Dissociative Adsorption of Hydrogen in Hydrogen-Blended Natural Gas Pipelines: A First Principles and Thermodynamic Analysis

Abstract

This study employs first principles calculations and thermodynamic analyses to investigate the dissociative adsorption of hydrogen on the Fe(110) surface. The results show that the adsorption energies of hydrogen at different sites on the iron surface are −1.98 eV (top site), −2.63 eV (bridge site), and −2.98 eV (hollow site), with the hollow site being the most stable adsorption position. Thermodynamic analysis further reveals that under operational conditions of 25 °C and 12 MPa, the Gibbs free energy change (ΔG) for hydrogen dissociation is −1.53 eV, indicating that the process is spontaneous under pipeline conditions. Moreover, as temperature and pressure increase, the spontaneity of the adsorption process improves, thus enhancing hydrogen transport efficiency in pipelines. These findings provide a theoretical basis for optimizing hydrogen transport technology in natural gas pipelines and offer scientific support for mitigating hydrogen embrittlement, improving pipeline material performance, and developing future hydrogen transportation strategies and safety measures.

1. Introduction

Amid escalating global climate change and a surging demand for carbon reduction, forging sustainable energy pathways has emerged as a global imperative. Within the spectrum of sustainable energy alternatives, hydrogen stands out for its clean energy characteristics and its pivotal role as an energy vector, making it essential in the shift towards a sustainable energy paradigm [1,2]. Notably, the approach of repurposing existing natural gas pipelines for the conveyance of clean hydrogen mixtures is increasingly recognized as a pragmatic strategy. This method not only significantly curtails greenhouse gas emissions but also boosts energy efficiency and catalyzes the growth of the hydrogen energy industry. Consequently, it contributes profoundly to enhancing the resilience, security, and diversity of the energy supply [3,4].

Despite the promising role of hydrogen in the sustainable energy transition, the process of transporting hydrogen encompasses several hurdles, notably hydrogen embrittlement and the aging of natural gas pipeline networks. These challenges pose substantial barriers to achieving safe and efficient hydrogen transportation [5,6]. Hydrogen embrittlement, which predominantly impacts high-strength steel materials, is governed by mechanisms such as hydrogen-enhanced localized plasticity (HELP) and hydrogen-enhanced decohesion (HEDE) [7,8]. These mechanisms critically influence hydrogen’s interaction with metals and consequently affect the mechanical properties of these materials [9,10].

When using existing natural gas pipelines to transport hydrogen-natural gas mixtures, there are two main types of hydrogen embrittlement that may occur [11]. The first type involves the hydrogen source produced by the electrochemical cathodic reaction (commonly referred to as cathodic hydrogen), which mainly occurs on metal surfaces undergoing cathodic protection or experiencing electrochemical corrosion [12,13]. These hydrogen atoms may either recombine into hydrogen molecules and be released from the surface or penetrate into the metal, causing hydrogen-induced cracking (HIC) [14,15]. Cracks may form under external stress or even in the absence of stress, and they extend as hydrogen accumulates at the crack tips, eventually leading to the failure of the metal parts [16]. The second type is called gaseous hydrogen embrittlement, which does not involve liquid electrolytes but occurs due to the direct contact and chemical reaction of hydrogen gas with metals [17,18]. Hydrogen molecules first dissociate into hydrogen atoms on the metal surface, a crucial step for the formation of gaseous hydrogen embrittlement [19,20]. The dissociated hydrogen atoms can stably adsorb on the steel surface and penetrate into the metal through surface diffusion or direct penetration, accumulating in the interstitial spaces of the steel lattice, causing lattice distortion and increasing internal stresses, ultimately leading to hydrogen embrittlement [21,22].

For gaseous hydrogen embrittlement, the process of dissociative adsorption of hydrogen represents the core step in its formation. Not only do these hydrogen molecules undergo chemical reactions on the metal surface, but they also affect the overall mechanical properties of the material, particularly in the context of pipeline operating conditions [23]. Therefore, gaining a deep understanding of the dissociative adsorption of hydrogen on metal surfaces and its behavior within the metal is crucial for enhancing the safety and efficiency of pipelines.

To address this issue, first principles calculations have played an irreplaceable role in studying the interaction between hydrogen and metals [24,25]. Dan’s research utilized first principles calculation methods to explore the adsorption mechanisms of hydrogen atoms on the Fe(100) surface, demonstrating how hydrogen atoms dissociate on the metal surface and further interact with the metal [26]. Jiang studied the thermodynamics of adsorption and diffusion of hydrogen on transition metals, revealing the influence of different metals on the dissociation of hydrogen molecules [27]. Liang Zhang analyzed the impact of elemental segregation on the properties of metal materials by calculating the charge density and state density of grain boundaries [28]. Du studied the interaction between hydrogen vacancies and grain boundaries in α-Fe and γ-Fe using first principles, finding that the grain boundary structure has larger vacancies, increasing solubility, with hydrogen having lower mobility within the grain boundaries, acting as traps for hydrogen [29]. Through these methods, researchers can delve into the adsorption mechanisms of hydrogen atoms on different metal surfaces, understand how hydrogen atoms dissociate and interact with metals, and understand how the migration and accumulation of hydrogen within metals affect the mechanical properties of materials.

Although existing research has provided us with important insights into the interactions between hydrogen atoms and metals, a deeper understanding of the adsorption and dissociation behaviors of hydrogen on metal surfaces and their impact on hydrogen embrittlement requires comprehensive consideration of the complexity of operational gas pipeline surfaces. This complexity arises not only from changes in microstructure, surface characteristics, and chemical composition due to the aging process of the pipelines but also includes surface by-products caused by environmental factors. Through computer simulation, we can precisely explore the adsorption mechanisms of hydrogen atoms on metal surfaces at the microscopic level. This approach offers new perspectives and strategies to ensure the safety and efficiency of hydrogen transport in natural gas pipelines [30]. This study utilizes first principles calculations to thoroughly investigate the dissociative adsorption process of hydrogen on the Fe(110) surface of X80 pipeline steel, aiming to address the key scientific issues related to the interaction between hydrogen molecules and pipeline steel surfaces. The research focuses on the microscopic mechanisms of hydrogen molecule dissociative adsorption on the Fe(110) surface, involving changes in system energy, bond length adjustments, and alterations in electron and charge distributions, and assesses the spontaneity influenced by environmental temperature and pressure, exploring the role of thermodynamic principles in this process.

Through a systematic examination of these issues, this study not only provides a theoretical basis for assessing the feasibility of transporting hydrogen through natural gas pipelines but also offers scientific support for developing safe and efficient hydrogen transport technology strategies. The findings will facilitate the optimization of hydrogen transport and distribution strategies within the natural gas pipeline system, significantly enhancing the performance of pipeline steel and ensuring the stability and safety of the transportation system.

2. Methodology

This research utilizes the CASTEP module within Materials Studio, leveraging spin-polarized Density Functional Theory (DFT) and the Ultrasoft Pseudopotentials (USPPs) method to accurately simulate the adsorption behavior of gaseous hydrogen on iron surfaces [31,32]. DFT, serving as a core computational tool, streamlines the complexity of electron systems, thus reducing computational difficulty and establishing it as an ideal choice for studying molecular structures and properties [33]. The USPPs method achieves an accurate simulation of complex electronic structures and enhances computational efficiency by describing the interaction between nuclei and electrons with a softer pseudopotential [34,35]. Meanwhile, the BFGS algorithm exhibits its efficiency and accuracy in optimizing the BCC lattice structure of iron, effectively accelerating the prediction process of lattice parameters and physical properties by approximating the Hessian matrix, thus becoming a preferred tool for analyzing complex lattice structures [36]. The simple 1s1 electron configuration of hydrogen atoms enables them to form chemical bonds with other atoms through electron sharing. For Fe, its electron configuration is Fe:1s22s22p63s23p63d64s2, with the valence electrons primarily located in the 3d and 4s orbitals. In studying the electronic interaction between hydrogen and iron, the USPPs method effectively manages this complex interaction [37].

This study selected the stable body-centered cubic structure of α-Fe as the subject material, specifically focusing on the atomic arrangement characteristics of the Fe(110) crystal plane. To simulate the dissociative adsorption process of hydrogen molecules (H₂) on the Fe(110) surface, a periodic cell model was employed. Computational parameters were carefully chosen, including a plane wave cutoff energy of 350 eV and a k-point grid size of 12 × 12 × 12. Brillouin zone integration was executed utilizing the Monkhorst-Pack scheme, with the aim of ensuring the high accuracy of the computational findings. The convergence criterion for self-consistent field (SCF) calculations was set at a rigorous threshold of 2.0 × 10⁻⁶ eV/atom, underscoring the precision of the calculation efforts. To simulate the real surface environment more accurately, a 15 Å vacuum layer was introduced above the Fe(110) surface, mirroring conditions closer to those in experimental settings.

The geometric optimization results indicated that the optimized lattice constant a of α-Fe is 2.844 Å, representing only a 0.77% deviation from the experimental value of 2.866 Å, thereby verifying the high accuracy of the model setup [38]. Furthermore, a model comprising 7 layers of Fe(110) crystal planes was constructed, with a 15 Å vacuum layer set to accurately simulate the surface environment. In this model, the positions of the bottom four layers of Fe atoms were fixed, whereas the top three layers of Fe atoms and the atoms adsorbed on them were permitted to relax, to more closely simulate real-world conditions. All simulation parameters underwent convergence tests to guarantee the reliability of this study’s results.

The computational workflow consists of five sequential stages. First, an initial geometry is constructed by placing a physisorbed H₂ molecule above the Fe(110) surface, followed by a pre-relaxation step at the Density Functional Theory (DFT) level. Second, static adsorption energies at 0 K are calculated for all high-symmetry adsorption sites—including top, bridge, and hollow positions—to identify the most thermodynamically favorable configurations. Third, the lowest-energy structures are subjected to full ionic relaxation to obtain fully optimized adsorbate–surface geometries. Fourth, finite-temperature and finite-pressure corrections are incorporated by combining the 0 K adsorption enthalpy with the temperature- and pressure-dependent chemical potential of H₂, yielding operational Gibbs free energies. Finally, the computed energies and geometries are benchmarked against existing literature, and a sensitivity analysis is conducted to evaluate the influence of key computational parameters—namely, plane-wave energy cutoff, k-point sampling density, and vacuum layer thickness—on the calculated energetic descriptors.

3. Results and Discussion

3.1. Adsorption of Hydrogen Molecules on the Surface of Iron

The Fe(110) surface, owing to its unique atomic arrangement and surface properties, exhibits significant representativeness in studies of the interaction between hydrogen and iron. The top, bridge, and hollow sites—these high-symmetry positions—are critical in exploring hydrogen’s adsorption behavior on iron surfaces, often displaying strong surface activity [39]. Previous studies indicate that the adsorption energies of hydrogen atoms on the Fe(110) surface amount to −1.98 eV for the top site, −2.63 eV for the bridge site, and −2.98 eV for the hollow site, highlighting the hollow site as hydrogen atoms’ preferred stable adsorption position, with the top site being relatively unstable [40]. Based on these findings, this study concentrates on analyzing the adsorption of hydrogen molecules at these two extremes—namely, the most stable and least stable positions. By positioning hydrogen molecules parallel to the Fe(110) surface and incrementally adjusting the distance between the hydrogen molecule and the iron surface, the simulation captured the approach of hydrogen molecules towards the iron surface, enabling the system to achieve an energy-minimized state at each step.

The total-energy profile of the H₂/Fe(110) system was obtained by varying the vertical distance d between the geometric center of the hydrogen molecule and the nearest surface Fe atoms. At each separation, the adsorption energy was evaluated as

$$E_{ads}=E_{sys}-E_{Fe}-{\displaystyle \frac{1}{2}}{E}_{H2}$$

(1)

where $E_{sys}$ is the total energy of the combined system, $E_{Fe}$ is the energy of the clean surface, and $E_{H2}$ is it the energy of an isolated H₂ molecule. Determining the minimum $E_{ads}$ allows the most favorable adsorption site to be identified, thereby providing the starting point for full geometry optimization [41]. The calculated values are summarized in

Table 1. Energy of the system with hydrogen molecules at different positions.

Distance (Å)	Top Site’s Energy (eV)	Hollow Site’s Energy (eV)
0.5	−10321.70	−10378.46
1	−10376.92	−10378.46
1.5	−10383.34	−10382.77
2	−10383.33	−10382.97
2.5	−10383.24	−10383.15

.

The analysis results (refer to Figure 1) show that as the hydrogen molecule approaches the iron surface to a proximity of approximately 2 Å, the system’s energy change begins to stabilize, indicating the initiation of interactions between the hydrogen molecule and the iron surface atoms. Further comparison of the energy changes at the top and hollow sites yields a definitive conclusion: the adsorption behavior of the hydrogen molecule at these two distinct symmetrical sites shows significant differences.

The fitted quadratic polynomial equation in Figure 1 is

$$E=33.4429D^2-126.2266D-10272.3340$$

(2)

The fitted quadratic polynomial equation in Figure 2 is

$$E=1.0716D^2-5.9927D-10375.1198$$

(3)

where D is in Å and E is in eV.

It’s critical to acknowledge that the analysis presented herein relies on system energy calculations that do not incorporate geometric optimization, thereby omitting the potential effects of chemical bonding between hydrogen molecules and iron atoms. For the purposes of this preliminary analysis, it is assumed that the hydrogen molecule retains its original molecular structure without alteration, and no geometry optimization is performed during this step. Observations indicate a marked reduction in system energy as the distance between the hydrogen molecule and the Fe(110) surface extends from 0.5 Å to 1.75 Å. This implies that, within this specified range and in the absence of chemical bonding, the interaction is predominantly influenced by van der Waals forces or alternative short-range repulsive forces. Notably, at the distance of 1.75 Å from the iron surface, where the system energy reaches a global minimum, this specific distance could denote the most favorable position for the physical adsorption of the hydrogen molecule. Beyond the distance of 1.75 Å, the variation in system energy stabilizes, indicating that past this juncture, the hydrogen molecule’s inclination towards physical adsorption or interaction weakens as the distance increases [41].

Further research indicates that within the distance range of 2 Å to 3 Å, as the distance between the hydrogen molecule and the iron surface gradually increases, the system energy shows a stable upward trend. This suggests that the effective interaction between the hydrogen molecule and the iron surface is gradually weakening and tends towards a state of detaching from the adsorption on the iron surface. Meanwhile, according to experimental data or theoretical calculations, the physical adsorption distance of hydrogen molecules at the iron surface’s hollow site is approximately 2.5 Å. Based on this, we can reasonably infer that on the Fe(110) surface, the ideal physical adsorption distance of hydrogen molecules at the top site is approximately 1.75 Å, while physical adsorption at the hollow site tends to occur around a distance of 2.5 Å. This helps to identify the lowest energy adsorption sites for hydrogen molecules on the iron surface.

During the geometric optimization of the Fe(110) interface system, the hydrogen-to-iron surface distance was initially set at 1.75 Å to identify the lowest energy configuration of the system. This optimization led to significant alterations in the electronic structure, marked by dynamic shifts in the band structure and density of electronic states. Figure 2 illustrates the atomic configurations before and after optimization during hydrogen adsorption on the Fe(110) surface. In the unrelaxed state (Figure 2a), the H–H bond measures 0.74 Å, with the molecular center located 1.75 Å above the topmost iron layer. Upon partial relaxation (Figure 2b), the H–H bond elongates to 1.067 Å, while the vertical distance to the surface contracts to 1.478 Å, signaling the onset of molecular dissociation and the formation of incipient Fe–H bonds, with bond lengths around 1.68 Å. Fully optimized configurations (Figure 2c) reveal that the hydrogen atoms have completely dissociated and migrated to hollow–bridge sites on the Fe surface, with Fe–H bonds stabilizing at approximately 1.612 Å and the H–H separation expanding further to 2.189 Å. Additionally, minor lateral displacements of Fe atoms are observed, consistent with structural reorganization induced by hydrogen chemisorption. Additionally, the iron atoms on the Fe(110) surface displayed slight positional adjustments as a result of the dissociative adsorption of hydrogen atoms. The computational findings align well with the literature, specifically references 14 and 29, affirming the model’s accuracy [27,42].

To gain a deeper understanding of the spontaneity of the reaction system, this paper will analyze the thermodynamic parameters of the reaction process. The change in Gibbs free energy $\Delta G$ serves as a key thermodynamic quantity for determining whether a chemical reaction will proceed spontaneously and is calculated by comparing the free energies of the products and reactants [43]. The calculation of Gibbs free energy is presented in Equation (4).

$$\Delta G=G_{\mathrm{products}}-\sum G_{\mathrm{reactants}}$$

(4)

where $G_{\mathrm{products}}$ represents the free energy of all products, while $\sum G_{\mathrm{reactants}}$ represents the sum of the free energies of all reactants.

Based on the calculated data obtained in this study, $G_{\mathrm{products}}$ = −12110.548 eV, $G_{Fe}$ = −12077.703 eV, and $G_{H2}$ = −31.31 eV. We can substitute the above data into the formula for the change in Gibbs free energy to obtain $\Delta G$ = −1.53 eV. Since the value of $\Delta G$ is less than zero, we can conclude that this reaction can proceed spontaneously.

3.2. Analysis of Hydrogen-Gas and Iron Surface Interactions Based on First Principles

The redistribution of charge density is crucial for understanding chemical reactions, especially in scenarios involving the transfer of electrons between molecules [44,45]. This phenomenon is particularly pronounced in the dissociative adsorption reaction of hydrogen molecules on the iron surface. The interaction between hydrogen and iron atoms triggers the redistribution of electrons, thereby altering the layout of charge density within the system. This change directly affects the formation of chemical bonds [46].

Through density functional theory, an in-depth simulation analysis of the iron-hydrogen adsorption model was conducted, aiming to quantify the overall and orbit-specific changes in the electron state density during the dissociative adsorption process of hydrogen on the iron surface. As shown in Figure 3, by comparing the changes in the total state density before and after hydrogen dissociative adsorption (represented by the red and blue areas, respectively), we observed a significant increase in the total state density near the Fermi level (energy range from −5 eV to 5 eV). This increase reflects an enhancement in the interaction strength between electrons, which could indicate the formation of new chemical bonds. The key changes in the electron state density provide important clues for understanding the microscopic mechanism of hydrogen’s dissociative adsorption on the iron surface. To further deepen the analysis, the changes in the electron state density were subdivided into three energy intervals: −10 eV to −5 eV, −5 eV to 5 eV, and above 5 eV. This subdivision helps in thoroughly discussing and analyzing the specific impacts of changes in electron state density within each energy interval.

The change in the s-orbital electron state density before and after hydrogen adsorption can be observed (as shown in Figure 4). Before hydrogen adsorption, near the Fermi level (0 eV), the state density diagram exhibits a sharp and high peak, reflecting the high state density of the lone electron on the hydrogen atom’s s-orbital. After hydrogen adsorption, this sharp peak disappears, and a new, broader peak appears in a lower energy range (approximately −10 eV to −5 eV). This indicates that electrons from the hydrogen atom’s s-orbital have interacted with the iron surface, leading to the transfer of electrons to the electronic states of iron and the formation of new chemical bonds [47]. This change reveals significant electron interaction between the hydrogen atom and the iron surface, resulting in the transfer of s-orbital electrons of hydrogen to the electronic states of iron and ultimately the formation of new chemical bonds. This phenomenon not only reflects the chemical adsorption process of hydrogen atoms on the iron surface but also demonstrates the process of electron reorganization.

The analysis of electron orbital hybridization reveals changes in electron behavior during the hydrogen adsorption process on the iron surface. As illustrated in Figure 3, new, broader peaks observed in the lower energy range (−10 eV to −5 eV) typically signify the formation of new energy levels through the hybridization process. These broader peaks indicate that the distribution of electron states becomes more extensive after hybridization, reflecting an enhancement in electron interactions and the splitting of energy levels.

Specifically, as demonstrated in Figure 5, the adsorption of hydrogen introduces a new peak in the density of states (DOS) within the same energy range for iron’s s-orbital, signaling the involvement of iron’s 4s orbital in the hybridization process. Concurrently, Figure 6 reveals that the DOS for iron’s d-orbital remains largely unchanged within the −10 eV to −5 eV energy range. This observation suggests that the hybridization primarily involves iron’s 4s orbital within this specified energy interval.

The redistribution of electronic states between the 4s orbitals of iron and the s orbitals of hydrogen atoms on the iron surface results in the formation of new hybrid orbitals at lower energy levels. This formation of new hybrid energy levels signifies the transition of electrons from higher to lower stable energy states, directly reflecting the pairing and sharing of electrons during the chemical adsorption process. The formation of new hybrid orbitals further reduces the total energy of the system, demonstrating the stability of the adsorption configuration and providing important theoretical support for understanding the hydrogen adsorption mechanism on the iron surface. Apart from the hybridization of the hydrogen 1s and iron 4s orbitals altering the total density of electronic states, Figure 5, Figure 6 and Figure 7 indicate that the s, d, and p orbitals of iron contribute to the increase in the total electronic density over the energy range of −5 eV to +5 eV.

Based on the analysis above, we can conclude that during the dissociative adsorption process of hydrogen, the interaction between hydrogen and iron atoms leads to the rearrangement of electrons, thereby affecting the distribution of charge density within the system and facilitating new chemical interactions between iron and hydrogen atoms. Furthermore, the electron rearrangement between iron and hydrogen atoms is primarily driven by orbital hybridization (especially the hybridization of hydrogen’s 1s orbital with iron’s 4s orbital) and interatomic interactions [48,49].

Through precise calculations of electron difference density, this study delves into the adsorption mechanism of hydrogen on the iron surface. The analysis results reveal changes in electron density induced by hydrogen adsorption, further deepening our understanding of the dynamics of electron rearrangement between atoms. Figure 8 details the changes in electron difference density during the hydrogen adsorption and dissociation process, clearly displaying the pattern of electron density changes during the dissociative adsorption process of hydrogen molecules on the iron surface. Here, color changes represent trends in electron density increase or decrease. Red areas indicate locations of increased electron density, suggesting electron concentration in these regions. Red areas near the hydrogen molecule suggest that electrons may be transferring from iron atoms to hydrogen atoms, facilitating the formation of Fe-H bonds. Conversely, blue areas show decreased electron density, possibly indicating the migration of electrons originally near iron atoms toward hydrogen atoms, thereby leading to a reduction in electron density around iron atoms. Such changes in electron density not only signify the migration of electrons from iron to hydrogen but are also key steps in the chemical adsorption process [50,51]. Therefore, electron rearrangement is the fundamental cause of changes in charge density. Charge density difference maps further showcase the redistribution of charge density after electron rearrangement. As shown in Figure 9, red areas indicate increased electron density, while blue areas denote decreased electron density. Especially, significant red areas near hydrogen atoms indicate an increase in electron density, enhancing the interaction between iron and hydrogen atoms and promoting the formation of chemical Fe-H bonds. This is consistent with the results of Figure 9, accurately describing the microscopic mechanism of dissociative adsorption of hydrogen molecules on the iron surface, i.e., the redistribution of charge density through electron migration. The areas with higher charge density exhibit enhanced interatomic interactions, which are key to the formation of chemical bonds.

3.3. Thermodynamic Analysis of Hydrogen Dissociative Adsorption on Pipeline Steel Surfaces

Understanding the adsorption behavior of hydrogen within natural gas pipeline systems is essential for maintaining the structural integrity of these pipelines and improving transport efficiency [52]. This, in turn, ensures the safety and efficacy of the energy supply chain. The Gibbs free energy offers a thermodynamic framework for elucidating the interactions between hydrogen molecules and the iron surface [53]. As illustrated in Figure 10, when examining the adsorption process of gas molecules on solid surfaces, our primary focus is on energy changes. These changes are predominantly driven by two factors: the alteration in adsorption energy and the variation in chemical potential, which stems from the fluctuation in the number of gas molecules [54,55]. As shown in Equation (5).

ΔG = ΔE _adsorption + Δ n_gas · μ(T,P)

(5)

where ΔG represents the total change in Gibbs free energy during the adsorption process, ΔE _adsorption is the change in adsorption energy, Δ n_gas is the change in the number of gas molecules, and ⋅μ(T,P) is the chemical potential at a specific temperature T and pressure P. This equation explicitly states that the spontaneity of the adsorption process under given temperature and pressure conditions is determined not only by the change in adsorption energy but also by the influence of changes in chemical potential due to the adsorption of gas molecules on the surface. By calculating ΔG, we can determine whether the adsorption process is spontaneous. If ΔG < 0, this indicates that the process occurs spontaneously, and the more negative the value of ΔG < 0, the higher the stability of the products.

3.3.1. Calculation of Adsorption Energy

The change in adsorption energy, ΔE adsorption, essentially corresponds to the enthalpy change, ΔH, reflecting the thermal effect during the adsorption process. The adsorption action on solid surfaces mainly involves the formation or breaking of chemical bonds; thus, ΔE adsorption directly indicates the change in system energy caused by the change in chemical bonds [56]. Specifically, if ΔE adsorption < 0, it implies that the adsorption process is exothermic, forming stable chemical bonds, which typically means that the process is spontaneous. The relevant information about the model and the computational results are presented in

Table 2. Model-related information and computational results.

Material	Structure	Atomic Count	Surface State	Pre-Reaction Energy	Post-Reaction Energy
Fe	Bcc	14	Fe(110)	−12077.62 eV	−12110.02 eV
H	Hydrogen Molecule	2	Hydrogen Molecule	−31.31 eV

.

The change in adsorption energy, ΔE adsorption, can be expressed by Equation (6):

$$\Delta E_{\mathrm{adsorption}}=E_{\mathrm{Sys}}-\left(E_{\mathrm{H}2}+E_{Fe}\right)$$

(6)

This equation indicates that the change in Gibbs free energy ΔG during the adsorption process can be calculated as the sum of the change in adsorption energy ΔE adsorption and the change in the number of gas molecules Δn gas multiplied by the chemical potential $\mu \left(T,P\right)$ at a specific temperature T and pressure P. This equation reveals the thermodynamic characteristics of the adsorption process, highlighting that the spontaneity of adsorption is influenced not only by the change in adsorption energy but also by the variation in the number of gas molecules during the adsorption and their change in chemical potential. This provides an important theoretical foundation for determining whether the adsorption process is spontaneous and for further understanding the adsorption mechanism.

3.3.2. Calculation of Chemical Potential

The chemical potential of hydrogen under specific conditions can be calculated using Equation (7) [57].

$$\mu \left(T,P\right)={\mu }_0\left(\mathrm{T}\right)+RTln\left({\displaystyle \frac{P}{P_0}}\right)$$

(7)

where $\mu \left(T,P\right)$ is the chemical potential at temperature $T$ and pressure $P$, ${\mu }_0\left(\mathrm{T}\right)$ The chemical potential is in the standard state, where for a pure substance at $P$ ₀ = 0.1 MPa, the chemical potential equals its Gibbs free energy in the standard state, R is the ideal gas constant, equal to 8.314 J/(mol K), T is the absolute temperature in Kelvin, $P$ is the actual pressure of the gas.

Given that the maximum design pressure is P = 12 MPa and room temperature is taken as 25 °C, or T = 298.15 K, substituting into the formula yields μ(T,P) ≈ 11.86 kJ/mol. The change in the chemical potential of hydrogen is approximately 0.123 eV.

3.3.3. Changes in Gibbs Free Energy and Chemical Potential

As the temperature increases, the value of the Gibbs free energy change ΔG shows a decreasing trend, which actually means a reduction in its absolute value. This phenomenon reveals that under conditions of rising temperatures inside steel pipes, the spontaneous dissociation tendency of hydrogen on the steel surface increases. In thermodynamics, when the change in Gibbs free energy ΔG for a process is less than zero, the process is considered spontaneous. Therefore, a decrease in the absolute value of ΔG actually reflects a trend of increased spontaneity in the hydrogen dissociation process. This point is crucial for understanding and predicting the adsorption behavior of hydrogen in natural gas pipeline systems, especially when considering the potential impact of temperature changes on pipeline safety and hydrogen transport efficiency.

At a set pressure of 12 MPa, the variations in the chemical potential and Gibbs free energy of hydrogen adsorption on steel pipe surfaces under different temperatures were investigated. The calculation results are shown in

Table 3. Chemical potential (μ) and Gibbs free energy (ΔG) at various temperatures under a pressure of 12 MPa.

T (°C)	ΔG (kJ/mol)	μ (kJ/mol)
−15	−115.444	10.275
0	−116.041	10.872
15	−116.638	11.469
25	−117.036	11.867
30	−117.235	12.066

, and the trend is illustrated in Figure 11. As the temperature rises, the chemical potential μ(T,P) also increases correspondingly. This phenomenon reveals that, in a constant pressure environment, the increase in temperature leads to an increase in the average energy of atoms or molecules in the system, thereby causing the chemical potential to rise. The increase in chemical potential means that, under higher temperature conditions, gas molecules are more inclined to adsorb onto solid surfaces. This trend is consistent with the decrease in the absolute value of the Gibbs free energy change ΔG into the negative range, further confirming that with the increase in temperature, the spontaneity of hydrogen adsorption and dissociation processes on steel surfaces significantly enhances.

In summary, at a working pressure of 12 MPa, as the temperature increases, the spontaneous adsorption and dissociation activities of hydrogen on steel surfaces show an enhanced trend. This observation is reflected not only in the increase in the absolute value of the negative ΔG but also in the continuous rise of the chemical potential μ, providing an important theoretical basis for a deeper understanding and optimization of hydrogen transportation and storage in natural gas pipelines.

At a set temperature of 25 °C, the variations in the chemical potential and Gibbs free energy of hydrogen adsorption on steel pipe surfaces under different pressures were investigated. The calculation results are shown in

Table 4. Chemical Potential (μ) and Gibbs Free Energy (ΔG) at Different Pressures at a Temperature of 25 °C.

P (MPa)	ΔG (kJ/mol)	μ (kJ/mol)
2	−112.595	7.426
4	−114.313	9.144
6	−115.318	10.149
8	−116.031	10.862
10	−116.584	11.415
12	−117.036	11.867
14	−117.418	12.249
16	−117.749	12.580

, and the trend is illustrated in Figure 12. The red curve reflects the trend of Gibbs free energy changes within a pressure range of 2 MPa to 16 MPa, showing that as the pressure increases, the negative value of ΔG decreases from about −113 kJ/mol to −118 kJ/mol, clearly indicating that the spontaneity of the adsorption process increases with pressure. The blue curve displays how the chemical potential μ changes with pressure, and it can be clearly seen that the chemical potential rises gradually from 8 kJ/mol to about 12 kJ/mol, suggesting that as the pressure increases, the tendency of hydrogen molecules to adsorb on the steel surface also gradually strengthens.

The trend of the negative value of ΔG decreasing as the pressure increases is consistent with previous predictions, indicating that under high-pressure conditions, the adsorption process of hydrogen tends to occur more spontaneously. A more negative value of free energy means an increase in the thermodynamic stability of the adsorption process. The trend of the chemical potential increasing with pressure further validates that under high-pressure conditions, the possibility of hydrogen molecules adsorbing to the steel surface increases, aligning with the trend of increased spontaneity in the adsorption process.

4. Conclusions

This study thoroughly investigates the dissociative adsorption process of hydrogen atoms on iron surfaces and observes significant changes in charge density due to electron rearrangement. These changes facilitate the formation of new Fe-H chemical bonds and the breaking of existing H-H bonds. Specifically, the electron density around iron atoms decreases, while it increases near hydrogen atoms. This electron transfer and the resulting increase in electron interactions strengthen the bond between hydrogen and iron atoms.

The dissociative adsorption process involves complex interactions between hydrogen and iron atoms, triggering electron rearrangement that affects the overall charge density distribution within the system. This electron rearrangement is primarily driven by orbital hybridization, particularly between hydrogen’s 1s orbital and iron’s 4s orbital, along with direct interatomic interactions.

Furthermore, thermodynamic analysis reveals that under operational conditions of 25 °C and 12 MPa, the Gibbs free energy change for hydrogen dissociation is −1.53 eV, indicating that the process is spontaneous under pipeline conditions. As temperature and pressure increase, the hydrogen adsorption process is enhanced, primarily due to a decrease in Gibbs free energy and an increase in chemical potential. Specifically, as the temperature rises from 15 °C to 30 °C, ΔG decreases, demonstrating the promoting effect of temperature on the spontaneity of the adsorption process. Therefore, precise control over temperature and pressure is critical in the design and operation of hydrogen-blended natural gas pipeline systems. This helps optimize hydrogen transport and distribution and plays a crucial role in maintaining the integrity of pipeline materials and energy efficiency management.

These findings provide essential theoretical support for developing more efficient and safer hydrogen transportation technologies. The research indicates that understanding the interaction between hydrogen and pipeline steel surfaces can offer theoretical foundations for mitigating hydrogen embrittlement, thereby ensuring safe and efficient hydrogen transport in natural gas pipelines. The results provide important theoretical support for future optimization of hydrogen transportation technologies and improvements in pipeline safety strategies, offering scientific insights for the sustainable use of hydrogen energy.