A novel methodology for forecasting gas supply reliability of natural gas pipeline systems

Abstract

In this paper, a novel systematic and integrated methodology to assess gas supply reliability is proposed based on the Monte Carlo method, statistical analysis, mathematical-probabilistic analysis, and hydraulic simulation. The method proposed has two stages. In the first stage, typical scenarios are determined. In the second stage, hydraulic simulation is conducted to calculate the flow rate in each typical scenario. The result of the gas pipeline system calculated is the average gas supply reliability in each typical scenario. To verify the feasibility, the method proposed is applied for a real natural gas pipelines network system. The comparison of the results calculated and the actual gas supply reliability based on the filed data in the evaluation period suggests the assessment results of the method proposed agree well with the filed data. Besides, the effect of different components on gas supply reliability is investigated, and the most critical component is identified. For example, the 48th unit is the most critical component for the SH terminal station, while the 119th typical scenario results in the most severe consequence which causes the loss of 175.61×10⁴ m³ gas when the 119th scenario happens. This paper provides a set of scientific and reasonable gas supply reliability indexes which can evaluate the gas supply reliability from two dimensions of quantity and time.

Keywords

natural gas pipeline system / gas supply reliability / evaluation index / Monte Carlo method / hydraulic simulation

1 1 Introduction

Global climate change represents one of the most severe environmental challenges the world is currently facing, with greenhouse gas emissions being the primary driver behind this phenomenon [1]. Carbon dioxide (CO₂) and methane (CH₄) are the two predominant greenhouse gases, accounting for a significant portion of total emissions. The rapid development of the global economy has led to a continuous increase in the emission of greenhouse gases, exerting substantial pressure on the environment and climate, thereby necessitating the urgent identification of effective emission reduction strategies. In response to the escalating environmental crisis, the international community has reached a consensus, with numerous countries signing the Paris Agreement, committing to various measures aimed at reducing greenhouse gas emissions in order to curb the trend of global warming [2,3]. In China, there has also been an active response to the challenges posed by global climate change, with goals set for “carbon peak” and “carbon neutrality” [4]. Efforts are being made to reduce CO₂ emissions through various measures, including enhancing energy efficiency, developing clean energy, and promoting low-carbon technologies [5–8]. Dry reforming of methane technology, as an effective method for converting CO₂ and CH₄ into useful chemicals (syngas), plays a significant role in reducing greenhouse gas emissions and achieving the circular utilization of carbon resources [9–13].

Precious metal catalysts exhibit commendable activity in the methane CO₂ reforming process [14–16]. However, considering the cost and production limitations, the use of precious metal catalysts is not feasible for large-scale industrial processes. Nickel, not only demonstrates catalytic activity comparable to that of precious metals but also has a significantly higher natural abundance and lower cost, increasingly attracting researchers’ attention [17]. Supported catalysts show superior catalytic performance compared to standalone active metal catalysts [18,19]. The support is another crucial component of supported catalysts. On the one hand, the support provides a large specific surface area for the dispersion of active metals, thus exposing more active sites and inhibiting metal agglomeration. On the other hand, the support can interact with the active metal, potentially altering the structure of catalyst and thereby affecting its catalytic performance [20,21]. Given that CO₂ is an acidic gas, catalysts supported on basic supports generally exhibit superior catalytic activity. Among common supports, MgO possesses a strong Lewis basicity, enhancing the chemical adsorption of CO₂. Therefore, researchers often choose MgO as the support for catalysts in their studies [22,23].

Coke is a primary cause of deactivation in Ni-based catalysts [24,25]. Researchers have identified that the sources of carbon deposition on catalysts stem from the deep cracking of methane and the disproportionation of CO [9,26,27]. However, the disproportionation reaction of CO is suppressed within the temperature range of the reaction, and thus most carbon deposition derives from the deep cracking of methane. The particle size of the active metal in Ni-based catalysts significantly influences the activity and stability of the catalyst. Extensive experimental studies have demonstrated that excellent activity and resistance to carbon deposition is exhibited by the catalysts with small active metal particles [28,29]. In their experiments, Lercher et al. [30] observed optimal performance of the catalyst against carbon deposition when the size of the active metal particles reached 2 nm on Ni/ZrO₂ catalysts. Zhang et al. [31] observed that achieving the best performance in Ni–Co/MgO catalysts required a Ni–Co size below 10 nm, thereby establishing 10 nm as the critical size in this system. Observations show that the catalyst consistently displays a superior resistance to coking when the active metal reaches a critical size. The critical size varies among different systems and reaction conditions but typically ranges from a few nanometers to around a dozen nanometers [32]. However, the size effect is widely observed in experiments, and its reaction mechanism remains unclear. Guo et al. [33] constructed catalyst models with Ni4, Ni8, and Ni12 active metal clusters supported on the MgO(100) surface and calculated the DRM reaction process on Ni particles of different sizes. The results indicated that on supported Ni catalysts, a smaller Ni particle is more efficient for the DRM reforming reaction. Researchers believe that the smaller the metal particle size, the higher the proportion of highly active Ni exposed on the catalyst, thereby enhancing the activity and stability of the catalyst. Although Guo et al. [33] conducted DRM-related studies on metal particles of different sizes, the models they constructed are focused on cluster particles, with no significant variation in size. Chen et al. [34] recently reported on the mechanism of CH₄ activation and C atom growth on the Nix/MgO surface, finding that particle size has a notable impact on CH₄ activation.

The activation of CO₂ and the generation of CO were not considered in previous work. Therefore, in this work, the DFT theory are utilized to thoroughly investigate the relationship between the variation in metal particle size and both CO₂ activation and CO generation. By comparing the adsorption energies of various species and the energy barriers along the reaction pathways, the impact of changes in Ni particle size on the CO₂ activation pathways and the CO generation reaction have been explored. This work could provide theoretical guidance for the preparation of catalysts for highly efficient Ni reforming reaction with an optimal chemical performance.

2 2 Computational details and models

2.1 2.1 Computational method

All density functional theories are calculated using the Dmol3 module in the Materials Studio software [35,36]. The electron exchange and correlation approach adopts the generalized gradient approximation (GGA) alongside the Perdue-Burke-Enzerhof (PBE) exchange-correlation functionals [37–39]. To achieve an optimal balance between computational accuracy and efficiency, the DFT half-core pseudopotential (DSPP) method is applied. For the convergence of energy, the self-consistent field (SCF), the maximum displacement, and the maximum force, the thresholds are respectively established at 2.0 × 10⁻⁵ Ha, 1 × 10⁻⁵ Ha, 5.0 × 10⁻³ Å, and 4.0 × 10⁻³ Ha/Å. To identify the transition state of reaction, the complete linear/quadratic synchronous transit (LST/QST) method is utilized. Considering the magnetic nature of Ni, calculations incorporate electron spin polarization. The smearing is adjusted to 0.05 Ha and vacuum layer is set to 20 Å.

The adsorption energy (E_ads), energy barrier (E_b), and reaction energy (ΔH) are obtained from

(1)$E_{\mathrm{a}\mathrm{d}\mathrm{s}}=E_{\mathrm{a}\mathrm{d}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{e}/\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}}-E_{\mathrm{a}\mathrm{d}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{e}}-E_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}},$

(2)$E_{\mathrm{b}}=E^{\mathrm{T}\mathrm{S}}-E^{\mathrm{I}\mathrm{S}},\mathrm{\Delta }H=E^{\mathrm{F}\mathrm{S}}-E^{\mathrm{I}\mathrm{S}},$

where E_{adsorbate/surf}, E_adsorbate, E_surf, E^IS, E^TS, and E^FS represent the electronic energy of the adsorption system, adsorbate alone, the clear metal surface, initial state (IS), transition state (TS), and final state (FS), respectively.

2.2 2.2 Structure model

Typically, the active metal particles of supported metal catalysts are adsorbed onto the support in a hemispherical shape [40]. Nix (x = 13, 25, 37) are constructed. A three-layer MgO(100) slab is used as the support [41]. The geometry optimization is calculated by set 3 × 3 × 1 k-point.

Research indicates that the interaction between the active metal and the support significantly alters the configuration of active metal clusters. Therefore, after loading the constructed active metal cluster particles onto the optimized MgO(100) surface, it is necessary to perform a comprehensive optimization of the entire catalyst model. During the optimization process of the catalyst model, the entire model is allowed to relax to ensure its rationality. In the following calculation process, MgO(100) is kept fixed. Fig.1 is the optimized catalyst model.

Fig.1 Models of Nix/MgO (x = 13, 25, 37) (Blue, Ni atoms; Red, O atoms; Green, Mg atoms) (adapted with permission from Chen et al. [34], copyright 2024, Royal Society of Chemistry).

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3 3 Results and discussion

3.1 3.1 Adsorption of CO₂, CO and intermediates

During the DRM process, there are many important intermediates, such as COOH and CHO. COOH serves as a critical intermediate in the hydrogen-assisted dissociation pathway of CO₂, playing a vital role in the study of CO₂ activation pathways. CHO, an intermediate formed by the reaction of CH generated from the cracking of CH₄ with O atoms produced from the dissociation of CO₂, also contributes to the formation of products CO and H through its dissociation. Moreover, the formation of CHO competes with the cracking reaction of CH, potentially hindering the formation of carbon atoms on the catalyst surface, making CHO an extremely important intermediate as well. This section delves into the adsorption behavior of CO₂, CHO, COOH, O, and CO.

Fig.2 illustrates the adsorption configurations of CO₂, intermediates, and products on Nix/MgO. Consistent with previous literature reports [42], CO₂ is found to preferentially adsorb at the interface between the active metal and the support on Nix/MgO. Studies have shown that free CO₂ molecules possess a linear structure with a bond length of 1.16 Å [43]. Upon adsorption on the Nix/MgO surface, CO₂ molecules undergo significant deformation, exhibiting a bent structure with altered C−O bond lengths, which are not identical within the molecule. On Ni13/MgO, the C−O bond lengths on the side closer to and further from the support are 1.33 and 1.26 Å, respectively; on Ni25/MgO, they are 1.32 and 1.28 Å; and on Ni37/MgO, they are 1.31 and 1.26 Å. On all three surfaces, the C−O bond closer to the support is longer than the other. This suggests that the MgO support plays a role in the adsorption of CO₂. For the intermediate COOH, it adsorbs perpendicularly on the top site of the first layer of Ni atoms on Ni13/MgO, while on Ni25/MgO and Ni37/MgO, it adsorbs at the interface between the active molecule and the support. On Ni25/MgO, COOH adsorbs vertically, whereas on Ni37/MgO, its adsorption is offset. For the intermediate CHO, its optimal adsorption site is on the top site of the topmost Ni atoms on Ni13/MgO, in the bridge site between the middle and bottom Ni atoms on Ni25/MgO, and most stably at the interface between the active component and the support on Ni37/MgO. The adsorption configurations of O atoms and CO molecules are relatively similar across the three catalyst surfaces. On Nix/MgO, O atoms adsorb in the hollow sites of Ni atoms in different layers, while CO adsorbs at the interface between the active metal and the support. Research findings indicate that variations in the size of active metal particles have an impact on the optimal adsorption sites of adsorbates on the catalyst surface, with the adsorption of intermediates COOH and CHO being most significantly affected.

Fig.2 Configurations of CO2, CO, and intermediates adsorption on Nix/MgO.

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The adsorption energy and charge transfer of various adsorbates on Nix/MgO are further investigated. Tab.1 records the adsorption energy and charge transfer for CO₂, intermediates, and products adsorbed on Nix/MgO. It demonstrates that adsorbates always gain charge from the catalyst surface for stable adsorption, and on the same catalyst surface, a greater amount of charge transfer correlates with a higher adsorption energy. Fig.3 further illustrates the impact of different sized Ni particles on Nix/MgO on the adsorption energy of adsorbates. It was found that the adsorption energies of CO₂ on Nix/MgO (x = 13, 25, 37) are −1.17, −1.37, and −1.22 eV. After adsorption on the Nix/MgO surface, CO₂ undergoes significant configurational changes, and the calculated adsorption energies are substantial, indicating that CO₂ adsorption on all three Nix/MgO surfaces is chemisorbed. CO₂ exhibits the strongest adsorption capability on Ni25/MgO, followed by Ni13/MgO, and the weakest on Ni37/MgO. For intermediates COOH and CHO, both exhibit the highest adsorption energy on Ni25/MgO, with the lowest on Ni13/MgO. For O atoms and CO molecules, their adsorption energies on the three different catalyst surfaces are similar. Notably, by comparing the adsorption configurations of O atoms and CO molecules on Nix/MgO surfaces, it was found that their adsorption configurations are also similar. This suggests that on Nix/MgO, the same adsorbate adsorbing at similar adsorption sites will have comparable adsorption energies. The different sizes of active metal particles on the catalyst primarily alter the optimal adsorption sites of adsorbates on the surface, thereby affecting the charge transfer and adsorption energy.

Tab.1 Adsorption energy and charge transfer of CO2, CO, and intermediates on Nix/MgO

	Ni13/MgO			Ni25/MgO			Ni37/MgO
	Eabs/eV	Charge/e		Eabs/eV	Charge/e		Eabs/eV	Charge/e
CO2	−1.17	0.16		−1.27	0.18		−1.01	0.14
COOH	−1.44	0.29		−1.89	0.22		−1.54	0.21
CHO	−1.25	0.20		−1.40	0.26		−1.39	0.23
O	−2.50	0.39		−2.50	0.35		−2.49	0.33
CO	−1.59	0.25		−1.60	0.25		−1.54	0.23

Fig.3 Adsorption energy of CO2, CO, and intermediates on Nix/MgO.

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3.2 3.2 Activation pathway of CO₂

Generally speaking, during the DRM process, CO₂ can undergo two possible activation pathways [44–46]: (1) Direct dissociation of CO₂ (CO₂ → CO + O), O subsequently participating in the oxidation of surface C atoms or CH oxidation reactions; (2) H-assisted dissociation of CO₂, where CO₂ reacts with dissociatively generated H atoms from CH₄ to form COOH (CO₂ + H → COOH), which then dissociate to yield OH and the product CO (COOH → CO + OH). The mode of CO₂ dissociation varies across different catalyst systems. This section investigates, in detail, the two activation pathways of CO₂ on Nix/MgO, comparing and analyzing the impact of variations in the size of active particles on the CO₂ activation pathways.

Fig.4 shows the initial, transition, and FSs of CO₂ direct dissociation on the surface of Nix/MgO. The results indicate that the direct dissociation of CO₂ occurs at the interface between the active component of the catalyst and the support. On the Ni13/MgO surface, during the activation process of adsorbed CO₂, the C−O bond farthest from the support breaks, with the distance between the O and C atoms stretching to 2.40 Å in the TS. Ultimately, the O atom is stably adsorbed in the hollow site of Ni atoms on the active metal side, while CO is adsorbed at the interface, with the detached O atom being 3.47 Å away from the C atom. On Ni25/MgO and Ni37/MgO, the process of direct dissociation of CO₂ is similar to that on Ni13/MgO, but the distances between the dissociated O and C atoms in the transition and FSs differ. On Ni25/MgO, the distance between the O and C atoms is 1.92 Å in the TS and 3.14 Å in the FS; on Ni37/MgO, these distances are 1.85 Å and 3.77 Å in transition and FSs. Comparative analysis reveals that the direct dissociation process of CO₂ on Nix/MgO is not significantly different, but the distances of atomic migration in the TS vary, being greatest on Ni13/MgO and similar on Ni25/MgO and Ni37/MgO. This suggests that the energy barrier for the direct dissociation process is highest on Ni13/MgO.

Fig.4 Reaction process of direct dissociation of CO2 on Nix/MgO.

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The energy barriers and reaction heats for the direct dissociation of CO₂ on Nix/MgO are presented in Tab.2. The results indicate that the energy barrier for direct CO₂ dissociation is highest on Ni13/MgO, with very similar values observed for Ni25/MgO and Ni37/MgO. This suggests, the direct dissociation of CO₂ is most difficult to occur from the kinetic aspect on Ni13/MgO, with the lowest catalytic activation for CO₂ dissociation observed. On catalysts with larger active metal particle sizes, the direct dissociation of CO₂ occurs more readily. This process is endothermic on both Ni13/MgO and Ni25/MgO surfaces, requiring more heat absorption on Ni25/MgO, while it is a mildly exothermic reaction on the Ni37/MgO surface.

Tab.2 Eb and ΔH for direct dissociation of CO2 on Nix/MgO surfaces

	Eb/eV	ΔH/eV
Ni13/MgO	1.40	0.08
Ni25/MgO	1.22	0.33
Ni37/MgO	1.24	−0.02

Fig.5 illustrates the initial, transition, and FSs of CO₂ undergoing hydrogenative dissociation on Nix/MgO surfaces. On Ni13/MgO, the specific process of CO₂ hydrogenative dissociation involves CO₂ adsorption at the interface between the active component and the support, with H atoms generated from CH₄ dissociation adsorbing at the bridge sites of the top-layer Ni atoms, forming a stable co-adsorption configuration. Initially, the distance between the H atom and the closest O atom in the CO₂ molecule is 4.27 Å. During activation, the O atom and the CO₂ molecule move upwards and gradually approach each other, with their distance reducing to 2.81 Å in TS1. Subsequently, the H atom bonds with CO₂ to form the intermediate COOH, where the O−H bond length is 1.00 Å. COOH is adsorbed perpendicularly to the support on the top site of the active metal Ni atom, with the C atom facing the metal particle and the O and H atoms facing the opposite side. Following this, COOH undergoes a dissociative activation, breaking the C−O bond. In TS2, the distance between the C atom in CO and the O atom in OH is 2.10 Å. In the FS, the produced CO is adsorbed at the interface between the active component and the support, and the generated OH is adsorbed on the top site of the top-layer Ni atom, forming a stable co-adsorption configuration with a C−O atom distance of 4.26 Å.

Fig.5 Reaction process of hydrogen-assisted dissociation of CO2 on Nix/MgO.

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On Ni25/MgO, the stable co-adsorption configuration of CO₂ with H atoms involves CO₂ adsorbed at the interface, with H atoms adsorbed in the hollow sites of active metal Ni atoms. The distance between the H atom and the O atom in CO₂ closest to H is 2.84 Å. During the reaction, the H atom approaches the O atom in CO₂, with the distance reducing to 1.47 Å in TS1. Afterwards, the H atom bonds with the O atom in CO₂ to form COOH, with an O−H bond length of 1.00 Å. Unlike the adsorption configuration of COOH on Ni13/MgO, COOH is adsorbed at the interface between the active component and the support on Ni25/MgO, with the C atom facing the active metal Ni side, and the O and H atoms facing the opposite side. During the formation of CO from the intermediate COOH, the C−O bond breaks, with the distance between the C and O atoms being 2.80 Å in TS2. In the FS, this distance becomes 3.77 Å, with CO adsorbed at the interface between the bottom Ni atoms and the support, and OH adsorbed on the metal Ni particle.

The process of CO₂ hydrogenative dissociation on Ni37/MgO is similar to that on Ni25/MgO. Initially, the distance between the H atom and the O atom in CO₂ closest to H is 3.40 Å, reducing to 1.89 Å in TS1, and after forming COOH, the O−H bond is 1.01 Å. During COOH dissociation, the C−O bond breaks, with the C and O atom distance being 2.06 Å in TS2, and 3.31 Å in the FS.

Comparative analysis reveals that variations in metal particle size lead to changes in the active sites where reactions occur. On Ni13/MgO, both the formation of COOH from CO₂ and H atoms, and the dissociation of COOH, take place on the active metal particles, whereas on the other two catalyst surfaces (Ni25/MgO, Ni37/MgO), these processes occur at the interface between the active metal and the support.

Tab.3 presents the energy barriers and reaction heats for the hydrogenative dissociation of CO₂ on Nix/MgO surfaces. Among these, the process on the Ni13/MgO surface exhibits the highest energy barrier and reaction heat, significantly exceeding the corresponding values on the other two surfaces, with the lowest energy barrier observed on the Ni25/MgO surface. The study results demonstrate that kinetically and thermodynamically, this reaction is most challenging to occur on the Ni13/MgO surface, while it proceeds most readily on Ni25/MgO. The reaction is endothermic on all three surfaces. Therefore, the intermediate COOH is less likely to form on the Ni13/MgO surface, whereas it is one of the main intermediates on the Ni25/MgO and Ni37/MgO surfaces. The dissociation of the intermediate COOH occurs very easily on all three surfaces, with little difference in the energy barriers. This indicates that the intermediate COOH is unlikely to remain stable on the surface, and the formed COOH readily dissociates into CO molecules and OH. On the Ni13/MgO and Ni37/MgO surfaces, this reaction is exothermic, whereas it is endothermic on the Ni25/MgO surface.

Tab.3 Eb and ΔH for hydrogen-assisted dissociation of CO2 on Nix/MgO

	CO2+H→COOH			COOH→CO+OH
	Eb/eV	ΔH/eV		Eb/eV	ΔH/eV
Ni13/MgO	1.72	0.61		0.73	−0.32
Ni25/MgO	0.93	0.20		0.72	0.07
Ni37/MgO	1.18	0.13		0.75	−0.34

Fig.6 illustrates the energy barrier for different CO₂ activation pathways on Nix/MgO surfaces. The study reveals that on the Ni13/MgO surface, the energy barrier for the reaction of CO₂ with H atoms to form COOH is significantly higher than that for direct dissociation. Although the subsequent dissociation barrier of COOH is lower, the overall pathway of CO₂ hydrogenative dissociation remains more challenging compared to direct dissociation. Thus, direct dissociation emerges as the predominant reaction pathway on Ni13/MgO. On the Ni25/MgO surface, in contrast to the direct dissociation of CO₂, the energy barrier for hydrogenative dissociation is lower, indicating that CO₂ hydrogenative dissociation occurs more readily on Ni25/MgO. Similarly, on Ni37/MgO, the energy barrier for CO₂ hydrogenative dissociation is also slightly lower than that for direct dissociation, making hydrogenative dissociation relatively easier to occur. In summary, the activation pathway of CO₂ on Ni13/MgO is primarily direct dissociation, while on Ni25/MgO and Ni37/MgO, CO₂ tends to undergo hydrogenative dissociation, making it the main activation pathway. The variation in the size of active metal Ni particles on the MgO support significantly influences the activation pathway of CO₂, leading to a change in the predominant mode of activation.

Fig.6 Energy curves of different activation paths of CO2 on Nix/MgO surfaces.

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3.3 3.3 Formation of CO

There are several sources of CO formation in DRM reactions, such as activation dissociation of CO₂, oxidation of surface C atoms, and dissociation of CHO species. Activation dissociation of CO₂ has been discussed in detail in Section 3.2, and this section focuses on exploring the other two reactions.

Fig.7 displays the structures of the IS, TS, and FS for the oxidation of surface carbon atoms. On Ni13/MgO, the carbon atom is adsorbed in the hollow site of the topmost Ni atoms, and the hydrogen atom is adsorbed at the hollow site of the side Ni atoms. In the IS, the distance between the carbon and oxygen atoms is 3.69 Å. During the reaction, the carbon and oxygen atoms move closer to each other, reaching a distance of 2.05 Å in the TS. The reaction proceeds to form a bond between the carbon and oxygen atoms, with a bond length of 1.21 Å in the FS. The CO molecule is adsorbed at the bridge site of the topmost Ni atoms, with the carbon atom closer to the Ni particle surface and the oxygen atom further from the surface. On Ni25/MgO, the most stable co-adsorption configuration has both the carbon and oxygen atoms adsorbed at the hollow sites on the side of the Ni particles, with an interatomic distance of 4.38 Å. During the reaction, the atoms move downwards and closer to each other, with the distance between them becoming 2.01 Å in the TS. In the FS, the formed CO molecule is adsorbed at the interface between the active metal and the support, with the carbon atom closer to the particle surface. The formed C−O bond length is 1.23 Å. On Ni37/MgO, in the IS, the carbon atom is adsorbed at the hollow site on the side of the Ni particles, and the oxygen atom is adsorbed at the bridge site, forming a stable co-adsorption configuration with an interatomic distance of 4.55 Å. During the reaction, the carbon atom moves downwards and the oxygen atom moves closer to the carbon atom, with the distance between the two atoms being 2.00 Å in the TS. In the FS, the formed CO molecule is also adsorbed at the interface between the carrier and the metal particles, with a bond length of 1.23 Å.

Fig.7 Reaction process of oxidation of C on Nix/MgO.

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Tab.4 presents the energy barriers and reaction heats for the oxidation of carbon atoms on Nix/MgO. The results indicate that, kinetically, the reaction is most favorable on Ni25/MgO, followed by Ni13/MgO, and is least favorable on Ni37/MgO. Thermodynamically, the reaction is endothermic on Ni13/MgO, while it is exothermic on Ni25/MgO and Ni37/MgO. Comparative analysis reveals that the oxidation of carbon atoms on Ni25/MgO is the most favorable both kinetically and thermodynamically, making it the most likely to occur.

Tab.4 Eb and ΔH for oxidation of C atoms on Nix/MgO surfaces

	Eb/eV	ΔH/eV
Ni13/MgO	1.52	0.09
Ni25/MgO	1.10	−1.31
Ni37/MgO	1.63	−0.83

CHO specie is important intermediates in DRM reactions, and the origin is generated by the reaction of CH generated from CH₄ dissociation with CO dissociation to generate O atoms. It is worth mentioning that this reaction is in competition with the reaction of CH depth dissociation to generate surface C atoms. Therefore, the study of CHO species in dry reforming is important.

Fig.8 illustrates the initial, transition, and FSs of the formation and dissociation reactions of CHO on Nix/MgO surfaces. On Ni13/MgO, CH and O are co-adsorbed in the hollow sites on the side of the metal particles, forming a stable co-adsorption configuration, with the oxygen atom 3.61 Å away from the carbon atom in CH. During the reaction, CH moves upwards while the oxygen atom moves toward CH, reaching a distance of 2.00 Å in the TS. In the FS, a C−O bond is formed with a bond length of 1.25 Å, and the resulting CHO is adsorbed at the bridge site of the topmost Ni atoms, with the carbon atom closer to the Ni particle surface and the hydrogen and oxygen atoms further from the surface. During the CHO dissociation process, the C−H bond breaks, with the distance between C and H increasing from 1.13 Å in the IS to 1.58 Å in the TS. The hydrogen moves to the top site of the topmost Ni atoms while CH moves downwards, resulting in a distance of 3.16 Å between C and H in the FS. The generated hydrogen atom and CO molecule are finally adsorbed at different bridge sites between the topmost Ni atoms.

Fig.8 Reaction process of CHO formation and dissociation on Nix/MgO.

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On Ni25/MgO, CH and the oxygen atom are adsorbed on the same side of the metal particle surface, with C and O 4.06 Å apart. During the reaction, the oxygen atom gradually approaches CH, reaching a distance of 1.90 Å in the TS. Subsequently, C and O form a bond with a bond length of 1.27 Å, and the resulting CHO is adsorbed at the interface between the active metal particle and the carrier. During the dissociation process of CHO, the C−H bond breaks, and the hydrogen atom moves toward another surface of the metal particle. The distance between the two atoms changes from 1.13 initially to 1.59 Å in the TS. In the FS, the generated CO molecule is adsorbed at the bridge site of Ni atoms on one side of the metal particle, while the hydrogen atom is adsorbed at the hollow site on the other side, ultimately 3.38 Å apart.

On Ni37/MgO, the specific process of CHO formation and dissociation involves CH being adsorbed at the hollow site on the side of Ni particles, with the oxygen atom adsorbed at a hollow site on an adjacent side. In the co-adsorbed configuration, C and O are 3.09 Å apart. During the reaction, CH moves downwards, and the oxygen atom moves toward CH, with the distance between C and O atoms being 1.35 Å in the TS. Subsequently, a C−O bond is formed, and the resulting CHO is adsorbed at the interface between the metal particle and the carrier, with a C−O bond length of 1.35 Å and a C−H bond length of 1.12 Å. During the CHO dissociation reaction, the C−H bond breaks, with the distance between C and H being 1.63 Å in the TS. The hydrogen atom moves upwards, and in the FS, a stable co-adsorption configuration is formed with the CO molecule adsorbed at the interface, the carbon atom closer to the Ni particle surface, the oxygen atom further from the particle surface, and the hydrogen adsorbed at the bridge site between the bottom and top layer Ni atoms, with a distance of 2.84 Å between them.

Tab.5 documents the energy barriers and reaction heats for the formation and dissociation processes of CHO. The research results indicate that on Ni13/MgO, the energy barrier for the formation of CHO is the highest, while on the other two surfaces, this reaction barrier is significantly lower, with the lowest observed on Ni25/MgO. This suggests that kinetically, the reaction is most favorable on Ni25/MgO and most challenging on Ni13/MgO. Furthermore, the reaction is exothermic on three catalyst surfaces, indicating it is thermodynamically feasible. The results demonstrate that CHO becomes one of the main intermediates on the surface of Ni37/MgO due to its easier formation and more challenging dissociation.

Tab.5 Eb and ΔH for CHO formation and dissociation on Nix/MgO surfaces

	CH+O→CHO			CHO→CO+H
	Eb/eV	ΔH/eV		Eb/eV	ΔH/eV
Ni13/MgO	1.37	−0.35		0.57	−0.07
Ni25/MgO	0.61	−0.39		0.59	−0.01
Ni37/MgO	0.78	−0.40		0.88	0.18

Fig.9 depicts the energy variation for the aforementioned processes. The research findings indicate that the optimal reaction pathway for C+O occurs on Ni25/MgO, suggesting that this reaction is more readily facilitated on its surface, and even a minimal generation of C atoms on the Ni particle surface can be quickly oxidized by O atoms. The optimal pathway for the CH + O reaction is also found on Ni25/MgO, demonstrating that the intermediate CHO is more likely to form on its surface. This reaction competes with the CH dissociation studied in previous work [35], with the energy barrier for CHO formation being lower than that for CH dissociation. CH on Ni25/MgO is more inclined to bond with O atoms other than dissociating into C atoms, which to some extent indicates that this catalyst has strong resistance to carbon buildup. Regarding the CHO dissociation reaction, the energy barriers on all three surfaces are below 1.0 eV, making this reaction relatively easy to occur. The dissociation of CHO also serves as a principal source of the product CO.

Fig.9 Energy variation. (a) C oxidation; (b) CHO production and dissociation.

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4 4 Conclusions

In this work, the mechanisms of CO₂ activation and the CO formation on Nix/MgO surfaces are explored. The impact of Ni particle size is examined from the adsorption of intermediates and products, and the formation pathways of reactants. The following is a summary of the key findings:

(1) The adsorption sites for CO₂, CHO and CO on different Nix/MgO surfaces are essentially the same, with similar corresponding adsorption energies. These species are chemisorbed on the Nix/MgO surface. The adsorption of COOH is significantly influenced by changes in the catalyst surface particle size, with its adsorption site transitioning from the metal particles to the interface between the particles and the support as the particle size increases.

(2) The primary activation pathway of CO₂ on the catalyst surface changes with the variation in Ni particle size. On Ni13/MgO, the direct dissociation of CO₂ into CO molecules and O atoms occurs more readily, with direct dissociation being the main pathway of activation. However, as the particle size increases, on Ni25/MgO and Ni37/MgO, the hydrogenation dissociation of CO₂ exhibits lower reaction barriers, leading to a shift in the main activation pathway toward hydrogenation dissociation.

(3) The oxidation reaction of surface C atoms exhibits the lowest reaction barrier (1.10 eV) on Ni25/MgO, with higher energy barriers observed on both Ni13/MgO and Ni37/MgO surfaces, making the oxidation of C atoms more challenging on the surfaces of Ni13/MgO and Ni37/MgO. The oxidation of CH occurs more readily on the Ni25/MgO surface, where CH is more inclined to combine with O atom rather than dissociating into C atom.

References

[1] Qiao W, Lu H, Zhou G, Azimi M, Yang Q, Tian W. A hybrid algorithm for carbon dioxide emissions forecasting based on improved lion swarm optimizer. Journal of Cleaner Production, 2020, 244: 118612

[2] Qiao W, Tian W, Tian Y, Yang Q, Wang Y, Zhang J. The forecasting of PM_2.5 using a hybrid model based on wavelet transform and an improved deep learning algorithm. IEEE Access: Practical Innovations, Open Solutions, 2019, 7: 142814–142825

[3] Flouri M, Karakosta C, Kladouchou C, Psarras J. How does a natural gas supply interruption affect the EU gas security? A Monte Carlo simulation. Renewable & Sustainable Energy Reviews, 2015, 44: 785–796

[4] Lochner S. Modeling the European natural gas market during the 2009 Russian–Ukrainian gas conflict: ex-post simulation and analysis. Journal of Natural Gas Science and Engineering, 2011, 3(1): 341–348

[5] Huang W. Reliability of large-scale natural gas pipeline network. Acta Petrolei Sinica, 2013, 34: 401–404

[6] Yuan Q, Li J, Liu H, Yu B, Sun D, Deng Y. Parametric regression of a multiparameter thixotropic model for waxy crude oil based on multiobjective strategy. Journal of Petroleum Science Engineering, 2019, 173: 287–297

[7] Yu W, Song S, Li Y, Min Y, Huang W, Wen K, Gong J. Gas supply reliability assessment of natural gas transmission pipeline systems. Energy, 2018, 162: 853–870

[8] Yuan Q, Liu H, Li J, Yu B, Wu C. Study on parametric regression of a complex thixotropic model for waxy crude oil. Energy & Fuels, 2018, 32: 5020–5032

[9] Su H, Zhang J, Zio E, Yang N, Li X, Zhang Z. An integrated systemic method for supply reliability assessment of natural gas pipeline networks. Applied Energy, 2018, 209: 489–501

[10] Rimkevicius S, Kaliatka A, Valincius M, Dundulis G, Janulionis R, Grybenas A, Zutautaite I. Development of approach for reliability assessment of pipeline network systems. Applied Energy, 2012, 94: 22–33

[11] Yu W, Zhang J, Wen K, Huang W, Min Y, Li Y, Yang X, Gong J. A novel methodology to update the reliability of the corroding natural gas pipeline by introducing the effects of failure data and corrective maintenance. International Journal of Pressure Vessels and Piping, 2019, 169: 48–56

[12] Kołowrocki K, Kwiatuszewska-Sarnecka B. Reliability and risk analysis of large systems with ageing components. Reliability Engineering & System Safety, 2008, 93(12): 1821–1829

[13] Zio E. Reliability engineering: old problems and new challenges. Reliability Engineering & System Safety, 2009, 94(2): 125–141

[14] Sukharev M, Karasevich A. Reliability models for gas supply systems. Automation and Remote Control, 2010, 71(7): 1415–1424

[15] Faertes D, Saker L, Heil L, Vieira F, Risi F, Domingues J, Alvarenga T, Mussel P, Carvalho E. Reliability modelling: petrobras 2010 integrated gas supply chain. In: 2010 8th International Pipeline Conference, Calgary, Alberta, Canada, 2010: 497–505

[16] Fan M, Gong J, Wu Y, Kong W. The gas supply reliability analysis of natural gas pipeline network based on simplified topological structure. Journal of Renewable and Sustainable Energy, 2017, 9(4): 045503

[17] Heuberger D, Wittenberg P, Moser A. Optimization of natural gas distribution networks considering the reliability of supply. In: PSIG Annual Meeting, Pipeline Simulation Interest Group, 2011

[18] Jensen H, Jerez D. A stochastic framework for reliability and sensitivity analysis of large scale water distribution networks. Reliability Engineering & System Safety, 2018, 176: 80–92

[19] Surendran S, Tanyimboh T, Tabesh M. Peaking demand factor-based reliability analysis of water distribution systems. Advances in Engineering Software, 2005, 36(11–12): 789–796

[20] Ostfeld A, Kogan D, Shamir U. Reliability simulation of water distribution systems – single and multiquality. Urban Water, 2002, 4(1): 53–61

[21] Qiao W, Yang Z, Kang Z, Pan Z. Short-term natural gas consumption prediction based on Volterra adaptive filter and improved whale optimization algorithm. Engineering Applications of Artificial Intelligence, 2020, 87: 103323

[22] Qiao W, Huang K, Azimi M, Han S. A novel hybrid prediction model for hourly gas consumption in supply side based on improved machine learning algorithms. IEEE Access: Practical Innovations, Open Solutions, 2019

[23] Yu W, Wen K, Li Y, Huang W, Gong J. A methodology to assess the gas supply capacity and gas supply reliability of a natural gas pipeline network system. In: 2018 12th International Pipeline Conference Calgary, Alberta, Canada, 2018

[24] Praks P, Kopustinskas V, Masera M. Probabilistic modelling of security of supply in gas networks and evaluation of new infrastructure. Reliability Engineering & System Safety, 2015, 144: 254–264

[25] Olanrewaju O, Chaudry M, Qadrdan M, Wu J, Jenkins N. Vulnerability assessment of the European natural gas supply. In: Proceedings of the Institution of Civil Engineers—Energy, 2015, 168: 5–15

[26] Vasconcelos C, Lourenço S, Gracias A, Cassiano D. Network flows modeling applied to the natural gas pipeline in Brazil. Journal of Natural Gas Science and Engineering, 2013, 14: 211–224

[27] Tran T, French S, Ashman R, Kent E. Impact of compressor failures on gas transmission network capability. Applied Mathematical Modelling, 2018, 55: 741–757

[28] Monforti F, Szikszai A. A Monte Carlo approach for assessing the adequacy of the European gas transmission system under supply crisis conditions. Energy Policy, 2010, 38(5): 2486–2498

[29] Szikszai A, Monforti F. GEMFLOW: a time dependent model to assess responses to natural gas supply crises. Energy Policy, 2011, 39(9): 5129–5136

[30] Liang G, Luo M, Zhang C, Pu H, Zheng Y. Analysis methods for hydraulic reliability of gas transmission pipeline networks. Natural Gas Industry, 2006, 26: 125–127

[31] Shaikh F, Ji Q, Fan Y. Evaluating China’s natural gas supply security based on ecological network analysis. Journal of Cleaner Production, 2016, 139: 1196–1206

[32] Su M, Zhang M, Lu W, Chang X, Chen B, Liu G, Hao Y, Zhang Y. ENA-based evaluation of energy supply security: comparison between the Chinese crude oil and natural gas supply systems. Renewable & Sustainable Energy Reviews, 2017, 72: 888–899

[33] Pambour K, Cakir Erdener B, Bolado-Lavin R, Dijkema G. SAInt—a novel quasi-dynamic model for assessing security of supply in coupled gas and electricity transmission networks. Applied Energy, 2017, 203: 829–857

[34] Yu W, Wen K, Min Y, He L, Huang W, Gong J. A methodology to quantify the gas supply capacity of natural gas transmission pipeline system using reliability theory. Reliability Engineering & System Safety, 2018, 175: 128–141

[35] Fu X, Zhang X. Failure probability estimation of gas supply using the central moment method in an integrated energy system. Applied Energy, 2018, 219: 1–10

[36] Fu X, Li G, Zhang X, Qiao Z. Failure probability estimation of the gas supply using a data-driven model in an integrated energy system. Applied Energy, 2018, 232: 704–714

[37] Zio E, Baraldi P, Patelli E. Assessment of the availability of an offshore installation by Monte Carlo simulation. International Journal of Pressure Vessels and Piping, 2006, 83(4): 312–320

[38] Zio E. The Monte Carlo Simulation Method for System Reliability and Risk Analysis. London: Springer, 2013

[39] Liu H, Lu Y, Zhang J. A comprehensive investigation of the viscoelasticity and time-dependent yielding transition of waxy crude oils. Journal of Rheology (New York, N.Y.), 2018, 62(2): 527–541

[40] Liu H, Zhang J, Lu Y. Yielding characterization of waxy gels by energy dissipation. Rheologica Acta, 2018, 57(6-7): 473–480

[41] Yu W, Gong J, Song S, Huang W, Li Y, Zhang J, Hong B, Zhang Y, Wen K, Duan X. Gas supply reliability analysis of a natural gas pipeline system considering the effects of underground gas storages. Applied Energy, 2019, 252: 113418

[42] Chaudry M, Wu J, Jenkins N. A sequential Monte Carlo model of the combined GB gas and electricity network. Energy Policy, 2013, 62: 473–483

[43] Qiao W, Huang K, Azimi M, Han S. A novel hybrid prediction model for hourly gas consumption in supply side based on improved whale optimization algorithm and relevance vector machine. IEEE Access: Practical Innovations, Open Solutions, 2019, 7: 88218–88230

[44] Qiao W, Yang Z. Modified dolphin swarm algorithm based on chaotic maps for solving high-dimensional function optimization problems. IEEE Access: Practical Innovations, Open Solutions, 2019, 7: 110472–110486

[45] Qiao W, Yang Z. An improved dolphin swarm algorithm based on Kernel Fuzzy C-means in the application of solving the optimal problems of large-scale function. IEEE Access: Practical Innovations, Open Solutions, 2020, 8: 2073–2089

[46] Qiao W, Yang Z. Solving large-scale function optimization problem by using a new metaheuristic algorithm based on quantum dolphin swarm algorithm. IEEE Access: Practical Innovations, Open Solutions, 2019, 7: 138972–138989

[47] Badea A C, Rocco S C M, Tarantola S, Bolado R. Composite indicators for security of energy supply using ordered weighted averaging. Reliability Engineering & System Safety, 2011, 96(6): 651–662

[48] Qiao W, Yang Z. Forecast the electricity price of US using a wavelet transform-based hybrid model. Energy, 2020, 193: 116704

[49] Zhou G, Moayedi H, Foong L. Teaching–learning-based metaheuri-stic scheme for modifying neural computing in appraising energy performance of building. Engineering with Computers, 2020, online, doi:10.1007/s00366-020-00981-5

[50] Qiao W, Bing F, Zhang Y. Differential scanning calorimetry and electrochemical tests for the analysis of delamination of 3PE coatings. International Journal of Electrochemical Science, 2019, 14: 7389–7400

[51] Cabalu H. Indicators of security of natural gas supply in Asia. Energy Policy, 2010, 38(1): 218–225

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