radicals than the benzyl radical. The possible pathways for their further reactions were studied, and it was found that the breakage of CO−SO bond leading to SO elimination is highly likely to take place after SO2 addition. Thereafter, the remaining O atom can carry out the oxidation of benzyloxy and methylphenoxy radicals through CO removal. This was found to be very similar to the pathways for benzene and toluene oxidation by O2 at high temperatures, where the O− O bond breaks in to facilitate the progress of their oxidation. The rate constant for CO−SO bond scission was found to be higher than that for O−O bond scission. This is possibly due to the high electronegativity of O atoms present on either sides of the S atom, which weakens the CO−SO bond. All of the pathways for benzyl and o-methylphenyl radicals had comparable overall activation energies with Pathway 1 having the lowest. Several routes for the formation of commonly observed species in the Claus furnace such as CO, CO2, OH, HCHO, CHO, SO, and S were identified. The energy profiles indicate that CO and SO would be forming in higher concentrations than the other species mentioned above since their elimination requires lower overall activation energy than the other products.

Figure 20. Comparison between the rate constants for the alternate pathways for CS1 and CS27 studied in this work.

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ASSOCIATED CONTENT

S Supporting Information *

Rate constants of the elementary reactions, and the energies, coordinates, vibrational frequencies, moments of inertia, and spin multiplicity for all chemical species and transition states are provided in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

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Figure 21. Rate constants for CO−SO bond scission reactions in CS1, CS27, CS63, CS65, and C6H5SO2. The rate constants for their reverse reactions leading to SO2 desorption are also provided. C7H7O2 = omethylphenylperoxy and C7H7O = o-methylphenyloxy.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been financially supported by the Gas Processing and Materials Science Research Centre, The Petroleum Institute, UAE.

present on the either side of the S atom that weakens the CO− SO bond. As discussed before, along with benzene and toluene, xylenes are also present as contaminants in the H2S gas stream. The mechanisms for their destruction by SO2 as well as the further decomposition of end products formed during toluene oxidation are required to be studied to determine, through simulations, the optimal process conditions for BTX destruction by SO2.

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