## 1 Introduction  
Global energy diversification, sustainability, and carbon reduction have been trending in recent years [1, 2]. As it is carbon-neutral, hydrogen energy is widespread [3, 4]. However, hydrogen use widely poses many risks, including combustion, explosion, and corrosion of pipelines. To enhance transport efficiency and minimize leakage in the utilization of hydrogen energy, it is customary to transmit a blend of hydrogen and natural gas [5, 6]. Research on hydrogen-blended natural gas (HBNG) transport has been conducted to varying extents in different nations [7]. As early as 2004, the EU launched a demonstration project called NaturalHy, which aimed to identify and address the problem of hydrogen blending into the natural gas network [8]. In 2008, the Sustainable Amelandproject was initiated by the Netherlands in Ameland, Netherlands, to investigate the effects of hydrogen-enriched natural gas on pipelines [9]. In 2013, NREL published \"Blending Hydrogen into Natural Gas Pipeline Networks: A Review of Key Issues.\" This comprehensive synthesis study covers US natural gas hydrogen doping technology research. Other significant international scientific findings are also considered [10]. In 2016, the H21 project launched in the UK aimed to assess the technological and economic feasibility of transitioning from natural gas to a 100% hydrogen supply [11]. In 2019, China established its first hydrogen doping pilot project in Chaoyang, Liaoning Province, to validate the core technologies of the HBNG \"production, storage, and transportation-doping-comprehensive utilization\" industrial chain [12]. In 2024, a comprehensive scientific and technological experimental platform was developed in Shenzhen for the hydrogen doping of town gas. This development represents a significant milestone in China's deployment of HBNG [13]. China's national standard [14; 15] allows gas pipelines to be included in utility tunnels. Nevertheless, if accidents occur in gas pipelines within natural gas compartments, there may be a high risk of explosion due to the flammability and explosiveness of natural gas, which can affect other compartments. Numerical modeling techniques are commonly used to study natural gas leakage patterns and explosion hazards in utility tunnels. [PERSON] analyzed the dispersion pattern of leaked natural gas under various ventilation conditions and its correlation with the effectiveness of ventilation dilution [16]. [PERSON] used numerical simulation to analyze the different factors affecting methane leakage in utility tunnels and established a prediction equation for the methane intrusion distance under natural ventilation conditions, which provides a reference for the installation distance of methane leakage alarm devices [17]. [PERSON] optimized the layout of sensors in the utility tunnels based on their ability to recover from human casualties and economic losses [18]. [PERSON] created an experimental setup to model natural gas explosions in utility tunnels, studied the effects of gas chamber length and pressure relief conditions on flame behavior, and examined several parameters related to natural gas explosion severity [19]. The addition of hydrogen to natural gas decreases the density of natural gas, resulting in a decreased minimum ignition energy and a significantly expanded explosion limit in comparison to utilizing it alone. These modifications impact the flow and dispersion of gas within the pipeline, affecting the ability to detect flammable gases after a leak and assess the consequences of an incident. Furthermore, upon entering the utility tunnel, the failure modes of natural gas pipelines primarily consist of small hole failures resulting from manufacturing defects, assembly defects, and corrosion. Therefore, it is of great significance to study the leakage law of natural gas small holes under hydrogen doping conditions to ensure the safe operation of pipelines.