Study on the potential risks under a hazardous gas leakage accident: effects of source characteristics and ambient wind velocities

In this study, a full-scale storage tank was established to investigate the potential risks of leakage accident. We have developed a series of leak scenarios that close to real accidents and have divided the ambient areas according to relevant regulations. Considering the variety and complexity of real-life accident scenarios, the presented work revealed the combined effect of source release intensity and ambient wind speed on dispersion features by classifying leakage scenarios into active or passive release. The environmental hazards in each area is evaluated under various leak scenarios. The results show that when the approaching wind speed is low, the leakage on the windward side is the most dangerous release pattern. With the increase of the wind speed, the case with jet angle perpendicular to the incoming wind produces the largest cloud volume. Top release is the least dangerous way among the studied leak scenarios. However, the results illustrate that under some release angles, the cloud volume near the tank is not sensitive to wind speed. In leak accidents, quantitatively analysis reveals that the commonly used dimensionless concentrations (Kc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{c}$$\end{document}) cannot be used as a suitable parameter to discuss the concentration field except under top/leeward passive release conditions. This study will be beneficial to on-site rescue and decision-making when leakage accidents occur and provide reasonable suggestions for subsequent research on the environmental impact of container leakage and the diffusion of pollutants.


Introduction
Accidental release of hazardous chemicals into air usually leads to an environmental emergency that poses an immediate threat to public health or the environment (Sittig 1991;Qu et al. 2016;Liu et al. 2011). In the past several decades, large volume storage facilities for chemicals are becoming increasingly used around the world, inspired by demand for energy and the innovation of chemical technology. This change has been accompanied by an increase in the potential risks of environmental incidents due to hazardous chemicals leakage (Wu et al. 2018;Hou et al. 2021). Since chemical substances are usually stored in storage tanks in liquid or gaseous form, leaked hazardous chemicals are more likely to spread around by flow of liquid or airborne routes, resulting in serious consequences (Li et al. 2014;Schmatz et al. 2021). Zhang and Zheng (2012) summarized 1632 hazardous chemical accidents (HCAs) happened in China from 2006 to 2010, and the results showed that accidents occurred in fixed facilities (1142 times) are more than twice as that during transport (490 times) in industrial process. According to statistics, 1015 people were killed and 2958 others were injured in the 5 years in China due to HCAs. As a commonly used container in the industrial process, storage tank accidents involve in hazardous chemical substance (HCS) have attracted the interests of many scholars, since failure of storage tanks may result in sever consequence due to the massive release of HCS (Yang et al. 2018;Cozzani et al. 2005; Barjoee et al. 2022).
Types and status of HCS leaked from storage tanks vary greatly from incident to incident. Chang and Lin (2006) made a statistic review on storage tank accidents worldwide, including 242 cases from 1960 to 2003. Notably, 64 cases occurred in the process of terminal or storage, which is the second most occurring segment of tank accidents. There were 15 cases caused by leakage alone, without counting accidents caused by other reasons accompanying HCS leakage. Moreover, 13 cases were clearly classified to toxic gas release in those 242 cases. Chang and Lin (2006) also pointed out that among the tanks involved in the accidents, atmospheric tanks were the most frequent type.
In fact, HCS gas leak from atmospheric storage tank has caused several remarkable disasters. For example, in 1984, methyl isocyanate (MIC) gas leaked from a storage tank in Bhopal, India. More than 40 t MIC escaped due to failure of valve and increased pressure inside the tank (Bowonder 1987;Broughton 2005). Gas cloud containing MIC and its reaction products settled down in surrounding area which led to 2500 nearby people died in the accident (Bowonder 1987). In 2012, 41 people were killed in an explosion at the Amuay refinery, Venezuela. Olefins vapors in storage tanks leaked due to a failed piping valve, and the gas cloud was ignited at a distance of 6 km away from leak source (Tauseef et al. 2018;Mishra et al. 2014). As reported by the Department of Emergency Management of Hebei Province (DEMHP), in 2018, a severe leakage accident occurred in Zhangjiakou city (DEMHP 2019; Wang et al. 2020a), Hebei Province, China. The accident resulted in 24 people being killed and 21 people injured. The pressure inside the storage tank was reported as 4 kPa, and the leaked vinyl chloride gas (VCG) was carried by the northwest low-speed wind (lower than 3 m/s, 0.9-1.9 m/s as reported) to the region across the road. A few minutes later, the gas was ignited in the southern region by a high-temperature furnace and explosion occurred. A similar accident occurred on April 24, 2019, in Inner Mongolia, China, which led to 4 deaths and 36 injuries. The VCG leaked from a cylinder gas container due to the mechanical failure and high pressure inside the container. Notably, the local wind velocity reached a Beaufort Wind Scale of 7 or 8 (10.8-17.1 m/s) as reported by the Ministry of Emergency Management of the People's Republic of China (MEMPRC) (MEMPRC 2021). The dense gas diffused to a workshop with a lower elevation and then been ignited.
In view of the serious consequences caused by leakage of gas-phase HCS from storage tanks, many scholars have investigated the diffusion behaviors of HCS leaking from containers. The main focus was generally on the effect introduced by approaching flow (velocity, direction, and atmospheric stability), leakage location, and ambient condition such as obstacles. For instance, Liu et al. (2009) developed a 2-D numerical model to study the transport distance of hydrogen accidentally leaking form high-pressure storage tank at various wind velocities, different ambient temperatures, as well as diverse diameters of leak orifice. The presence of obstacles was also taken into account in this work. Lin et al. (2021) numerically studied dispersion characteristics of natural gas in cofferdam area, and the impacts of wind directions, cofferdam height, and leak locations were carefully considered in computational cases. Hort and Robbins (2002) presented a series of experimental results of dense gas diffusion around single storage tank or a smallscale tank group under neutral or stable atmospheric stability. Ohba et al. (2004) validated the accuracy of wind tunnel experiment and numerical methods in predicting dispersion of LNG leaking from storage tank. Gases with different specific gravities were adopted in numerical simulation to reveal the concentration distributions near ground. Wang et al. (2020b) investigated the effects of tank spacing on gas diffusion and vapor cloud explosion by CFD method based on analyzing Chinese National Standards (GB 50160 2018) and the Flammable and Combustible Liquids Code by American National Fire Protection Association (NFPA 30 2018). The abovementioned researches illustrate that diffusion characteristics of HCS could be significant different when the impact factors change. Therefore, the representations of real accident scenarios are particularly important for the study of HCS diffusion, especially for dense gas diffusion, since it may pose a great threat to personnel safety due to its ease of settling into the ground in the air (Xin et al. 2021;Scargiali et al. 2011).
The above researches provided valuable experience for the subsequent studies on HCS dispersion after a leakage accident happened, while few studies have related the leakage characteristics of HCS to the actual operating conditions of the storage tank, such as pressure, which may lead to the generation of high-speed jet at the leak orifice. Due to the complicated interaction between high-speed jet and the ambient wind on the dispersion of HCS gas, the combined effect of leakage features and approaching wind needs to be investigated in detail. In addition, many researches have focused on large-scale leaks from storage container, while the National Institute for Occupational Safety and Health (NIOSH) (Barsan 2007) notes that even low concentrations of HCS may pose a serious hazard to humans. Zinke et al. (2020) made a theoretical derivation on the emission intensity of floating roof tank during normal operation, revision and rim seal damage, and the results showed that the mass flow rate of released HCS was conservatively estimated to be below 40 kg/h. However, to facilitate presentation of the results, this small-scale leakage was not applied to the subsequent simulations.
In this paper, numerical simulation was used to explore the diffusion characteristics of HCS gas when accidentally leaking from a storage tank, and a series of three-dimensional (3-D) leakage scenarios were established. The leakage scenarios were built considering the effects of wind velocities and wind directions, while the possible leakage locations and leakage pressures were also considered. In the "CFD validation" section, grid independent check and model validation of numerical simulation method were presented. The "Details of numerical simulation" section described the details of computational fluid dynamics (CFD) setups for leak scenarios, some key parameters with reference to actual accidents and relevant codes were also explained. The discussions of simulation results were presented in the "Results" section. Influences of wind velocities and source locations on diffusion behaviors were firstly evaluated by analyzing distribution of hazardous gas cloud within specific zones. While specially, the combined effects of environmental wind velocity and source release intensity on dispersion features were then examined, by means of categorizing the leakage scenarios into active and passive release, respectively.

Description of the wind-tunnel experiments
Two wind-tunnel experiments (Cantwell and Coles 1983;Giedt 1951) were selected to verify the accuracy of numerical methods employed in this paper. Cantwell and Coles (1983) used the wind tunnel and flying-hot-wire technique to investigate the transport process in the wake near the circular cylinder at a Reynolds number of 140,000. The height of the stainless-steel circular cylinder used here was 2.97 m with a diameter of 0.1014 m. End-plates were mounted at both the ends of the cylinder to avoid the influence of the boundary layers generated on the tunnel walls. The air flow near the middle part of the cylinder was acceptably twodimensional (2-D). It is worth mentioning that the cylinder was well polished and the surface can be considered as smooth. Additional details of the experiment are available in the studies by Cantwell and Coles (1983). The normalized mean centerline velocity (U/U 0 at y = 0) and the streamwise mean velocity at x/D = 1 (U/U 0 at x/D = 1) in the experiment were selected for comparison to verify the reliability of the prediction results on airflow around a cylinder-shaped structure. Giedt (1951) carried out a series of experiments in an open-throat-type tunnel in University of California. A circular cylinder with a diameter of 0.1016 m was used for surface pressure measurement at different Reynolds numbers. Plates were also installed on both sides of the cylinder which were parallel to the air flow. Further details on the experimental setups can be found in the study by Giedt (1951). Experimental data of C p on the surface of the cylinder at Re of 172,000 were extracted to compare with simulation results. Considering the HCS gas is released from the container and the diffusion is initially near to the container's surface, C p was selected for comparison to check the accuracy of the numerical methods in predicting the flow in the near-wall region of the cylinder-shaped structure.

CFD simulation settings
With the tremendous progress made in computer science, CFD has become a vital tool for solving problems in real life that relates to fluid dynamics, such as dispersion of hazardous materials and prediction of wind pressure (Vasilopoulos et al. 2021;Liu et al. 2013). It is generally accepted that the accuracy of simulation results can be sensitive to a great number of parameters. In order to test the accuracy and reliability of the numerical methods, a 3-D model was established. The computational domain size and the names of the boundaries are shown in Fig. 1. The lateral sides were extended to a length of 7D (D represents diameter of cylinder here) away from the cylinder to ensure the blockage ration below 8% (Ramamurthy and Ng 1973). In the z-direction, the domain height is set as 4D, which is larger than the typical values of 2D and D (Breuer 2000). The boundary conditions of the computational model were summarized in Table 1.
The uniform flow was applied in the inlet of the computational domain, which was consistent with the experiments. Mean velocities of the approach-flow were adjusted to ensure that Re numbers the same with those in the two experiments, respectively. The commercial CFD code FLU-ENT 19.2 which is based on the finite volume method was used in present work, and four kinds of Reynolds-averaged Navier-Stokes turbulence models (standard k − , SST k − , RNG k − , and realizable k − ) were selected to solve the steady-state isothermal flow past the cylinder. Then, the simulation results were compared with the measured data.

Grid independence check and model validation
The structural hexahedral mesh was used in all the computational cases here, and three grid arrangements were employed for grid sensitive analysis, with the total number were 0.86 million (coarse grid), 1.70 million (basic grid), and 2.66 million (fine grid), respectively. Cells near the wall were adjusted to keep the value of y + an appropriate range based on the selected near-wall treatment methods. And the stretching ratio was kept under 1.2 in the whole computational domain.
Grid sensitive analysis and the comparisons between different near wall treatments were firstly performed and the results are shown in Fig. 2. The normalized wind velocities along the red lines (in both streamwise and spanwise directions) were selected for comparisons, while the C p values were presented with different angles ( ) along the cylindrical surface. The results obtained by basic grid (with standard wall function) and fine grid (with enhanced wall function) were similar, and showed acceptable agreement with experimental data. Comparing with the basic grid, the size of nearwall cell was larger in the coarse grid, and a poor agreement with experimental data was observed. Thus, the basic grid was selected to conduct the model validation.
Simulation results for the four selected turbulence models were summarized in Fig. 3. As presented in Fig. 3a and b, realizable k − model performed much better in predicting the flow field in the wake behind the cylinder than any other models comparing with experimental data. Additionally, numerical results in Fig. 3c indicated that both RNG and realizable k − models were sufficient to capture the main characteristics in the very near-wall region around the cylinder.
According to the discussions above, the realizable k − model was selected in the following studies, and the nearwall treatment was kept the same as the basic grid after an overall consideration of computational cost and numerical accuracy.

Geometry configurations and case setup
In this section, a full-scale cylinder-shaped storage tank was established to investigate dense gas diffusion and the  In tank failures, leakage of storage tank is commonly caused by corrosion of metal or crack (Chang and Lin 2006). Thus, the leak orifice can be very small and the release of hazardous gas could be maintained at a small but stable level. In this study, a 10 mm square-shaped orifice was designed, which is considered as a medium-sized hole according to America Petroleum Institute (API) (API 2008; Wang et al. 2020c). Other small obstructions on the tank were omitted except the leak orifice. The source locations (orifice locations) were set in the center of the top wall or half the height of the sidewall. For large welded tanks, these positions are usually the areas where the welds locate and are more prone to corrosion than unwelded metal (API 2009;Hassanzadeh and Rahmani 2021).
For a cylinder tank, since the leaking HCS jet is perpendicular to the wall, setting a different approaching wind direction can also be seen as a corresponding change in the location of the leak orifice. To facilitate the model description and the discussions of the results below, the jet angle of HCS ( β ) was used as the parameter to characterize the source location. β was defined as the angle between the jet direction and the negative direction of the x-axis, varying from 0 • to 180 • . = 0 • indicates a windward release while β = 180 • represents a leeward release scenario. In order to investigate the effects of different jet angles, β set in this paper was 0 • , 45 • , 90 • , 135 • , and 180 • , respectively. Top release was also discussed as an additional case considering vertical jet situation.
The computational domain was set based on guidelines summarized by Franke et al. (2007) and Tominaga et al. (2008). The lateral sides and the top of the domain were extended to 5D away from the storage tank. As for the streamwise direction, a distance of 5D in the front and 12D in the wake was adopted, respectively. Whole computational domain dimensions were L × W × H = 288 m × 176 m × 96 m. Details of model configures and the computational domain setup can be seen in Fig. 4.
Based on the descriptions above, the case scenarios considered in this paper are summarized in Table 2. The design of U ref was close to real accidents.
According to Re-independence theory, the flow field will enter the Re-independent regime when the Reynolds number (Re) exceeds a certain critical value, and the flow field do not change as Re increases. While critical values presented  by previous researchers ranging from 2 × 10 3 to 1 × 10 5 for building-height-based Reynolds number (calculated by U ref D∕ here) (Dai et al. 2019;Uehara et al. 2003;Chew et al. 2018;Saathof et al. 1995) or larger than 2.5 for roughness Reynolds number (calculated by u * z 0 ∕ ) (Snyder 1972). The Reynolds number in previous validation cases are 1.42 × 10 5 and 1.72 × 10 5 , respectively. While for the cases presented in this section, the building-height-based Reynolds numbers ranging from 2.6 × 10 6 to 1.5 × 10 7 and the roughness Reynolds numbers are large than 10 3 . Based on the above considerations, both the validation and analysis cases have reached the Reynolds-independent state, and the mesh arrangement near the walls in the analytical cases were kept the same with validation cases.

Governing equations and physical models
This paper presented a numerical study of the potential risks of HCS leakage from a cylinder-shaped storage tank, and the three-dimensional Navier-Stokes equation and continuity equation for incompressible, viscous flow in RANS models are presented as follows.
Momentum equation: Continuity: where U i , P , and S ij are mean velocity, pressure, and mean strain-rate tensor, respectively. u , i represents the fluctuation component of velocity and t is the time. S ij is calculated by the following equation.
Additionally, present work focuses on the diffusion of VCG in air, and the advection-diffusion equation is used.
in which C , D , and c , represents the mean concentration, the molecular diffusion coefficient and the fluctuation component of concentration, respectively.
As can be seen from Eqs.
(1) to (4), the RANS equations cannot be solved since two terms are introduced ( u , i u , j and u , j c , ). In order to derive a closed system of equations, the two-equation turbulence models, such as the selected realizable k − model (Shih et al. 1995), are developed. The (1) transport equations of turbulent kinetic energy (k) and turbulent dissipation rate ( ) can be written as follows: k equation equation In the two equations, G k and G b is the turbulence kinetic energy produced by mean velocity gradients and buoyancy, respectively. The calculation of C 1 and C 4 can be found in the relevant literature (Shih et al. 1995;Launder and Spalding 1972). The model constants used in this study are:

Boundary conditions and mesh arrangements
Atmospheric boundary layer (ABL) was used in this paper. The approaching wind velocities described by a logarithmic law was imposed in the domain inlet, as shown in Eq. (7). The turbulent kinetic energy (k) and turbulent dissipation rate ( ) are given by Eq. (8) and Eq. (9), according to previous study by Tominaga et al. (2008). A suburban terrain was adopted here, and the aerodynamic roughness length was taken as 0.1 (Holmes 2015). The three constants g, , and k took the value of 9.81, 1, and 0.42, respectively. Based on the Zhangjiakou accident (DEMHP 2019; Wang et al. 2020a) and Inner Mongolia accident (Chang and Lin 2006), wind velocities at the height of storage tank (defined as U ref ) were set as 3 m/s, 10 m/s, and 17 m/s, respectively. The two lateral sides and domain top were set as symmetries, while no-slip walls were applied in the domain bottom and storage tank. Surface of storage tank was assumed to be smooth, since the surface was usually well cleaned and then painted (API 2009).
The inlet profiles for wind speed and turbulence features are of importance since they represent the turbulent conditions upstream (Gorlé et al. 2009), which are the basis for obtaining accurate simulation results. has been identified as dissipation rate of kinetic energy and it acts only to reduce kinetic energy (a minus sign in Eq. (5)). The role of k is to increase momentum mixing. Study by Ramponi and Blocken (Ramponi and Blocken 2012) indicates that centerline velocity become higher with k increases for a single room with open. In addition, an underestimation of velocity can be observed in the wake of an isolated building due to the underestimation of k (Blocken 2014). For dispersion problems, Gorlé et al. (2009) found that lower value of k results in a higher concentration near the source. Figure 5 shows the profiles of k and at the inlet in this paper.
The design pressure in an atmospheric tank is usually below 3.5 kPa (NFPA 30 2018). In this study, the gauge pressure inside tank was set to 1 kPa and 5 kPa, as listed in Table 2, which represent the pressure under normal operation and excessively high pressure that may cause accident, respectively. The pressures were converted to jet velocities ( ) by Eqs. (10) (Dong et al. 2002) and (11). Ambient pressure ( p a ) is maintained at a constant value of 101 kPa. Referring to the Zhangjiakou accident (DEMHP 2019; Wang et al. 2020a), the leaked gas was set to VCG. Temperature of released gas was set the same as ambient temperature (T = 293 K), since the mass flow rate is relatively small and the process of heat exchange can be neglected. The compressible factor (Z) and adiabatic index ( ) of VCG was set as 1 and 1.3, respectively. The densities of VCG and air were 2.78 kg/m 3 and 1.205 kg/m 3 . The molecular weight of VCG was 62.5 and viscosity was set as 9.2 × 10 −6 Pa ⋅ s . The boiling point of vinyl chloride is 7 • F (259.1 K) according to NIOSH (Barsan 2007), which is much lower than the ambient temperature (293 K) and the gas state is assumed to be stable during the diffusion process. Given that the Reynolds numbers in all cases were larger than 30,000, the empirical discharge coefficient (E) was taken as 0.61 (Dong et al. 2002).
As shown in Fig. 4, boundary conditions used in this paper are summarized in Table 3. Here, u, v, and w represent the velocity component in the x-, y-, and z-direction, respectively.
Mesh used in this paper were specially designed for various leakage scenarios to avoid excessive number of grids, ranging from 3.43 million to 4.20 million in different occasions. The height of the first grid layer near the walls was kept at 0.002 m, and the stretch ratio was kept below 1.2 in all the adopted meshes. The grid near the orifice was also carefully encrypted. Detailed grid arrangements near the target storage tank are shown in Fig. 6, and the exact positions of the leak orifices can be seen in this figure. (10)

Data analysis methods
VCG is classified as a flammable gas by NIOSH, with a lower explosion limit (LEL) of 3.6% (Barsan 2007). NIOSH also points out that VCG can cause severe symptoms of death through respiratory and dermal exposure. Based on Acute Exposure Guideline Levels for Selected Airborne Chemicals (AEGLs) by National Research Council (2009), acute exposure concentration of human should not exceed 70 ppm for VCG, which is much smaller than the LEL. Given the obvious differences between these two thresholds, a discussion of the results from a personnel safety perspective is necessary to thoroughly consider the potential hazards posed. Figure 7a shows the VCG concentration contour on the tank surface and the y = 0 plane under = 0 • at a lower ambient wind velocity (case 2). The white areas are where the concentration value exceeds 70 ppm, which can be observed in the front and the lateral side of the storage tank. Although the VCG that settled on the ground is swept up and spread to the top and the near wake of the tank due to the presence of vortices, extremely high concentration cannot be observed at the back and the top of the tank. As the wind velocity increases, the total volume of highly concentrated clouds (> 70 ppm) will further decrease.
On the other hand, VCG, a colorless gas, has an odor threshold ranging from 10 to 25,000 ppm, which means that long-term human exposure at a low concentration (less than 10 ppm) is relative possible. NIOSH has proposed a ceiling recommended exposure limit of 5 ppm for VCG (Barsan 2007), thus relying on acute exposure concentration threshold alone to discuss exposure risk clearly results in an underestimation. As can be seen in Fig. 7b, the iso-surface at 5 ppm extends further to the side and rear of the tank, and it remains at a certain height even at a location far from the tank, which indicates the potential threat to people even far away from storage tank due to hazardous pollutants. Therefore, from the Iso-surface at 5 ppm safety point of view, 5 ppm was selected as the threshold value, and the distribution of gas cloud with concentration value larger than 5 ppm near the storage tank (define as hazardous gas cloud) was discussed. According to NFPA 30 (2018), the area around the storage tank can be divided into four regions with the center of the tank as the origin, as described in Fig. 8. The impacts of wind velocities and jet angles on hazardous gas cloud volumes in these regions will be presented in the sections "Impacts of wind velocities on volume of hazardous gas cloud" and "Impacts of jet angles on volume of hazardous gas cloud", in order to quantitatively reveal the exposure risks at different locations.
According to Table 22.4.1.1 in NFPA 30, 5.3 m represents one third of the tank diameter, while 15 m, 30 m, and 60 m represent 0.5 L, L, and 2 L,respectively. L is a specified minimum spacing that can be find in Table 22.4.1.1(b) in NFPA 30. Based on the capacity of the full scale tank, L = 100f t(30m) was adopted.
The diffusion characteristics of dense gas are not only related to the properties of the gas itself, but are also influenced by ambient factors and source features (jet angles and release intensity). The release of dense gas can be determined as "active release" or "passive release" according to the Britter's criterion (Britter 1989) (see Eq. (12)), which took into account the combined effects of wind velocity and release intensity on the diffusion of dense gas.
where g � = g | | − a | | ∕ a . When BC ≤ 0.15 , the release is seen as "passive", otherwise it is considered "active". At this point, the combined effects of ambient wind velocities and source feature (release intensity q v ) on dispersion convert to the effects of active and passive releases on diffusion behaviors. The non-dimensional concentration K c (see Eq. (13)), as a parameter commonly used to characterize the concentration field (Tominaga and Stathopoulos 2009;Gousseau et al. 2011;Liu et al. 2020;Zheng and Yang 2021), is selected, since the combined effects of ambient wind velocity ( U ref ) and the source feature (release intensity q v ) are also took into account in K c . The dispersion of VCG under the combined effects of ambient wind velocities and source features (jet angles and release intensities), especially the adaptability of K c under various jet angles, are discussed and presented in the "Combined impacts of wind velocity and source release intensity" section.

Impacts of wind velocities on volume of hazardous gas cloud
Given the potential for a more serious consequence when gas leaking at a higher pressure, the cases with a leakage pressure of 5 kPa are firstly selected for discussion. Referring to Table 2, the scenarios in this section involve all the cases with even number from case 1 to case 18. Figure 9 shows the gas cloud volumes (> 5 ppm) in each region under different wind velocities. As expected, when the wind velocity increases, the gas cloud volume in each region generally decreases regardless of the jet angles and region locations. This is due to the fact that the leaked VCG is carried to the far field by the high-speed wind before it can spread in the near-tank regions. In addition, with the increase of ambient wind velocity, the cloud volume in each region shows an essential trend that the further away from the tank, the higher percentage of volume decrease, except in region 1 and region 2 under β = 180 • and top release conditions. Among different jet angles, β = 0 • shows the most sensitive to wind velocity. Under this jet angle, when the wind velocity increases from 3 Fig. 8 Schematic of specific regions. 5.3 m represents minimum distance from public way or important building; 15 m, 30 m, and 60 m represent minimum distance from property line that is or can be built upon under different tank protection measures, respectively; 8 m is the radius of storage tank (NFPA 30 2018) to 17 m/s, the gas cloud volume in each region decreases by 81.1%, 82.9%, 90.3%, and 97.0%, respectively. As to different regions, region 4 is the most sensitive region to the wind velocity, where both the largest and smallest volumes of gas clouds are observed. The cloud volume reduces by more than 60% when the wind speed increases by 14 m/s regardless of the jet angles (see Fig. 9d). Since this region is far away from the storage tank, and the effect of vortices near the storage tank that prevent VCG from being wrapped to the far field is greatly diminished. As the closest region to the storage tank, with the increasing wind speed, the gas cloud volumes in region 1 decrease by 38.9% and 47.4% for β = 180 • and top release, which are only about a half of that under β = 0 • (81.1%, see Fig. 9a). However, although the gas cloud volume at a wind velocity of 17 m/s when β = 0 • is quite small compared to other cases, it still maintains a total volume of 1956.9 m 3 in the four regions and the cloud is near the ground which cannot be overlooked. That's to say, in the case of accidental leak of storage tank, even in the most favorable leak scenario, the nearby personnel should be evacuated in a timely manner.

Impacts of jet angles on volume of hazardous gas cloud
Based on the discussions above, a low wind velocity is not conducive to the environmental safety during tank leakage. Thus, in this section, the results at leakage pressure of 5 kPa with an ambient wind speed of 3 m/s are presented, and the effects of different jet angles on the distribution patterns of gas clouds are evaluated. The cases with a wind velocity of 10 m/s are also provided for comparisons, as shown in Fig. 10. As listed in Table 2, the scenarios involved in this section are case 2, case 4, case 6, case 8, case 10, case 12, and cases from case 19 to case 24.
As indicated by Fig. 10, after introducing new jet angles ( β = 45 • , β = 90 • , and β = 135 • ), the overall trend is consistent with the findings observed in the previous section when the ambient wind velocity increased. The volumes of the gas clouds in the four regions generally decrease with the increase of wind speed, and region 4 still performs the most sensitive to the wind velocity. While focusing on specific regions, the differences under various jet angles can be observed.
For region 1 which represents the very near region of storage tank, when the jet angles are 45 • , 90 • , and 135 • , the wind velocity does not have a significant effect on the gas cloud volume. This suggests that under these three jet angles, although the higher wind velocity limits the diffusion of VCG in spanwise direction, it enhances the mixing of airflow in the leeward side, resulting in a less pronounced limitation on cloud volume. Differently, under β = 0 • , the high wind velocity not only limits the spanwise diffusion but also suppresses the cloud volume in front of the storage tank; thus, the volume decreases with the wind velocity increases. With top release condition, the total volume of gas cloud in four regions is the minimum comparing with other jet angles under both presented wind velocities. However, when considering the largest gas cloud volume in each region under various jet angles, the wind effect cannot be ignored. When the wind velocity is 3 m/s, jet release of VCG under β = 0 • produces the largest cloud volume in each region. And the volume distributions of the gas clouds under different jet angles are similar in region 2 and region 3. As the wind velocity increases to 10 m/s, jet release under β = 90 • becomes the most dangerous release condition except for region 4.

Combined impacts of wind velocity and source release intensity
This section explores the combined effects of ambient wind and source release intensity on the dispersion of heavy gas released from the container surface by classifying leak scenarios into active and passive releases. Three jet angles,β = 0 • (windward release),β = 180 • (leeward release) and top release are selected as typical leakage scenarios. The simulation cases from case1 to case18 are adopted in this section. A commonly used normalized concentration ( K c ) along three different lines (line-x, line-y, and line-z) are presented and shown in Fig. 11d. These lines are parallel to the coordinate axes with a distance of 2D away from the storage tank.
Release intensity is characterized by the leakage pressure, and it is only related to the pressure value when the size of the leak orifice is fixed, as indicated by Eq. (10) and Fig. 6. When the wind velocity is taken into account, the combined effect becomes more complicated. With U ref = 3 m/s, the release is classified as active under both leakage pressures (1 kPa and 5 kPa). For a moderate wind velocity (c) Region3 (d) Region4 ( U ref =10 m/s), the release is active for higher pressure (5 kPa) and passive for lower pressure (1 kPa), respectively; When U ref = 17 m/s, the releases become passive under both leakage pressures. Figure 11 shows the values of K c along line-z under different leak scenarios. When we ignore the specific incoming wind velocity and release intensity, consider merely the active or passive release conditions in each of the three leakage scenarios (windward release, leeward release and top release), the K c shows significantly different. That indicates the following discussions should be focus on data obtained under the same leakage scenario and ambient wind velocity.
When focusing on windward release (see Fig. 11a), it is clear that no regularity can be observed for the distribution of K c . Examining the results with the same wind velocity, K c values for both release intensities are obviously different, even though both release conditions are passive at a wind velocity of 17 m/s. From these discussions we can conclude that for the windward jet release of dense gas, K c cannot be used as a suitable parameter to characterize the concentration field in any case, since the changes of K c under windward release show a great randomness to the source release intensities and environmental wind speeds.
However, the leeward release ( β = 180 • ) and the top release are different from the windward release, as presented by Fig. 11b and Fig. 11b, the K c values can still be inconsistent. The same conclusions can also be found in Fig. 11c. Comparing Fig. 11b (or Fig. 11c) with Fig. 11a, the reason that K c values remain different under windward passive release can be attributed to the mutual offset of the jet and the approaching wind. In other words, windward release could not be regarded as passive in accidental release scenario of container.
As for line-x and line-y, considering the limitation of paper length, the K c distributions alone these two lines are presented in Fig. 12 with a wind speed of 17 m/s, and similar conclusions can be drawn. The results shown in this section suggest that the consistency of K c values for the accidental leeward and top release of dense gas is subjected to the following two conditions.
1. Ambient wind velocity and source locations are the same 2. Gas release with various intensities should be passive

Conclusions
Leakage of HCS from a storage tank will generate large amounts of contaminants, forming a dangerous gas cloud that can damage the environment and threaten the safety of personnel. In the present work, typical hazardous gas leak scenarios that close to the real accidents were established by CFD method, and the characteristics of hazardous gas cloud around the container influenced by wind velocities and jet angles were investigated. The results could be helpful to provide valuable references for the protection of personnel and environment when such accident occurs. In addition, this paper explored the combined effects of ambient wind velocity and source release intensity on dense gas diffusion characteristics, and put forward reasonable suggestions on the concentration field analysis. The main conclusions obtained in this paper are as follows.
1. For gas release at a low wind velocity, windward release ( β = 0 • ) is the most dangerous pattern, producing the largest cloud volume. As wind speed increases, the jet perpendicular to the approaching wind ( β = 90 • ) becomes the worst scenario. However, with the wind velocity below 10 m/s, the top release produces the smallest total volume of clouds, acting as the least dangerous release pattern. 2. For dense gas leak from the storage container, the total volume of hazardous gas cloud around the tank decreases with the increase of wind velocity as expected, while the volume performs the most sensitive to the wind in the areas away from the container (region 4). In spite of this, the total cloud volume in the nearby regions still remains large even at a high wind velocity, requiring immediate evacuation of personnel in the event of gas leak. 3. When focusing on the very near region around storage tank (region 1), hazardous gas cloud produced by jet releases under β = 45 • , β = 90 • and β = 135 • exhibit insensitive to wind velocity. In the event of a leakage, special attentions should be paid to these release patterns, which may be helpful for decision-makers in emergency response planning. 4. For β = 0 • (windward release), K c cannot be employed as a suitable parameter for discussing the concentration field. While under top/leeward passive release, it is appropriate to adopt K c . Regardless of the ambient wind speed, accidental release from windward side should always be viewed as an active release. Absolute concentration values could be a better alternative to characterize the concentration filed.
It is worth mentioning that many other impact factors, such as environmental characteristics (air temperature and humidity), HCS temperature, and presence of obstacles, can significantly affect the diffusion behavior of HCS and we will consider the effects of these factors in the next step of our work. Data availability All data analyzed during current study are included in this article.