Numerical Simulation of Diffusion Characteristics and Hazards in Multi-Hole Leakage from Hydrogen-Blended Natural Gas Pipelines
Abstract
1. Introduction
2. Method
2.1. Assumptions of the Model
- The soil, as a porous medium, is considered isotropic, and changes in its spatial structure before and after leakage are neglected;
- Due to the leak hole diameter being less than 5% of the pipeline diameter, pressure variations within the pipeline before and after leakage are neglected;
- Given the minimal gas leakage volume, temperature changes induced by pressure variations after leakage are neglected;
- The gas within the pipeline comprises only methane and hydrogen, with the effects of other gases neglected;
- The influence of soil moisture is neglected.
2.2. Governing Equation
2.2.1. Mass Conservation
2.2.2. Momentum Conservation Equation
2.2.3. Continuity Equation
2.2.4. Transport Equation
2.2.5. Equation of Gas State
2.2.6. Soil Conditions
2.2.7. Mass Diffusivity
2.3. Numerical Modeling of Multi-Hole Leakage
2.3.1. Geometric Dimension
2.3.2. Numerical Modeling
2.4. Numerical Model Analysis
2.5. Simulated Scene
2.6. Numerical Analysis Model Validation
2.6.1. Grid Independence Validation
2.6.2. Model Reliability Validation
3. Results and Discussion
3.1. Diffusion Characteristics of Multi-Hole Leakage
3.2. The Influence of the Leakage Hole Number
3.3. The Influence of Inter-Hole Spacing
3.4. The Influence of HBR
3.5. The Influence of Soil Porosity
4. Conclusions
- The multi-hole leakage diffusion of HBNG exhibits three distinct evolutionary phases. Initially, during the independent diffusion phase, the two leakage plumes remain spatially separated, with concentration distributions mirroring single-hole leakage characteristics. Subsequently, in the interaction-accelerated diffusion phase, overlapping gas plumes in the soil matrix generate intensified concentration gradients, forming a peanut-shaped concentration contour with significantly enhanced vertical migration velocity along the inter-hole axis. Eventually, when the diffusion envelope exceeds the inter-hole spacing, the merged leakage field transitions into a Unified-Source diffusion mode, characterized by circular or runway-shaped surface concentration profiles approximating unified aperture diffusion patterns. Hydrogen, due to its low-density properties, exhibits limited lateral migration confined near leakage sources and undergoes only two diffusion stages. In contrast, methane progresses through all three phases, ultimately forming extensive circular distribution patterns. The hazardous potential of the gas mixture is predominantly governed by methane’s expansive diffusion footprint rather than hydrogen’s localized accumulation.
- The multi-hole and single-hole leakage scenarios exhibit similarity in gas concentration gradients along both axial and horizontal directions. When leakage hole diameters are identical, the distribution distance along the central axis equals the algebraic sum of the single-hole diffusion distance and the inter-hole spacing. Radial distribution patterns also demonstrate comparable characteristics, where the number of leakage holes does not influence gas diffusion along LB2. Under equivalent total leakage hole areas, multi-hole leakage configurations present higher hazard potential compared to single-hole scenarios.
- The inter-hole spacing significantly influences the gas diffusion characteristics in multi-hole leakage scenarios. When leakage holes are in closer proximity, the interacting gas plumes rapidly coalesce, causing the diffusion behavior to approximate single-hole dynamics with an extended FDD. Conversely, increased inter-hole spacing restricts the diffusion process to only the first two evolutionary phases while generating a substantially expanded GDR
- Compared to pure methane leakage and diffusion behavior, low HBR (<30%) increases post-leakage hazard potential but primarily modifies near-source gas concentration distribution characteristics, with minimal influence on GDR. When hydrogen blending reaches 30%, the surface hazardous zone expands by only 3% compared to natural gas leakage. This occurs because hydrogen’s superior diffusivity generates localized dilution effects without significantly altering methane’s expansive diffusion footprint. Therefore, for low HBR, critical parameters like GDR can be conservatively estimated using natural gas leakage models.
- The hazard potential of HBNG leakage is significantly influenced by soil porosity variations. Using yellow cinnamon soil as a representative example, increased porosity reduces both inertial and viscous resistances to gas migration, thereby accelerating subsurface diffusion and expanding GDR. Consequently, engineering interventions aimed at decreasing soil porosity can substantially mitigate leakage-related risks through controlled modification of subsurface transport pathways.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
p | pressure (Pa) |
g | gravitational acceleration (m/s2) |
v | leak velocity (m/s) |
t | time (s) |
ui | velocity in the x, y, z direction (m/s) |
Si | resistance loss in porous media |
R | general gas constant (J/(mol K)) |
T | temperature (K) |
M | molecular mass of the component |
DP | soil particle diameter |
C2 | inertial resistance coefficient |
d | diffusion distance |
s | inter-hole spacing |
D | diffusion coefficient |
Greek letters | |
ρ | density (kg/m3) |
α | soil permeability |
1/α | viscous resistance coefficient (1/m2) |
γ | soil porosity |
ε | turbulence dissipation rate (J/(kg s)) |
μ | viscosity (kg/ms) |
ω | mass fraction of the component |
Abbreviations
HBNG | hydrogen-blended natural gas |
LEL | lower explosive limit |
HBR | hydrogen blending ratio |
FDT | first dangerous time |
FDD | farthest dangerous distance |
GDR | ground dangerous range |
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Item | Information |
---|---|
Scheme | PISO |
Viscous Model | DES |
RAWS Model | Spalart-Allmaras |
Gravity | −9.81 m/s2 |
Temperature | 300 K |
Transient Formulation | Second Order Implicit |
Time step size | 0.5 s |
Total time | 5000 s |
Case | Leakage Hole Number | Leakage Hole Diameter/mm | Leakage Hole Area/mm | Inter-Hole Spacing/m | HBR | Soil Porosity |
---|---|---|---|---|---|---|
1 | 1 | 10 | 25 π | —— | 0.3 | 0.43 |
2 | 1 | 14.4 | 50 π | —— | 0.3 | 0.43 |
3 | 1 | 17.3 | 75 π | —— | 0.3 | 0.43 |
4 | 2 | 10 | 25 π | 0.5 | 0.3 | 0.43 |
5 | 2 | 10 | 25 π | 1 | 0.3 | 0.43 |
6 | 2 | 10 | 25 π | 2 | 0.3 | 0.43 |
7 | 2 | 10 | 25 π | 3 | 0.3 | 0.43 |
8 | 2 | 10 | 25 π | 4 | 0.3 | 0.43 |
9 | 3 | 10 | 25 π | 2 | 0.3 | 0.43 |
10 | 2 | 10 | 25 π | 2 | 0 | 0.43 |
11 | 2 | 10 | 25 π | 2 | 0.1 | 0.43 |
12 | 2 | 10 | 25 π | 2 | 0.2 | 0.43 |
13 | 2 | 10 | 25 π | 2 | 0.3 | 0.32 |
14 | 2 | 10 | 25 π | 2 | 0.3 | 0.54 |
Maximum Size of the Surface Mesh | Number of the Surface Mesh | Maximum Cell Length | Number of the Volumetric Mesh |
---|---|---|---|
50 mm | 143,572 | 66.04006 | 701,026 |
100 mm | 47,194 | 143.3163 | 119,224 |
150 mm | 30,950 | 200.657 | 63,883 |
200 mm | 24,964 | 256.0571 | 50,551 |
Case | Dp (mm) | γ | A (m2) | 1/α (1/m2) | C2 (1/m) |
---|---|---|---|---|---|
13 | 0.05 | 0.32 | 1.18 × 10−12 | 8.47 × 1011 | 1.45 × 106 |
6 | 0.05 | 0.43 | 4.08 × 10−12 | 2.45 × 1011 | 5.02 × 105 |
14 | 0.05 | 0.54 | 1.24 × 10−11 | 8.06 × 1010 | 2.04 × 105 |
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Wang, H.; Tian, X. Numerical Simulation of Diffusion Characteristics and Hazards in Multi-Hole Leakage from Hydrogen-Blended Natural Gas Pipelines. Energies 2025, 18, 4309. https://doi.org/10.3390/en18164309
Wang H, Tian X. Numerical Simulation of Diffusion Characteristics and Hazards in Multi-Hole Leakage from Hydrogen-Blended Natural Gas Pipelines. Energies. 2025; 18(16):4309. https://doi.org/10.3390/en18164309
Chicago/Turabian StyleWang, Haolin, and Xiao Tian. 2025. "Numerical Simulation of Diffusion Characteristics and Hazards in Multi-Hole Leakage from Hydrogen-Blended Natural Gas Pipelines" Energies 18, no. 16: 4309. https://doi.org/10.3390/en18164309
APA StyleWang, H., & Tian, X. (2025). Numerical Simulation of Diffusion Characteristics and Hazards in Multi-Hole Leakage from Hydrogen-Blended Natural Gas Pipelines. Energies, 18(16), 4309. https://doi.org/10.3390/en18164309