H2s 3p6c6x

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APPLIED CHEMISTRY Hydrogen Sulfide Combustion: Relevant Issues under Claus Furnace Conditions Ivan A. Gargurevich Combustion & Process Technologies, San Diego, California 92122

The major chemical paths for the combustion of hydrogen sulfide under conditions typical of the Claus furnace (i.e., fuel-rich conditions) are presented. The manuscript begins with a brief survey of recently published research that involves sulfur chemistry in high-temperature environments, including the results of sensitivity analysis for some of the systems involved. Recommended values for the heats of formation of sulfur species are included. The reaction mechanism that is presented consists of more than 150 reactions. Issues such as the formation and destruction of COS and CS2 are presented: new chemical paths for the formation of COS and CS2 (not involving elementary carbon) are illustrated, on the basis of sound thermochemical and kinetic considerations. The formation of COS and CS2 is of great importance in the design of sulfur plants in industry. Possible reactions of COS and CS2 with SO2, and CO2 with H2S and sulfur species, also are discussed, prompted by experimental observations in flow reactors. The mechanism can explain the formation of hydrogen, which also is an important issue in sulfur plant design and associated tail gas units. Species such as H2S2 seem to have an important role during the combustion of hydrogen sulfide. Higher-molecular-weight linear H2Sx species are also considered, and it is concluded that their role is possibly minor. The chemical steps leading to the formation of Sx species by molecular growth are presented. The ring structure of some of the Sx species is discussed, as well as intramolecular ring conversions for S8, S7, S6, and S5. The possibility of H,OH radical recombination catalyzed by oxygenated sulfur species may explain the delayed oxidation of hydrocarbon species in the Claus furnace that has been observed in previous experiments by other authors. This could be an important design consideration for Claus plants to minimize the coking of catalyst beds in the process. The most likely chemical paths for the radical quench are presented and based on past observations. Controversy persists in regard to the actual mechanism and the rate constants of the reactions involved in the radical recombination, as well as the thermochemistry of some of the oxygenated sulfur species involved. More studies are needed to resolve the issues. The study also reveals the lack of high-temperature data for the kinetic coefficients of some of the reactions. Much rate data are based on atmospheric studies, rather than high-temperature oxidation. Similarly, better thermodynamic data are lacking for some important oxygenated sulfur species in the mechanism. This is most important for temperature- and pressure-dependent reactions, such as unimolecular reactions and chemically activated reactions. Studies that involve hydrogen sulfide flames under fuel-rich conditions are lacking. Most of the studies have been limited to the impact of sulfur species on the formation of other species, such as CO and NOx, in flames or reactors. Introduction This manuscript examines the gas-phase combustion of hydrogen sulfide under reducing conditions such as those found in the Claus process, for example. The main chemical species resulting from the combustion process are identified, and, most importantly, the main chemical paths in the combustion are identified based on chemical principles and thermodynamics (see Table 5 later in this work). The manuscript does not attempt to develop any chemical reaction rate coefficients for the reactions; this is left for future work. Nevertheless, the work of other authors is presented, introducing rate coefficients for * To whom correspondence should be addressed. Tel: (858)5696742. E-mail: [email protected].

reactions that lead to major species such as SO, SO2, S2, H2S2, H2, S2, COS, CS2, CO, and CO2. It has been the finding of the author that not much information is available, in either experimental or computational quantum chemistry, concerning the rate coefficients of many of the reactions in Table 5 at high temperatures that are typical of flames. Recent developments in computational chemistry and the advent of faster computers have made it possible to develop large chemical kinetic models that are composed of hundreds of elementary reactions. The purpose is often to predict the formation of trace species. These species often have an important environmental impact, e.g., the well-known formation of NOx in the hot region of flames.1

10.1021/ie0492956 CCC: $30.25 © 2005 American Chemical Society Published on Web 08/23/2005

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7707 Chart 1. Process Flow Diagram of the Overall Claus Plant.

Despite the aforementioned discussion, the combustion of hydrogen sulfide has not received much consideration at the molecular level. A review of sulfur chemistry by Johnsson and Glarborg2 indicates that most of the chemistry has been concerned mainly with the effect of sulfur on the emissions of other pollutants, such as NOx and CO (there will be more discussion about this point later in this paper). In this respect, the work of Chernyshera et al.,3 which involved the mechanism of H2S oxidation at high temperatures, is an exception. Most of the work involving the industrial aspects of H2S combustion that has been published only considers the main overall reactions that occur during the hightemperature oxidation of hydrogen sulfide.4-6 The work of Monnery et al.6 also shows that empirical correlations used to determine gas-phase composition (e.g., COS and CS2 concentrations at the exit of the waste heat boiler during the Claus process) are often inadequate. One very important application of hydrogen sulfide combustion is the Claus reaction. Other applications such as the high-temperature decomposition of hydrogen sulfide to form hydrogen are also being considered.7 The thermodynamics of super-adiabatic partial oxidation of hydrogen sulfide in an inert porous media has also been studied by Slimane et al.8 The study considered various acid gas and oxidizer feeds, equivalence ratios, interstitial gas velocity, and temperatures. Most of the calculations involved temperatures well in excess of 1000 K. The results of the equilibrium calculations show favorable conversions to hydrogen. Thermodynamic equilibrium modeling can be representative of flame temperatures and product compositions, and this is most significant in the case of fast chemical kinetics during the process. Thermodynamic predictions are usually less useful at low temperatures, because of slower rates of the chemical reactions in the process. Claus Reaction Refinery fuel gas, as well as other refinery hydrocarbon streams, will contain quantities of hydrogen sulfide; this is the result of the distillation of crude oil in the main crude distillation column or treatment of the distillation cuts in hydrotreaters and other treatment units. The resulting fuel gas is treated to remove hydrogen sulfide in amine units, which is a dangerous substance, resulting in a hydrogen sulfide-rich stream to be treated in Claus plants.9,10

The Claus plant or sulfur recovery units make use of the well-known Claus reaction:

3 2H2S + SO2 T Sx + 2H2O x

(1)

To obtain the necessary SO2 for the reaction above, onethird of the hydrogen sulfide is combusted in a hightemperature furnace, or

H2S + 1.5O2 T SO2 + H2O

(2)

The overall reaction is then

1 1 H2S + O2 T Sx + H2O 2 x

(3)

The temperature in the combustion furnace can be as high as 2000 °F. The overall Claus plant is depicted in Chart 1. Both acid gas and, in some cases, sour water stripper gas are fed to the main furnace. After partial oxidation of H2S in the furnace, the high-temperature gas is cooled in a waste heat boiler; the gas then proceeds to a condenser, where the gas is cooled to its dew point. Low-pressure steam is generated for this purpose. The Claus plant then consists of various stages of gas reheating, catalytic reaction, and condensation of sulfur. In the catalytic reactor, Claus reaction 1 proceeds at much lower temperature (450-610 °F), thanks to an alumina-based catalyst. The gas is reheated in the reheaters to bring it to reaction temperature. Care is taken to reheat the gas to a sufficiently high temperature, so that the gas exiting the catalytic reactor that follows is above the sulfur dew point. This way, plugging of the reactor is avoided. After reheating, the gas then proceeds to the catalytic reactor to form sulfur via the Claus reaction. Finally, the gas flows to the sulfur condenser, where the gas is cooled to its sulfur dew point by producing low-pressure steam in a shell-and-tube exchanger. The process described above is repeated several times to increase conversion to sulfur. The flow diagram in Chart 1 depicts three catalytic stages. An important problem in modeling Claus plants is the estimation of the gas composition as the gas flows from the reaction furnace to the waste heat boiler. The gas composition in the furnace is very close to equilibrium (because of the high temperature and residence time).

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As the gas is cooled in the waste heat boiler, the gas continues to react and follow the temperature drop to some extent, depending on the reaction that is being considered. The waste heat boiler exit temperature is typically 700 °F.4,6 Most process simulators (SULFSIM, TSWEET) simulate the conditions at the waste heat boiler, based on equilibrium considerations and/or estimated quench temperatures for reactions of some species such as hydrogen, CO, and CO2. A difficulty in the simulation is the prediction of trace species such as COS, CS2, and mercaptans, because no chemical kinetic mechanism is featured in these software programs. The results of equilibrium calculations indicate that significant amounts of H2 and CO are produced in the reaction furnace.6 The hydrogen is most likely produced by the thermal decomposition of H2S. There is some debate in regard to the mechanism of CO formation. Plant samples taken after the waste heat boiler seem to indicate the reassociation of H2 and S2 to form H2S. Similarly, CO formed in the furnace seems to react in the waste heat boiler to form COS.6 Plant samples taken after the waste heat boiler also seem to indicate substantially higher concentrations of COS and CS2 than what is predicted by equilibrium calculations at furnace conditions.6 CS2 formation seems to correlate well with the amount of hydrocarbon in the feed gas. As previously indicated, an important problem is that empirical correlations are often inadequate in predicting gas composition. The work of Clark and co-workers4,11 is also important in this matter. They conducted studies using an externally heated tubular reactor to simulate Claus furnace conditions with variable quenching of the hot gas. They found that CO2/sulfur species do not result in CS2, but hydrocarbons do react with sulfur to produce CS2. Under the partial oxidation conditions of the furnace, they found that H2S is destroyed more quickly than any hydrocarbon in the feed gas (the author gives a possible explanation for this in this manuscript, below). They also studied new chemical pathways that involved the reaction of CS2 and COS with major species such as SO2, CO2, and H2. The destruction of COS and CS2 by reaction with water occurs very rapidly. COS is also known to react with hydrogen; CS2, on the other hand, does not seem to react with hydrogen.4,6 The author does not know of any recent comprehensive studies that examine the chemistry of H2S combustion under reducing conditions that are typical of the Claus process. The work of Kennedy12 and Zachariah and Smith13 are important in this respect; however, their kinetic mechanisms do not include the molecular growth that leads to S8. Similarly, the chemistry of COS, and CS2, is not considered. Their mechanisms include the chemistry that leads to the formation of SO, SO2, SO3, and S2, as well as other chemical paths for the destruction of H2S. Another important source of chemistry and kinetics data that is more recent can be found in the University of Leeds, U.K. Sulfur Mechanism (which can be found on the Internet at www.chem.leeds.ac.uk/Combustion/Combustion.html). Other considerations beyond the scope of this work are fluid dynamics and residence time within the reaction furnace of the Claus plant. Both are important in determining the real approach to equilibrium within the furnace.14,15 Computational methods, including turbulent combustion, have been reviewed by Eaton et al.16

Table 1. Chemical Species under Consideration in Equilibrium Calculation Hydrogen Sulfide Combustion-Reducing Conditions (Claus Process) Major Species O2, N2, NH3, NO, H2O2, H2, H2O CO, CO2, COS, CS2, HCN, CH4, C2H6, C2H2, C2H4 CH2O SO, SO2, SO3, H2S2, H2S3, H2S4, H2S5, H2S6, H2S7, H2S8 S2O2, H2SO2, CH3SH, C2H5SH S2, S5, S6, S7, S8 Radical Species O, OH, HO2, H CS, CN, CH3S, C2H5S, CH3, CH2, CH, C2H5, C2H, C2H3 CHO, CH3O S2O, S, S3, S4, HSO, HSO2 HS2, HS3, HS4, HS5, HS6, HS7, HS8

Reaction furnace design considerations are further discussed by Hyne.5 Discussion A first step in the assembly of the main chemical paths is to consider all or some of the possible species, radical or stable, that can partake in the destruction of the initial mixture that contains hydrogen sulfide. These are listed in Table 1.10,17,18 This table must include species that lead to the formation of elemental sulfur in the Claus furnace as well as important trace species such as COS and CS2. In addition to hydrogen sulfide, acid gas may contain hydrocarbons such as methane and ethane. Furthermore, there are instances when sour water stripper gas that contains ammonia must be treated in the Claus plant;9 for this reason, ammonia is included in Table 1. The oxidation of methane has been studied extensively (see, for example, GRI Mechanism 3.0, which can be found on the Internet at www.me.berkeley.edu/ gri_mech), as well as comprehensive discussions and reaction compilations in dissertations by Gargurevich,17 and Wang19 (more below); the hydrocarbon species considered in Table 1 are taken from these references. It is important to assess the concentration level of these species under typical reaction conditions in the Claus furnace and waste heat boiler. For this reason, equilibrium simulations were performed with ASPEN Plus 10.1. The simulations consisted of isotherms at different temperatures including the adiabatic temperature. It must be noted that similar calculations have been conducted by Meisen and Bennett.10 The results of the calculations for this manuscript are shown in Figures 1-7. The well-known fact that radicals can be present in flames in excess of their equilibrium values must be considered when producing the elementary chemical steps of the combustion process. Before proceeding, it is important to become familiar with the molecular geometry of some of these species. This is very relevant to the discussion of the reactions that can occur during the combustion process. Table 2 shows the molecular structure for some of the sulfur species in Table 1. Sulfur, as well as oxygen, has six valence electrons and requires two more to satisfy the octet rule. There is no indication that the sulfur in the species SO2, SO3 shown in Table 2 makes use of d orbitals.20 Both involve double-bonded resonance structures. It is important to note that the oxygenated species SO, SO2, and SO3 provide double bonds for radical

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7709

Figure 1. Concentration plot of the CO, CO2, and H2 species in the furnace gas over a range of temperatures.

Figure 2. Concentration plot of the sulfur species (S1-S8) in the furnace gas over a range of temperatures.

addition reactions to occur. These reactions are important in the flame, e.g.,

SO2 + O T SO3

(4)

It is well-known that S8 in the vapor phase forms a puckered ring structure. There are several alleotropes of solid sulfur, and the most common ones are the rhombic and monoclinic crystal structures; the rhombic form is the most stable of the two. It is seldom discussed in the literature that species such as S7, S6, and S5 can also form ring structures.21,22 The ring structutre of S5 is similar to that of cyclopentane; similarly, the S6 ring structure is an hexagonal chair that is similar to that of cyclohexane. S7 has also been shown to have a chairlike structure. However, the

smaller species (S3, S4) seem to have a linear geometry.21 Yet, at the high temperatures of combustion, it should be possible to open up the rings previously described to produce the linear geometry. The energy required to open the S8 ring is estimated to be 33.8 kcal/mol.23 Raghavadari et al.21 also gives energy estimates for the following ring conversions:

8 S8(c) T S5(c) 5

(29.1 kcal/mol)

(5)

8 S8(c) T S6(c) 6

(9.2 kcal/mol)

(6)

8 S8(c) T S7(c) 7

(5.2 kcal/mol)

(7)

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Figure 3. Concentration plot of the COS and CS2 species in the furnace gas over a range of temperatures.

Figure 4. Concentration plot of the H2S2, HSO, S2O, SO, and H2SO2 species in the furnace gas over a range of temperatures.

At the high combustion temperatures, these reactions should occur. No mechanism is given for the conversions described by Raghvadari et al.21 A. Hydrogen Sulfide Combustion: Chemical Equilibium Calculations. As previously noted, the concentration of chemical species under equilibrium conditions can only be considered as a guide to their importance in the combustion process. Measurements of radicals in laminar flames with microprobes, for example, have shown that these species can be found in levels exceeding their equilibrium concentrations during the combustion process. However, temperatures and residence times typical of Claus furnace designs make it possible to achieve a close approach to equilibrium, and the chemical com-

positions shown by the calculations in this section at the higher temperatures should be viewed as a close representation of the furnace products in typical applications. Thus, the results presented here are most relevant in understanding the chemistry that occurs in the furnace at high temperatures. As stated previously, chemical equilibrium calculations have been conducted by other authors10 for a mixture of hydrogen sulfide and air under conditions typical of the operation of Claus units. This author performed calculations at the adiabatic temperature and isotherms ranging from 600 °F to 2000 °F. Species for which concentration profiles were provided are shown in Table 3. The minimum concentration reported was on the order of 1 ppmv (parts per million by volume).

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Figure 5. Concentration plot of the H2S3, H2S4, and NH3 species in the furnace gas over a range of temperatures.

Figure 6. Concentration plot of the H, HO, HS, HS2, and HS3 species in the furnace gas over a range of temperatures.

They found that the amounts of the radical species H, OH, and O reach concentrations at the ppm level only at the highest temperatures (2400-3100 °F). This is what is expected from what is known about combustion chemistry. The calculations show that, for temperatures of >800 K, the most abundant species are S2, S3, S4, and HS, with S2 being the predominant molecule. Sulfur species such as S5, S6, S7, and S8 become abundant at lower temperatures (well below 1330 °F). Monatomic sulfur (S) does not become significant until temperatures above 1700 °F are reached. The relative abundance of S and HS from H2S decomposition could be due to the lower bond energy in S-H (89 kcal/mol), as compared to the C-H bond energy in CH4, for example (104 kcal/mol).

Significant amounts of COS are formed at temperatures above 970 °F. CS2 formation is at the ppmv level at temperatures above 1330 °F. These species are thought to involve reactions of CO2 and CO (more about this observation will be presented later in this paper). The importance of CO, H2, and CO2 chemistry has been previously discussed. The work of Meisen and Bennett10 showed that significant amounts of CO and H2 are formed above 620 °F. The concentrations of both species continue to increase with increasing temperature. They found almost insignificant amounts of ammonia that was created from the feed nitrogen. At the highest temperatures, the amount of SO2 exceeds that of H2S, which suggests that elemental sulfur competes successfully for oxygen.

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Figure 7. Concentration plot of the H2O, H2S, and SO2 species in the furnace gas over a range of temperatures.

The maximum in sulfur yield under adiabatic conditions occurs under conditions where the oxygen consumption is given by the overall reaction

1 1 H2S + O2 T Sx + H2O 2 x

(8)

This is a well-known fact to Claus plant operators when optimization of the operation of the Claus process is attempted.24 As part of the work presented here, as well as to expand on the previously given results, equilibrium calculations were performed for a mixture of the following composition for acid gas and sour gas: H2S, 87.31 vol %; CO2, 3.82 vol %; NH3, 1.51 vol %; C1, 1.62 vol %; C2, 1.62 vol %; H2O, 4.12 vol %; total, 100.00 vol %. This gas composition would be the type that is treated in a Claus unit designed to handle acid gas and sour water stripper gas that contains ammonia at 10 psig. For the equilibrium calculations, the gas was burned with air by the stoichiometry of eq 3, adiabatically and isothermally, in the temperature range of 400-2200 °F. The results of the calculations are shown in Figures 1-7. Table 4 shows both stable and radical species exceeding the ppmv concentration level. For purpose of the calculations, the COMBUST thermodynamic databank of the ASPEN package was used. This is based on the JANAF Thermochemical Tables, which were published by Dow Chemical Co., Midland, MI, in 1979. The databank contains the ideal gas heat capacity, free energy of formation, and enthalpy of formation for many species, and these values are accurate at the high temperatures that are typical of combustion for more than 59 stable and radical species. Generally, the results are in agreement with the work of Meisen and Bennett.10 Figure 1 shows the concentration of major species such as CO, CO2, and H2. As with the work of Meisen and Bennett,10 the concentrations of CO and H2 increase significantly at temperatures

above 620 °F. The concentrations of both CO and H2 increase with temperature, reaching an equilibrium mole fraction of ∼0.01 in both cases at the highest temperature shown or 2400 °F. Figure 2 shows the distribution of the sulfur species S, S2, S3, S4, S5, S6, S7, and S8. The smaller species, such as S1, S2, and S3, are significant at the higher temperatures and above 1000 °F. Elemental sulfur (S2) is the predominant species at these temperatures. Molecules such as S5, S6, S7, and S8 become most significant at lower temperatures (<700 °F). S8 overtakes all the other species such as S6 and S7 as the temperature approaches 500 °F or lower. Figure 3 shows that the formation of COS and CS2 does not become significant until the temperature reaches 1000 °F or above, with the COS mole fraction being higher by 2 orders of magnitude, or 100 ppmv. The simulations also show that the concentrations of species such as H2S2 and H2S3 start becoming significant at temperatures higher than 600 °F (see Figures 4 and 5). The mole fraction of H2S2 peaks at 1000 ppmv, only to decrease slightly at temperatures above 1000 °F. H2S3 displays the same behavior peaking at a mole fraction of 10 ppmv at 1000 °F. The oxygenated species SO can reach a mole fraction of 1000 ppm levels at the higher temperatures shown or 2300 °F. In contrast, S2O is most important, even at lower temperatures; it peaks at 1000 °F with a mole fraction as high as 1000 ppmv, or 3 orders of magnitude higher than the concentration of SO at the same temperature. The levels of species such as HSO and H2SO2 are not as significant as SO or S2O above (see Figure 4). The mole fraction of HSO can reach ∼1 ppmv, at the higher temperature shown or 2300 °F, whereas H2SO2 remains well below 1 ppmv even at the highest temperatures or above 2000 °F. The concentrations of radical species such as HS and HS2 reach levels as high as 1000 ppmv (for HS radical), at temperatures of ∼2000 °F (see Figure 6). In com-

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7713 Table 2. Molecular Structure of Sulfur Species chemical formula SO

Table 3. Species under Consideration in the Modeling of Chemical Equilibrium Calculationsa

molecular structure

Species

SdO

SO2

SO3

H2SO2 HSO2 S2O S2O2 S2 CS CS2 COS S3 S4

a

H-S-O-O- -H H-O-O- -S S-O- -S S-O-O- -S SdS C)S SdCdS OdCdS S-S- -S S-S-S- -S

H, OH, O CS, HS S, S3, S4 HS, SN

Table 4. Species Used in Chemical Equilibrium Calculations and Showing Concentrations in the Parts per Million by Volume (ppmv) Rangea Species

S6(c) a

S7(c)

S8(c) H-S-S-S-S-S-S-S-S- -H H-S-S-S-S-S-S-S- -H H-S-S-S-S-S-S- -H H-S-S-S-S-S- -H H-S-S-S-S- -H H-S-S-S- -H H-S-S- -H CH3- -SH CH3-CH2- -SH

parison, HS3 is not as significant; its concentration is lower by 3 orders of magnitude. Species such as H2S2 and H2S3 could have an important role in the combustion chemistry of H2S. The concentration of H2S2 peaks at 1000 °F, reaching 1000 ppmv (see Figure 4), only to decrease slightly at the higher temperatures. H2S3 displays a similar behavior, but its highest concentration is only 10 ppmv (see Figure 5). In contrast, a larger molecule, such as H2S4, reaches considerably lower concentrations than the aforementioned H2S2 or H2S3 (<1 ppmv) (see Figure 5). Equilibrium calculations show insignificant amounts of hydrogenated species such as H2S5, H2S6, H2S7, and H2S8. This could be due to hydrogen elimination reactions, such as

H2S5 T S5(c) + H2

radical

H2O, H2, O2 NO, NH3 CO, CO2, COS, CS2 S2, S5, S6, S7, S8 SO2, SO, S2O, SO3 H2S, H2S2 Data from Meisen and Bennett.10

S5(c)

H2S8 H2S7 H2S6 H2S5 H2S4 H2S3 H2S2 CH3SH C2H5SH

stable

(16 kcal/mol, ESTIM) (9)

H2S6 T S6(c) + H2

(9 kcal/mol, ESTIM)

(10)

H2S7 T S7(c) + H2

(7 kcal/mol, ESTIM)

(11)

H2S8 T S8(c) + H2

(3 kcal/mol, ESTIM)

(12)

The reactions result in the formation of the ring structures for the sulfur species. The heats of reaction are given parentheses and are based on average bond energies. These reactions could easily occur at flame temperatures.

stable

radical

CO, CO2 H2, H2O COS, CS2 NH3 H2S2, H2S3, H2S4 SO2, S2O, SO, H2SO2 S2, S5, S6, S7, S8

H, OH HS, HS2, HS3 S, S3, S4 HSO

Data from this work.

B. Chemical Reactions Found in Combustion (Illustrating the Chemistry Typical in Combustion). This section is a short tutorial in combustion chemistry fundamentals. Combustion involves radical species and radical-chain mechanisms.17 The existence of radical species such as H and OH in the gas phase is possible because of the high temperature of combustion. Chain mechanisms consist of initiation, propagation, and termination steps. The type of reactions have been described by Pryor:23 (a) Initiation reactions involving molecular cleavage, producing the pool of radical species that start the chain, e.g.,

Cl2 T 2Cl

(13)

(b) Propagation reactions can be of four different types:

atom transfer, such as hydrogen abstractions, e.g.,: R′ + RH T R′H + R (14) addition reactions, e.g.; Cl + RCHdCH2 T RCH-CH2Cl (15) fragmentation reactions, e.g.; RCH2-CH2 T R + CH2dCH2 (16) and

radical rearrangement reactions, e.g.; CH3-C(H)-CH2Cl T CH3-C(HCl)-CH2 (17) where the Cl atom transfers to the second C atom in the molecule. (c) Termination reactions are radical-radical addition reactions or,

R + Cl T RCl

(18)

These result in a decrease of the radical species in the gas phase.

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Table 5. Chemical Paths for the Combustion of H2S-Reducing Conditionsa Heat of Reaction Data reaction

heat of reaction (kcal/mol)

notes

H2S + H ) H2 + HS H2S + OH ) H2O + HS H2S + O ) OH + S H2S + O ) SO + H2 H2S + S ) HS + HS HS + HS + M ) H2S2 + M HS + HS ) H2S + S HS + HS ) S2 + H2 HS + OH ) S + H2O HS + H ) S + H2 H2S2 + H ) HS2 + H2 H2S2 + OH ) HS2 + H2O H2S2 + O ) HS2 + OH H2S2 + S ) HS + HS2 H2S2 + M ) 2HS + M H2S2 + H ) H2S + SH H2S2 + HS ) H2S + HS2 HS2 + M ) HS + S + M HS2 + OH ) S2 + H2O HS + S2 ) HS2 + S HS2 + M ) 2HS + M HS2 + S2 ) HS3 + S HS2 + HS ) H2S + S2 HS2 + H ) 2SH HS2 + H ) H2 + S2 HS2 + H ) H2S + S H2S + S ) S2 + HS HS2 + HS2 ) H2S2 + S2 HS + O2 ) SO + OH HS + O2 ) S + HO2 HS + O2 ) HSO + O HS + O2 ) SO2 + H S3 + H2 ) HS3 + H HS3 + H2 ) H2S3 + H HS3 + H2S ) H2S3 + HS HS3 + S ) HS + S3 HS3 + HS ) H2S + S3 HS3 + OH ) S3 + H2O H2S3 + OH ) HS3 + H2O H2S3 + S ) HS3 + HS H2S3 + HS ) H2S + HS3 S4 + H2 ) HS4 + H H2S4 + OH ) HS4 + H2O H2S4 + S ) HS4 + HS H2S4 + HS ) HS4 + H2S HS4 + H2 ) H2S4 + H HS4 + H2S ) H2S4 + HS HS4 + S ) HS + S4 HS4 + HS ) H2S + S4 HS4 + OH ) S4 + H2O HS3 + M ) HS2 + S + M HS4 + M ) HS3 + S S2 + O ) SO + S S + O + M ) SO + M S + O2 ) SO + O SO2 + O + M ) SO3 + M SO + O + M ) SO2 + M SO + S + M ) S2O + M S + S + M ) S2 + M S2 + S + M ) S3 + M S3 + S + M ) S 4 + M S4 + S + M ) S5(c) + M S5 + S + M ) S6(c) + M S6 + S + M ) S7(c) + M S7 + S + M ) S8(c) + M S2 + S3 + M ) S5(c) + M S2 + S4 + M ) S6(c) + M S2 + S5 + M ) S7(c) + M S2 + S6 + M ) S8(c) + M S3 + S ) S2 + S 2 S4 + S ) S3 + S 2 S5 + S ) S4 + S 2

-13.9 -28.91 20.91 -54.65 5.25 -66.6 -5.25 -35.89 -15.53 -19.16 -49.46 -44.92 -28.05 -29.37 64.48 -26.65 -36.42 77.36 -58.6 47 64.48 47 -14.78 9.77 -14.93 2.72 -7.7 21.64 -22.48 33.45 -0.4 -52.14 23 23 0 0 0 -30 -30 -8 -8 23 -30 -8 -8 23 0 0 0 -30 54 54 -22.5 -124.29 -5.19 -83.14 -131.75 -66.24 -101.78 -7 -54 -96 -103 -106 -108 -49 -56 -59 -61 -94 -47 -47

JANAF JANAF JANAF JANAF JANAF JANAF JANAF JANAF JANAF JANAF JANAF JANAF JANAF JANAF Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 JANAF JANAF ESTIM, BE Hynes and Wine28 ESTIM, BE Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 JANAF JANAF JANAF JANAF ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTM. BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE JANAF JANAF JANAF JANAF JANAF JANAF JANAF Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28

reaction rate coefficient data Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS UNIV LEEDS UNIV LEEDS UNIV LEEDS UNIV LEEDS Sendt et al.32 Sendt et al.32 Sendt et al.32 UNIV LEEDS UNIV LEEDS Kennedy12 Sendt et al.32 Kennedy12 Sendt et al.32 Sendt et al.32 Sendt et al.32 Sendt et al.32 Sendt et al.32 Sendt et al.32 Kennedy12 Kennedy12 Kennedy12 Kennedy12

Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS Kennedy,12 UNIV LEEDS NIST

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7715 Table 5 (Continued) Heat of Reaction Data reaction

heat of reaction (kcal/mol)

notes

S6 + S ) S5(c) + S2 S7 + S ) S6(c) + S2 S8 + S ) S7(c) + S2 S5(c) ) M ) S5 + M S6 (c) + M ) S6 + M S7(c) + M ) S7 + M S8(c) + M ) S8 + M S3 + S3 + M ) S6(c) + M S3 + S4 + M ) S7(c) + M S3 + S5 ) + M S8(c) + M S4 + S4 ) + M S8 (c) + M S8(c) T 8/5S5(c) S8(c) T 8/6S6(c) S8(c) T 8/7S7(c) HS2 + S3 ) S5(c) + H HS2 + S2 ) S4 + H HS2 + S4 ) S6(c) + H HS2 + S5 ) S7(c) + H HS2 + S6 ) S8(c) + H HS2 + HS2 ) S4(c) + H2 HS3 + S2 ) S5(c) + H HS3 + S2 ) HS4 + S HS3 + HS3 ) S6(c) + H2 HS3 + HS2 ) S5(c) + H2 HS4 + S2 ) HS5 + S HS4 + S2 ) S6(c) + H HS4 + HS4 ) S8(c) + H2 HS4 + HS3 ) H2 + S7(c) HS + S4 ) S5(c)+ H HS + S5 ) S6(c) + H HS + S6 ) S6(c) + H HS + S7 ) S8(c) + H CO + S + M ) COS + M COS + H ) CO + HS COS + OH ) CO2 + HS COS + O ) CO2 + S COS + O ) CO + SO COS + S ) CO + S2 C + S + M ) CS + M CS + S + M ) CS2 + M C + S2 ) CS + S CS + S2 ) CS2 + S CS2 + O ) COS + S CH3+ O2 ) CH2O + OH CH3O + M ) CH2O + H + M CH2O + HS ) CHO + H2S S2 + CHO ) COS + HS CH3 + S2 + M ) CH3-S-S + M CH3-S-S + H2S ) HS + CH3-S-SH CH3-S-SH + M ) CH3S + HS + M CH3S + HS ) H2S + CH2dS CH2dS + HS ) H2S + CHdS CHdS + S2 + M ) S-S-CHdS + M S-S-CHdS + H2S ) S ) CH-S-SH + HS SdCH-S-SH + M ) SdCH-S + HS SdCH-S + HS ) H2S + CS2 S + C2H2 T HCS + CH CHS + M T H + CS + M CH3SH + H ) CH3 + H2S C2H5SH + H ) C2H5 + H2S CH3SH + HS ) CH3 + H2S2 C2H5SH + HS ) C2H5 + H2S2 CH3SH + S ) CH3 + HS2 C2H5SH + S ) C2H5 + HS2 CH3 + S2 ) CH2 ) S + HS CH2dS + HS ) CHdS + H2S CHdS + S2 ) CS2 + H2S CH3 + HS ) CH3SH CH3 + HS ) H2 + CH2S CH3SH + H ) CH3 + H2S CH3SH + H ) CH3S + H2 CH3S + H ) CH2S + H2 CH2S + H) HCS + H2 HCS + H ) H2 + CS HS + CS ) H + CS2

-89 -96 -98 30 32 33 33 -103 -105 -107 -107 29.1 9.2 5.2 -15 74 -21.7 -23.8 -28.1 -50 32 47 -44.7 -38 47 25.3 -51.1 -46.8 -15 -21.7 -23.8 -28.1 -72.91 -11.91 -37 -56.5 -52.9

Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Pryor23 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Raghavachari et al.21 Raghavachari et al.21 Raghavachari et al.21 ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE ESTIM, BE JANAF JANAF JANAF JANAF JANAF

-170.54 -105.29 -68.4 -3.51 -54.3 -53.2 20.50 -0.1 -76.4 47.5 7 54 -63 10 -18 7 54 -63 92 51 -16.72 -41.52 7.01 -17.8 -3.75 -28.6 -3.9 3.9 --39.10 -74.44 -41.50 -16.70 -16.77 -54.47 -9.1 -55.67 -21.0

JANAF JANAF JANAF JANAF JANAF JANAF JANAF JANAF JANAF Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 JANAF JANAF JANAF JANAF JANAF JANAF JANAF JANAF Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28

reaction rate coefficient data

UNIV OF LEEDS NIST, UNIV LEEDS NIST, UNIV LEEDS NIST, UNIV LEEDS NIST, UNIV LEEDS NIST, UNIV LEEDS UNIV OF LEEDS UNIV OF LEEDS UNIV OF LEEDS UNIV OF LEEDS NIST Gargurevich,17 GRI MECH Gargurevich,17 GRI MECH

NIST NIST

Petherbridge et al.36 Petherbridge et al.36 Petherbridge et al.36 Petherbridge et al.36 Petherbridge et al.36 Petherbridge et al.36 Petherbridge et al.36 Petherbridge et al.36

7716

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005

Table 5 (Continued) Heat of Reaction Data reaction

heat of reaction (kcal/mol)

notes

reaction rate coefficient data

CO2 + S ) SO + CO CO2 + HS ) HSO + CO H + SO2 + M T HSO2 + M H + HSO2 T SO2 + H2 OH + SO + M T HSO2 + M OH + HSO2 T SO2 + H2O H + SO + M T HSO + M HSO + H T H2 + SO HSO + H T H2S + O HSO + H T SH + OH HSO + OH T H2O + SO HSO + O T SO + OH HSO + O T H + SO2 HSO + O T HS + O2 HSO + O2 T SO + HO2 SH + HSO T H2S + SO

2.9 7.69 6.0 -110.0 -23.49 -80.2 -52.3 -54.2 -5.0 -7.6 -13.0 -47.10 -77.50 -23.28 7.15 -35.73

JANAF JANAF Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28 Hynes and Wine28

Zachariah and Smith13 Zachariah and Smith13 Zachariah and Smith13 Zachariah and Smith13 Zachariah and Smith13 Zachariah and Smith13 Zachariah and Smith13 Zachariah and Smith13 Zachariah and Smith13 Zachariah and Smith13 Zachariah and Smith13 Zachariah and Smith13 Zachariah and Smith13 Zachariah and Smith13

a ”UNIV LEEDS” refers to the University of Leeds, U.K., Sulfur Mechanism (http://garfield.chem.elte.hu/Combustion/Combustion.html). “GRI Mech” refers to the GRI Mechanism 3.0 for Methane Combustion (www.me.berkeley.edu/gri_mech). “NIST” refers to the kinetic database provided by the National Institute of Standards (www.nist.gov).

Another important process that is common in combustion systems is the process of chemical activation. A reaction involving addition, such as a radical addition to a double bond, leads to the formation of a chemically activated adduct that possesses excess energy due to the bond formation. This adduct can further react, leading to products. One such reaction leading to the formation of formaldehyde is the addition of a methyl radical to the double bond in oxygen, or

CH3 + O2 T [CH3-O-O]* T CH2dO +OH (19) The chemically activated adductsin this case, CH3-OO* has excess energy and leads to the formation of products. The reader can find more-complete discussions of chemical activation in ref 25. Warnatz has published an interesting manuscript that examined the issues of hydrocarbon oxidation and high-temperature chemistry.26 It describes the main chemical paths in the combustion of hydrocarbons that are common to most molecules. Hydrogen sulfide combusts then via chemical paths that are similar those previously mentioned. A summary of the elementary chemical reactions considered in this study is given in Table 5. The table includes the heat of reaction for each reaction. One must recall that, because of the concentration factor in the rate of a chemical reaction, typically, radical-radical reactions should not be as important as radical-stable-species reactions. C. A Brief Discussion of Recently Published Sulfur Chemistry. It is not the objective of this section to present a comprehensive review of published chemistry; this has been done by other authors who will be mentioned below. This part of the manuscript will attempt to describe the main results of previous studies, as well as show some very relevant and important conclusions: (i) there is a lack of high-temperature kinetic data; (ii) accurate thermodynamic data for some important sulfur species are also lacking; (iii) most studies examine H2S combustion at high temperature only indirectly, and their aim is to observe the effect of the sulfur species on the formation of pollutants such as CO and NOx; and (d) the effect of combustion conditions on the formation of SO3 is examined. A comprehensive review of the combustion of gaseous sulfur compounds was conducted by Cullis and Mulcahy

in 1972.18 The review examines the chemistry of sulfur compounds that either undergo combustion themselves or may be present in other gaseous combustion systems. Their study is based on low-temperature photolysis experiments and flame studies. In some ways, this is the starting point for later works on sulfur chemistry and oxidation. They identify the final and intermediate products of combustion: SO2 is always the main product, with small amounts of SO3, depending on the stoichiometric conditions. Other sulfur oxides of interest are SO and S2O, which are intermediates. Other products of combustion under substoichiometric conditions are H2S, COS, and elemental sulfur. Cullis and Mulcahy18 continued by identifying some of the elementary reactions of interest. These are listed as follows. H Atoms.

H + H2S T HS + H2

(20)

H + HS T H2 + S

(21)

H + CH3SH T H2 + CH3S

(22)

H + SO2 + M T HSO2 + M

(23)

S2 + O T SO + S

(24)

H2S + O T SO + H2

(25)

O + H2S T OH + SH

(26)

O + SH T SO + H

(27)

COS + O T SO + CO

(28)

COS + O T CO2 + S

(29)

CS2 + O T CS + SO

(30)

O + CS T CO + S

(31)

S + O2 T SO + O

(32)

SO + O + M T SO2 + M

(33)

O Atoms.

They agree that the main reaction for formation of SO3 is

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7717

O + SO2 + M T SO3 + M

(34)

Table 6. Sulfur Species Heat of Formationa species

OH Radicals.

OH + SO T SO2 + H

(35)

Other Reactions. Other reactions that will be significant in our work include

CH3 + H2S T CH4 + HS

(36)

The presence of methyl radicals from fossil fuel would accelerate the decomposition of H2S. S Atoms.

S + H2 T H + HS

(37)

H + COS T CO + SH

(38)

S + CH4 T CH3 + SH

(39)

A reaction of high interest, because it could lead to CS2 during the combustion of H2S, when in the presence of hydrocarbons, is

S + C2H2 T HCS + CH

(40)

Also,

HCS T H + CS

(41)

S + COS T S2 + CO

(42)

S + O2 T SO + O

(43)

Molecular growth occurs via the reactions

277.0 ( 0.3 142 ( 8 109 ( 8 114 ( 8

S S3 S5 S7 SO SO2

5.0 ( 1.3 -296.8 ( 0.2

SH H2S

143 ( 3 -20.5 ( 0.8

CS2

117 ( 1

295 ( [10] 125 ( 2 -22.9 ( 0.6 112.4 ( 0.8 -37.5 ( 0.5 -24.2 ( 1.0 72 ( 5 82.1 ( 1.2 -84 ( 1 115.0 ( 0.4

H2CS CH3SH C2H5SH H2CdCdS CH3SCH2 CH3SSSCH3 CH3SSS CH3SC2H5 (C6H5)2S C4H8S

115 ( [10] 214 ( 9 -46.3 + 0.6 165 ( [15] 135 ( 3 11 ( [10] 86 ( 5 -59.6 ( 1.1 231 ( 3 -34.1 ( 0.9

CH3SO CH3SO2 (CH3)2SO CH2CH2SO (C6H5)2SO CH3C(O)SH CH3S(O)OH SCSOH HSNO HNCS CH3SCN (NH2)2CS

-62 ( [15] -238 ( [15] -151.3 ( 0.8 -30 ( [15] 107 ( 3 -175 ( 8 -360 ( [25] 110 ( [10] 94 ( [20] 126 ( 115] 160 ( [15] -25 ( [15]

CH3SOO CH3SO3 (CH3)2SO2 (C2H5)2SO (CH3O)2SO CH3SOH CH3SO3H (CH3)2SOH NS CH3NCS (SCN)2 CH3C(S)NH2

76 ( 4 -350 ( [5] -373 ( 3 -205.6 ( 1.5 -483 ( 2 -90 ( [25] -567 ( [25]60 ( [10] 263 ( 105 131 ( [15] 350 ( 6 10 ( 1

SF2

-297 ( 17

(46)

HS + O2 T OH + SO

(49)

OH + H2S T H2O + HS

(50)

SO + O2 T SO2 + O

(51)

O + H2S T H2 + SO

(52)

O + H2S T OH + HS

(53)

Unfortunately, the early work of Cullis and Mulcahy18 lacks information on the thermodynamics and kinetic data for much of the information presented, and, as noted previously, much of the referenced experimental data have been obtained at temperatures much lower than the combustion temperatures. However, it is a good starting point for any sulfur compound combustion or decomposition mechanism. Johnsson and Glarborg2 presented developments in the sulfur chemistry of combustion. The point is made that there are studies for the purpose of kinetic modeling in shock tubes, flow reactors, and flames. They stated that earlier models suffered from a lack of

18 ( [15] -188 ( 15 -735.1 ( 8.4

HCS CH3S CH3SH C6H5SH CH3SCH3 CH3SSCH3 CH3SS c-CH2CH2S (C2H5)2S C4H4S

FS

(48)

27 ( [20] 16 ( 15

280 ( 25 -138.4 ( 0.5

CIS Cl2S

H2S + M T H + HS + M

HS2 HSSH

-56 ( 34 -395.8 ( 0.7

CS COS

(45)

(47)

S2O SO3

128.6 ( 0.3 146 ( 8 102 ( 8 100.4 ( 0.6

HOS HOSO H2SO4(g)

S + S2 + M T S3 + M

H2S + O2 T HO2 + HS

S2 S4 S6 S8

∆f H°298 (kJ/mol)

-4 ( 3 -54 ( 15 -385 ( [10] -814.0 ( 0.7

(44)

Their summary mechanism for the combustion of H2S under fuel-lean conditions consists of the main reactions

species

HSO HSO2 HOSO2 H2SO4(l)

S + S + M T S2 + M S3 + S T 2S2

∆f H°298 (kJ/mol)

13.0 ( 6.3 156 ( 17 17.6 ( 3.3 -1220.5 ( 0.8

SF6

S2C1 Br2S SF5C1

SF4Cl2 SF4Cl SF3 F2CS CH3SCl C6H5SCl CH3SCH2Cl

-858 ( 13 -741 ( [20] -503 ( 34 -350 ( [15] -28 ( 6 106 ( 6 26 ( 5

SF5 SF4 HSI Cl2CS CH3SI CH3SCH2Cl

FSSF BrSSBr C6H5SSCl

-335 ( 42 35 ( [10] 113 ( 6

ClSSCl CH3SSCl

78.6 ( 8.4 21 ( 17 -1039 ( 11 -908 ( 15 -763 ( 21 42 ( 3 -27 ( [15] 30 ( 3 -90 ( [5] -16.7 ( 4 -21 ( 6

F2SO

-544 ( 21

Cl2SO

-213 ( [20]

Br2SO Cl2SO2

-107 ( [20] -354.8 ( 2.1

F2SO2 FClSO2

-758.6 ( 8.4 -557 ( 21

a

Data from Hynes and Wine.28

accurate thermodynamic and kinetic data. Rate constants for important reactions involving SO2 and SO3 are presented. Sulfur dioxide catalyzes the recombination of the main chain carriers in the flame (this will be discussed further below) and it impacts the concentration of CO and NOx in flames. The reaction mechanism of Glarborg et al.27 is recommended, because of its completeness in thermodynamic data. Hynes and Wine28 expanded on the work of Cullis and Mulcahy18 in an attempt to update the species thermodynamics (see Table 6) and rate coefficients. They note that kinetic studies have focused on low-temperature chemistry, as required to obtain rate coefficient data for

7718

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005

atmospheric modeling studies. Most rate data would seem to apply to a temperature in the proximity of 1000 K, and extrapolations are required for flame temperatures. The rate coefficients and chemistry of ∼48 elementary reactions are presented, with the applicable temperature being as high as 2500 K. The reactions involve species such as SO2, SO3, H2S, HS, S, S2, HSO2, CH3SH, CH3SCH3, CS2, COS, and CS. The work of Alzueta et al.29 has some important observations concerning the inhibition of moist CO oxidation by SO2 in flow reactors. Their main objective is to re-examine the interaction of SO2 with the radical pool under different conditions of temperature, SO2 concentration, and stoichiometry (ranging from very lean to rich). The reactor temperature ranged from 800 K to 1500 K at a pressure of 1.05 bar. For this purpose, they assembled a reaction mechanism that was comprised of 82 reactions and sulfur species such as SO, SO2, SO3, HSO, HOSO, HSO2, HOSO2, S, SH, S2, HS2, and H2S2. The mechanism used in their modeling is essentially that reported by Glarborg et al.27 They found that the extent of CO inhibition is dependent on the stoichiometry and the amount of SO2. Under very lean conditions, SO2 inhibits CO oxidation via the following reaction that captures O radicals:

erties of species such as HOSO, as well as the issue of H-radical recombination in flames, requires further investigation to elucidate the real chemistry that occurs in SO2 inhibition. Schofield’s study46 is interesting because it questions previous studies by other authors that have involved flames and sulfur chemistry. It presents equilibrium calculations and kinetic modeling of flames of H2, CH3OH, and C3H8 in air at several equivalence ratios (fuelrich) and isotherms and doped with amounts of SO2 (0.3%-0.9%). Their work seems to substantiate a partial equilibrium assumption involving the reactions of HS, S2, S, SO2, SO, H, and OH:

SO2 + O + M T SO3 + M

(54)

However, at near-stoichiometric conditions, the promotion of CO oxidation occurs, because of the increase in the radical pool by the reactions

SO2 + H T SO + OH

(55)

SO + O2 T SO2 + O

(56)

and

The overall reaction results in radical chain branching:

H + O2 T O + OH

(57)

On the other hand, under fuel-rich conditions, SO2 inhibits the oxidation of CO:

H + SO2 + M T HOSO + M

(58)

HOSO + O2 T SO2 + HO2

(59)

HOSO + H T SO2 + H2

(60)

They note that, to match the experimental data with their mechanism, they had to modify the heat of formation of HOSO to a value of -236.3 kJ/mol (versus -188 kJ/mol in Table 6 from Hynes and Wine28). They determined that, in the flame experiment of Zachariah and Smith,13 the H-atom recombination by the sulfur species could also be explained (using their mechanism) by the reaction sequence

H + SO + M T HSO + M

(61)

H + S2 + M T HS2 + M

(62)

This is in contrast to the reaction originally proposed by Zachariah and Smith13 to produce HOSO:

SO2 + H + M T HOSO + M

(63)

As this work illustrates, both the thermodynamic prop-

HS + H2 T H2S + H

(64)

H + S2 T HS + S

(65)

S + H2 T HS + H

(66)

H + SO2 T SO + OH

(67)

S + OH T SO + H

(68)

S2 + OH T S2O + H

(69)

H2 + OH T H2O + H

(70)

For kinetic modeling, they seem to prefer Zachariah and Smith,13 because of its validation against experimental data, and measurements of OH, H, and O radicals in their flames. They present a system of 16 reactions that involves the formation of COS from CS and the destruction of COS in fossil-fueled flames. One interest point is that nonequilibrium has a tendency to move the sulfur speciation in the direction of SO2, SO, and S. At the temperatures considered, species such as HSO, HSO2, HSO3, H2S2, S2O, S3, etc. contribute little to the overall sulfur balance. The report by Glarborg et al.27 is, without a doubt, one of the most quoted papers tha tinvolves reaction mechanisms for sulfur species oxidation. They studied the impact of SO2 and NO on CO oxidation using flow reactors. They note that previous studies of flames, shocks, and flow reactors provided some understanding of sulfur chemistry, although the modeling efforts lacked accurate thermodynamic data and rate data. Their experiments determined that SO2 inhibits CO oxidation, and it is most pronounced at high O-atom concentrations. The addition of NO significantly reduces the impact of SO2. They revised the thermochemistry for the H/S/O system, based on recent experimental and theoretical results. Their work included revised thermodynamic properties for the HxSOy species, as well as QRRK treatment for reactions involving these species. The mechanism consists of 67 reactions and more than 15 species. The work of Frenklach et al.30 also is often quoted. Their experimental and modeling work directly involved H2S oxidation in shock tubes (induction times). The experimental conditions were 4%-22% H2S in air, with 2%-13% H2O. The experiments were conducted at a pressure of 1 atm and a temperature of 950-1200 K. The kinetic model consisted of 17 species and 57 reactions. The agreement between experiment and model is reported to be satisfactory. Frenklach et al.30 conducted a rate and sensitivity analysis for their mechanism. The main reactions are listed below, be-

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7719

cause of its power to illustrate the most important reactions for oxidation of H2S at high temperature:

tary reactions.31 It includes species such as O, S, S2, SO, S2O, CS, COS, SO2, and SO3. For the most part, the kinetic data are estimates for the reactions in the mechanism. As with the model for H2S, the predictions for ignition delay and the concentration of major species in flames are well-correlated (no intermediates are reported). Their comment is that, generally, the mechanism will need refinements (reaction channels, rate coefficients). The most important reactions in CS2 oxidation are identified as (fuel-lean conditions)

H + O2 T OH + O

(71)

H + O2 + M T HO2 + M

(72)

HO2 + H T OH + OH

(73)

HO2 + HO2 T H2O2 + O2

(74)

H2O2 + M T OH + OH + M

(75)

S + O2 T SO + O

(76)

CS2 + O T CS + SO

(100)

SO + O2 T SO2 + O

(77)

SO + O2 + M T SO3 + M

SO + O2 T SO2 + O

(101)

(78)

H + H2S T H2 + HS

(79)

CS2 + O2 T COS + SO

(102)

HS + HS T H2S + S

(80)

S + O2 T SO + O

(103)

HS + H T H2 + S

(81)

CS + O T CO + S

(104)

H2S + O T OH + HS

(82)

For the oxidation of COS (fuel-lean):

H2S + O T SO + H2

(83)

H2S + O T HSO + H

(84)

H2S + OH T H2O + HS

(85)

HS + O2 T SO + OH

(86)

HS + O2 T SO2 + H

(87)

HS + HO2 T H2S + O2

(88)

HS + O T SO + H H + SO + M T HSO + M HSO + O2 T HO2 + SO

(89) (90) (91)

HO2 + SO2 T SO3 + OH

(92)

The work of Chernysheva and co-workers,3,31 which examined mechanistic issues in the gas-phase oxidation of hydrogen sulfide and carbon disulfide, is also an important step in the understanding of the most relevant chemistry in both processes. The H2S oxidation model3 consists of 201 reactions and 23 species, and it describes experimental data in a wide range of temperature, although the data available were limited to ignition delay and the concentration of the major species (no intermediates are reported). The model includes species such as S, S2, HS, HS2, H2S2, SO, S2O, HSO, HOS, HSO2, HOSO2, (HSO)2, SO2, and SO3. They noted that the mechanism should still be considered to be an approximation for the high-temperature oxidation of H2S. The ignition studies reveal some important reactions under stoichiometric conditions:

COS + O T CO + SO

(105)

S + O2 T SO + O

(106)

CO + SO T CO2 + S

(107)

COS + O T CO2 + S

(108)

SO + O T S + O2

(109)

CO2 + S T CO + SO

(110)

The work of Sendt et al.32 is also important, because it elucidates the importance of the chemical species H2S2 (HSSH) in the thermolysis of H2S and H2 sulfidation. Their objective is to validate a chemical kinetic mechanism that consists of 21 reactions and the species H2S, S2, H2, HSSH, HSS, SH, S, and H. The mechanism was validated against a diverse collection of published data for flow reactors (residence time of 0.2-1800 s, temperature of 873-1423 K, pressure of 0.04-3 bar, H2S mole fractions of 0.02-1.0). To estimate the rate constants, computational methods were often used, such as transition-state theory, QRRK methods, and quantum chemistry estimates of energy barriers. A sensitivity analysis of their mechanism results show that the most important reactions are as follows (shown with the heat of reaction):

H2S + M T H2 + S + M H + HSS T 2SH HSSH + M T 2SH + M

(71.05 kcal/mol)

(111)

(9.77 kcal/mol)

(112)

(64.48 kcal/mol) (113)

H2S + O2 T HS + HO2

(93)

HS + O2 T OH + SO

(94)

HS + O2 T SO2 + H

(95)

For the species HSS, the decomposition reaction is

HS + O2 + M T HSO2 + M

(96)

HSS + M T S2 + H + M

SO + O2 T SO2 + O

(97)

H2S + O T HS + OH

(98)

H2S + OH T HS + H2O

(99)

The carbon disulfide mechanism consists of 70 elemen-

HSSH + H T H2S + SH

(-26.65 kcal/mol) (114)

(76.35 kcal/mol)

(115)

The HSSH species decomposes mainly by

HSSH + M T 2HS + M

(64.48 kcal/mol)

(116)

The channel HSSH T H + SSH is not considered to be important.

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HSS will react according to the sequence

HSS + SH T H2S + S2

(-14.78 kcal/mol)

(117)

H + HSS T H2 + S2

(-14.93 kcal/mol)

(118)

H + HSS T H2S + S S + HSS T S2 + SH

(2.72 kcal/mol) (119) (-7.70 kcal/mol)

HSS + HSS T HSSH + S2

(120)

(21.64 kcal/mol) (121)

Finally, HSSH reactions include

HSSH + H T HSS + H2

(-49.46 kcal/mol) (122)

HSSH + H T H2S + SH

(-26.65 kcal/mol) (123)

HSSH + SH T H2S + HSS

(-36.42 kcal/mol) (124)

HSSH + S T HSS + SH

(-29.37 kcal/mol) (125)

D. Results of this Study: H2S Combustion Chemical Paths. The heats of reaction calculated for the reactions shown below were obtained from the JANAF Themochemical Tables. For some of the reactions involving stable and radical sulfur species, the recent data of Hynes and Wine,28 as presented in Table 6, was used as indicated. The errors associated with the heats of formation are indicated in Table 6. If data was lacking, in this work estimates were made using bond energies. As Hynes and Wine28 have noted, the thermochemistry of sulfur species in combustion phenomena is a subject of active research. The recommended heats of formation in Table 6, which contains over 100 sulfur compounds, show that the values for many key oxygenated sulfur species remain unacceptably high. Some of these species are HOS, HSO2, HOSO, HOSO2, H2SO4 (g), CH3SO, CH3SO2, CH3SO3, CH3SOH, CH3S(O)OH, and CH3SO3H. Many these species have a role in the mechanism of radical recombination by SO2, as will be discussed below. Prior to the discussion, some important considerations that have a significant role in considering chemical paths must be noted. The rate of reaction is dependent on the concentration of the chemical species and the magnitude of the rate constant. In the chemical paths depicted below, radical-molecule reactions would be considered typically more important than radicalradical reactions, because of concentration effects. Reactions that involve radical-radical additions, as well as chemically activated reactions, such as a radical addition to a double bond, usually have favorable activation energies. Reactions that involve atomic abstraction by O, OH, and H radicals in the combustion process also involve, typically, relatively low activation energies. It is useful to realize that the energy barrier for endothermic reactions is at least equal to the heat of reaction. Chemicals paths that involve O, OH, and H radicals are fundamental to high-temperature combustion phenomena,34 because they participate in the radical-chain mechanism. D.1. Formation of Oxygenated Species: SO, SO2, SO3, and S2O. The formation of oxygenated sulfur

species occurs via radical addition reactions.12 Consideration must be given to the reducing conditions under which the Claus process occurs; thus, H and OH radicals should be more abundant than O. The addition of S and HS to oxygen leads to the formation of SO:

S + O2 T SO + O HS + O2 T SO + OH

(-5.19 kcal/mol) (126) (-22.48 kcal/mol) (127)

Because of the lower O radical concentration, the addition to elemental sulfur should be secondary:

S2 + O T SO + S

(-22.50 kcal/mol) (128)

The bond between sulfur and oxygen in SO is a double bond. The formation of SO2, and SO3, occurs via similar chemical paths:

HS + O2 T SO2 + H

(-52.14 kcal/mol) (129)

SO + O + M T SO2 + M

(-132.0 kcal/mol) (130)

SO2 + O + M T SO3 + M

(-83.14 kcal/mol) (131)

Both SO2 and SO3 consist of resonance structures in which the oxygen is double-bonded to sulfur. In this work, because of the reducing conditions, no significant amounts of SO3 were calculated at equilibrium. The previously described mechanism would seem to confirm this, because its formation involves O radicals, which are less abundant in fuel-rich flames. Finally, the formation of S2O would seem to follow the path

SO + S + M T S2O + M

(-66.24 kcal/mol) (132)

D.2. Formation of Sulfur Vapor (S2). The thermal decomposition of H2S leads to an abundance of S and HS radicals in the Claus furnace. Elemental sulfur vapor (S2) is formed via the following chemical paths:

HS + HS T S2 + H2

(-35.89 kcal/mol)

(133)

This reaction leads to the formation of hydrogen, which is a species with important design considerations for the Claus Plant.

M + S + S T S2 + M

(-101.78 kcal/mol) (134)

D.3. Destruction of Hydrogen Sulfide. The initial decomposition of hydrogen sulfide is initiated by its unimolecular decomposition at high temperature, or

M + H2S T H + HS + M

(90.30 kcal/mol)

(135)

The decomposition then follows paths that involve radical-molecule reactions12 typical of combustion, or

H2S + H T H2 + HS

(-13.90 kcal/mol)

(136)

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7721

This reaction leads to the formation of hydrogen, which is an important species in Claus plant design.

H2S + OH T HS + H2O H2S + S T HS + HS

(-28.91 kcal/mol) (137) (5.25 kcal/mol) (138)

S5 + S + M T S6(c) + M (-121.9 kcal/mol; from Hynes and Wine28) (151) S4 + HS2 T S6(c) + H

This continues to form sulfur (S):

HS + OH T S + H2O

(-15.53 kcal/mol) (139)

HS + H T S + H2

(-19.16 kcal/mol) (140)

HS + HS T S + H2S

The growth continues to form S6 and S7 species:

(-5.25 kcal/mol)

(141)

These are radical-radical reactions; however, the concentration of HS radicals was shown to be high in our equilibrium calculations. Reactions that involve HS, S, and O can lead to SO and SO2, as described previously. D.4. Molecular Growth of Sulfur in the Gas Phase. The equilibrium calculations show that concentrations of S, HS, S2, H2S2, and HS2 are relatively high, and molecular growth to S8 could involve all of these species. To a lesser extent, species such as H2S3 and H2S4 can also participate. The first step would be the formation of S3, or

S2 + S + M T S3 + M (-9 kcal/mol; from Hynes and Wine28) (142)

(-18.90 kcal/mol; from Hynes and Wine28) (152) S4 + S2 + M T S6(c) + M (-95.3 kcal/mol; from Hynes and Wine28) (153) HS4 + S2 T S6(c) + H (-37.8 kcal/mol; from Hynes and Wine28) (154) HS + S5 T S6(c) + H (-37.8 kcal/mol; from Hynes and Wine28) (155) S6 + S + M T S7(c) + M (-117.4 kcal/mol; from Hynes and Wine28) (156) S5 + HS2 T S7(c) + H (-7.2 kcal/mol; from Hynes and Wine28) (157)

which is followed by

S5 + S2 + M T S7(c) + M

S3 + S + M T S4 + M (-65.25 kcal/mol; from Hynes and Wine28) (143) S2 + HS2 T S4 + H (49.8 kcal/mol; from Hynes and Wine28) (144) The growth continues, or

S4 + S + M T S5(c) + M (-129 kcal/mol; from Hynes and Wine28) (145) S3 + HS2 T S5(c) + H

(-83.5 kcal/mol; from Hynes and Wine28) (158) HS + S6 T S7(c) + H (-33.2 kcal/mol; from Hynes and Wine28) (159) S6(c) + M T S6 + M

(32 kcal/mol, ESTIM) (160)

S7(c) + M T S7 + M

(33 kcal/mol, ESTIM) (161)

Finally, S8 is formed: 28

(-16.3 kcal/mol; from Hynes and Wine ) (146) S3 + S2 + M T S5(c) + M 28

(-38.6 kcal/mol; from Hynes and Wine ) (147) HS3 + S2 T S5(c) + H (15.2 kcal/mol; from Hynes and Wine28) (148) HS + S4 T S5 (c) + H (-44.95 kcal/mol; from Hynes and Wine28) (149) where, for thermodynamic reasons, the ring or cyclic structure of S5(c) would be formed. Depending on temperature, an equilibrium would be formed between the open linear structure and its ring counterpart, or

S5(c) + M T S5 + M

(30 kcal/mol, ESTIM) (150)

S7 + S + M T S8(c) + M (-127.5 kcal/mol; from Hynes and Wine28) (162) S6 + HS2 T S8(c) + H (-8.8 kcal/mol; from Hynes and Wine28) (163) S6 + S2 + M T S8(c) + M (-85.13 kcal/mol; from Hynes and Wine28) (164) HS + S7 T S8(c) + H (-39.36 kcal/mol; from Hynes and Wine28) (165) S8(c) + M T S8 + M (33 kcal/mol; from Pryor23) (166)

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Other reactions that can also occur, but at lower temperatures (because of concentration effects), are

S3 + S3 + M T S6(c) + M (-151.5 kcal/mol; from Hynes and Wine28) (167) S3 + S4+ M T S7(c) + M (-149.6 kcal/mol; from Hynes and Wine28) (168) S3 + S5 + M T S8(c) + M (-144 kcal/mol; from Hynes and Wine28) (169) S4 + S4 + M T S8(c) + M (-153.8 kcal/mol; from Hynes and Wine28) (170) There is the question concerning the magnitude of the activation energies for the reactions responsible for the formation of cyclic sulfur species up to S8. Radical addition reactions typically have relatively low activation energies, which is a well-known fact. The ringopening reactions are endothermic in nature, and the activation energy should be at least equal to the heat of reaction. The work of Huang et al.33 in a similar reaction that involved C atoms and examined the decyclization of the phenyl radical to C6H5 would seem to indicate that, for the larger molecules (such as S6 and S8), the energy barrier may be close to the heat of reaction. For smaller molecules (such as S5), semiempirical quantum chemistry calculations by Gargurevich,17 which involved five carbon species, would indicate that the decyclization energy could be somewhat higher than the heat of reaction. The same studies would seem to indicate that the magnitude of the energy barriers for cyclization of linear sulfur species to its ring structure should be fairly low. D.5. Formation of Trace Species CS2 and COS. The chemical paths leading to the formation of carbon disulfide (CS2) and carbonyl sulfide (COS) also involve radical-addition reactions. The most important path leading to the formation of COS is the addition of the S radical to the triple bond of CO, or

M + CO + S T COS + M

(-72.91 kcal/mol) (171)

Studies indicate that there is a good correlation between the formation of COS and the presence of CO and sulfur.6 The formation of formaldehyde and CH3O are wellknown chemical paths during the oxidation of hydrocarbons.17 COS could very well form following pathways that involve these two species. First, CH3 and SO2 are abundant species during the combustion of H2S laden with hydrocarbon species. Thus, the addition of CH3 to SO2 leads to a chemically activated adduct that results in the formation of CH3O and SO:

CH3 + SO2 T [CH3-O-S-O]* T CH3O + SO (-15.5 kcal/mol) (172) The NIST Database shows a rate coefficient of 1.1 ×

10-13 exp[(-1.50 kcal/mol)/(RT)] (in units of cm3 molecule-1 s-1) for the formation of the stabilized adduct CH3SO2 at 298 K. Other data show a rate coefficient of 2.92 × 10-13 cm3 molecule-1 s-1 for the formation of products at 298 K. The nature of the products is not reported. This is similar reaction to the addition of CH3 to O2 (for the validity of this type of approach to the development of kinetic models, see ref 34, with a low energy barrier of 8.9 kcal/mol):

CH3 + O2 T CH2O + OH (∆Hf ) -53.20 kcal/mol, Ea ) 8.9 kcal/mol) (173) In this reaction, a chemically activated adduct is produced in which a bridge can be formed between the last O atom, and a hydrogen attached to carbon, which results in the elimination of OH. The net reaction has an activation energy of 8.94 kcal/mol.17 For the theoretical treatment of O2 addition reactions, see, for example, the work of Sheng et al.;35 that paper involves the more-complex addition of C2H5 to oxygen, leading to a multiplicity of products. The formation of CH3 and SO is followed by the formation of formaldehyde:

CH3O + M T CH2O + H + M

(20.50 kcal/mol) (174)

Formaldehyde then reacts with sulfur species, leading to COS:

CH2O + HS T CHO + H2S

(-0.10 kcal/mol) (175)

The comparable reaction CH2O + O ) CHO + OH has an activation energy of 2.772 kcal/mol.17

S2 + CHO T [S-SCHdO]* T CSO + HS (-76.4 kcal/mol) (176) This reaction involves a chemical adduct, which leads to HS elimination and COS formation. The comparable addition of CHO to O2 has a low activation energy. A very simple mechanism for the formation of CS2 involves C and S radical species:

C + S + M T CS + M

(-170.54 kcal/mol)

CS + S + M T CS2 + M

(177)

(-105.29 kcal/mol) (178)

This is not very likely, because Claus furnaces should not be operated in a manner that leads to coke formation; it would lead to coking of the catalytic reactors. The formation of CS2 seems to correlate well with the presence of hydrocarbons in the Claus furnace.6 A mechanism for the formation of CS2 is given by Clark

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7723

et al.4 The mechanism is given below and it starts with the reaction of methyl radicals with sulfur:

H + CH3S T CH2S + H2 (-54.47 kcal/mol; Ea ) 0 kcal/mol) (192)

CH3 + S2 + M T CH3-S-S + M

H + CH2S T HCS + H2 (-9.1 kcal/mol; Ea ) 2.99 kcal/mol) (193)

(-48.3 kcal/mol; from Hynes and Wine28) (179) CH3-S-S + H2S T HS + CH3-S-SH 28

(4.4 kcal/mol; from Hynes and Wine ) (180) CH3-S-SH + M T CH3S + HS + M (46.6 kcal/mol; from Hynes and Wine28) (181) CH3S + HS T H2S + CH2dS (-41.5 kcal/mol; from Hynes and Wine28) (182) CH2dS + HS T H2S + CHdS (4.8 kcal/mol; from Hynes and Wine28) (183) CHdS + S2 + M T S-S-CHdS + M (-18 kcal/mol; ESTIM) (184) S-S-CHdS + H2S T SdCH-S-SH + HS (7 kcal/mol; ESTIM) (185)

H + HCS T H2 + CS (-55.67 kcal/mol; Ea ) 0 kcal/mol) (194) SH + CS T H + CS2 (-21.0 kcal/mol; Ea ) 0.5 kcal/mol) (195) They experimentally determined the concentration of species such as CH4, C2H2, CH3, H2S, CS2, and CS, using molecular beam mass spectroscopy in microwaveactivated gas mixtures. Their model agrees fairly well with the experimental data, even after experimental errors in the species concentrations have been taken into consideration. A mechanism for the formation of CS2 that is proposed here again uses a reaction similar to the formation of formaldehyde from CH3, or, as above,

CH3 + O2 T [CH3-O-O]* T CH2dO + OH (-53.2 kcal/mol; Ea ) 8.94 kcal/mol) (196) Thus, the first step in the formation of CS2 would be

SdCH-S-SH + M T SdCH-S + HS (54 kcal/mol; ESTIM) (186) S)CH-S + HS T H2S + CS2 (-63 kcal/mol; ESTIM) (187) Their work does not provide rate coefficients for the aforementioned reactions. Petherbridge et al.36 presented a sequence of reactions leading to the formation of CS2. Their work involved the simulation of gas-phase reactions that were occurring in a representative gas-phase environment used to grow sulfur-doped diamond films via chemical vapor deposition (CVD) for use in electronic devices. For the C/H system, the GRI-Mech 3.0 was used, and the chemistry of the sulfur species was gathered from literature or estimated. Some estimates of the rate coefficients involving the sulfur species were also made; mixtures of H2S/CH4/H2 and CS2/H2 were studied. The sequence leading to CS2 used in their mechanism is as follows:

SH + CH3 T CH3SH (-74.44 kcal/mol; Ea ) 0 kcal/mol) (188) The heat of reaction is taken from Hynes and Wine,28 as is the case for the reactions below.

SH + CH3 T H2 + CH2S (-41.50 kcal/mol; Ea ) 0 kcal/mol) (189) H + CH3SH T CH3 + H2S (-16.70 kcal/mol; Ea ) 1.66 kcal/mol) (190) H + CH3SH T CH3S + H2 (-16.77 kcal/mol; Ea ) 2.59 kcal/mol) (191)

CH3 + S2 T [CH3-S-S]* T CH2dS + HS (-3.9 kcal/mol; from Hynes and Wine28) (197) In this reaction, a chemically activated adduct is also produced, and, in this case, a transition state is formed, in which a bridge is formed between the last S atom and a hydrogen attached to carbon, leading to HS elimination. The work of Petherbridge et al.36 would indicate that the net reaction would have a very low activation energy. The reaction that follows is then

CH2dS + HS T CHdS + H2S (3.9 kcal/mol; from Hynes and Wine28) (198) The estimate for the activation energy would be on the order of 3.0 kcal/mol for the net reaction.36 Finally,

CHdS + S2 T [S-S-CHdS]* T CS2 + HS (-39.10 kcal/mol; from Hynes and Wine28) (199) The magnitude of the activation energy can be estimated from the work of Petherbridge et al.36 as 1 kcal/mol for the overall reaction. This is a much more simple and elegant mechanism that leads to CS2. It is very favorable thermodynamically, and the order of magnitude of the estimated activation energies is relatively low. Another path for the formation of CS2 has been outlined in the work of Cullis and Mulcahy18 and was discussed previously; it involves acetylene, which is an

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intermediate that is formed during the fuel-rich combustion of methane:

S + C2H2 T HCS + CH

(92 kcal/mol)

HCS + M T H + CS + M

(200)

(51 kcal/mol) (201)

This is also a much simpler path to carbon disulfide. D.6. Destruction of COS and CS2 by Water or Hydrogen. The overall reactions that seem to explain the destruction of COS or CS2 best are as follows:

COS + H2O T H2S + CO2 COS + H2 T CO + H2S

(-8.08 kcal/mol) (202) (1.76 kcal/mol)

CS2 + 2H2O T CO2 + 2H2S

(203)

(-16.21 kcal/mol) (204)

The hydrogenation of COS should follow the following chemical paths involving an activated adduct:

COS + H T [H-S-CdO]* T CO + HS (-11.91 kcal/mol) (205) The proposed mechanism for the destruction of COS by water is as follows:

COS + OH T [S-C(OH)dO]* T CO2 + HS (-37 kcal/mol) (206) A chemically activated adduct is formed. The sulfur and hydrogen (attached to oxygen in the proximity) form a bridge that leads to the elimination of HS. The formation of CO2 as a major product is in agreement with the experiments of Clark et al.11 The aforementioned hydrogenation of COS can then be followed by the wellknown reaction

CO + OH T CO2 + H

(-24.85 kcal/mol)

(207)

The hydrolysis of CS2 involves the following reaction:

CS2 + OH T [S-C(OH)dS]* T COS + HS (-37 kcal/mol) (208) Again, a chemically activated adduct is formed, which can lead to HS elimination and formation of COS. The COS that is formed decomposes via the previously described mechanisms (hydrolysis and hydrogenation). The formation of COS as an intermediate during the reaction of CS2 with water is in agreement with the work of Clark et al.11 D.7. Reactions of CS2 and COS with SO2. Both CS2 and COS have been observed to undergo reactions in the presence of SO2 in tubular reactors4,11 to form sulfur, CO2, and CO. The mechanism can involve the thermal decomposition of the SO2 reactant, which would provide O radicals:

SO2 + M T SO + O + M

(131.75 kcal/mol) (209)

SO + M T S + O + M

(124.29 kcal/mol) (210)

This would be followed by the oxidation of COS and CS2 by O radicals, involving chemical activation:

COS + O T [S-C(O)dO]* T CO2 + S (-56.5 kcal/mol) (211) COS + O T [O-S-CdO]* T CO + SO (-52.9 kcal/mol) (212) For CS2, the chemical paths are

CS2 + O T [S-C(O)dS]* T COS + S (-54.3 kcal/mol) (213) This is followed by the oxidation of the COS, as previously discussed. D.8. The Oxidation of Methane. Issues relevant to the oxidation of hydrocarbons at high temperature have been well-discussed by Warnatz.26 The overall scheme for the combustion of methane is well-known, and it involves, depending on the conditions, species such as CH3, CH2O, CHO, CO, CO2, C2H6, C2H4, C2H2, CH2, CH, C3H3, and C6H6. The two-carbon molecules become more important under fuel-rich conditions. In this respect, the work of Westbrook and Dryer37 is also very revealing: methane oxidation is a hierarchical process that consists of CO, H2, and C2 sub-mechanisms. It is not the purpose of this study to dwell on these issues, except to refer the reader to the proper sources for further study. Our main intention here is to show the main chemical paths for methane oxidation in the presence of sulfur species. Simmie38 provided an excellent review of the recent developments in the kinetic modeling of hydrocarbons (methane, as well as heavier molecules). He discussed several methane oxidation mechanisms: GRI-Mech 3.0 (325 reactions, 53 species, 1000-2500 K), the University of Leeds, UK Mechanism (351 reactions, 37 species), and the mechanism that has been attributed to Alexander Konnov (1200 reactions, 127 species) (found at http://homepages/vub.ac.be/∼akonnov/), among others. The discussion here will rely heavily on the extensive work by Wang19 and Gargurevich,17 because these are comprehensive discussions on the issues of methane combustion, rather than reviews or summaries. The features described here have much in common with the work of the previously mentioned authors. In the absence of hydrogen sulfide, methane combustion, under fuel-rich conditions, is initiated by

CH4 + H T CH3 + H2

(0.61 kcal/mol)

CH4 + OH T CH3 + H2O

(214)

(-14.40 kcal/mol) (215)

However, under the conditions prevalent in the Claus process, S and HS radicals are also abundant and the following reactions would be expected:

CH4 + S T CH3 + HS

(19.78 kcal/mol)

(216)

CH4 + HS T CH3 + H2S

(14.51 kcal/mol)

(217)

The destruction of CH3 can then proceed as follows:

CH3 + HO2 T CH3O + OH

(-77.67 kcal/mol) (218)

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7725

COS and SO2 in the reaction of CO2 with S2.11 SO2 would form according to

Formaldehyde is also formed according to

CH3 + O2 T CH2O + OH

(-53.20 kcal/mol) (219)

CH3O + M T CH2O + H + M

(20.50 kcal/mol) (220)

followed by

CH2O + H, S, HS T CHO + H2, HS, H2S (14.00 kcal/mol, 4.60, -0.10) (221) CH2O + OH T CHO + H2O

(-29.01 kcal/mol) (222)

The following reaction can also be important if the amount of hydrocarbons is high in the initial mixture.

CH2O + CH3 T CHO + CH4

(-14.61 kcal/mol) (223)

CHO radicals decompose according to

CHO + M T H + CO + M

(15.29 kcal/mol) (224)

Also important is

CHO + O2 T HO2 + CO

(-36.31 kcal/mol) (225)

Carbon dioxide forms via the well-known reaction

CO + OH T CO2 + H

(-24.85 kcal/mol) (226)

D.9. Reactions of CO2 with H2S and S2. Monnery et al.6 noted that plant data seems to indicate the formation of CO via reactions of the type

1 CO2 + H2S T CO + H2O + S2 2 2CO2 + H2S T 2CO + H2 + SO2

D.10. Ethane Oxidation. The chemical reactions for the combustion of ethane under fuel-rich conditions have been discussed fully by Wang19 and Gargurevich.17 The presence of radicals such as S and HS introduce additional paths for the decomposition. The initial decomposition occurs according to

C2H6 + H, OH, S, HS T C2H5 + H2, H2O, HS, H2S (-52.07, -67.08, -32.91, -38.17 kcal/mol) (234) The ethyl radical continues to react, according to the following reactions:

C2H5 + O2 T C2H4 + HO2

(33.26 kcal/mol) (235)

C2H5 + H, S, HS T C2H4 + H2, HS, H2S (-19.34, -0.18, 5.44 kcal/mol) (236) Ethylene (C2H4) continues to react:

C2H4 + H, S, HS T C2H3 + H2, HS, H2S (-52.92, -33.77, -39.02 kcal/mol) (237) C2H4 + OH T C2H3 + H2O (-67.93 kcal/mol) (238) Then,

C2H3 + O2 T CH2O + CHO C2H3 + H T C2H2 + H2

(-29.02 kcal/mol) (239) (-9.63 kcal/mol) (240)

C2H3 + S, HS T C2H2 + HS, H2S (9.52, 4.27 kcal/mol) (241)

(69.23 kcal/mol) (228)

The equilibrium calculations did not result in any significant amounts of C2H2. This component reacts to form CO:

CO2 + S T SO + CO

(2.90 kcal/mol) (229)

HS + CO2 T HSO + CO

(7.69 kcal/mol) (230)

They are both chemically activated reactions that lead to CO formation. The formation of COS follows:

(-72.91 kcal/mol) (231)

Sulfur could then be formed by the reaction

SO + S T S2 + O

(-131.75 kcal/mol) (233)

(-0.61 kcal/mol) (227)

The reactions involve the CO2 constituent in the Claus feed gas only. The major products of reaction are H2, CO, COS, and S2.11 The second reaction is highly endothermic, in comparison to the first reaction, and is not very likely. The mechanism for these reactions should involve S and HS radicals that have been produced from the decomposition of H2S, or

CO + S + M T COS + M

SO + O + M T SO2 + M

(22.5 kcal/mol)

(232)

This same mechanism would explain the formation of

C2H2 + O T CH2 + CO

(-47.81 kcal/mol)

(242)

D.11. Mercaptans. The equilibrium calculations did not result in any significant amounts of mercaptans. Perhaps this is due to the lower bond energy of the C-S bond. Methyl and ethyl mercaptan react as follows:

CH3SH + H T CH3 + H2S

(-16.72 kcal/mol) (243) (-41.52 kcal/mol) C2H5SH + H T C2H5 + H2S (244) CH3SH + HS T CH3 + H2S2 (7.01 kcal/mol) (245) C2H5SH + HS T C2H5 + H2S2 (-17.80 kcal/mol) (246) (-3.75 kcal/mol) CH3SH + S T CH3 + HS2 (247) C2H5SH + S T C2H5 + HS2 (-28.60 kcal/mol) (248)

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Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005

Table 7. Simple Combustion Mechanism for H2S and SO/SO2/SO3/S2 Formationa From Kennedy et al.12

From Zachariah and Smith13

reaction

A

n

E (cal/mol)

A

n

E (cal/mol)

H + O2 T OH + O O + H2 T OH + H 2OH T O + H2O OH + H2 T H2O + H H + O2 + M T HO2 + M H2O/12./H2/2.5/ H + HO2 T 2OH H + HO2 T H2 + O2 OH + HO2 T H2O + O2 H + H + M T H2 + M H2O/6.5/O2/0.4/H2/1/N2/0.4/ H + OH + M T H2O + M H2O/12./H2/2.5/ HO2 + HO2 T H2O2 + O2 H2O2 + M T OH + OH + M H2O/15./H2/2.5/ H2O2 + OH T H2O + HO2 O + HO2 T O2 + OH H + HO2 T O + H2O H + O + M T OH + M H2O/12./H2/2.5/ O + O + M T O2 + M H2O/12./H2/2.5/ H2O2 + H T H2O + OH H2O2 + H T HO2 + H2 O + OH + M T HO2 + M H2 + O2 T 2OH S and SOx Section S + O2 T SO + O O + S2 T SO + S SO + O2 T SO2 + O SO + SO T SO2 + S SO + O + M T SO2 + M SO2 + O + M T SO3 + M SO + O2 + M T SO3 + M SO3 + O T SO2 + O2 SO3 + SO T SO2 + SO2 SO + S + M T SO2 + M 2S + M T S2 + M S2 + H T S2O + H S and H Section H2S + M T S + H2 + M H + H2S T H2 + SH SH + SH T H2S + S H2S + S T SH + SH H2 + S T SH + H HS + H T H2 + S SH + S T H + S2 S, H, and O Section H2S + O T OH + SH H2S + OH T H2O + SH SH + H2O2 T HO2 + H2S SH + O2 T SO + OH SH + O2 T SO2 + H SH + HO2 T H2O2 + S SH + HO2 T H2S + O2 SH + O T OH + S SH + O T SO + H SH + OH T H2O + S OH + SO T SO2 + H OH + S T SO + H HO2 + S T SH + O2 SO3 + H T SO2 + OH HSO2, HSO Reactions H + SO2 + M T HSO2 + M H + HSO2 T SO2 + H2 OH + SO + M T HSO2 + M OH + HSO2 T SO2 + H2O OH + HSO2 T SO2 + H2O H + SO + M T HSO + M HSO + H T H2 + SO HSO + H T H2S + O HSO + H T SH + OH HSO + OH T H2O + SO

3.52 × 1016 5.06 × 104 6.00 × 108 1.17 × 109 6.76 × 1019

-0.7 2.67 1.3 1.3 -1.42

17070 6290 0 3626 0

1.20 × 1017 1.50 × 107 1.50 × 109 1.00 × 108 2.00 × 1018

-0.91 2 1.14 1.6 -0.8

16422 7542 0 3295 0

1.70 × 1014 4.28 × 1013 2.89 × 1013 1.80 × 1018

0 0 0 -1

874 1411 -497 0

1.50 × 1014 2.50 × 1013 2.00 × 1013 2.00 × 1018

0 0 0 -1

1003 692 0 0

2.20 × 1022

-2

0

2.20 × 1021

-2

0

3.02 × 1.20 × 1017

0 0

1390 45500

7.08 × 1012 2.00 × 1013 3.10 × 1013 6.20 × 1016

0 0 0 -0.6

1430 0 1720 0

2.00 × 1013

0

0

6.17 × 1015

-0.5

0

1.00 × 1013 4.79 × 1013 1.00 × 1016 1.70 × 1013

0 0 0 0

6.30 × 1011 6.30 × 101 1.80 × 1011 3.30 × 1011 1.20 × 1022

0.5 0.5 0 0 -1.8

0 0 0 2250 0

1.20 × 1022 1.00 × 1018 1.80 × 1013

-1.8 -1 0

0 0 0

1.20 × 1013 1.00 × 1014

0 0

1710 1430

2.00 × 1014 5.16 × 1014 1.40 × 1013

0 0 0

76600 21000 478

4.36 × 1012 1.40 × 1013

0 0

322 886

6.31 × 101 3.56 × 1014

0.5 0

1.80 × 1013 7.20 × 1013

0 0

0 642

7.30 × 1016 1.60 × 1012 7.00 × 1016 6.80 × 1013

0 0 0 0

0 0 0 1772

1.60 × 1020 5.00 × 1011 5.00 × 1010 5.00 × 1011 5.00 × 1013

-1.5 0.5 0.5 0.5 0

0 2222 4520 4520 1006

1012

2.00 × 106 3.98 × 1012 6.20 × 103 2.00 × 1012 1.10 × 1022 4.00 × 1028 1.00 × 1015 1.30 × 1012 1.00 × 1012

1.93 0 2.42 0 -1.84 -4 0 0 0

3590 7950 0 47780 -1400 0 3050 4000 0 5250 0 6100 4000

2.00 × 1014 1.20 × 107

0 2.1

66000 700

4.00 × 1014 6.00 × 1014

0 0

15100 24000

2.69 × 1013

0

0

6.40 × 107 2.70 × 1012 1.00 × 1011 1.10 × 1011 2.00 × 1011 1.00 × 1011 6.00 × 1012 2.29 × 1011 1.00 × 1014 1.00 × 1013 5.20 × 1013 4.00 × 1013 1.00 × 1012 1.00 × 1012

1.78 0 0 0 0 0 0 0.67 0 0 0 0 0 0

1.00 × 1015

0

2840 0 0 5400 5400 0 0 1920 0 0 0 0 0 0

0

8060 642

Ind. Eng. Chem. Res., Vol. 44, No. 20, 2005 7727 Table 7 (Continued) From Kennedy et al.12 reaction HSO2, HSO Reactions HSO + O T SO + OH HSO + O T H + SO2 HSO + O T HS + O2 HSO + O2 T SO + HO2 SH + HSO T H2S + SO a

A

n

From Zachariah and Smith13

E (cal/mol)

1.00 × 1012

0

0

1.00 × 1012

0

0

A

n

E (cal/mol)

5.00 × 101 1.00 × 1014 5.00 × 1011 5.00 × 1011

0.5 0 0.5 0.5

2222 26200 4520 2222

Values determined using the rate equation in Arrhenius form: k ) ATn exp[-E/(RT)]. Units involved include cm, mol, and s.

D.12. The Effect of SO2 on Radical Chemistry. Zachariah and Smith,13 as well as Tseregounis and Smith,39 have noted the effect of small amounts of SO2 on the radical chemistry, i.e., reactions that involve H, O, and OH in H2/O2/Ar flames under fuel-rich conditions. This study has been selected because of the existence of experimental data, including measurements of the H, OH, O radicals. They have noted that SO2, and HSO2 (see Table 7), lead to radical recombination reactions of the type

X + SO2 + M T XSO2 + M

(249)

XSO2 + Y T XY + SO2

(250)

for H, Y ) H, OH. For example,

H + SO2 + M T HSO2 + M

(251)

H + HSO2 T H2 + SO2

(252)

OH + HSO2 T H2O + SO2

(253)

Similarly, for the O radical (from Smith et al.40),

O + SO2 + M T SO3 + M

(254)

SO3 + O T SO2 + O2

(255)

Tseregounis and Smith determined, for example, that the addition of SO2 leads to a substantial depletion of atomic hydrogen. As the previously discussed reaction between H and HSO2 shows, the presence of SO2 catalyzes the formation of H2 from H atoms. Zachariah and Smith13 also have noted the role of HSO2 as a channel for radical recombination. Smith et al.40 have highlighted the role of SO2 as a catalyst for radical recombinaton in CO/O2/Ar fuel-lean flames, as shown by the last set of reactions previously presented involving atomic oxygen radicals.They noted the importance of HSO2 to be able to better model flames that have been doped with SO2. This could be an important consideration during the combustion of H2S in the Claus process. Clark et al.4 noted in their study of Claus chemistry that H2S combusts more quickly than the hydrocarbons that were present in the initial gas mixture. The aforementioned discussion would seem to indicate that this could be the result of the formation of SO2 in large quantities in the Claus process and the resultant H and OH radical recombination, which would then slow the hydrocarbon decomposition. This should be an area of further study. The equilibrium calculations in this study did not result in any significant quantities of HSO2. This is in agreement with the study of Smith et al.40 on CO/O2/ Ar flames under fuel-lean conditions. However, as mentioned earlier, H2SO2 molecules seem to form at the

higher temperatures or above 2000 °F. This could be the end product of HSO2 formation in the combustion process. The work of Alzueta et al.29 on the effects of SO2 on the radical pool has been presented earlier. This is a study conducted at a later time than the Zachariah and Smith experiments and somehow is in contradiction with what is presented here. The arguments presented by Alzueta et al. seem to indicate that the effect of SO2 on the radical pool, as well as the mechanism for radical recombination in flames, require further study. The problem seems to involve a lack of better kinetic and thermodynamic data. D.13. Reaction Rate Coefficients. This work will not address issues relating to methods for the construction of any detailed chemical kinetic model composed of many reactions, as shown in Table 5, and the estimation of chemical kinetic coefficients. Several sources can be found that address the subject, including the work of Wang19 and Gargurevich.17 These are also good sources for the treatment of chemically activated reactions, some of which have been presented in this manuscript The treatment of chemically activated reactions can also be found in the work of Westmoreland et al.,25 Deanet al.,41 and Kazakov et al.42 It is important to note here the conclusion reached by Hynes and Wine28 in their review of thermochemical and kinetic data of sulfur reactions: “The paucity of high-temperature kinetic data on elementary reactions of sulfur is a substantial roadblock to understanding sulfur combustion. More high-temperature studies are needed for almost all of the reactions of sulfur species.” “Modeling studies of sulfur chemistry under combustion conditions have been handicapped by the lack of a regularly upgraded, evaluated high-temperature database similar to the NASA or CODATA compilations used for atmospheric modeling”. This consideration is most important for temperatureand pressure-dependent reactions (such as unimolecular reactions) and chemically activated reactions, which have a fundamental role in combustion. The dependence of the rate coefficient on reaction conditions must be taken into . The author has not found a comprehensive study of H2S combustion in the fuel-rich flames and experimental studies of the reactions presented in this manuscript. Table 7 illustrates the kinetic models of Kennedy12 and Zachariah and Smith.13 These models only examine the formation of simple sulfur species (such as SO, SO2, SO3, and S2) and are fairly similar. They are a good starting point for kinetic data. Kennedy’s work12 is representative of a high-temperature model under reducing conditions. The work of Zachariah and Smith,13 as noted previously, provide both a model and the experimental

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data to it, but with reservations on the thermodynamic and kinetic data, which would need to be updated. The work of Radi et al.43 uses a novel spectroscopic technique (multiplex spectroscopy) and it is applied to measure S2 and OH concentration profiles in H2/Air/ SO2 flames obtained stabilized on a flat flame burner at atmospheric pressure. The sulfur chemistry used in their mechanism is taken from Zachariah and Smith13 for low-pressure H2/O2/SO2 flames. The experimental results for the OH and S2 concentration profiles are in good qualitative agreement with the mechanism results. Discrepancies in the S2 concentration profile are attributed to the fact that the mechanism of Zachariah and Smith13 was developed for low-pressure flames. To improve their mechanism, corrections must be made to pressure-dependent reactions for the higher experimental pressure in their flame experiments. Table 5 shows, for each reaction, the most recent sources of chemical kinetic rate coefficient data. A good source is also the NIST Database (which can be found via the Internet at www.nist.gov). The sulfur mechanism by the University of Leeds, U.K. presents kinetic data that are based on the work of Alzueta et al.,29 including the most recent data for the HxSOy system of reactions; it can be found at http://garfield.chem.elte.hu/ Combustion/Combustion.html. The compilation of Hynes and Wine28 consists of 48 elementary reactions that involve sulfur-containing species and it is also an updated resource. For the combustion of simple hydrocarbons, the extensive compilations by Baulch and coworkers,44,45 Wang,19 and Gargurevich17 are good resources. Experimental rate coefficients (at high temperatures) for reactions leading to sulfur S8(c), and the novel reactions leading to COS and CS2, as presented in this study, have not been found by the author. Because experimental data is lacking, further studies will be necessary to improve the rate coefficients and thermodynamics of the reactions in Table 5 by the methods described by Gargurevich17 and Senkan.34 Computational quantum chemistry can also be used for the estimation of activation energies and the heats of formation of the molecular species. Experimental studies would also need to be pursued, to validate the model depicted in Table 5, after the reaction rate coefficients have been estimated. Conclusions The main objective of this study has been to present the relevant chemical reactions that occur in the combustion of hydrogen sulfide under Claus furnace (i.e., fuel-rich) conditions. As a result of a survey of literature, fundamental chemical laws, and radical reactions fundamental to combustion phenomena, a chemical reaction mechanism consisting of over 150 elementary reactions is presented. The mechanism is able to explain the high-temperature oxidation of H2S. The formation of hydrogen, which is an important consideration in Claus plant design, can be explained by the mechanism. Hydrogen generation impacts the design of the Claus plant tail gas treating units. Most importantly, novel chemical paths for the formation of COS and CS2 are presented, based on fundamental chemical laws. The heats of reaction and activation energies for the reactions are estimated and seem to indicate that the chemical paths presented could

have an important role. These are trace species with important environmental impact, which must be considered in the design of sulfur treatment plants in modern refineries. Existing process simulators such as TSWEET and SULFSIM rely on empirical correlations or an approach to equilibrium to determine the amounts of H2, COS, and CS2 produced in the Claus plant as the gas is cooled to the sulfur dew point. Unfortunately, many of these empirical correlations cannot represent all of the conditions that may occur in the design of Claus plants. The study introduces a plausible explanation for the observed reduced rate of hydrocarbon oxidation in the Claus furnace, which is due to radical recombination catalyzed by SO2. This should be an important consideration in the design of the combustion furnace of Claus plants to minimize carbon deposition in the catalytic reactors downstream of the furnace. The molecular growth to S8, starting with S2, is also included in the mechanism. Evidence is provided for the ring structure of S5, S6, and S7; in contrast, S4 is a linear molecule. Intramolecular reactions involving S8 and leading to S7 and S6 are introduced. Heats of reaction and activation energy estimates for the cyclization reactions of Sx species are estimated. The energy barriers for cyclization are favorable at the high temperatures that are typical of the Claus process. Reactions of COS and CS2 with SO2 are investigated prompted by observations in flow reactor experiments. For similar reasons, reactions of CO2 with H2S and S2 are considered. The study highlights the consensus, in regard to the lack of high-temperature kinetic data, as well as studies of fuel-rich H2S flames. These are needed for a validation of the elementary reaction chemistry presented in the manuscript. Similarly, experimental studies at high temperature are needed to better elucidate the phenomena of radical recombination by SO2. Literature Cited (1) Bowman, C. T. Kinetics of Pollutant Formation and Destruction in Combustion. Prog. Energy Combust. Sci. 1975, 1, 3345. (2) Johnsson, J. E.; Glarborg, P. Sulphur Chemistry in Combustion I. Sulphur in Fuels and Combustion Chemistry. In Pollutants from Combustion: Formation and Impact on Atmospheric Chemistry; Vovelle, C., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2000; p 263. (3) Chernysheva, A. V. et al. Mechanism of Gas-Phase Oxidation of Hydrogen Sulfide at High Temperatures; N. N. Semenov Institute for Chemical Physics, Academy of Sciences of the USSR: Moscow. (Translated from Izv. Akad. Nauk SSSR, Ser. Khim. 1990, (9), 1956-1966.) (4) Clark, P. D.; Dowling, N. I.; Huang, M. Chemistry of the Claus Front-End Reaction Furnace: Hydrocarbon Reactions and the Formation and Destruction of CS2. In ASR Quarterly Bulletin, Vol. XXXIII, No. 4, Jan.-Mar. 1997; Alberta Sulphur Research: Calgary, Alberta, Canada, 1997; pp 1-49. (5) Hyne, J. B. Optimum Furnace Configuration for Sulphur Recovery Units. Sulphur 1988, 198 (September-October), 2439. (6) Monnery, W. D.; Svreck, W. Y.; Behie, L. A. Modelling the Modified Claus Process Reaction Furnace and the Implications on Plant Design and Recovery. Can. J. Chem. Eng. 1993, 71, 711. (7) Slimane, R. B.; Lau, F. S.; Abbasian, J. Hydrogen Production by Superadiabatic Combustion of Hydrogen Sulfide. In Proceedings of the 2000 Hydrogen Program Review, Paper No. NREL/-57028890. (8) Slimane, R. B.; Lau, F. S.; Khinkis, M.; Bingue, J. P.; Saveliev, A. V.; Kennedy, L. A. Conversion of Hydrogen Sulfide

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Received for review August 4, 2004 Revised manuscript received June 25, 2005 Accepted July 25, 2005 IE0492956