
==== Front
ACS Omega
ACS Omega
ao
acsodf
ACS Omega
2470-1343
American Chemical Society

10.1021/acsomega.4c06414
Article
Analysis of Leakage and Diffusion Characteristics and Hazard Range Determination of Buried Hydrogen-Blended Natural Gas Pipeline Based on CFD
https://orcid.org/0000-0002-2810-7112
Bu Fanxi *†
He Yuheng †
Lu Qingxiu †
Liu Ming ‡
Bai Jinyu †
Lv Zhuoran †
Leng Chunmiao †
† Key Laboratory for Enhanced Oil and Gas Recovery of the Ministry of Education, Northeast Petroleum University, Daqing, Heilongjiang 163318, China
‡ Daqing Petrochemical Engineering Co. Ltd., Daqing Heilongjiang 163711, China
* Email: bufanxi_nepu@163.com.
06 09 2024
17 09 2024
9 37 3920239218
11 07 2024
30 08 2024
27 08 2024
© 2024 The Authors. Published by American Chemical Society
2024
The Authors
https://creativecommons.org/licenses/by-nc-nd/4.0/ Permits non-commercial access and re-use, provided that author attribution and integrity are maintained; but does not permit creation of adaptations or other derivative works (https://creativecommons.org/licenses/by-nc-nd/4.0/).

Injecting hydrogen into natural gas pipelines is an economical and efficient method of hydrogen transportation. However, the addition of hydrogen leads to significant hydrogen corrosion and embrittlement in the pipelines, especially in harsh and concealed underground conditions, where leak accidents are frequent and difficult to detect. This Article uses Le Chatelier’s Principle to determine the hazardous range of hydrogen-blended natural gas (HBNG) by employing numerical simulation, it examines the gas leakage and diffusion characteristics before and after hydrogen injection as well as under different hydrogen blending ratio (HBR). Additionally, considering the density of the mixed gas, a prediction model for the diffusion hazard range of hydrogen-mixed natural gas is established based on multivariate regression theory. The results show that after a leakage occurs in HBNG the diffusion range in soil is wider compared to methane, with higher corresponding pressure and velocity values. Moreover, as the HBR increases, the farthest danger range (FDR) of the HBNG also increases. When the leakage of the buried HBNG pipeline occurs for 1 min, the difference in FDR between HBR 25% and HBR 5% is 0.005 m. After 30 min, this difference increases to 0.019 m, indicating that with longer leakage duration, the potential explosion risk resulting from increased HBR becomes greater. Factors such as pipeline pressure increase, larger leak hole size, and decreased burial depth all contribute to an increase in FDR, with pipeline pressure change having the greatest impact and burial depth change having the smallest impact. The maximum error of the predicted model for the diffusion hazard range of hydrogen-mixed natural gas is 9.385%, and the average error is 2.376%, demonstrating the accuracy of the prediction results. This study provides guidance for monitoring underground hydrogen-blended natural gas pipeline leaks, offers a basis for determining the repair range of pipelines, and ensures the safe transportation of hydrogen-mixed natural gas pipelines.

Key Research and Development Program of Heilongjiang 10.13039/100017366 JD22A004 Guiding Innovation Fund of Heilongjiang Provincial Undergraduate Universities NA 2023YDL-04 Northeast Petroleum University 10.13039/501100009407 2022KQ05 National Natural Science Foundation of China 10.13039/501100001809 52074090 document-id-old-9ao4c06414
document-id-new-14ao4c06414
ccc-price
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pmc1 Introduction

With the exacerbation of global greenhouse effect, the environmental issues brought about by traditional fossil fuels have garnered increasing attention.1 To meet the development plans for green and low-carbon initiatives, and to reduce carbon emissions from fuel, many countries have been pursuing reliable and stable clean energy sources.2,3 Many clean energy sources are influenced by geographical factors such as solar energy and tidal energy. This leads to significant fluctuations in the stability and sustainability of the energy supply. In contrast, hydrogen energy can provide a sustainable and stable energy supply, with the added benefits of zero emissions, renewability, and wide availability.4,5 It has been acclaimed as “the most promising clean energy source of the 21st century”.6

The transportation and storage of hydrogen is still one of the main reasons limiting the development of hydrogen energy.7,8 Currently, hydrogen is mainly transported in liquid and gaseous form. Among them, hydrogen loss in gaseous transportation is smaller. For example, in the case of tube trailer transportation, the compression cost consumed is only 40% of that of liquid hydrogen transportation.9 Yin et al.10 studied the current development status of hydrogen storage and transportation, they believed that traditional hydrogen storage and transportation methods are inefficient and costly. The pipeline transportation through HBNG is a necessary condition for the large-scale and widespread utilization of hydrogen energy.

HBNG has broader application prospects than natural gas,11 but it also poses greater safety risks. Hydrogen, being the lightest element in terms of relative atomic mass, has a higher escape velocity compared with natural gas. After blending hydrogen gas into methane, the new mixture has a lower density compared to pure methane, this density difference results in greater leakage flow rate in HBNG pipelines.12 During pipeline operation, hydrogen embrittlement can occur when many materials come into contact with hydrogen, the phenomenon of hydrogen embrittlement can lead to changes in the toughness and load-bearing capacity of pipeline materials, increasing the risk of pipeline rupture.13,14 According to relevant statistics, pipeline failures are one of the common causes of safety incidents in hydrogen energy systems among 120 hydrogen-related accidents that occurred from 1999 to 2019. In order to avoid dangerous accidents in hydrogen energy transportation pipelines, it is essential to strengthen pipeline safety research.15

Pipeline leakage is one of the common causes of pipeline accidents and has always attracted attention from scholars around the world. Using high-pressure gas cylinders as a gas source and deploying sensors to monitor gas leakage are common methods for simulating pipeline leaks. Zhu et al.16 used a mixed hydrogen-natural gas steel cylinder as the gas supply system for underground gas pipelines and placed methane concentration monitors and hydrogen concentration monitors in the soil. Explored the impact of different leak directions, HBR, and pipeline pressure on the leakage of medium- and high-pressure HBNG pipelines through experiments. They found that the diffusion distance of HBNG along the three o’clock direction from the leak was greater than that along the 12 o’clock direction. Stefano et al.17 studied the leakage of hydrogen gas in a small enclosed space. Discovering that due to the significantly lower density of hydrogen compared to air, a difference in density leads to the formation of different concentration layers of hydrogen and air within an enclosed space, and when hydrogen gas collides with obstacles in the space, it loses some energy, resulting in an increase in the final time required for uniformization. Houssin-Agbomson et al.18 conducted experiments by setting the size of the leak in a high-pressure buried pipeline to 12 mm to study the impact of pipeline leaks on the ground surface. They compared the leakage of methane and hydrogen gas and found that the formation of volcanic vents was unrelated to the type of gas but had a significant correlation with the pipeline pressure and leak direction. The higher the pressure and vertically upward the leak direction, the greater the probability of forming volcanic vents. Bonnaud et al.19 further studied the ground vents formed by pipeline leaks, considering the influence of soil moisture content, and found that a lower soil water content is more conducive to the formation of a crater at the leak site. Kobayashi et al.20 conducted low-temperature compressed hydrogen gas leakage diffusion experiments under different leakage apertures. The experimental setup had a hydrogen gas pressure of 90 MPa, a flow rate of 100 kg/h, and temperatures ranging from 50 to 300 K. The experiment shows that the hydrogen leakage flow rate increases with the decrease of supply temperature. Daniel et al.21 studied the risk of flashback in HBNG burners and found a significant risk of flashback when the HBR exceeded 34.7%. They suggested that the HBR in the gas should not exceed 30% while equipment reliability was ensured and user safety. Zhao et al.22 further discussed the risk of flashback limit in HBNG, continuously increasing the proportion of hydrogen in the gas mixture. It was found that the flashback limit of the HBR is 25%.

In recent years, with the development of computational fluid dynamics, many scholars have used numerical simulations as a research method to analyze pipeline leakage situations. Zeng et al.23 according to the numerical simulation results, the diffusion of parallel buried gas pipelines in tunnel airspaces can be divided into three stages: the initial leakage stage, the diffusion stage, and the stable stage. After entering the diffusion stable stage, natural gas exhibits a clear concentration stratification within the tunnel. Shao et al.24 established a three-dimensional model based on actual public engineering tunnels to simulate the different leakage scenarios of CH4 and H2 after small hole leakage occurs in the tunnel. Study found that the diffusion rate and concentration of H2 were faster. Bu et al.25 analyzed the leakage and diffusion of methane in public engineering tunnels through numerical simulations, and found that the ventilation effect is good when the ventilation frequency is higher than 15 times/h, at this time, the concentration of methane at different monitoring points in the tunnel is below the lower explosive limit. Wang et al.26 considered the interaction between CH4 and H2 and proposed an improved nonideal multicomponent mixture diffusion model. This model was used to simulate the leakage of HBNG in tunnels under different ventilation conditions. The study showed that the addition of hydrogen would accelerate the leakage rate of the leaking gas in the tunnel. Bezaatpour et al.27 considered the influence of soil anisotropy on buried pipeline leakage accidents. Based on collected data on soil mechanical and hydraulic properties in reality, they established a buried gas pipeline model with anisotropic soil. The study found that the velocity of the leaked gas was mainly affected by the mechanical and hydraulic properties of the soil and the direction of gas diffusion was mainly influenced by the slope of the soil. Liu et al.28 obtained an empirical leakage rate estimation model for air in the soil through buried pipeline experiments, which was verified and corrected through numerical simulations. The error of this model was −2.2% to −1.1%. They further established a diffusion model for methane in the soil, with leakage rate error and diffusion concentration error both less than 7.2% and 15%, respectively, validating the reliability of the model. Moghadam et al.29 simulated the leakage of natural gas pipelines by establishing a stable, compressible turbulent computational equation. The study showed that after a leakage occurred in a buried pipeline, subsonic flow would appear near the leakage point due to soil resistance. The study showed that after a leakage occurred in a buried pipeline, subsonic flow would appear near the leakage point due to soil resistance. In general, gas diffusivities increase with pressure.30 Nagase et al.31 studied the leakage of high-pressure hydrogen pipelines through numerical simulation, considering the effect of pipeline valve closure during accidents. They proposed a predictive model for the distribution of the mass flow rate and pressure drop inside the pipeline. During a long pipe leakage process, this model matched well with the flow characteristics obtained from numerical simulations. Bu et al.32 studied the leakage of buried gas pipelines and simulated different operating conditions such as pipeline burial depth, pipeline diameter and soil type. They defined the FDR, which refers to the farthest dangerous range of methane in the soil after pipeline leakage occurs and established a predictive model for the hazardous boundary after natural gas pipeline leakage. Zhang et al.33 studied the leakage of medium-pressure buried hydrogen pipelines and conducted numerical simulations under different soil, pressure, and soil type conditions. They performed multivariate fitting of pipeline pressure, leakage orifice size, soil resistance coefficient, and ground hazard radius, obtaining a time-varying nonlinear fitting equation. Wang et al.34 considered the heat exchange between the gas inside the pipeline and the external environment, and improved the leakage model of nonadiabatic pipelines. They simulated pipeline leaks with different heat transfer coefficients, HBR, and pipeline pressures and found that the temperature change of the gas inside the pipeline is mainly determined by the heat transfer coefficient of the pipeline. Sun et al.35 conducted a numerical simulation to study the leakage of natural gas under different wind speeds and hydrogen blending concentration. They discussed the diffusion height, horizontal dispersion width, and horizontal dispersion distance of hydrogen and methane and designed monitoring probe layout schemes based on gas diffusion simulation results and the explosion limits of hydrogen and methane.

Previous studies have extensively researched the operational safety analysis of buried gas pipelines. However, there is limited research on buried HBNG pipelines, especially regarding the leakage and diffusion characteristics of HBNG in soil after leakage occurs. The leakage volume of buried gas pipelines is estimated to be 75–85% of that of overhead pipelines.36 Leakage incidents in buried pipelines are less easily detected. Furthermore, the introduction of hydrogen gas exacerbates the embrittling effect on the pipeline, thereby increasing the leakage risk of buried HBNG pipelines compared with traditional buried natural gas pipelines.

This paper presents a 3D model for the leakage and dispersion of buried HBNG pipelines in soil. The Le Chatelier’s Principle is used to determine the explosion limits of HBNG, and the influence of mixed gas density changes on the leakage process is considered. The study investigates the leakage and diffusion characteristics of buried HBNG pipelines in soil under different HBR, pipeline operating pressures, pipeline burial depths, and pipeline leakage port apertures. By using the least-squares method and multiple regression analysis, a predictive model for FDR based on the aforementioned variables is established. This model provides data support for determining the hazardous range after leakage of buried HBNG pipelines.

2 Method

2.1 Physical Model

For study of the leakage of buried HBNG pipeline in soil, a 3D physical model was established as shown in Figure 1a. In this model, a 5 m × 3 m × 2.5 m soil model is established with the center of the soil bottom as the origin of the coordinate axis. The distance between the center of the pipeline and the ground is 1.5 m. Ignoring the influence of the pipe wall, the diameter of the pipeline is 100 mm. The leakage port is located in the center of the pipeline, with a diameter of 20 mm. The leakage direction is vertical to the ground and upward.

Figure 1 Model diagram: (a) Schematic diagram of the physical model. (b) Schematic diagram of Test points and line.

For better understanding the leakage of the buried HBNG pipeline in the soil, 8 monitoring points are set in the soil as shown in Table 1. At the same time, in order to explore the change of FDR, a monitoring line is set along the pipeline direction at the leakage port, as shown in Figure 1b.

Table 1 Test Point Numbers and Locations

No.	coordinate	No.	coordinate	
A	(0,1.2,0)	P3	(1,0.5,0)	
B	(0,2,0)	P4	(0,1.5,0)	
P1	(0,0.5,0)	P5	(0,1.5,–1)	
P2	(0,0.5,–1)	P6	(1,1.5,0)	

2.2 Mathematical Modeling

To simplify the model and reduce the computational workload, the following series of assumptions were made:(1) Soil is an isotropic, homogeneous, porous medium.

(2) The internal pores of the soil are filled with dry air, irrespective of the effect of moisture in the soil.

(3) No change in pipeline pressure during leakage.

(4) The leakage gas is an ideal gas.

(5) Leaking gases do not react with air in the soil.

Based on the above assumptions, the mathematical equations required for this simulation include the mass continuity equation, the momentum conservation equation, the gas mixture density equation, the component transport equation, the turbulence model, the soil leakage model, and the equations.(1) Continuity conservation equation:371

In the formula, the φ is the soil porosity; ρ is the density of mixed gas (kg/m 3); t is the time (s),vi is the velocity of mixed gas in different directions (m/s), i = x,y,z.

(2) Momentum conservation equation:382

In the formula, the φ is the soil porosity; ρ is the density of mixed gas (kg/m3); vi is the velocity of mixed gas in different directions (m/s), i = x, y, z; p is the gas pressure (Pa); μ is the dynamic viscosity of gas (Pa·s), Si is the source term, i = x, y, z.

(3) The density equation for the gas mixture:3

In the formula, the ω is the mass fraction of the leaking gas component; η is the hydrogen mixing ratio; p is the gas leakage diffusion pressure (Pa); Ma is the relative molecular mass of air; Mc is the relative molecular mass of methane; Mh is the relative molecular mass of hydrogen.

When ω = 1, ρ is the leakage gas density4

(4) Species transport equation:395

In the formula, ω is the mass fraction of the leaking gas component; D is the diffusion coefficient (m2/s).

(5) Due to the high gas pressure inside the pipe, the gas velocity at the leak point is high. The standard k – ε equation model40 was used to solve the turbulent equation, which can well describe the turbulent flow near the leak point.6

7

In the formula, k is the turbulent kinetic energy (J); μ is the dynamic viscosity of gas (Pa·s); μt is turbulent viscosity (Pa·s); ε is the turbulent dissipation rate; the prk and prε are the turbulent Prandtl numbers of the k equation and ε equation, respectively; the Gk represents the production term of turbulent kinetic energy K due to the mean velocity gradient; C1ε and C2ε are empirical constants.

(6) Soil leakage modeling and equations:

Set the air volume fraction in the soil fluid domain as 100%, the initial relative pressure as 0 MPa, and the soil temperature as 300 k. Assume that the soil is isotropic porous medium and the viscous resistance coefficient of different types of soil (1/α) and inertial drag coefficient,41 as in eqs 8 and 9 shown; three soil characteristics39 are shown in Table 2.8

9

In the formula, the Dp is the average diameter of soil particles

Table 2 Characteristics of the Soils

soil type	particle diameter Dp (mm)	porosity φ	viscous resistance 1/α (1/m2)	inertial resistance C2 (1/m)	
clay	0.01	0.3	2.72e+13	9.07e+5	
loam	0.05	0.43	2.45e+11	5.02e+5	
sandy	0.5	0.25	2.16e+10	3.36e+5	

2.3 Explosive Limits of Gas Mixtures

Determining the percentage of different gas components4210

where VC is the volume percentage of methane; VH is the percentage by volume of hydrogen; VT is the total percentage of the gas mixture.

Using Le Chatelier’s Principle43 to calculate the explosion limit of mixed gas:11

In the formula, LC and LH represent the explosion limits of methane and hydrogen, respectively, and Lm represents the explosion limit of the mixed gas.

2.4 Boundary Conditions

In this study, in the simulation parametrization of pipeline leakage, the energy equation is enabled, and the choice of k – ε equation model, considering the influence of gravity, the pressure velocity coupling is calculated by PISO algorithm; The time step is set as 0.1 s, and the maximum number of iterations for each time step is 200. The gas leakage within 1800 s of pipeline leakage is calculated. Set the pipe inlet as pressure inlet, the pipe outlet and the soil boundary as pressure outlet, and the leakage outlet as internal. The specific settings are shown in Table 3.

Table 3 Type of Boundary Conditions

boundary	type	parameter setting	
leakage hole	interior	 	
pipeline inlet	pressure inlet	gauge pressure, turbulence, species	
pipeline outlet	pressure outlet	gauge pressure, species	
pipe wall	wall	no slip, wall roughness	
soil boundaries	pressure outlet	gauge pressure, species	
soil zone	interior	 	

2.5 Case Parameter Setting

In this simulation, the control variable method is used to study the leakage of the buried HBNG pipeline in the soil. By changing HBR, pipeline pressure, pipeline burial depth, and other factors, the impact of the above variables on the leakage is explored. The specific working conditions are shown in Table 4.

Table 4 Case Conditions

scenario	HBR (%)	pressure (MPa)	buried depth (m)	leak size (m)	pinhole location	soil type	
1	0	0.4	1.5	0.02	top	loam	
2	5	0.4	1.5	0.02	top	loam	
3	10	0.4	1.5	0.02	top	loam	
4	15	0.4	1.5	0.02	top	loam	
5	20	0.4	1.5	0.02	top	loam	
6	25	0.4	1.5	0.02	top	loam	
7	15	0.01	1.5	0.02	top	loam	
8	15	0.1	1.5	0.02	top	loam	
9	15	0.2	1.5	0.02	top	loam	
10	15	0.3	1.5	0.02	top	loam	
11	15	0.4	0.3	0.02	top	loam	
12	15	0.4	0.6	0.02	top	loam	
13	15	0.4	0.9	0.02	top	loam	
14	15	0.4	1.2	0.02	top	loam	
15	15	0.4	1.5	0.01	top	loam	
16	15	0.4	1.5	0.015	top	loam	
17	15	0.4	1.5	0.025	top	loam	
18	15	0.4	1.5	0.03	top	loam	
19	15	0.4	1.5	0.02	bottom	loam	
20	15	0.4	1.5	0.02	side	loam	
21	15	0.4	1.5	0.02	top	sandy	
22	15	0.4	1.5	0.02	top	clay	

2.6 Validation of Mesh-Independent Solution

The number of mesh divisions significantly affects the computational workload and the accuracy of the simulation results, and the number of meshes should be reduced as much as possible under the premise of guaranteeing the calculation accuracy.

In this study, the physical model was partitioned using an unstructured mesh. During the mesh partitioning, the mesh was refined at the leak point of the pipeline and at the pipe wall, as shown in Figure 2. Using the physical model of Case 1 for mesh division, and the grid number of 372478, 573119, 776375, 1011271, 1220119 was obtained. The mesh mentioned above was used to simulate the leakage of an underground pipeline. The methane concentration changes at the monitoring point (0,1.4,0) within 30 s are shown in Figure 3. The curve variation indicates that, as the number of mesh divisions increases, the concentration values at monitoring points also rise. When the number of mesh is 372478, the relative error is 8.78% with the number of mesh 1220119, and when the number of mesh is not less than 776375, the relative error is reduced to less than 3%, it can be assumed that when the number of mesh divisions exceeds 776375, the effect of further increasing grid divisions on the calculation results is relatively small. While ensuring the accuracy of the computation results, efforts should be made to minimize computational workload; therefore, the mesh division scheme with 776375 mesh divisions will be employed for subsequent calculations.

Figure 2 Detailed information on mesh generation.

Figure 3 Mesh independence verification.

2.7 Validation of Mathematical Model

This study validates the reliability of the numerical simulation by comparing it with the experimental results of Zhu et al.16

According to the experimental settings,16 there are 12 cases in total, and this paper selects one set of settings for simulation. The soil area of the experiment is 4 m long, 4 m wide, and 1.8 m deep, the buried depth of the pipeline is 1.4 m, the diameter of the pipeline is 25 mm, the transmission pressure is 4 MPa, the gas transported in the pipeline is HBNG, its HBR is 10%, the diameter of the leakage port is 1 mm, the leakage direction is 12 o’clock, the vertical distance from the monitoring point to the leakage port is 0.5 m, and the horizontal distance is 2 m. Figure 4 shows the change in the methane concentration at the monitoring point after the leakage occurred. As shown in the figure, there are discrepancies between the experimental and simulated values during the leakage process. This could be attributed to the simplification of soil structure in the simulation settings. In the simulation, soil is assumed to be an isotropic and homogeneous porous medium, while real soils are often more complex. In addition, during the experiment, the leaked gas will also affect the soil structure, leading to changes in the experimental results. The maximum relative error obtained by comparing the simulated values with the experimental values is 18.7%, and the average relative error is 5.12%. It can be considered that the results obtained from this numerical model are reliable.

Figure 4 Model validation by experiment.

3 Results and Discussion

3.1 Comparison of Flow Fields before and after Natural Gas Blending with Hydrogen

This section compares the difference of pressure, speed, streamline, and leakage gas concentration between Case 1 (CH4) and Case 4 (HBNG, HBR = 15%) and discusses the influence of adding hydrogen into natural gas on leakage.

3.1.1 Pressure Field Comparison

Such as shown in Figure 5, the gas transported by the buried pipeline under the two working conditions is methane and natural gas with HBR of 15%. Under the same other conditions, the pressure time curve at monitoring points A and B after pipeline leakage. The curve indicates that the pressure values at both monitoring points rapidly increased after the pipeline leakage, reaches the peak at the fourth second, then drops slightly and gradually becomes stable. Comparing the pressure curves of different leaked gases, it can be found that the pressure change trend of the two is basically the same, but after the pressure value is stable, the pressure value of HBNG at detection point A is slightly higher than the pressure value after the methane leakage, and the pressure value at point B is close to the pressure value after the pure methane leakage.

Figure 5 Pressure variation of methane and HBNG at different monitoring points over time.

Thirty minutes after the leakage, the pressure cloud along the pipe axis slices for both conditions. As shown in Figure 6, the pressure gradient is distributed in an elliptical shape. The pressure in a small range at the leak can reach more than 40000 Pa, and the leakage pressure range above the pipeline is greater than that below the pipeline. In order to compare the differences between the two more clearly, the contour is magnified. Taking the 8000 Pa pressure contour line as an example, the intersection of methane and the Y axis is at Y = 1.22 m, while the 8000 Pa pressure contour line of HBNG has exceeded Y = 1.22 m. This is consistent with the law shown in Figure 5. After hydrogen gas is blended into natural gas, the pressure of the leaked gas in the soil will increase.

Figure 6 Pressure contours of methane and HBNG.

3.1.2 Velocity Field Contrast

As shown in Figure 7, the gas flow velocity at monitoring points A and B rapidly rises to the peak value within 3 s after the pipeline leakage occurs, then decreases slightly and then rises again, gradually becoming stable. Due to the different vertical distances between monitoring points A and B and the leakage port, the speed of different monitoring points varies greatly. The rising speed of the flow rate at monitoring point A is greater, and the stabilized flow rate is faster. Due to greater soil resistance at monitoring point B, the rising speed of the leakage gas flow rate after the pipeline leakage is gentle, and the stabilized flow rate is slower. By comparing the flow rate curves of different leaked gases after the leakage, it can be found that the rising trend of the two is roughly the same, but the peak flow velocity of the leaked gas and the stabilized flow velocity of HBNG at monitoring point A are slightly higher than the flow velocity of the gas after the leakage of pure methane, while the flow velocity curve of monitoring point B is similar to that of pure methane.

Figure 7 Velocity variation of methane and HBNG at different monitoring points over time.

Thirty minutes after the leakage of the pipeline, the velocity cloud of the two conditions sliced along the axis of the pipeline is shown in Figure 8. At a distance of 0.2 m from the ground, the air resistance near the ground is lower than the soil resistance in the geological strata, the range of 0.0001 m/s velocity contour line of leakage gas will be slightly expanded, and the gas will accelerate to escape from the soil to the air. For better comparison of the differences between the two conditions, the cloud map was magnified. Taking the 0.0008 m/s velocity contour line as an example, the 0.0008 m/s velocity contour line of pure methane intersected with 0.51 m of the X axis of the cloud map, while the intersection of the 0.0008 m/s velocity contour line of HBNG and the X axis of the cloud map significantly exceeded 0.51 m. This is consistent with the law shown in Figure 7. After hydrogen gas is blended into natural gas, it will cause an increase in the velocity of the leaked gas in the soil.

Figure 8 Velocity contours of methane and HBNG.

3.1.3 Comparison of Flowcharts

Thirty min after the leakage, the streamline distribution of methane and HBNG in the soil along the axial slice of the pipeline as shown in Figure 9. Because of the soil is isotropic porous medium, the streamline of leakage gas is evenly distributed in the soil, and the streamline in different horizontal directions is symmetrical about the leakage port. The leaked gas diffuses freely to the soil boundary in the soil, where the streamline is almost perpendicular to the soil boundary. By comparing the streamline maps of the two, the leakage velocity direction of methane and HBNG in the soil is the same, and the streamline distribution is similar, which indicates that the influence on the streamline distribution of leakage gas in the soil can be ignored after hydrogen is added to methane.

Figure 9 Gas streamlines distribution in the soil.

3.1.4 Concentration Comparison

In order to better analyze the leakage in different directions after pipeline leakage, this paper compares the concentration changes from monitoring point 1 to monitoring point 6 in Case 1 and Case 4, as shown in Figure 10. Taking Case 1 as an example, since monitoring point 4 is the closest to the pipeline leak, the concentration at monitoring point 4 rises the fastest, rising to the peak at 201 s when the leak occurs, and the concentration reaches 100%. Compared with monitoring point 1 directly below the leak, the concentration at monitoring point 1 rises slower than that at monitoring point 4. The concentration at monitoring point 1 rises to the peak at 734 s after the leak occurs, and the concentration reaches 100%. The concentration values at monitoring points 2, 3, 5, and 6 did not reach 100% within 30 min of leakage. Among them, the rising speed and concentration value of the leakage gas concentration at monitoring points 5 and 6 above the pipeline leakage outlet are greater than those at monitoring points 2 and 3. By comparing the monitoring points in different directions on the same horizontal plane, due to the isotropy of the soil, the gas concentration change at the radial monitoring point of the pipeline is consistent with that at the axial monitoring point of the pipeline. By comparing the concentration changes of methane and HBNG at the monitoring points, the gas concentration rise rate of HBNG at each monitoring point is greater than that of methane at each monitoring point, which indicates that the concentration diffusion rate of leaked gas in soil will be increased after adding hydrogen to natural gas.

Figure 10 Concentration contours of methane and HBNG at different monitoring points over time.

Figure 11 shows the comparison of the concentration cloud images of Case 1 and Case 4 sections along the pipeline axis, and the upper right part of the cloud image is enlarged. Compared with the two working conditions, the concentration diffusion range distribution is circular with the leakage mouth as the center, but the diffusion range of HBNG in the soil is wider. In the vertical direction, the 80% concentration contour line of HBNG has diffused to near the soil surface, while the methane is not close to the soil surface. In the horizontal direction, the 5% concentration contour line of HBNG has spread to 1.6 m away from the leak, but the methane has not yet reached. It indicates that the diffusion range of HBNG in soil is larger than that of methane after the leakage of buried pipeline.

Figure 11 Concentration contours of methane and HBNG.

3.2 Influence of Different HBR on the Diffusion Characteristics of HBNG in Soil

This section compares the pressure, velocity, diffusion range, and FDR of HBNG with different HBR in the soil after the leakage of buried pipelines and discusses the impact of different HBR on the leakage of HBNG in the soil.

3.2.1 Pressure Field Comparison

Figure 12 shows the pressure change curves at monitoring points A and B under different HBR. As shown, after the pipeline leakage occurs, the pressure values at the two monitoring points rise rapidly, rise to the peak value at the fourth second, and then slightly decrease, and then tend to be stable. Because the distance between the two monitoring points and the leakage port is different, the pressure value at the monitoring point A, which is closer to the leakage port, is much higher than that at the monitoring point B. By comparing the leakage of different cases, it can be found that the change trend of the pressure value of different cases is similar, but after the pressure value rises to the peak value and tends to be stable, the higher the HBR of the leakage gas is, the higher the pressure value at the corresponding monitoring point is. This indicating that with the increase of HBR, the pressure of leakage gas in the soil will also increase accordingly.

Figure 12 Pressure variation of HBNG with different HBR values at different monitoring points over time.

3.2.2 Velocity Field Contrast

Figure 13 shows the speed change curves of monitoring points A and B under different HBR. As shown, after the pipeline leakage occurs, the speed values of the two monitoring points rise rapidly, rise to the peak at the third second and then slightly decrease, rise again slightly at the fifth second, and then tend to be stable. Compared with the leakage of different cases, it can be found that the change trend of the speed value of different cases is similar, but after the speed value becomes stable, the higher the HBR of the leaked gas, the higher the corresponding velocity values at the monitoring points. This indicating that with the increase of HBR, the leakage velocity of leaked gas in soil will also increase.

Figure 13 Velocity variation of HBNG with different HBR at different monitoring points over time.

3.2.3 Comparison of Diffusion Ranges

Due to the change of HBR, the lower explosive limit of leakage gas of different HBR will change. Based on the lower explosive limit for methane (5%) and the lower explosive limit for hydrogen (4%), through eq 11, the lower explosive limit of leakage gas for different HBR is calculated. As shown in Table 5, when HBR is 5%, 10%, 15%, 20%, and 25%, the corresponding lower explosive limit is 0.04938, 0.04878, 0.04819, 0.04762, and 0.04706. It shows that with the increase of HBR, the lower explosion limit of leaked gas will also be reduced, and the explosion risk will be greater.

Table 5 Lower Explosive Limit Corresponding to Different HBR

HBR (%)	LEL	
5	0.04938	
10	0.04878	
15	0.04819	
20	0.04762	
25	0.04762	

Based on the definition of FDR by Bu et al.,32 this paper believes that the furthest dangerous range of horizontal diffusion of HBNG in soil after pipeline leakage is FDR. For investigate the impact of different HBR on FDR, the leakage gas concentration on monitoring line 1 at different times is shown in Figure 14. The dashed lines in different colors correspond to the lower explosive limit of the corresponding color HBR, and the corresponding FDR value can be obtained through the intersection points of the two. Since each curve is relatively close, the intersection points are amplified. For example, when HBR is 15%, the corresponding FDR reaches 0.6016 m 60 s after leakage and 1.323 m 600 s after leakage, which is twice that of 60 s after leakage, and 1.681 m 1200 s after leakage, which is 2.8 times that of 60 s after leakage, and it reached 1.935 m 1800 s after the leak, which is 3.2 times that of 60 s after the leakage. The data show that the increase rate of FDR decreases with the increase in leakage time. Compared with the leakage conditions of different HBR, taking the leakage 1800 s after the occurrence of HBR as an example, when the HBR is 5%, the FDR is 1.926 m. When the HBR is increased to 25%, the FDR is 1.945 m. This indicates that with the increase of HBR, the corresponding increase of FDR will also occur. The FDR changes of different HBR at different leakage time points were compared. When the leak occurred for 60 s, the FDR difference between 5% HBR and 25% HBR was 0.005 m, and when the leak occurred for 1800 s, the FDR difference rose to 0.019 m. This indicates that with the increase of leakage time, the influence of HBR change on FDR is increasing and the potential explosion risk corresponding to high HBR is also increasing.

Figure 14 Monitoring line 1, the HBNG concentration value under different HBR values: (a) t = 60 s, (b) t = 600 s, (c) t = 1200 s, and (d) t = 1800 s.

3.3 Influence of Various Factors on the Dispersion Range of Leaked Gas in the Soil

3.3.1 Influence of Pipeline Pressure

The influence of pipeline operating pressure on FDR is explored by comparing the change of leakage gas concentration at monitoring line 1 under different pipeline operating pressures. Figure 15 shows the leakage gas concentration value at each time point of monitoring line 1 under different pipeline operating pressures, and the dashed line is the lower explosion limit of the leakage gas. As shown in the figure, it is obvious that with the increase of pipeline operating pressure, the diffusion range of leaking gas increases, and the corresponding FDR also increases. Taking the pipeline pressure of 0.2 and 0.3 MPa as an example, after 60 s of leakage, the corresponding FDR is 0.496 m and 0.559 m, respectively, with a difference of 0.063. The increase of pipeline operating pressure leads to a significant increase in FDR. When the leakage occurred for 600 s, the corresponding FDR were 0.884 and 0.971 m, respectively, and the difference increased to 0.087, indicating that the influence of pipeline pressure on FDR was also increasing with the increase of leakage time.

Figure 15 Monitoring line 1, the HBNG concentration value under different pipeline pressures: (a) t = 60 s, (b) t = 600 s, (c) t = 1200 s, and (d) t = 1800 s.

3.3.2 Influence of Pipeline Burial Depth

The influence of the pipeline burial depth on the FDR was explored by comparing the changes in the concentration of leaking gas at monitoring line 1 under different pipeline burial depths. Figure 16 shows the concentration of leaking gas at different time points of monitoring line 1 under different pipeline burial depths, and the dashed line shows the lower explosion limit of leaking gas. As shown in the figure, in the initial stage of leakage, the FDR corresponding to different pipeline burial depths are close to each other. With the increase of leakage time, the FDR difference corresponding to different pipeline burial depths becomes larger and larger, and the deeper the pipeline burial depth, the higher the corresponding FDR. In each working condition, the FDR corresponding to the buried depth of 0.3 m is the most different from other working conditions, because when the buried depth of the pipeline is shallow, the leaking gas will escape to the ground faster after pipeline leakage. Taking the FDR corresponding to the buried depth of 0.3 and 1.5 m as an example, the difference of FDR is 0.06 m after 60 s of leakage, and increases to 0.15 m after 600 s of leakage. It shows that with the increase of leakage time, the influence of the pipeline burial depth on FDR is increasing.

Figure 16 Monitoring line 1, the HBNG concentration value under different pipeline burial depths: (a) t = 60 s, (b) t = 600 s, (c) t = 1200 s, and (d) t = 1800 s.

3.3.3 Influence of Leak Diameter Size

The influence of the leakage gas diameter on FDR was explored by comparing the change in the leakage gas concentration at monitoring line 1 under different leakage port diameters. Figure 17 shows the leakage gas concentration value at each time point of monitoring line 1 under different leakage port diameters, and the dashed line is the lower explosive limit of the leakage gas. As shown in the figure, it is obvious that with the increase of the diameter of the leakage port, the diffusion range of the leakage gas increases and the corresponding FDR also increases. Taking the leak diameter of 0.01 and 0.015 m as an example, after 60 s of leakage, the corresponding FDR is 0.477 and 0.544 m, respectively, with a difference of 0.067. The increase of leak diameter leads to a significant increase of FDR. When the leakage occurred for 600 s, the corresponding FDR values were 1.076 and 1.211 m, respectively, and the difference increased to 0.135, indicating that with the increase of leakage time, the influence of leakage port diameter on FDR was also increasing.

Figure 17 Monitoring line 1, the HBNG concentration value under different leakage hole diameters: (a) t = 60 s, (b) t = 600 s, (c) t = 1200 s, and (d) t = 1800 s.

3.3.4 Influence of the Direction of the Leakage Outlet

The influence of different leakage directions is discussed by comparing the leakage conditions of Case 19 (the leakage direction is downward), Case 20 (the leakage direction is leftward), and Case 4 (the leakage direction is upward). Figure 18 shows the leakage situation of the above cases at each monitoring point and monitoring line. Figure 18a shows the time varying curve of leakage gas concentration at monitoring points 1 and 4. Since the monitoring point 4 is located above the pipeline, when the leakage port is upward, the leakage gas first rises and reaches the peak value, followed by the leakage port on the left, and when the leakage port is downward, the leakage gas is monitored at the latest time point and takes the longest time to reach the peak value. The opposite is true for monitoring point 1 below the pipeline. Since the leakage directions of Case 4 and Case 19 are opposite in the vertical direction, and monitoring points 2 and 5 are two symmetrical points in the vertical direction, the concentration curve of Case 4 at monitoring point 2 is similar to that of Case 19 at monitoring point 5, and the concentration curve of Case 4 at monitoring point 5 is similar to that of Case 19 at monitoring point 2. When the leakage direction is left, the leaked gas will escape to the ground, and the concentration curve of monitoring point 4 is slightly larger than that of monitoring point 1. Figure 18b shows the time varying curve of leakage gas concentration at monitoring points 2 and 5. Since both monitoring points 2 and 5 are located on the left side of the pipeline, Case 20 with the leakage port on the left side was first monitored, and the rising speed and concentration value of the concentration curve of Case 20 were both greater than those of Case 4 and Case 19. Figure 18c shows the time varying curve of leakage gas concentration at monitoring points 3 and 6. Since monitoring points 3 and 6 are arranged along the pipeline, Case 20 is monitored late at the time point, and the rising speed and concentration value of the concentration curve are low. Case 19 and Case 4 are monitored earlier at nearby monitoring points, and the corresponding rising speed and concentration value of the concentration curve are also higher. Figure 18d shows the concentration value at line 1 of the monitoring line 600 s after the leakage occurred. As shown in the figure, Case 4 has the widest diffusion range at monitoring line 1, and Case 19 has the smallest diffusion range, so the potential explosion risk is greatest when the leakage port is upward.

Figure 18 HBNG concentration in different leakage directions: (a) P1 and P4 over time, (b) P2 and P5 over time, (c) P3 and P6 over time, and (d) monitoring line 1 at 30 min

3.3.5 Influence of Soil Type

The impact of different soil types is discussed by comparing the leakage of Case 21 (sandy soil), Case 22 (clay soil), and Case 4 (loam soil). Figure 19 shows the leakage situation of different soil types at various monitoring points and monitoring lines. Figure 19a shows the leakage at monitoring points 1 and 4. Taking monitoring point 1 as an example, when the soil type is sandy soil, the concentration of leaked gas rises at the maximum speed and reaches the peak value at the earliest time. When the soil type is loam, the rising speed is slower than that of sandy soil, and the time required to rise to the peak value is longer. When the soil type is clay, the rising speed is the slowest. When the leakage occurs 600 s later, the concentration value at the monitoring point is still at a low level and does not exceed 0.1. Figure 19b shows the leakage situation at monitoring points 2 and 5, which is consistent with the leakage situation at monitoring point 1. The concentration rising speed is in the order that the sand is greater than the loam and the clay. Figure 19c shows the leakage situation at monitoring points 2 and 5. Since soil is isotropic, the diffusion velocity of leaking gas in different directions on the same horizontal plane should be the same, so the concentration curve of Figure 19c corresponds to that of Figure 19b. Figure 19d shows the concentration value at the monitoring line 1 after the leak occurred for 600 s. When the soil type is sandy, the leakage gas diffusion range is the largest, and the FDR reaches 2.063 m; when the soil type is loam, the FDR is 1.377 m; when the soil type is clay, the leakage gas diffusion range is the smallest, and the FDR is 0.443 m. Therefore, the potential explosion risk is greatest when the soil type where the pipeline leak occurs is sandy.

Figure 19 HBNG concentration in different soil types: (a) P1 and P4 over time; (b) P2 and P5 over time; (c) P3 and P6 over time; (d) monitoring line 1 at 30 min.

3.4 Predictive Model of FDR

3.4.1 Establishment of the Predictive Model

It can be seen from the simulated data that HBR, pipeline operating pressure, pipeline burial depth, leak hole diameter, and leak time will all affect FDR. Since changes in HBR can lead to changes in the density of leaking gas and thus affect the gas leakage diffusion process, the impact of changes in gas density should also be considered when calculating FDR. Based on the data obtained from numerical simulations, a multiple regression analysis is conducted to establish a multivariate regression predictive model for gas density, HBR, pipeline operating pressure, pipeline burial depth, leak hole diameter, and leak time with respect to FDR. The predictive model and the applicable range of each variable are shown in eqs 12 and 13. This model is applied to an underground HBNG pipeline with a diameter of 100 mm, where the leak direction is upward and the backfill soil is loam.12

13

In the formula, r is FDR (m); η is HBR; h is the pipeline burial depth (m); t is the duration of pipeline leakage (s); P is the operating pressure of the leaking pipeline (MPa); ρ is the leakage gas density (kg/m3); d is the pipe leakage hole diameter (m).

3.4.2 Validation of the Predictive Model

To verify the reliability of the prediction model, one set of data was randomly selected from each of the four control groups for comparison of HBR, pipeline pressure, pipeline burial depth, and leak orifice size for comparison. The comparison between simulated values and predicted values is shown in Figure 20. Figure 20 illustrates the variation of the FDR with time for different cases. In particular, when Case 9 experiences a leak at 1 min, the relative error between the predicted value obtained from eq 12 and the simulated value is 9.385%, which is the maximum relative error, as shown in Figure 20b. Case 4 has the highest average relative error among the four comparison cases, which is 2.376%, as shown in Figure 20a, while Case 12 has the smallest average relative error of 1.479%, as shown in Figure 20c. It can be considered that the prediction model, eq 12, is reliable.

Figure 20 Simulated and fitted values of different cases: (a) Case 4, (b) Case 9, (c) Case 12, (d) and Case 16.

4 Conclusion

In this paper, a three-dimensional leakage model of a buried HBNG pipeline is established to study the leakage process of a buried HBNG pipeline in soil. The influence of different variables on the diffusion process was discussed by the control variable method, and the prediction model of the farthest danger range of buried HBNG pipeline leakage under different working conditions was established, which provided a reference for the construction of a high HBR pipeline in the future. Specific conclusions are as follows:(1) After the pipeline leakage occurs, the pressure and speed values of the leakage gas at 1 m above the leakage port will rapidly rise to the peak value within 5 s before the leakage and then slightly fall back and tend to be stable after rising to the peak value. Compared with the leakage of the natural gas pipeline in soil, the leakage rate of the HBNG pipeline in soil is faster, the pressure is greater, and the concentration is higher, which indicates that the leakage risk will be increased after natural gas is mixed with hydrogen, and because the lower explosion limit of HBNG is lower than that of natural gas, the explosion risk caused by leakage is also higher.

(2) With the increase of HBR, the lower explosive limit of HBNG will also decrease. The lower the explosive limit, the higher the explosion risk. By comparing the leakage of HBNG pipelines with different HBR in the soil, the higher the HBR, the higher the pressure value, diffusion rate, and gas concentration of HBNG in the soil, which led to the rise of FDR with the rise of HBR. After 30 min of leakage, the FDR corresponding to HBR 0.25 was 0.019 m higher than that corresponding to HBR 0.05.

(3) With the increase of pipeline pressure, leak size and pipeline burial depth, the FDR of HBNG pipeline after leakage also increases. The direction of the leakage port has little influence on FDR, and the FDR corresponding to different leakage port directions is similar, but it has a greater influence on the diffusion speed in different directions in the soil. When the leakage port direction is the side, the HBNG concentration value of the monitoring point on the side is significantly higher than the concentration value when the leakage port direction is up and down. Different soil types have a great impact on the leakage, among which HBNG has the fastest diffusion speed in sand and the slowest diffusion speed in clay. After 10 min of leakage, the FDR corresponding to sand is about 4.6 times that of clay.

(4) The paper considers the impact of gas density changes caused by HBR variations on the leakage process. Through multiple regression analysis, a multivariate regression prediction model for FDR is obtained based on HBR, gas density, pipeline operating pressure, pipeline burial depth, leak aperture, and leakage time. The average error of the prediction model is within 2.986%, and there is a high degree of agreement between predicted and simulated values. This model can provide data support for assessing the danger zone after leakage from buried HBNG pipelines, thereby facilitating the rational planning of personnel evacuation plans and the positioning of leakage monitoring points.

(5) Currently, most countries globally set the maximum value of HBR for HBNG pipelines at 10% or below. This paper discusses the HBR range from 0% to 25% and explores the leakage situation of buried HBNG pipelines under high HBR conditions. It is found that an increase in HBR has a relatively small impact on the leakage diffusion process of HBNG in soil, providing reference significance for the construction of future high-hydrogen pipelines.

The authors declare no competing financial interest.

Acknowledgments

The work presented in this paper was financially supported by the National Natural Science Foundation of China (52074090). The Key Research & Development Program of Heilongjiang Province (No. JD22A004), Guiding Innovation Fund of Heilongjiang Provincial Undergraduate Universities (No. 2023YDL-04), and Northeast Petroleum University Scientific Research Foundation, China (No. 2022KQ05) are also gratefully acknowledged.
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