Numerical Simulation Study of Gas Stratification in Hydrogen-Enriched Natural Gas Pipelines

Abstract

Hydrogen blending in natural gas pipelines facilitates renewable energy integration and cost-effective hydrogen transport. Due to hydrogen’s lower density and higher leakage potential compared to natural gas, understanding hydrogen concentration distribution is critical. This study employs ANSYS Fluent 2022 R1 with a realizable k-ε model to analyze flow dynamics of hydrogen–methane mixtures in horizontal and undulating pipelines. The effects of hydrogen blending ratios, pressure (3–8 MPa), and pipeline geometry were systematically investigated. Results indicate that in horizontal pipelines, hydrogen concentrations stabilize near initial values across pressure variations, with minimal deviation (maximum increase: 1.6%). In undulating pipelines, increased span length of elevated sections reduces maximum hydrogen concentration while maintaining proximity (maximum increase: 0.65%) to initial levels under constant pressure. Monitoring points exhibit concentration fluctuations with changing pipeline parameters, though no persistent stratification occurs. However, increasing the undulating height elevation difference leads to an increase in the maximum hydrogen concentration at the top of the pipeline, rising from 3.74% to 9.98%. The findings provide theoretical insights for safety assessments of hydrogen–natural gas co-transport and practical guidance for pipeline design optimization.

1. Introduction

The global intensification of energy crises coupled with escalating environmental deterioration has rendered the establishment of sustainable energy systems implementing carbon-neutral technologies an imperative societal objective [1]. Hydrogen emerges as a leading next-generation energy vector, distinguished by its combustion producing water vapor without greenhouse gas emissions or particulate matter generation. With a gravimetric energy density of 143 MJ·kg⁻¹ [2,3], this lightweight gas delivers specific energy content exceeding conventional liquid hydrocarbons (diesel/petrol) by nearly threefold. Critical technological impediments persist, however, in establishing economically viable storage and transportation infrastructure that ensures both operational safety and material integrity.

The escalating hydrogen economy demands have driven comprehensive multidisciplinary investigations into retrofitting fossil-derived gas transportation frameworks with hydrogen compatibility protocols [4,5,6]. This cross-domain synergy leverages legacy pipeline assets’ structural sunk capital while maintaining hydraulic integrity, simultaneously achieving two essential energy transition objectives: infrastructure interoperability preservation and hydrogen vectorization at gigawatt-hour scalability thresholds [7,8].

The rapid expansion of China’s natural gas pipeline infrastructure has heightened scientific attention to operational shutdown events [9,10], known to induce significant thermodynamic variations including temperature and pressure fluctuations within pipeline systems [11,12,13]. While extensive research has addressed critical operational challenges such as blockage mitigation, shutdown duration safety thresholds, and thermal dissipation patterns, scientific investigation of hydrogen-enriched natural gas pipeline shutdown phenomena remains comparatively underdeveloped. Current experimental studies primarily focus on density-driven stratification dynamics, demonstrating that gas mixtures with substantial density differentials [14] inherently develop compositional stratification—a process independent of pressure conditions [15], thermal gradients [16], or external environmental factors [17,18,19]. This stratification mechanism, exacerbated by extended transport distances and shutdown durations, raises material safety concerns through localized hydrogen accumulation in pipeline systems [20,21,22].

Numerous researchers have investigated gas mixtures under gravitational influence; however, considerable controversy still exists regarding the stratification behavior of hydrogen–methane mixtures. Tong [23] established a 2.96 m (width) × 2.24 m (height) one-dimensional model to investigate gas distribution under varying hydrogen fluxes. Results indicate more uniform hydrogen distribution at low Froude numbers where stratification is gravity-dominated. Peng et al. [24] systematically studied equilibrium distribution of hydrogen–methane mixtures in gravitational fields by integrating molecular dynamics simulations with thermodynamics and diffusion theory. Their findings demonstrate that partial pressures of hydrogen and methane decrease with increasing height. Due to its lower molar mass, hydrogen exhibits a slower decrease rate, leading to accumulation at the pipeline top. However, significant stratification occurs only under substantial height differences, with stabilization time increasing proportionally to the height differential. Pitts et al. [25] constructed a two-car garage chamber to explore hydrogen dispersion following vehicular leaks. After ground-level central release, a hydrogen concentration gradient forms with peak concentrations near the ceiling, though concentration differences remain minor. Collectively, stratification of hydrogen-methane mixtures in gravitational fields remains contentious, with limited studies in horizontal/undulating natural gas pipelines, necessitating systematic quantitative investigations of stratification behavior.

Under conventional operating conditions, the gas flow in pipelines is predominantly turbulent, which promotes the thorough mixing of natural gas and hydrogen, preventing stratification. However, once the pipeline is shut down for maintenance or repair, the situation changes. Due to the significant density differences between hydrogen and natural gas, hydrogen tends to separate from the mixture and accumulate at the top when the gas is at rest, leading to stratification. If this stratification results in a sharp increase in hydrogen concentration at the top, it significantly raises the risk of hydrogen-induced cracking in the pipeline, posing a safety threat.

Therefore, understanding the stratification mechanism, the spatiotemporal variation of hydrogen concentration, and the time required to reach a stable stratified state during the gas standing process after pipeline shutdown is critical for determining the safety maintenance window of hydrogen-blended pipelines. Unfortunately, current research in this area is insufficient both domestically and internationally, and further exploration is urgently needed to fill this knowledge gap.

2. Research Background and Current Status of the Study

When considering the integration of hydrogen into natural gas pipeline systems for transportation, the primary task is to determine an appropriate hydrogen blending ratio. However, this is not a straightforward process, as it is influenced by numerous complex factors, including but not limited to pipeline material compatibility, changes in the physical properties of the gas mixture, and the adaptability of end-use equipment. As a result, no global unified standard has been established to date. Different countries, based on their own technical conditions, safety regulations, and economic considerations, have set varying thresholds for the upper limits of hydrogen blending. For instance, in Europe [26], Finland has taken a conservative approach, setting the upper limit at 1%, while Switzerland [27], Austria [28], and Spain [29,30] have raised this value to 2%, 4%, and 5%, respectively, showing a more open attitude. Meanwhile, a study by the Australian Renewable Energy Agency indicates that when the hydrogen blending ratio is kept below 10% [31], its impact on existing natural gas pipeline infrastructure, end-use equipment, and current regulatory systems is negligible or minimal, providing the industry with operational flexibility and a reference point.

In China, significant strides are being made in the utilization of hydrogen energy. For example, the “Chaoyang Renewable Energy Hydrogen Blending Demonstration Project Phase I” successfully achieved a hydrogen blending ratio of approximately 5%, accumulating valuable experience for hydrogen transportation technology in the country. However, it is important to note that China has not yet issued clear laws, regulations, or technical standards regarding the upper limits of hydrogen blending in natural gas pipelines and networks. This presents both a wide space for industry innovation and a need for continuous learning from practice, gradually establishing a comprehensive standard system to guide the healthy and orderly development of the hydrogen energy industry [32].

2.1. Hydrogen-Blended Natural Gas Pipeline Transportation Cases

Although the development of hydrogen pipelines in China started relatively late, it has been accelerating in recent years. The total length of the hydrogen pipeline network currently approaches 400 km, primarily concentrated in the Bohai Economic Rim and Yangtze River Delta regions, reflecting a regionalized layout. Notably, the hydrogen pipeline connecting Jiyuan City and Luoyang City in Henan Province marks a significant breakthrough in China’s hydrogen transportation technology. With a length of 25 km, an oversized diameter of 508 mm, a hydrogen transport pressure of up to 4 MPa, and an annual hydrogen transport capacity exceeding 100, 400 tons, this pipeline has become a leader in the field of hydrogen pipeline construction in China.

Internationally, the development of hydrogen pipelines has a long history, dating back to the late 1930s, marking the early emergence of hydrogen pipeline transportation technology. Although the total length of hydrogen pipelines globally has accumulated to approximately 4500 km, this figure is still relatively small compared to the vast network of oil and gas pipelines, showing a significant gap. Focusing on Europe, by the end of 2016, about 1598 km of hydrogen pipelines had been laid, with operating pressures typically ranging from 2 to 10 MPa. These pipelines are mainly made of seamless steel, with diameters ranging from 0.3 to 1.0 m. In terms of material selection, pipeline steels such as X42, X52, and X56, which are low-strength but highly adaptable, have become mainstream. Notably, Germany has a long history of hydrogen pipeline construction. As early as 1939, Germany constructed a 208 km-long hydrogen pipeline with a 254 mm diameter and a 2 MPa operating pressure, achieving a hydrogen transport rate of 9000 kg per h. This achievement not only highlighted Germany’s pioneering position in hydrogen energy technology but also set a benchmark for the global development of hydrogen pipelines.

Table 1. Hydrogen Pipelines in Different Regions of the World.

Regions	Pipeline Length
	km	Miles
U.S.	2608	1621
Europe	1598	993
Rest of World	337	209
World total	4542	2823

provides detailed information on the specific lengths of hydrogen pipelines in different regions, based on statistics available as of the end of 2016. These figures offer a quantitative reference for the development trajectory of the hydrogen energy sector. The primary owners of major hydrogen pipelines are Liquefied Gas Companies and Air Products, with respective pipeline lengths of approximately 1936 km and 1140 km. Detailed data can be found in

Table 2. Hydrogen Pipelines of Different Global Companies.

Companies	Pipeline Length
	km	Miles
Air Liquide	1936	1203
Air Products	1140	708
Linde	244	152
Praxair	739	459
Others	483	300
World total	4542	2823

.

2.2. Theoretical Analysis of Distribution in Mixed Gas Systems at Rest

From the perspective of the second law of thermodynamics, the process of non-uniform concentration distribution of gases in a pipeline from a fully mixed state is a process of entropy reduction and does not occur spontaneously. However, in reality, the gases in the pipeline are not ideal gases and are affected by the gravitational field. Due to the differences in molecular weights of the components in the gas mixture, a concentration gradient can develop in the vertical direction. The existence of the thin upper atmosphere on Earth serves as proof of this possibility.

To study the macroscopic motion of a large number of particles, Boltzmann proposed the highly influential principle of equiprobability, which forms the foundation of classical statistical mechanics. This principle asserts that when an isolated system reaches equilibrium, all possible microscopic states occur with equal probability. Therefore, we can derive the most probable distribution at the microscopic level—the Maxwell–Boltzmann distribution.

For typical building heights near the Earth’s surface, it is assumed that the temperature remains constant at room temperature (25 °C or 298 K). Taking a mixture of 20% hydrogen and 80% methane as an example, the concentration ratio of the two gases along height variations is shown in

Table 3. The concentration variation in the hydrogen and methane mixture at different heights.

Height (m)	H2/CH4	H2 Percentage	CH4 Percentage
0	0.2500	20.00%	80.00%
30	0.2504	20.03%	79.97%
60	0.2508	20.05%	79.95%
90	0.2513	20.08%	79.92%
120	0.2517	20.11%	79.89%
1000	0.2642	20.90%	79.10%

.

As seen in the table, with the increase in height, the proportion of the lighter H₂ in the mixed gas increases, while the volumetric fraction of the heavier gas, CH₄, decreases. Within typical building heights, the change in the concentration ratio of the mixed gas is less than 1%. Specifically, even for a mixed gas column at a height of 1 km, the change in the concentration ratio of the components is only about 1%. Scholars who have studied these issues have all adopted the aforementioned derivations. V.V. Azatyan et al. [33] studied the gravitational stratification possibility of a propane-hydrogen mixture, concluding that the gravity distribution of the gases follows the Boltzmann distribution. Based on this, they derived the variation in the concentration ratio of hydrogen and propane with height, noting that under static conditions at a height of 15 m, the change in the concentration ratio was less than 0.2%. If natural convection is considered, the difference becomes even smaller.

It is widely believed that gas stratification occurs in areas with little flow, such as caves and sewers filled with CO₂ in nature. Badino G [34] provided mathematical analysis and theoretical derivation of the behavior of such gases in confined conditions, suggesting that the stratification of underground gas layers with specific components is not due to gravity, but rather because there is no air movement around the gas source. Stratification does occur, but it requires a static air column several kilometers high to have an effect. The occurrence of stratification in nature is not due to density differences, but because these gases are constantly generated in caves and diffuse very slowly, leading to localized concentration at certain heights. In high-altitude non-homogeneous layers, where the temperature remains constant, there is a tendency for gas stratification. In higher layers, components with smaller molar masses have higher concentrations, and when the height is sufficiently high, the components with larger molar masses may even disappear, though this occurs at altitudes of tens of kilometers.

3. Numerical Simulation Methodology

Due to the complexity of the gas mixing process, it is difficult to measure the concentration changes at various points. CFD (Computational Fluid Dynamics) simulation has become a promising approach to address this issue. Some scholars argue that due to the influence of gravity, when gases with different densities are mixed, concentration non-uniformity occurs. Other scholars, however, adhering to the theory of molecular thermal motion, believe that stratification is unlikely to occur on a small scale. These issues can be explored, observed, and studied using advanced and mature CFD tools, while small-scale experiments can be conducted for validation. However, it should be noted that since CFD software does not operate at the molecular scale, the simulation results tend to be more conservative.

3.1. Governing Equations

Considering gas compressibility, the unsteady Reynolds-Averaged Navier–Stokes (RANS) equations are employed to solve the mixing process of hydrogen and natural gas in high-pressure pipelines [35]. The Boussinesq eddy-viscosity approach establishes the relationship between Reynolds stresses and mean velocity gradients [36]:

$${ \tau }_{ij}=-\rho v_{m, i}^{, }{v}_{m, j }^{, }=2{\mu }_t{S}_{ij}-{\displaystyle \frac{2}{3}}\rho k{\delta }_{ij}$$

(1)

where

$${\mu }_t=C_{\mu }\rho {\displaystyle \frac{k^2}{\epsilon }},S_{ij}={\displaystyle \frac{1}{2}}\left({\displaystyle \frac{\partial v_{m, i}}{\partial x_j}}+{\displaystyle \frac{\partial v_{m, j}}{\partial x_i}}\right)$$

where τ_ij is Reynolds stress, Pa, i and j is coordinate component indices (I, j = 1, 2, 3), k and ε represent turbulent kinetic energy and turbulent energy dissipation rate, respectively, S_ij is strain, μ_t is the eddy viscosity coefficient, C_μ is the empirical constant, C_μ = 0.09, δ_ij is kronecker delta, v_m is mixture gas velocity, m/s, ρ is the gas density, kg/m³.

Studies indicate that the Reynolds Stress model is suitable for three-dimensional complex flows but exhibits poor convergence and requires greater computational time and memory. The Standard k-ε turbulence model yields distorted results when applied to curved surface flows. Both Realizable and RNG k-ε models address this limitation; however, compared to RNG, the Realizable k-ε turbulence model demonstrates broader applicability in non-separated flow problems with superior convergence and lower computational costs [37,38]. The realizable k-ε turbulence model closes the governing equations, including:

$${\displaystyle \frac{\partial {\rho }_{m}k}{\partial t}}+{\displaystyle \frac{\partial {\rho }_m{v}_{m, j}k}{\partial x_j}}={\tau }_{ij}{\displaystyle \frac{\partial v_{m, j}}{\partial x_j}}+{\displaystyle \frac{\partial }{\partial x_j}}\left[\left({\mu }_m+{ \mu }_t\right){\displaystyle \frac{\partial k}{\partial x_j}}\right]-{\rho }_m\epsilon$$

(2)

$${\displaystyle \frac{\partial {\rho }_m\epsilon }{\partial t}}+{\displaystyle \frac{\partial {\rho }_m{v}_{m, j}\epsilon }{\partial x_j}}=C_{\epsilon 1}{\tau }_{ij}{\displaystyle \frac{\epsilon \partial v_{m, j}}{k\partial x_j}}+{\displaystyle \frac{\partial }{\partial x_j}}\left[\left({\mu }_m+{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\right){\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right]+C_{\epsilon 2}{\displaystyle \frac{{\rho }_{m{\epsilon }^2}}{k}}$$

(3)

where t is time, s, ρ_m is the density of the mixed gas, kg/m³, μ_m is the dynamic viscosity of the mixed gas, Pa∙s, σ_ε, C_ε1, C_ε2 are empirical constants, taken as σ_ε = 1.3, C_ε1 = 1.45, C_ε2 = 1.90.

For multiphase flow modeling: The VOF model requires distinct interfaces between fluids, rendering it unsuitable for hydrogen–natural gas mixing simulations. The Euler model entails excessive computational demands. Consequently, the Mixture model—applicable to homogeneous dispersed multiphase flows—is selected. The governing equations for hydrogen–natural gas stratification solved by the Mixture model are as follows [35]:

$${\displaystyle \frac{\partial \left({\rho }_m\right)}{\partial t}}+\nabla \cdot \left({\rho }_m{v}_m\right)=0$$

(4)

$$\begin{array}{c}{\displaystyle \frac{\partial \left({\rho }_m{v}_m\right)}{\partial t}}+\nabla ·\left({\rho }_m{v}_m\times v_m\right)=-\nabla p+\nabla ·\left[{\mu }_m\left(\nabla v_m+\nabla v_m^T\right)\right]\\ +{\rho }_{m}g+\nabla ·\left({\displaystyle \sum _{k=1}^N}{\alpha }_k{\rho }_k{v}_{dr,k}\times v_{dr,k}\right) \end{array}$$

(5)

where

$${\rho }_m={\sum }_{k=1}^N{\alpha }_k{\rho }_k,v_m={\sum }_{k=1}^N{\alpha }_k{\rho }_k{v}_{dr,k}/{\rho }_m,v_{dr,k}=v_k-v_m,$$

$$\nabla ={\displaystyle \frac{\partial i}{\partial x}}+{\displaystyle \frac{\partial j}{\partial x}}+{\displaystyle \frac{\partial k}{\partial x}},{\mu }_m=\sum _{k=1}^N{\alpha }_k{\mu }_k$$

where ρ_k is the k-th phase density, kg/m³; V_m and V_k are the average velocity of the mixture and the velocity of the k-th phase, respectively, m/s; α_k is the volume fraction of the k-th phase (H₂ and natural gas); N is the number of phases; μ_k is the k-th phase dynamic viscosity, Pa∙s; dr, V_k is the drift velocity, m/s; P is static pressure, Pa; g is gravitational acceleration, m/s².

3.2. Problem Description and Grid Generation

The computational domain used in the simulation is a horizontal pipeline with a length of 30 m and a diameter of 500 mm. Three monitoring points are set along the pipe axis: P1 (0, 0245, 15), P2 (0, 0, 15), and P3 (0, −0245, 15) to monitor the hydrogen concentration distribution along the pipeline. The geometric diagram is shown in Figure 1.

During the long-distance transportation of natural gas through pipelines, complex terrain conditions, such as mountains and rivers, may be encountered. This chapter focuses on the study of static stratification in undulating natural gas pipelines that may be encountered in actual field conditions. The two-dimensional model of the undulating pipeline used in this study is shown in Figure 2.

Static stratification simulations in horizontal pipelines investigate the effects of internal pressure and initial hydrogen concentration (volume fraction, φ_H2,I) on hydrogen-natural gas mixtures, determining whether stratification occurs and quantifying its patterns. Simulations in undulating pipelines conduct sensitivity analyses of hydrogen concentration, elevation difference (H), top span length (L₂), and number of spans (n) to establish stratification patterns in undulating pipelines. Detailed simulation conditions are listed in

Table 4. Simulation parameters.

Pipeline Type	Internal Pressure (MPa)	φH2,I (%)	H (m)	L2	n
Horizontal pipeline	3	3, 5, 10, 50	-	-	-
	5	3, 5, 10, 50	-	-	-
	8	3, 5, 10, 50	-	-	-
Undulating pipeline	8	3	10, 30, 50	10	1
	8	10	10	5	3, 5
	8	10	10	10, 50, 100	1

.

Structured meshing was applied to the geometric models shown in Figure 1 and Figure 2, as illustrated in Figure 3 and Figure 4, with local refinement implemented at bends of the undulating pipeline. All boundaries were set as stationary walls with the no-slip condition. A grid independence study was conducted to eliminate the influence of mesh density on simulation results. For an internal pressure of 8 MPa and 3% hydrogen concentration, stabilized hydrogen concentrations for models with different mesh counts are presented in

Table 5. Grid independence verification.

Pipeline Type	Mesh Count	P1 Stabilized Hydrogen Concentration (%)	Variation Rate (%)
Horizontal pipeline	75,462	3.56	-
	254,566	3.70	3.93
	446,213	3.72	0.54
Undulating pipeline	101,245	3.63	-
	405,612	3.74	3.03
	620,145	3.75	0.27

. The data demonstrate that for static stratification in horizontal pipelines, hydrogen concentration stabilizes when the mesh count exceeds 250,000. Balancing computational accuracy and efficiency, the mesh count was set to 254,566. For static stratification in undulating pipelines, hydrogen concentration remains nearly constant above 400,000 elements. Considering computational precision and efficiency, the mesh count was set to 405,612.

3.3. Model Validation

At present, there are relatively few experimental studies on the stratification of H₂–methane mixed gas. Ren [39] injected methane into a sealed tank filled with air and observed vertical stratification of the gas mixture after static placement. Ren employed a sealed vessel (height: 0.33 m; diameter: 0.14 m). Initial internal pressure was 0.1 MPa. Following the partial pressure principle, a gas mixture was introduced to establish initial methane volume fractions of 5%, 10%, and 15%. Methane volume fractions at different locations were measured after an equilibration period. The numerical model was validated against these experimental data using identical operational parameters. As shown in Figure 5, simulated results demonstrate good agreement with experimental measurements. The simulated concentrations were overestimated as only gravitational effects were considered without accounting for thermal molecular motion, but a maximum deviation of 4.75% was observed between simulated and experimental values. Computational results demonstrate good agreement with experimental data. The numerical simulation methodology employed in this study accurately captures the dynamic process of gas stratification. This confirms the model’s capability to effectively simulate mixing-diffusion and stratification processes in H₂-blending natural gas systems.

4. Study on the Static Concentration Distribution Pattern of Medium in Horizontal Pipelines

4.1. Static Stratification in a Horizontal Pipe at 3 MPa Internal Pressure

Based on the above numerical model, a simulation analysis of stratification in a hydrogen-blended pipeline under static conditions was conducted. The simulation conditions included internal pipe pressures of 3 MPa, with an internal pipe temperature of 300 K. The stratification phenomenon in horizontal pipes was compared for different hydrogen concentrations in natural gas, specifically 3%, 5%, 10%, and 50%.

Figure 6 shows the variation of hydrogen concentration along the vertical line at different time intervals (t = 400 s, 800 s, 1200 s, 1600 s, 2000 s, 4000 s, 6000 s, 10,000 s, 2000 s) in horizontal pipes with different initial hydrogen concentrations. It is evident that as time progresses, the hydrogen concentration at the top of the pipeline increases, while the concentration at the bottom decreases. At t = 2000 s, the rate of increase in hydrogen concentration accelerates, and around t = 10,000 s, the hydrogen concentration reaches a stable value. Figure 7 presents the variation of hydrogen concentration over time at the z = 15 m cross-section in horizontal pipes with different initial hydrogen concentrations.

Table 6. Static stratification results for the horizontal pipe at 3 MPa internal pressure.

Internal Pressure (MPa)	φH2, I (%)	φH2, max (%)	Stabilization Time (s)
3	3	3.33	10,000
	5	5.43	10,000
	10	10.73	10,000
	50	50.90	10,000

displays the static stratification results for the horizontal pipe at 3 MPa internal pressure. As the hydrogen blending ratio increases, the percentage increase in hydrogen concentration at the top of the pipe after stabilization becomes smaller. The final stabilization time shows no significant change, fluctuating around t = 10,000 s, and exhibits minimal influence from the initial concentration.

4.2. Static Stratification in Horizontal Pipes at 5 MPa and 8 MPa Internal Pressures

As the variation of hydrogen concentration along the vertical line and the variation pattern of hydrogen concentration over time at the z = 15 m cross-section in horizontal pipes exhibit consistent patterns across different pressures and hydrogen concentrations, additional figures are not provided. Figure 6 and Figure 7 can be referred to.

Table 7. Static stratification results in horizontal pipelines at 5 MPa and 8 MPa internal pressures.

Internal Pressure (MPa)	φH2,I (%)	φH2,max (%)	Stabilization Time (s)
5	3	3.50	10,000
	5	5.70	10,000
	10	11.07	10,000
	50	51.18	10,000
8	3	3.70	10,000
	5	5.73	10,000
	10	11.54	10,000
	50	51.6	10,000

presents the static stratification results for horizontal pipes at 5 MPa and 8 MPa internal pressures. With increasing pressure, the final stabilized concentration shows a slight increase. That is because increased pressure enlarges the density difference between hydrogen and methane, intensifying the gravity-driven segregation phenomenon. Additionally, hydrogen’s partial molar volume advantage becomes more pronounced under high pressure, promoting its migration towards the top.

The final stabilization time exhibits no significant change, occurring at approximately t = 10,000 s, and is minimally affected by the initial concentration and internal pressure. Although increased pressure reduces the diffusion coefficient, potentially prolonging the time to reach equilibrium, the enhanced natural convection due to the larger density difference under high pressure accelerates the upward movement of hydrogen and downward movement of methane, promoting segregation and shortening the equilibrium time. These two effects counteract each other, resulting in similar equilibrium times.

5. Study on the Static Concentration Distribution of Medium in Undulating Pipelines

5.1. Effect of Elevation Difference on Static Stratification in Undulating Pipelines

Based on the aforementioned numerical model, a simulation analysis of the stratification in undulating pipes was conducted. The simulation conditions are as follows:

Analysis was conducted using an elevation difference of 10 m. Figure 8 shows the hydrogen concentration distribution on the vertical cross-section of the undulating pipeline at nine time points: t = 1000 s, 2000 s, 4000 s, 10,000 s, 30,000 s, 50,000 s, 100,000 s, 150,000 s, and 280,000 s. The contour plot of hydrogen concentration along the longitudinal section reveals that hydrogen initially accumulates at the top of the undulating pipeline while decreasing gradually at the bottom over standing time. This occurs because gas molecules migrate downward under gravity, with molecular density decreasing exponentially with height, resulting in a non-uniform spatial distribution characterized by a sparse upper and dense lower profile. After 280,000 s (3.24 days), the hydrogen concentration at the pipeline top reaches 3.74%, representing a 24.6% increase from the initial state.

Figure 9 displays the hydrogen concentration at cross-sections of the upper and lower horizontal segments in the 10 m elevation difference pipeline. Within the first 10,000 s of standing, no stratification occurs between hydrogen and natural gas, with both gases distributed uniformly throughout the pipeline. As standing time increases further, the hydrogen concentration at the top gradually rises. Figure 10 presents concentration curves at monitoring points within the undulating pipeline. With prolonged standing time, concentration increases at the top monitoring point while decreasing at the bottom point. After 280,000 s (3.24 days), the maximum hydrogen concentration reaches 3.74% at the monitoring points.

Table 8. Static stratification simulation results for undulating pipelines with different elevation differences.

Internal Pressure (MPa)	L2 (m)	n	H (m)	φH2,I (%)	φH2,max
8	10	1	10	3	3.74%
			30		6.63%
			50		9.98%

shows simulation results for different elevation differences under a fixed top span length (L₂ = 10 m). The data indicate that when operational conditions and pipeline geometry remain unchanged, increasing the elevation difference leads to higher maximum hydrogen concentrations at the pipeline top after 3 days of standing—rising from 3.74% at 10 m to 9.98% at 50 m. This is because within the inclined sections of an undulating pipeline, shear-induced airflow moving upwards and downwards is formed due to the velocity difference between gas near the wall and at the center. An increase in the elevation difference intensifies this gas shearing effect, leading to more pronounced hydrogen concentration accumulation across the crown and thereby increasing the hydrogen concentration.

5.2. Effect of Top Span Length on Static Stratification in Undulating Pipelines

Analysis was conducted using a top span length of 50 m (Figure 11). Figure 12 shows the hydrogen concentration distribution on the vertical cross-section of the undulating pipeline at ten time points: t = 1000 s, 2000 s, 4000 s, 10,000 s, 30,000 s, 50,000 s, 100,000 s, 150,000 s, 200,000 s, and 280,000 s (top span length: 50 m). With increasing standing time, hydrogen concentration gradually rises at the pipeline top while decreasing at the bottom. Due to the density difference between methane and hydrogen molecules, molecular density decreases exponentially with height withFin the undulating pipeline, resulting in a non-uniform spatial distribution characterized by a sparse upper and dense lower profile. At t= 280,000 s (3.24 days), the hydrogen concentration at the pipeline top reaches 10.45%, representing a 0.45% increase from the initial state.

Figure 13 displays hydrogen concentration curves at monitoring points on cross-sections of the upper (points b, c) and lower (points a, d) horizontal segments (top span length: 50 m). Concentration increases over time at upper monitoring points but decreases at lower points, with the rate of concentration increase diminishing over time. The trend of hydrogen concentration change at point a is consistent with that at point d. After 280,000 s (3.24 days), the maximum hydrogen concentration (10.45%) occurs at upper monitoring points (Figure 14).

Under the condition of constant internal pressure and initial hydrogen concentration, as the top span length (L₂) increases, the maximum hydrogen concentration at the top of the undulating pipe tends to decrease after 3 days of settling, from 10.65% at a span length of 10 m to 10.38% at 100 m (

Table 9. Comparison of Simulation Results for Settling Stratification in Wavy pipelines with Different L₂.

Internal Pressure (MPa)	L2 (m)	n	H (m)	φH2,I (%)	φH2,max
8 MPa	10 m	1	10 m	10	10.65%
	50 m				10.45%
	100 m				10.38%

). A larger top span length in an undulating pipeline allows for more complete flow development, leading to reduced hydrogen concentration at the crown. Conversely, with a shorter top span length, disturbances induced by the inclined pipe sections do not fully dissipate before entering the opposing inclined section, resulting in a short residence time for disturbances and a more rapid initiation of gravity-driven stratification. In configurations with a larger top span length, disturbances generated by the inclined sections persist longer within the top pipe section or may even dissipate there, inducing more vigorous fluid disturbances. This increases the degree of gas mixing and consequently lowers the hydrogen concentration at the crown.

5.3. Effect of Number of Spans on Static Stratification in Undulating Pipelines

An analysis was conducted for n = 3 spans (Figure 15). Figure 16 shows hydrogen concentration on the vertical cross-section at ten time points: t = 1000 s, 2000 s, 4000 s, 10,000 s, 30,000 s, 50,000 s, 100,000 s, 150,000 s, 200,000 s, and 280,000 s (n = 3). Under gravity, molecules accumulate downward with molecular density decreasing exponentially with height. Since methane molecules exhibit higher density than hydrogen molecules, this results in a non-uniform spatial distribution characterized by a sparse upper and dense lower profile. At t = 280,000 s (3.24 days), hydrogen concentration at the top reaches 10.8%, representing a 0.8% increase from the initial state.

As shown in Figure 17, the hydrogen accumulation rate progressively decreases with standing time. After 280,000 s (3.24 days), the maximum hydrogen concentration at monitoring points reaches 10.65% (Figure 18).

When operational pressure and initial hydrogen concentration remain constant, the maximum hydrogen concentration at the top of the undulating pipeline exhibits a decreasing trend with an increasing number of spans after 3 days of standing (

Table 10. Comparison of Settling Stratification Simulation Results for Different Numbers of Spans.

Internal Pressure (MPa)	L2 (m)	n	H (m)	φH2,I	φH2,max
8 MPa	5 m	3	10 m	10%	10.8%
		5			10.78%

).

The gas mixture within the undulating pipeline does not reach a steady state even after 72 h of standing. Compared to horizontal pipelines, the stratification process requires significantly longer time. After 72 h, the maximum hydrogen concentration accumulated at the pipeline top increases with larger elevation differences but decreases with greater top span lengths or higher numbers of spans. However, the maximum hydrogen concentration remains close to the initial concentration, indicating insignificant stratification.

6. Conclusions

Computational fluid dynamics (CFD) models were developed to systematically analyze the flow dynamics and spatial distribution patterns of methane–hydrogen mixtures in both horizontal and undulating pipeline configurations. The simulations elucidate the coupled effects of hydrogen blending ratio and operational pressure on mixture stratification in horizontal pipelines, while further investigating the multifactorial interplay of blending ratio, pressure gradients, and elevation differentials in undulating pipeline systems. Key findings are summarized as follows:

(1)

In horizontal hydrogen-blended natural gas pipelines, progressive pressurization (from 3 MPa to 8 MPa) induced a transient stabilization phase, beyond which the equilibrium hydrogen concentration exhibited negligible deviation from the initial blending ratio.

(2)

In undulating pipelines, hydrogen concentration evolution at pipeline crests after a 72 h stagnation period exhibited the following patterns:

(i)

The data indicate that when operational conditions and pipeline geometry remain unchanged, increasing the elevation difference leads to higher maximum hydrogen concentrations at the pipeline top after 3 days of standing—rising from 3.74% at 10 m to 9.98% at 50 m.

(ii)

Under constant operational pressure and initial hydrogen concentration, the maximum hydrogen concentration exhibited a decreasing trend with increased crest span length. However, the peak concentration remained proximate to the initial value, indicating homogeneous methane–hydrogen mixing.

(iii)

Under fixed operational pressure and initial hydrogen concentration, the maximum hydrogen concentration remained proximal to the initial value with increasing span count, demonstrating enhanced homogeneity in methane–hydrogen mixtures.