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. 2023 Nov 27;8(48):46013–46026. doi: 10.1021/acsomega.3c06910

Density Functional Theory Investigation of the Sulfur–Iron Compound Formation Mechanism in Petrochemical Facilities

Siyuan Wu †,‡,*, Mengxin Zhang †, Baichao Shi †, Jiancun Gao †,‡, Renyou Zhang †,‡, Tianhao Chen †, Yiting Zou †
PMCID: PMC10702202  PMID: 38075837

Abstract

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In order to investigate the formation mechanism of hydrogen sulfide corrosion products in petroleum and petrochemical facilities, the interaction mechanism between iron oxides and H2S was studied by density functional theory (DFT). First, the adsorption of H2S on Fe2O3 clusters and Fe3O4 clusters was studied. The results indicated that H2S was more inclined to adsorb on the Fe site. After adsorption, the S–H bond changed from 1.356 to 1.360 Å in the gas phase, which was the main reason for the decomposition of H2S. On this basis, the reaction paths of Fe2O3 clusters and Fe3O4 clusters with H2S and the rate-determining steps of different reaction paths were calculated. The thermodynamic parameters and kinetic parameters of the rate-determining step of each path are analyzed. The results indicated that reaction path 1 of H2S and Fe2O3 clusters is the best reaction channel. The reaction will gradually form products such as S, H2O, and Fe2S2, which can release a total of 622.23 kJ/mol heat. The reaction path 2 of H2S and Fe3O4 clusters is the best reaction channel. The reaction will gradually form products such as S, H2O, and Fe3S2, which can release a total of 260.40 kJ/mol heat. Finally, the reaction paths of Fe2S2, Fe3S2, and S2 were further calculated, and it was observed that the products formed by hydrogen sulfide corrosion were easy to react with S2 to form sulfur–iron compounds with different iron–sulfur ratios. This is consistent with the corrosion products including FeS, FeS2, and Fe3S4 observed in the experiment. It lays a theoretical foundation for the subsequent study of the effect of associated elemental sulfur on the spontaneous combustion of sulfur–iron compounds.

1. Introduction

Hydrogen sulfide gas can be dissolved in water and crude oil. Hydrogen sulfide gas may exist in the processes of oil extraction, transportation, processing, and refining.1−3 Petroleum and petrochemical plant facilities and their oxidation products can be corroded by hydrogen sulfide to form iron sulfide compounds.4−6 Iron sulfide compounds can spontaneously combust and release a lot of heat at room temperature in contact with air and then ignite the surrounding combustible materials and induce fire and explosion accidents.7−10 Therefore, the study of the formation mechanism of different sulfur–iron compounds is an important component of the study of the spontaneous combustion of corrosion products in petroleum and petrochemical facilities. The formation process of iron sulfides is very complicated. At present, the reaction mechanism of the formation of iron sulfides is not clear. Most of the research on H2S corrosion of rust focuses primarily on experimental studies. Many scholars have studied the formation principle of iron sulfide compounds.11−14 At the same time, some scholars have directly studied the corrosion products formed by the reaction of H2S and rust through experiments.15−17 However, the formation conditions and processes of elemental sulfur and various iron sulfides in the product as well as the impact of elemental sulfur on the formation and spontaneous combustion of iron sulfides remain as areas that require further understanding. In particular, the effect of elemental sulfur on the formation and spontaneous combustion of different iron sulfides is not clear and is difficult to achieve in experiments. This has hindered theoretical research on the influence of associated elemental sulfur on the spontaneous combustion of pyrite compounds and the study of prevention and control technologies for pyrite compound spontaneous combustion to a certain extent.

At present, the research on iron oxides is mainly focused on the reaction mechanism of hydrogen, NO, and other molecules on their surfaces.18−23 Yang et al.19 computed hydrogen adsorption on the Fe3O4(111) surfaces at the level of density functional theory. Song et al.21 used density functional theory to investigate the synergistic effect of Fe2O3 and CuO on simultaneous catalytic hydrolysis of COS and CS2. Fang et al.22 calculated the adsorption energy of ammonia and nitric oxide on α-Fe2O3(001), γ-Fe2O3(001), and Fe3O4(111) surfaces by density functional theory (DFT) calculations. These scholars have extensively studied the mechanisms and properties of iron oxides involved in reactions. However, they have not studied the reaction mechanism of H2S corrosion of rust in petroleum and petrochemical facilities for the purpose of studying spontaneous combustion, especially concerning the reaction of the cluster structure of rust with H2S. The cluster structure can explore the chemical reaction path, structure, and properties of atoms, molecules, and their aggregates, providing certain ideas and scientific basis for the study of microscopic reaction mechanisms.24 Most of the studies on the interaction between iron oxides and H2S are about the interaction mechanism between the α-Fe2O3 surface and H2S. Zhou et al.25 investigated the adsorption mechanism of hydrogen sulfide on α-Fe2O3(001) surfaces by density functional theory with geometrical relaxations. Song et al.26 investigated the interaction mechanism of H2S and the α-Fe2O3(001) surface during the desulfurization by the density functional theory (DFT) method within a periodic slab model. The interaction mechanism of the H2S dissociation process was clarified, and the formation process of H2 and H2O was studied. Unfortunately, the research background does not involve the formation mechanism of iron sulfides in petroleum and petrochemical facilities. In petrochemical facilities, the primary components of oxidized rust are Fe2O3 and Fe3O4. Therefore, this study uses density functional theory to study the interaction between hydrogen sulfide gas molecules and Fe2O3 clusters and Fe3O4 clusters, including H2S adsorption, charge distribution, and reaction paths. On this basis, the formation mechanism of different sulfur–iron compounds is further studied, which lays a theoretical foundation for the subsequent study of the influence of associated elemental sulfur on the spontaneous combustion of sulfur–iron compounds.

2. Computational Methods and Models

2.1. Computational Methods

In this work, all calculations were performed under the Dmol3 module in Materials Studio software. The generalized gradient approximation (GGA-PBE) with the Perdew–Burke–Ernzerhof exchange correlation function is used. The transition metal core electrons are calculated using all-electron calculations. The valence electron wave function uses a double numerical polarization basis set (DNP). The energy threshold for structural optimization is within 1 × 10–5 Hartree, and the atomic displacement is less than 0.005 Å (1 × 10–10 m). The convergence limit of the structural optimization force is 0.002 hartree/Å, and the self-consistent field (SCF) convergence standard is 1 × 10–6 Hartree. Since the system contains transition metal Fe atoms, all calculations take into account the influence of the electron spin. The formal spin is used as the initial value to test the spin state of the structure, and the structure optimization and frequency analysis of all structures in this paper are carried out to obtain the ground-state stable structure. The LST/QST method27 is used to search the reaction transition state and calculate the frequency of the transition state to ensure that the transition state has a unique imaginary frequency. On the stable structure, the adsorption of H2S at different positions was considered and the adsorption energy of each adsorption site was calculated to obtain the most stable adsorption structure. The adsorption energy Eads is defined as follows

2.1. 1

or

2.1. 2

In the formula, Eads represents the adsorption energy, EFe2O3/H2S and EFe3O4/H2S represent the total energy of the system, EFe2O3 represents the ground-state energy of Fe2O3, EFe3O4 represents the ground-state energy of Fe3O4, and EH2S represents the ground-state energy of H2S. According to the definition, the value of the negative number represents the exothermic process and the larger the value, the stronger the adsorption.

According to Eyring transition state theory (TST), the reaction rate constant k of the elementary reaction is defined as follows

2.1. 3

In the formula, k is the reaction rate constant, kB is the Boltzmann constant, T is the temperature, h is the Planck constant, ΔGb is the Gibbs free energy barrier, and R is the gas constant.

In the calculation of reaction thermodynamics, the equilibrium constant is defined as follows

2.1. 4

In the formula, GP and GR represent the Gibbs free energy of the product and the reactant, respectively, R represents the gas constant, T represents the temperature, and K represents the reaction equilibrium constant.

The energy gap Egap is defined as follows

2.1. 5

In the formula, ELUMO represents the LUMO orbital energy level and EHOMO represents the HOMO orbital energy level. The energy gap reflects the ability of electrons to transition from occupied orbitals to empty orbitals and, to some extent, can indicate the strength of a molecule ’s ability to participate in chemical reactions. The smaller the energy gap, the easier the electronic transition and the more active the molecular chemical activity. When the energy gap value is large, it is believed that the stability of the cluster is strong.

2.2. Computational Models

Based on the crystal mode,28,29 the amorphous cluster model was established. In our study, since Fe2O3 clusters and Fe3O4 clusters contain multiple Fe atoms, two magnetic configurations are considered of Fe2O3 clusters, + – and + +, and three magnetic configurations are considered of Fe3O4 clusters, + + +, + – +, and + – −, where + and – are designated as the up-spin and down-spin directions of the cluster Fe sites, respectively, as shown in Figure 1. The cluster model of iron oxide and the molecular model of H2S were geometrically optimized using the Dmol3 module to obtain a stable structure, as shown in Figure 2. Our calculation shows that the Fe2O3 antiferromagnetic arrangement (+ −) and Fe3O4 antiferromagnetic arrangement (+ – −) induce the most stable and accurate structure, which is in agreement with the previous theoretical work.30,31

Figure 1.

Figure 1

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Magnetic structures of Fe2O3 clusters and Fe3O4 clusters (the arrow represents the spin direction of the Fe sites, purple represents the Fe atom, red represents the O atom).

Figure 2.

Figure 2

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Stable structures of the ground-state Fe2O3 cluster (left) and the ground-state Fe3O4 cluster (middle) and the molecular model of H2S (right) (purple represents the Fe atom, red represents the O atom, yellow represents the S atom, white represents the H atom) (bond length unit: Å, 1 Å = 1 × 10–10 m).

It can be seen from Figure 2 that Fe2O3 and H2S have a planar structure, in which the length of the Fe–Fe bond is 2.322 Å, the length of the Fe–O bond is 1.808 and 1.630 Å, and the length of the S–H bond is 1.356 Å. The length of the Fe–Fe bond in the Fe3O4 cluster is 2.471 Å, and the length of the Fe–O bond is 1.837 and 1.906 Å.

3. Results and Discussion

3.1. Adsorption of H2S on Iron Oxide Clusters

In order to study the interaction mechanism between H2S and iron oxides, it is necessary to first investigate the adsorption of H2S on different sites of Fe2O3 clusters and Fe3O4 clusters and obtain the most stable adsorption structure for subsequent reaction studies. In our study, different adsorption methods such as H2S adsorption at the top of the Fe atom, Fe–O bond bridge site adsorption, and O atom top adsorption were considered. Each adsorption method considers different adsorption angles and adsorption distances. The geometric structures of different adsorption modes were optimized to determine the most stable adsorption structure at each adsorption site and calculate the adsorption energy. The adsorption sites and adsorption energies for each adsorption structure are listed in Figure 3. The formation of chemical bonds between atoms can cause changes in charge density. Therefore, in order to observe the transfer of charge during atomic bonding and obtain more information about atomic bonding. The differential charge density and Mulliken charge population of the adsorption structure were calculated. The electron transfer, charge distribution, and interaction in the adsorption process were analyzed. In order to illustrate the effect of H2S adsorption on the structure of Fe2O3 and Fe3O4 clusters, the energy gaps of Fe2O3 and Fe3O4 clusters before and after H2S adsorption were calculated.

Figure 3.

Figure 3

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(a) Adsorption energy of H2S on different active adsorption sites on Fe2O3 clusters and (b) adsorption energy of H2S on different active adsorption sites on Fe3O4 clusters (purple represents the Fe atom, red represents the O atom) (bond length unit: Å, 1 Å = 1 × 10–10 m).

3.1.1. Adsorption of H2S on Fe2O3 Clusters

The adsorption structure of H2S on different active sites of Fe2O3 clusters and the charge density diagram of each adsorption structure are shown in Figure 4. In Figure 4(a), when H2S is adsorbed on the top of the Fe atom, H2S is in a perpendicular state with Fe–Fe, and the bond length of S–Fe is 2.362 Å. The S–H bond extends from 1.356 Å in the gas phase to 1.362 Å. The color of the Fe–S atoms after the adsorption of H2S is red, indicating that a large amount of charge is distributed between the Fe and S atoms. Due to the difference in electronegativity between the S atoms and the Fe atoms, a chemical bond is formed between them, indicating that H2S undergoes chemisorption with Fe2O3. Furthermore, according to the Mulliken charge population analysis, after H2S adsorption, Fe2O3 clusters are on the electron-gaining side and H2S is on the electron-losing side, losing a total of 0.18e electrons, indicating an electron transfer from H2S to the Fe2O3 cluster. The low charge magnitude suggests that chemical adsorption is not strong. The adsorption energy for this adsorption mode is −90.77 kJ/mol. Before and after H2S adsorption, the energy gap of Fe2O3 clusters changes from 1.81 to 0.01 eV, indicating that the structural activity increases after adsorption. In Figure 4(b), when H2S was adsorbed at the top of the O adsorption site 1, the S atom was adsorbed on the Fe atom, and the bond length of the formed S–Fe is 2.333 Å. Additionally, the S–H bond is extended from its gas phase value of 1.356–1.362 Å. A large number of charges were distributed around the Fe–S bond, indicating that this adsorption mode also belongs to chemisorption. The adsorption energy for this adsorption mode is −88.84 kJ/mol. Furthermore, according to the Mulliken charge population analysis, H2S lost a total of 0.17e electrons. Before and after H2S adsorption, the energy gap of Fe2O3 clusters changes from 1.81 to 0.02 eV, indicating that the structural activity increases after adsorption. In Figure 4(c), when H2S was adsorbed at the Fe–O bond bridge site 1, the S atom was also adsorbed on the Fe atom and the bond length of the formed S–Fe is 2.333 Å. A large number of charges were distributed around the Fe–S bond, indicating that this adsorption mode also belongs to chemisorption. The adsorption energy for this mode is −89.24 kJ/mol. Before and after H2S adsorption, the energy gap of Fe2O3 clusters changes from 1.81 to 0.01 eV, indicating that the structural activity increases after adsorption. In Figure 4(d), when H2S was adsorbed at the top of the O adsorption site 2, there was repulsion between the O and S atoms, while the O atom tends to adsorb the H atom. As a result, the S–H bond is extended from its gas phase value of 1.356–1.373 Å. The Mulliken charges for H2S and Fe2O3 are 0.06e and −0.06e, respectively, indicating that under this adsorption mode, H2S does not participate in chemical adsorption with Fe2O3 clusters. The calculated adsorption energy is −46.12 kJ/mol. Before and after H2S adsorption, the energy gap of Fe2O3 clusters changes from 1.81 to 0.01 eV, indicating that the structural activity increases after adsorption. In Figure 4(e), when H2S was adsorbed at Fe–O bond bridge site 2, the S atom was adsorbed on the Fe atom and the bond length of the formed S–Fe is 2.570 Å. Additionally, the S–H bond is slightly extended from its gas phase value of 1.356 to 1.358 Å. According to the Mulliken charge population analysis, H2S lost a total of 0.18e electrons. The adsorption energy for this adsorption mode is −47.64 kJ/mol. Before and after H2S adsorption, the energy gap of Fe2O3 clusters changes from 1.81 to 0.03 eV, indicating that the structural activity increases after adsorption.

Figure 4.

Figure 4

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Adsorption structure of H2S on different active sites of Fe2O3 clusters and the charge density diagram of each adsorption structure. ((a) Fe Site, (b) O Site 1; (c) bridge Site 1, (d) O Site 2, (e) bridge Site 2) (bond length unit: Å, 1 Å = 1 × 10–10 m).

3.1.2. Adsorption of H2S on Fe3O4 Clusters

The adsorption structure of H2S on different active sites of Fe3O4 clusters and the charge density diagram of each adsorption structure are shown in Figure 5. In Figure 5(a), when H2S was adsorbed at the top of Fe adsorption site 1, H2S attached to the Fe atom, forming an S–Fe bond with a bond length of 2.428 Å. Additionally, the S–H bond is slightly extended from its gas phase value of 1.356–1.360 Å. The color of the Fe–S atoms after adsorption of H2S is red, indicating that a large amount of charge is distributed between the Fe and S atoms. Due to the difference in electronegativity between the S atoms and the Fe atoms, a chemical bond is formed between them, indicating that H2S undergoes chemisorption with Fe3O4. Furthermore, according to the Mulliken charge population analysis, after H2S adsorption, Fe3O4 clusters are on the electron-gaining side and H2S is on the electron-losing side, losing a total of 0.19e electrons, indicating an electron transfer from H2S to the Fe3O4 cluster. The low charge magnitude suggests that the chemical adsorption is not strong. The adsorption energy for this mode is 69.10 kJ/mol. The energy gap of Fe3O4 clusters did not change before and after H2S adsorption, indicating that H2S adsorption had little effect on the structural activity. In Figure 5(b), when H2S was adsorbed at the top of Fe adsorption site 2, H2S also attached to the Fe atom, forming an S–Fe bond with a bond length of 2.391 Å. Additionally, the S–H bond is slightly extended from its gas phase value of 1.356–1.360 Å. A large number of charges were distributed around the Fe–S bond, indicating that this adsorption mode also belongs to chemisorption. The adsorption energy for this adsorption mode is −49.97 kJ/mol. Furthermore, according to the Mulliken charge population analysis, H2S lost a total of 0.19e electrons. Before and after H2S adsorption, the energy gap of the Fe3O4 clusters changes from 0.01 to 0.02 eV, indicating a decrease in structural activity after adsorption. In Figure 5(c), when H2S was adsorbed at Fe–O bond bridge site 1, the S atom was also adsorbed on the Fe atom. The bond length of the formed S–Fe is 2.474 Å and the S–H bond is extended from 1.356 Å in the gas phase to 1.358 Å. A large number of charges were distributed around the Fe–S bond, indicating that this adsorption mode also belongs to chemisorption. The adsorption energy for this adsorption mode is −49.48 kJ/mol. Before and after H2S adsorption, the energy gap of the Fe3O4 clusters changes from 0.01 to 0.02 eV, indicating a decrease in structural activity after adsorption. In Figure 5(d), when H2S was adsorbed at the top of O adsorption site 1, there was repulsion between the O and S atoms. As a result, one of the S–H bonds breaks, while the O–H bond forms, with the O atom showing a preference for adsorbing the H atom. The adsorption energy for this mode is −58.24 kJ/mol. In Figure 5(e), when H2S was adsorbed at the top of O adsorption site 2, there was no bonding between the O and S atoms. The adsorption energy for this adsorption mode is −17.83 kJ/mol. The energy gap of Fe3O4 clusters did not change before and after H2S adsorption, indicating that H2S adsorption had little effect on the structural activity. In Figure 5(f), when H2S was adsorbed at Fe–O bridge site 2, the S atom was adsorbed on the Fe atom and the bond length of the formed S–Fe is 2.50 Å. Additionally, the S–H bond is slightly extended from its gas phase value of 1.356 to 1.357 Å. According to the Mulliken charge population analysis, H2S lost a total of 0.18e electrons. The adsorption energy for this adsorption mode is −48.51 kJ/mol. Before and after H2S adsorption, the energy gap of the Fe3O4 clusters changes from 0.01 to 0.02 eV, indicating a decrease in structural activity after adsorption.

Figure 5.

Figure 5

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Adsorption structure of H2S on different active sites of Fe3O4 clusters and the charge density diagram of each adsorption structure. ((a) Fe site 1, (b) Fe site 2, (c) bridge site 1, (d) O site 1, (e) O site 2, (f) bridge site 2) (bond length unit: Å, 1 Å = 1 × 10–10 m).

The above-mentioned analysis indicates that when H2S is adsorbed in the molecular state, S tends to adsorb around the Fe atoms of Fe2O3 clusters and Fe3O4 clusters rather than around the O atoms. The elongation of the S–H bond from its gas phase value of 1.356 to 1.360 Å is the main reason for the decomposition of H2S. This is consistent with the result proven by Song et al.26 through density functional theory calculations that the H2S molecule undergoes two dehydrogenation processes on the α-Fe2O3(001) surface. After adsorption of H2S, the most stable adsorption result is obtained when adsorbing around the Fe atoms. The activity of the Fe2O3 structure increases, while the activity of the Fe3O4 structure remains unchanged or decreases. When H2S is adsorbed on Fe2O3, the most stable adsorption result is obtained at the top of the Fe atom, releasing 69.10 kJ/mol energy. When H2S is adsorbed on Fe3O4, the most stable adsorption result is obtained at the top of Fe adsorption site 1, releasing 90.77 kJ/mol energy and providing an energy foundation for the subsequent reaction process.

3.2. Reaction Path of H2S on Iron Oxide Clusters

In order to understand the formation mechanism of corrosion products, based on the most stable adsorption structure of H2S on Fe2O3 clusters and Fe3O4 clusters, the reaction pathways of Fe2O3 clusters and Fe3O4 clusters with H2S were studied and calculated. The reaction potential energy distribution diagram of the reaction process between H2S and Fe2O3 clusters is shown in Figures 6, 7, and 8. The reaction potential energy distribution diagram of the reaction process between H2S and Fe3O4 clusters is shown in Figures 10to 12. The initial adsorption structure is denoted by R; TS represents the transition state, and IM represents the intermediate. The initial reactant energy is used as the zero point to compute the energy difference of each intermediate, transition state, and product with regard to the reactants. Based on different intermediate states, the reactions between H2S and Fe2O3 clusters as well as H2S and Fe3O4 clusters are each divided into two paths for further discussion. At the same time, the rate-determining steps of different reaction pathways are calculated and the thermodynamic and kinetic parameters of each pathway are analyzed. Each reaction pathway is comprehensively analyzed to determine the optimal reaction pathway. The rate-determining step of a reaction is the slowest elementary reaction and is generally the step with the highest activation energy barrier.

Figure 6.

Figure 6

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First-stage reaction path of the interaction between Fe2O3 clusters and H2S.

Figure 7.

Figure 7

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Second-stage reaction path of the interaction between Fe2O3 clusters and H2S.

Figure 8.

Figure 8

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Third-stage reaction path of the interaction between Fe2O3 clusters and H2S.

Figure 10.

Figure 10

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First-stage reaction path of the interaction between Fe3O4 clusters and H2S.

Figure 12.

Figure 12

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Third-stage reaction path of the interaction between Fe3O4 clusters and H2S.

3.2.1. Reaction Path of Fe2O3 Clusters with H2S

3.2.1.1. Path 1

H2S initially adsorbs onto the Fe atom of the Fe2O3 cluster, and the stable adsorption structure of H2S on Fe2O3 clusters is represented as the reactant R. This step releases 90.77 kJ/mol heat, as shown in Figure 6. The reactant R forms stable intermediate IM1 through transition state TS1, where the first dehydrogenation process (H2S → SH + H) happens. The dissociated H atom diffuses to the adjacent O atom, forming an O–H bond. This process requires overcoming an energy barrier of 27.78 kJ/mol and releases 113.43 kJ/mol heat. Subsequently, the second dehydrogenation process (HS → S + H) occurs, breaking the S–H bond and forming an O–H bond. Through transition state TS2, stable intermediate IM2 is formed. This process requires overcoming an energy barrier of 92.37 kJ/mol. Compared to IM1, IM2 requires a larger energy barrier, indicating a weak interaction between H2S molecules and the cluster structure, while HS exhibits a strong interaction with the cluster structure. The intermediate IM2 overcomes the energy barrier of 56.65 kJ/mol through TS3 to form the first stage product P1. In this process, the O in Fe–O attacks the Fe atom in Fe–S to bond with Fe and forms the S atom, and the remaining part is incompletely reacted Fe2O3H2.

When Fe2O3H2 continues to react with H2S, H2S also preferentially adsorbs onto the Fe atoms. The Fe2O3H2 cluster adsorbs H2S to release an energy of 125.67 kJ/mol to form intermediate IM4 and then overcomes the energy barrier of 28.72 kJ/mol through transition state TS6 to form intermediate IM5. The dissociated H atom diffuses to an O atom that has not yet formed a bond with H, forming an O–H bond. Intermediate IM5 overcomes an energy barrier of 11.05 kJ/mol through transition state TS7 to form intermediate IM6. During this process, the Fe–O bond breaks, releasing 56.06 kJ/mol energy. Then, the S–H bond breaks and the dissociated H atom combines with OH to form H2O. Intermediate IM6 overcomes an energy barrier of 29.89 kJ/mol through transition state TS8 to form second-stage product P3. In this step, the process is endothermic. The remaining part consisted of incompletely reacted Fe2O2SH2.

When Fe2O2SH2 continues to react with H2S, the stable adsorption structure of H2S adsorbed on the Fe2O2SH2 cluster is intermediate IM9, and the heat released in this step is 129.44 kJ/mol. Intermediate IM9 overcomes an energy barrier of 76.81 kJ/mol, forming intermediate IM10 through transition state TS11 and releasing 41.41 kJ/mol energy. During this process, the Fe–O bond breaks and S in Fe–S forms a bond with another Fe atom, resulting in the formation of two Fe–S bonds. The dissociated H atom diffuses to the adjacent O atom and combines with OH to form H2O, while Fe2S2OH2 remains incompletely reacted. Intermediate IM11 overcomes an energy barrier of 18.22 kJ/mol through transition state TS12, forming intermediate IM12. During this process, the Fe–O bond breaks and S in S–H forms a bond with Fe, releasing 12.45 kJ/mol energy. Intermediate IM12 overcomes an energy barrier of 63.35 kJ/mol, forming the final products Fe2S2 and H2O through transition state TS13. During this process, the S–H bond breaks and the dissociated H atom diffuses to O, combining to form H2O. The remaining complete reaction reacted Fe2S2, releasing 23.16 kJ/mol energy.

3.2.1.2. Path 2

In reaction path 2, intermediate IM1 undergoes the second dehydrogenation process (HS → S + H) through transition state TS4, overcoming an energy barrier of 197.8 kJ/mol to form intermediate IM3. This step is an endothermic process. The dissociated H atom diffuses to the adjacent O atom, forming H2O. Compared with reaction path 1, IM1 is more likely to form intermediate IM2 through TS2. However, when the reaction heat is sufficient to overcome the energy barrier at TS4, the H atom easily migrates to form intermediate IM3. Intermediate IM3 overcomes an energy barrier of 4.75 kJ/mol through transition state TS5 to form product P2. This step is an exothermic process. In this process, the O in Fe–O attacks the Fe atom in Fe–S to bond with O and forms the S atom, and the remaining part is incompletely reacted Fe2O2.

When Fe2O2 continues to react with H2S, H2S also preferentially adsorbs onto the Fe atoms. The Fe2O2 cluster adsorbs H2S, releasing 126.71 kJ/mol energy to form intermediate IM7. Then, through transition state TS9, intermediate IM8 is formed. The dissociated H atom diffuses to the adjacent O atom, forming an O–H bond. This process requires overcoming an energy barrier of 37.67 kJ/mol and releases 79.72 kJ/mol energy. Subsequently, the S–H bond breaks and the dissociated H atom diffuses to another adjacent O atom, forming an O–H bond. Intermediate IM8 overcomes an energy barrier of 85.85 kJ/mol to form P4 and releases 30.81 kJ/mol energy. P4 represents incompletely reacted Fe2O2SH2, so its subsequent reaction process is the same as the third stage in path 1.

When seen as a whole, the stage reaction is effectively a continuous reaction process. Through analysis, it can be seen that each stage of the reaction between Fe2O3 clusters and H2S is exothermic, which is conducive to the reaction. The reaction heat of each stage is shown in Table 1. In reaction path 1, the adsorption of H2S on the Fe2O3 clusters generates 90.77 kJ/mol heat, providing the foundation for subsequent reactions. The maximum energy barrier encountered in the first stage is 92.37 kJ/mol, releasing 212.24 kJ/mol heat. In the second stage, the maximum energy barrier encountered is 29.89 kJ/mol and the heat released is 250.60 kJ/mol. In reaction path 2, the maximum energy barrier encountered in the first stage is 197.8 kJ/mol and the heat released is 223.58 kJ/mol. The heat released from the adsorption and the heat released when reactant R forms intermediate IM1 through transition state TS1 are 204.20 kJ/mol, sufficient to sustain the normal progression of all paths. In the second stage, the maximum energy barrier to overcome is 85.85 kJ/mol, releasing a total of 237.24 kJ/mol heat. The reaction path of the third reaction stage of path 1 and path 2 is consistent. In the third stage, the reaction releases 159.39 kJ/mol heat and forms Fe2S2 and H2O. Overall, both reaction paths in the entire reaction process are exothermic. The reaction products for pathways 1 and 2 are Fe2S2, S, and H2O, with S being an intermediate formed during the reaction process.

Table 1. Reaction Heats at Different Stages of the Reaction between the Fe2O3 Clusters and H2S.
process reaction path heat of reaction/kJ·mol–1
stage 1 path 1 Fe2O3 + H2S → P1 –212.24
path 2 Fe2O3 + H2S → P2 –223.58
stage 2 path 1 Fe2O3 + H2S → P3 –250.60
path 2 Fe2O2 + H2S → P4 –237.24
stage 3   Fe2O2SH2 + H2S → P5 –159.39
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Based on the above-mentioned analysis, the rate-determining step for path 1 is from IM1 to IM2, while for path 2, it is from IM1 to IM3. Path 1 and path 2 are competitive in terms of kinetics. The thermodynamic parameters for the rate-determining step of the reaction between H2S and the Fe2O3 cluster are shown in Table 2. In the temperature range of 298.15–1000 K, the Gibbs free energy change ΔG of the rate-determining step of path 1 is less than 0, indicating that path 1 can spontaneously proceed. The Gibbs free energy change ΔG of the rate-determining step of path 2 is greater than 0 at 298.15 K and the ΔG is less than 0 as the temperature increases. This indicates that path 2 cannot react spontaneously at 298.15 K, and as the temperature increases, it is beneficial to the reaction. At the same temperature conditions, the equilibrium constants for the rate-determining steps in path 1 are all greater than the equilibrium constants for the rate-determining steps in path 2. This indicates that the reaction in path 1 has a higher degree of progress. In conclusion, path 1 is thermodynamically more favorable. The calculated results of the reaction rate constants for the rate-determining steps of the reaction between H2S and Fe2O3 clusters are shown in Figure 9. The calculation of the reaction rate constant shows that the reaction rate constant for the rate-determining step in path 1 increases with temperature and reaches its maximum value of 9.0 × 107 s–1 at 1000 K. This rate constant is the highest among all paths involving H2S and Fe2O3 clusters. In contrast, the rate constant for the rate-determining step in path 2 shows no significant variation with temperature. Therefore, path 1 exhibits a kinetic advantage, and combined with thermodynamic analysis, it is considered to be the optimal channel for the reaction of H2S with Fe2O3 clusters.

Table 2. Thermodynamic Parameters of the Rate-Determining Steps of the Two Reaction Paths between H2S and Fe2O3 at Different Temperatures.
  path 1
 path 2
temperatures/K ΔG/(kJ·mol–1) ln(K) ΔG/(kJ·mol–1) ln(K)
298.15 –46.35 18.70 14.38 –5.80
400 –44.94 13.51 –1.82 0.55
500 –44.33 10.66 –6.14 1.48
600 –43.70 8.76 –10.37 2.08
700 –43.03 7.39 –14.52 2.49
800 –42.33 6.36 –18.61 2.80
900 –41.61 5.56 –22.64 3.03
1000 –40.85 4.91 –26.63 3.20
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Figure 9.

Figure 9

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Variation trend of the reaction rate constant k for the rate-determining steps of the reaction between H2S and the Fe2O3 cluster with changing temperature.

3.2.2. Reaction Path of Fe3O4 Clusters with H2S

3.2.2.1. Path 1

When H2S comes into contact with Fe3O4, H2S preferentially adsorbs onto the Fe atom of the Fe3O4 cluster. The stable adsorption structure of H2S on the Fe3O4 cluster is reactant IM13, with a heat release of 69.10 kJ/mol, as shown in Figure 10. The reactant IM13 undergoes transition state TS14 to form stable intermediate IM14, undergoing the first dehydrogenation process. The dissociated H atom diffuses to the adjacent O atom, forming an O–H bond. This process requires overcoming an energy barrier of 58.36 kJ/mol and releases 88.10 kJ/mol heat. Subsequently, the second dehydrogenation process was carried out, the S–H bond was broken, and the second O–H bond was formed. IM14 passed through transition state TS15 to overcome the energy barrier of 37.35 kJ/mol to form the intermediate IM15. Compared with IM14, the energy barrier to be overcome is smaller, indicating that the interaction between HS and the cluster structure is weakened after the first dehydrogenation process of the H2S molecule. At this time, the second H2S molecule continued to adsorb on the Fe site to form IM16. The intermediate IM16 undergoes two dehydrogenation processes through transition state TS16 and TS17 to form the product P6. The dissociated H atom diffuses to the O atom that is not bonded with H to form an O–H bond. The energy barriers to be overcome are 52.51 and 89.02 kJ/mol. In this stage, a total of 368.71 kJ/mol energy is released. At this time, the second H2S molecule continues to adsorb onto Fe, forming IM16. Intermediate IM16 undergoes transition states TS16 and TS17, experiencing two dehydrogenation processes to form intermediate product P6. The dissociated H atom diffuses to the unbound O atom, forming an O–H bond, with energy barriers of 52.51 and 89.02 kJ/mol that need to be overcome. During this stage, a total of 368.71 kJ/mol energy is released.

When P6 continues to react with H2S, the Fe3O4S2H4 cluster adsorbs H2S and releases 70.19 kJ/mol energy to form intermediate IM21. Subsequently, it undergoes transition state TS21 to form intermediate IM22. The dissociated H atom diffuses to the adjacent O atom to form H2O, requiring the achievement of an energy barrier of 50.78 kJ/mol and release of 18.09 kJ/mol energy during this process. Intermediate IM23 overcomes an energy barrier of 115.03 kJ/mol through transition state TS22 to form intermediate IM24. This is an endothermic process where the Fe–O bond and S–H bond break and the dissociated H atom combines with O–H to form H2O. Intermediate IM25 forms stage product P8 through transition states TS23 and TS24. During this process, the Fe–S bond breaks, forming S2, with energy barriers of 2.10 and 107.04 kJ/mol that need to be overcome. The formation of S2 from IM26 through transition state TS24 requires an absorption of 107.02 kJ/mol heat (Figure 11).

Figure 11.

Figure 11

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Second-stage reaction path of the interaction between Fe3O4 clusters and H2S.

When the second-stage reaction product Fe3O2SH2 continues to react with H2S, the stable adsorption structure of H2S adsorbed on the Fe3O2SH2 cluster is intermediate IM32, and the heat released in this step is 58.33 kJ/mol. Intermediate IM32 overcomes an energy barrier of 28.88 kJ/mol through transition state TS30 to form intermediate IM33. This step is an exothermic process, releasing 44.58 kJ/mol energy. During this process, the Fe–O bond breaks and the S in Fe–S bonds with another Fe atom. The dissociated H atom diffuses to the adjacent O atom and combines to form H2O. Intermediate IM34 overcomes an energy barrier of 46.55 kJ/mol through transition state TS31 to form the final product P10. During this process, the Fe–O and S–H bonds break and the dissociated H atom diffuses to O and combines to form H2O. The remaining fully reacted product is Fe3S2. This step is an endothermic process, requiring the absorption of 49.40 kJ/mol energy (Figure 12).

3.2.2.2. Path 2

In reaction path 2, intermediate IM13 forms intermediate IM19 through transition states TS18 and TS19. During this process, H2S undergoes two dehydrogenation processes and the dissociated H atom diffuses to adjacent O atoms, forming O–H bonds with energy barriers of 18.72 and 25.50 kJ/mol. Compared with reaction path 1, IM13 easily forms intermediate IM18 through TS18 at this stage. At this time, the second H2S molecule continues to adsorb at the Fe site to form IM20 and intermediate IM20 overcomes the energy barrier of 52.90 kJ/mol through TS20 to form product P7. In this process, the H atom dissociated from H2S combines with OH to form H2O and the remaining part is incompletely reacted Fe3O3S2H2. A total of 314.15 kJ/mol energy is released in this stage.

As Fe3O3S2H2 continues to react, the H atom dissociated from HS diffuses to the adjacent O atom, forming an O–H bond, requiring an energy barrier of 46.06 kJ/mol to overcome. In IM27, the Fe–S bonds gradually break, with the S atom moving to another Fe–S bond, forming S2. The remaining part is Fe3O3H2 that is not completely reacted. This process involves two transition states, TS26 and TS27, with energy barriers of 6.57 and 92.54 kJ/mol, respectively, and the breaking of Fe–S bonds is an endothermic process. When Fe3O3H2 continues to react with a new H2S molecule, it adsorbs and forms intermediate IM30. The H atom dissociated from H2S attacks the adjacent O atom, forming an O–H bond. Subsequently, another H atom dissociates and attacks the O atom bonded in the O–H bond, leading to the formation of intermediate products H2O and Fe3O2SH2 through transition state TS29. This process involves two transition states, TS28 and TS29, with energy barriers of 41.50 and 18.78 kJ/mol, respectively (Figure 11).

When Fe3O2SH2 continues to react with H2S, the stable adsorption structure of H2S on the Fe3O2SH2 clusters is intermediate IM35. The heat released during this step is 56.42 kJ/mol. The difference from path 1 is that H2S adsorbs on a different Fe site in this case. Subsequently, in intermediate IM35, the Fe–O bond breaks and the H atom dissociated from H2S migrates to the O atom, forming H2O and overcoming an energy barrier of 29.99 kJ/mol, while releasing 47.77 kJ/mol heat. IM37 overcomes the energy barrier of 54.62 kJ/mol through transition state TS33 to form the final product P11. In this process, the Fe–O bond and S–H bond break and the dissociated H atom diffuses to the O atom to form H2O, leaving Fe3S2 with a complete reaction. This step is an endothermic process and needs to absorb 49.74 kJ/mol energy (Figure 12).

Through calculations, it is evident that the first stage of the reaction between the Fe3O4 cluster and H2S is exothermic, while the second stage is an endothermic reaction. The reaction heats for each stage are shown in Table 3. After the adsorption of H2S by Fe3O4 clusters, a heat of 69.10 kJ/mol was generated, which laid the foundation for the subsequent reaction. In the reaction path 1, the maximum energy barrier encountered in the first stage reaction was 89.02 kJ/mol and the released heat was 368.71 kJ/mol. In the second stage, the maximum energy barrier encountered is 115.03 kJ/mol, and during this stage, the formation of H2O and S2 occurs. In the third stage, the maximum energy barrier for the reaction is 46.55 kJ/mol, ultimately resulting in the formation of product Fe3S2. In reaction path 2, the first stage involves the formation of H2O, encountering a maximum energy barrier of 52.90 kJ/mol and releasing 314.15 kJ/mol heat. In the second stage of the reaction, the maximum energy barrier to be overcome is 92.54 kJ/mol and a total of 55.10 kJ/mol of heat is absorbed. In this stage, S2 is formed. In the third stage of the reaction, the maximum energy barrier encountered is 54.62 kJ/mol, ultimately forming product Fe3S2. Both paths 1 and 2 lead to the formation of products Fe3S2, S2, and H2O.

Table 3. Reaction Heats at Different Stages of the Reaction between Fe3O4 Clusters and H2S.
process reaction path heat of reaction/kJ·mol–1
stage 1 path 1 Fe3O4 + H2S → P6 –368.71
path 2 Fe3O4 + H2S → P7 –314.15
stage 2 path 1 Fe2O4S2H4 + H2S → P8 46.23
path 2 Fe3O3S2H2 + H2S → P9 55.10
stage 3 path 1 Fe3O2SH2 + H2S → P10 –1.12
path 2 Fe3O2SH2 + H2S → P11 –1.35
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Based on the analysis mentioned above, the rate-determining step for path 1 is from IM23 to IM24, while for path 2, it is from IM28 to IM29. Moreover, the rate-determining step in path 2 has a higher rate than that in path 1. The thermodynamic parameters for the rate-determining steps of the reaction between H2S and Fe3O4 clusters are shown in Table 4. Within the range of 298.15–1000 K, both the ΔG values for the rate-determining steps in path 1 and path 2 are greater than 0. This indicates that both reactions in path 1 and path 2 are nonspontaneous within this temperature range. The equilibrium constants for the rate-determining steps in paths 1 and 2 increase gradually with the temperature rise, indicating that an increase in temperature favors the progress of the reactions. When the temperature is greater than 900 K, under the same temperature conditions, the reaction equilibrium constant of path 1 is lesser than that of path 2, indicating that the reaction of path 2 proceeds more rapidly as the temperature increases. The calculation results of the reaction rate constants for the rate-determining steps of the reaction between H2S and Fe3O4 clusters are shown in Figure 13. The rate constant calculations indicate that with increasing temperature, the reaction rate constant for the rate-determining step in path 1 shows no significant variation. However, for the rate-determining step in pathway 2, the reaction rate constant increases with temperature and reaches its highest value of 1.1 × 109 s–1 at 1000 K. This value is the largest rate constant of all paths of H2S and Fe3O4 clusters. Therefore, path 2 has more advantages in kinetics, and combined with thermodynamic analysis, it is considered that path 2 is the best channel for the reaction of H2S and Fe3O4 clusters.

Table 4. Thermodynamic Parameters of the Rate-Determining Steps of the Two Reaction Paths between H2S and Fe3O4 at Different Temperatures.
  path 1
 path 2
temperatures/K ΔG/(kJ·mol–1) ln(K) ΔG/(kJ·mol–1) ln(K)
298.15 65.30 –26.34 91.62 –36.96
400 66.85 –20.10 82.27 –24.74
500 67.52 –16.42 79.80 –19.20
600 68.28 –13.69 77.33 –15.50
700 69.11 –11.87 74.88 –12.87
800 70.00 –10.52 72.44 –10.89
900 70.94 –9.48 69.99 –9.35
1000 71.92 –8.65 67.55 –8.12
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Figure 13.

Figure 13

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Variation trend of the reaction rate constant k for the rate-determining steps of the reaction between H2S and Fe2O3 clusters with changing temperature.

3.3. Reaction Paths of Fe2S2, Fe3S2, and S2

Based on the calculations of the interactions between the Fe2O3 cluster and H2S as well as between the Fe3O4 cluster and H2S, in order to further study the effect of elemental sulfur in H2S corrosion products on the spontaneous combustion of sulfur–iron compounds, the reaction paths of Fe2S2 and Fe3S2 with S2 were calculated.

3.3.1. Reaction Path of Fe2S2 and S2

The reaction potential energy distribution during the interaction between Fe2S2 and S2 is shown in Figure 14. S2 first adsorbs at both ends of the Fe atoms, and the stable adsorption structure of S2 on the Fe2S2 cluster is intermediate IM23. The adsorption process releases 135.46 kJ/mol heat. Afterward, the S–S bond breaks, and the intermediate IM23 overcomes an energy barrier of 3.34 kJ/mol to form intermediate IM24, releasing 15.82 kJ/mol heat. The intermediate IM24 overcomes an energy barrier of 7.54 kJ/mol and forms intermediate IM25 through transition state TS23. During this process, the S atom moves to another Fe atom, forming a Fe–S–Fe bond. Intermediate IM25 overcomes an energy barrier of 11.23 kJ/mol to form product Fe2S4, releasing 24.57 kJ/mol heat.

Figure 14.

Figure 14

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Reaction path of the Fe2S2 and S2 interaction.

The analysis shows that the reaction of Fe2S2 with S2 to form Fe2S4 is an exothermic reaction, releasing a total of 199.92 kJ/mol heat. The maximum energy barrier overcome by the reaction is 11.23 kJ/mol, and the adsorption of S2 by the Fe2S2 cluster releases 135.46 kJ/mol heat, which is sufficient to sustain the reaction. At 298.15 K, the free energy change ΔG of the rate-determining step of the Fe2S2 and S2 paths is less than 0, indicating that the reaction can proceed spontaneously. Therefore, the reaction could proceed under normal conditions. After the Fe2O3 clusters react with H2S to produce Fe2S2 and elemental sulfur, the two easily react to produce Fe2S4.

3.3.2. Reaction Path of Fe3S2 and S2

The reaction potential energy distribution during the interaction between Fe3S2 and S2 is shown in Figure 15. The stable adsorption structure of S2 molecules on the Fe3S2 clusters is intermediate IM41, and the adsorption process releases 272.02 kJ/mol heat. During this process, the S–S bond breaks and Fe–S–Fe bonds are formed. Subsequently, another S atom moves toward the center of the structure, forming intermediate IM42, which is Fe3S4. At this point, Fe3S4 continues to react with a new S2 molecule, adsorbing and forming intermediate IM43. During this process, the S–S bond breaks, and one of the S atoms moves toward the adjacent Fe atom, resulting in the formation of product Fe3S6. The energy barrier overcome by intermediate IM43 is 29.25 kJ/mol. The calculation results indicate that in the reaction pathway of Fe3S2 with S2, intermediate product Fe3S4 is initially formed. Subsequently, Fe3S4 continues to react with S2 to form product Fe3S6. Therefore, both Fe3S4 and Fe3S6 may coexist in the products.

Figure 15.

Figure 15

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Reaction path of the Fe3S2 and S2 interaction.

Through the above-mentioned analysis, after the reaction of Fe2O3 clusters and Fe3O4 clusters with H2S to form products, the associated elemental S in the product easily reacts with sulfur–iron compounds to form sulfur–iron compounds with different iron–sulfur ratios. Shang et al.32 demonstrated through experiments that both Fe2O3 and Fe3O4 can generate the same type of iron–sulfur compounds after sulfiding, but the microstructure and elemental distribution of these iron–sulfur compounds are different. This result is consistent with our simulated reaction pathway results.

4. Conclusions

The corrosion products of petroleum and petrochemical equipment can spontaneously ignite when in contact with air at room temperature. In order to explore the formation mechanism of hydrogen sulfide corrosion products in petroleum and petrochemical facilities, we used density functional theory (DFT) to study the interaction mechanism between iron oxides and H2S. On this basis, the reaction paths of Fe2S2 and Fe3S2 with S2 were further studied. The following conclusions were reached:

  • (1)

    After adsorption of H2S, stable adsorption is formed on the top of the Fe atoms in the Fe2O3 clusters or Fe3O4 clusters. H2S is the electron-losing party, and the breaking of the S–H bond is the main cause of H2S corrosion.25

  • (2)

    The reaction path calculation of Fe2O3 clusters and Fe3O4 clusters with H2S indicates that the reaction of Fe2O3 clusters and Fe3O4 clusters with H2S will form S, H2O, and iron sulfide compounds, releasing a large amount of heat. The reaction heat of the reaction path 1 between Fe2O3 clusters and H2S is −622.23 kJ/mol, and the reaction heat of reaction path 2 is −620.21 kJ/mol. The reaction heat of reaction path 1 of the Fe3O4 cluster with H2S is −323.6 kJ/mol, and the reaction heat of path 2 is −260.40 kJ/mol.

  • (3)

    The thermodynamic parameters and kinetic parameters of the rate-determining step of the path show that the free energy change ΔG of the rate-determining step of reaction path 1 of H2S and Fe2O3 clusters is less than 0, indicating that the reaction can proceed spontaneously, and reaction path 1 is the best reaction channel. The free energy change ΔG of the rate-determining step of the reaction between H2S and Fe3O4 clusters is greater than 0, indicating that the reaction cannot proceed spontaneously.

  • (4)

    The calculated reaction pathways of Fe2S2 and Fe3S2 with S2 indicate that both Fe2S2 and Fe3S2 readily react with S2 to form iron–sulfur compounds with different iron-to-sulfur ratios. This is consistent with the experimental results of Dou et al.33 that FeS transforms into Fe3S4 and FeS2 with increasing temperature. It lays a theoretical foundation for the subsequent study of the effect of associated elemental sulfur on the spontaneous combustion of sulfur–iron compounds.

Acknowledgments

This work was supported by the Beijing Natural Science Foundation (No. 2214071).

The authors declare no competing financial interest.

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