# Model for Cryogenic Flashing LNG Leak
## 3 Results
### Simulation Finding  
Natural gas (NG) is flammable between 5% and 15% methane concentration in the air. The 5% concentration is called the lower flammable limit (LFL), and the 15% concentration is called the upper flammable limit (UFL). The LFL distance covered by each simulated scenario is presented in Table 2. The LFL distance is the furthest distance from the leak source where the methane concentration has been diluted to 5% in air.  
Among the five simulated scenarios, the horizontal leak with tailwind had the furthest LFL distance at 49.83 m, which can be explained by three reasons. The first reason is that  
Figure 3: Grid use for the simulation.  
it was non-impinged, unlike the vertical downward leak. An impinged leak has the help of obstruction to redirect dispersion flow, leading to a smaller LFL distance. Figure 4a shows the plane view of the downward leak overall spread across the ground. Figure 4b shows the section view of the downward leak at the leak source. The colour depicts the methane concentration at the location. Deep red represents methane concentration at UFL or higher, and deep blue represents the methane concentration at LFL. Concentrations of lower than LFL are not shown in the figure. The gas height measured 0.65 m from the ground, reflecting a low laying gas dispersion, which is a phenomenon observed in past LNG experiments [26; 27; 28].  
The second reason is that horizontal leak experienced lower wind speed as compared to vertical upward leak. The FLACS wind boundary was modelled based on the Monin and Obukhov theory, and the wind velocity increased logarithmically with elevation [29]. Figure 5a shows the section view of wind velocity (north direction) distribution. It can be observed that the wind speed above 10 m elevation is approximately 2 m/s, 10 times more than the wind speed of 0.2 m/s found below 2 m elevation. For the horizontal leak, the gas dispersion barely surpassed 1 m elevation. In the case of the vertical upward leak, the leak reached up to a height of 11 m with an LFL distance of 16.72 m, as shown in Figure 5b. The higher wind speed experienced by the vertical upward leak led to faster gas dilution, resulting in a shorter LFL distance.  
The third reason is that a tailwind leak will not suffer \"push back\" as a headwind would. The opposing headwind reduced the leak velocity, leading to a smaller LFL distance. Figure 6a,b show the section view of tailwind and headwind leak, respectively. The LFL distance was 49.83 m for the tailwind leak and 32.53 m for the headwind.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Leak Direction** & **Wind Direction** & **Furthest LFL Distance (m)** \\ \hline Vertical upward & North & 16.72 \\ Vertical downward & North & 35.70 \\ Horizontal & East (tailwind) & 49.83 \\ Horizontal & West (headwind) & 32.53 \\ Horizontal & North-east (crosswind) & 47.04 \\ \hline \hline \end{tabular}
\end{table}
Table 2: LFL distance of leaks.  
Figure 4: (**a**) Plane view of the downward leak spreading across the ground with LFL distance of 35.7 m; (**b**) section view of the downward leak at the leak source with a height of 0.65 m.  
The LFL distance difference between the horizontal leak with tailwind and crosswind was 2.79 m. The slight difference is likely due to the manifold and hose geometry influencing the wind flow around the leak source. Overall, the five LFL distances differences are explained, and the results do not contradict each other.