# A Model for Assessing the Potential Impact Radius of Hydrogen Pipelines Based on Jet Fire Radiation

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## Abstract

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## 1. Introduction

- (1)
- The pressure inside the hydrogen pipeline decays with time;
- (2)
- The rupture leads to a double-ended gas release.

^{2}as the radiation threshold, Equation (1) and the value 0.099 are derived [13]. It is to be noted that the single point source model takes the jet fire as one single point and neglects the influence of flame shape on radiation. The previous model for the potential impact radius (Equation (1)) was validated by the data from the National Transportation Safety Board (NTSB) of the United States and the Transportation Safety Board (TSB) of Canada. In total, 12 practical cases were validated, and Equation (1) shows the reasonable and conservative results. One possible explanation is that Equation (1) assumes immediate ignition. While in real cases, the actual time for ignition is longer. Thus, the mass flow rate in Equation (1) is more conservative than the real cases [13]. It is to be noted that Equation (1) is limited to natural gas pipelines and is not applicable to hydrogen pipelines. The pipeline diameter (d, m) and operating pressure (p, Pa) are utilized in Equation (1) to determine the potential impact radius (r, m):

## 2. Radiation Threshold for Potential Impact Radius

- (1)
- The people located outdoors when failure happens would be exposed to a low and finite chance of fatality.
- (2)
- The property represented by a typical wooden structure would not ignite and burn, thereby providing indefinite protection for people indoors when failure happens.

^{2}, accounting for the impact on the effect of thermal load on both people and property [13]. Assuming an individual is exposed to radiation for 30 s and would remain in position for 1–5 s to evaluate the situation and then run with a 2.5 m/s speed towards a shelter, the estimated distance of people traveling within this period is 60 m. It is assumed that a shelter is located within 60 m of individuals. Then, under 30 s of exposure, 15.8 kW/m

^{2}is the significant threshold leading to a 1% chance of fatality [13,20,21]. And when a wooden structure is exposed to 15.8 kW/m

^{2}radiation, spontaneous ignition is improbable, and piloted ignition will only occur after approximately 20 min of exposure [20]. Therefore, it is posited that when the radiation is below 15.8 kW/m

^{2}, the wooden structures would not be destroyed and would provide indefinite protection for the individuals [13]. This 15.8 kW/m

^{2}threshold of radiation is applicable for hydrogen pipelines, as indicated in ASME B31.12 [16].

## 3. A Model for Assessing Potential Impact Radius

#### 3.1. Equivalent Mass Release Rate

_{d}is the frictional coefficient and has no unit; ${A}_{h}$ (m

^{2}), which is calculated as $\pi {d}^{2}/4$, is the area of the leakage hole of the hydrogen pipeline cross-section; d is the diameter of the rupture, namely the pipeline diameter in the present work (m) [13]; $\gamma $ is the adiabatic constant; ${P}_{1}\left({P}_{0}+{P}_{a}\right)$ (Pa) is the absolute pressure inside the pipeline; ${P}_{2}$(${P}_{0}+{\rho}_{w}g{H}_{0},\text{}$ Pa) is the absolute atmosphere pressure; ${P}_{0}$(Pa) is the effective gauge operating pressure; ${P}_{a}$ (Pa) is the ambient pressure; $\rho $ (kg/m

^{3}), which is calculated as $\frac{\left({P}_{0}+{P}_{a}\right){M}_{w}}{R{T}_{1}},$ is the ideal gas density; ${M}_{w}$ (kg/mol) is the molar mass of hydrogen; R (Jmol

^{−1}K

^{−1}) is the ideal gas constant; and T

_{1}(K) is the temperature of hydrogen. By further considering the pressure drop and the double-ended leakage of hydrogen pipelines, as well as the integration of the release rate decay factor $\mathsf{\lambda}=0.33$ [13,23], the equivalent mass release rate ${\left({\dot{m}}_{RG}\right)}_{equ}$ is obtained, as shown in Equation (4):

#### 3.2. Flame Radiation Model

_{i}to each point. The heat release rate P (kW) is calculated using Equation (5). The radiation of each point is understood as an independent part, and the radiation of part i is calculated individually, as shown in Equation (6). As shown in Equation (7), w

_{i}is used because the intensity of each part is different. The total radiation of the entire flame is the sum of each point, as illustrated in Equations (5)–(9) [24,25]:

_{2}in the path. One should note that the transmissivity is constant through the whole flame in the present work. Equation (1) considers the incomplete combustion of natural gas, whose main component is methane. The minimum ignition energy and the flammable limits of methane are 0.28 mJ and 5% to 15%, while the minimum ignition energy and flammable limits of hydrogen are 0.017 mJ and 4.25% to 75%. Compared with methane, the minimum ignition energy of hydrogen is low and the flammable limits of hydrogen are wide; therefore, the combustion efficiency of the hydrogen jet fire is 1.

^{2}). The hollow triangles in Figure 1 indicate the experimental results of Schefer, with the leakage diameter of 3.175 mm. The initial temperature is assumed to be 294 K, and the initial pressure is 15.3 MPa [28]. The solid dots in Figure 1 indicate the experimental results of Schefer regarding different times after leakage, with the leakage diameter of 7.94 mm and the initial pressure of 15.5 MPa. The gas temperature at the jet exit is predicted to be 258 K to 284 K. The radiation changes with time as the pressure changes with time [27]. In previous work, the visible, infrared (IR), and ultraviolet (UV) digital images of the flame were used to obtain the flame shape. The average flame length over five successive frames was then taken to discuss the flame properties and to provide quantitative data, and the visible flame lengths from the averaged visible digital images were used for the radiation calculation [28]. The curved lines indicate the results calculated by the weighted multi-source model. In total, 59 experimental data points from previous works are used to validate Equation (10). Nineteen data points are derived from the experimental condition when the leakage diameter is 3.175 mm and the initial pressure is 15.3 MPa [27]; these are the black hollow triangles is Figure 1. Additionally, 40 data points are derived from the experimental condition when the leakage diameter is 7.94 mm and the initial pressure is 15.5 MPa [27]; these are the green, blue, purple, pink, and yellow solid points in Figure 1. This comparison demonstrates that the weighted multi-source model effectively captures the characteristics of high-pressure hydrogen leakage.

#### 3.3. Potential Impact Radius for Hydrogen Pipelines

^{2}. The radiation is calculated with the aforementioned model in Section 3.2, with the pipeline diameter varying from 300 mm to 610 mm and operation pressure from 2 MPa to 6.3 MPa. And the temperature inside the hydrogen pipeline is 294 K. A total of 60 cases were computed with Equations (1)–(9), as depicted in Figure 2. It is to be noted that these conditions encompass real-world hydrogen pipelines. All the conditions are shown in Table 1. The calculated values of the potential impact radius increase with the increase in pipeline diameter and operating pressure, affirming the applicability of Equation (8) for the potential impact radius calculation.

## 4. Results and Discussion

## 5. Conclusions

^{2}. Previous methodologies relied on the single point source model to calculate radiation, overlooking the impact of the flame shape. This study, encompassing 60 cases, introduces a novel model for the potential impact radius and considers the geometric characteristics of the jet flame induced by high-pressure leakage. The key findings include:

- (1)
- A model for assessing the potential impact radius is proposed, including an equivalent mass release rate that considers the pressure drop of the hydrogen pipeline leakage and a radiation model based on a weighted multi-source model;
- (2)
- A simplified correlation (Equation (10)) is proposed to calculate the potential impact radius and to provide a reference for industrial use. The proposed model consistently yields more accurate results than the single point source model. The validation against an actual pipeline leakage demonstrates good agreement with real-world scenarios.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Comparison of ASME [16] (Equation (2)) and new proposed model (Equation (10)) for hydrogen pipeline leakage with the same pipeline diameter.

**Figure 5.**Comparison of ASME [16] (Equation (2)) and new proposed model (Equation (10)) for hydrogen pipeline leakage with the same operation pressure.

Operation Pressure (MPa) | Pipeline Diameter (mm) |
---|---|

6.3, 6, 5.5, 5, 4.5, 4, 3.5, 3, 2.5, 2 | 610, 600, 500, 450, 400, 325, 300 |

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**MDPI and ACS Style**

Lin, Y.; Yu, A.; Liu, Y.; Liu, X.; Zhang, Y.; Kuang, C.; Lu, Y.; Dang, W.
A Model for Assessing the Potential Impact Radius of Hydrogen Pipelines Based on Jet Fire Radiation. *Fire* **2024**, *7*, 38.
https://doi.org/10.3390/fire7020038

**AMA Style**

Lin Y, Yu A, Liu Y, Liu X, Zhang Y, Kuang C, Lu Y, Dang W.
A Model for Assessing the Potential Impact Radius of Hydrogen Pipelines Based on Jet Fire Radiation. *Fire*. 2024; 7(2):38.
https://doi.org/10.3390/fire7020038

**Chicago/Turabian Style**

Lin, Yujie, Anfeng Yu, Yi Liu, Xiaolong Liu, Yang Zhang, Chen Kuang, Yuan Lu, and Wenyi Dang.
2024. "A Model for Assessing the Potential Impact Radius of Hydrogen Pipelines Based on Jet Fire Radiation" *Fire* 7, no. 2: 38.
https://doi.org/10.3390/fire7020038