## 2 Materials and Methods
The inlet point, labeled as dispensed gas, represents the gas line responsible for filling the vehicle tank, where a mass flow rate sensor measures the transfer speed. The pressure sensor monitors the tank's current pressure, providing real-time data to the control unit, while the temperature sensor detects the gas temperature inside the tank. The vehicle tank is modeled using internal convection and heat conduction mechanisms, where internal convection accounts for heat transfer within the tank, and heat exchange with the surroundings is represented through internal conduction and external convection. The thermal properties of the tank wall are incorporated via the wall mass component, considering conductivity and heat capacity in the heat transfer process. Heat dissipation to the environment is modeled using the conduction tank and external convection components, while the environment temperature component simulates the ambient temperature effects on overall heat transfer. The values and material properties used in the heat transfer calculations are provided in Table 3.  
The experimental dataset used for validation in this study was originally presented by [PERSON] [56], based on a fast-fill CNG operation with cascade storage. This dataset has also been widely used in previous research for benchmarking and validation purposes, notably by [PERSON] et al. [27] and [PERSON] et al. [47]. In these studies, the model predictions showed high consistency with the experimental results, reinforcing the reliability of the dataset. Figure 5 illustrates the variation of mass flow rate over time, comparing the simulation results with the experimental data. The experimental conditions are consistent with those reported in [27, 47], where the initial pressure of the NGV cylinder is 72 bar and the volume is 52 L. The mass flow rate varies between 0.29 kg/s and 0.04 kg/s, managed through a cascade storage system. The fast-filling process starts at 24 s and ends at 60 s. The experimental data are shown as a blue dashed line, while the perfect gas and real gas simulation results are represented by black and red lines, respectively. These results indicate that the real gas model provides a closer alignment with the experimental measurements, especially at the peak flow rate and during the decline phase. The perfect gas model underestimates the maximum flow rate and shows noticeable  
Figure 5: Comparison between the simulations and experimental results for the mass flow rate. discrepancies in the decreasing region. These findings confirm that considering real gas behavior improves the accuracy of mass flow predictions during high-pressure filling. Figure 6 shows the pressure variation in the NGV cylinder over time. Initially, the pressure remains low and then increases rapidly after approximately 24 s. Both gas models (perfect and real) showed a high degree of agreement with the experimental results, particularly during the pressure rise phase. However, the final pressure predicted by both simulations was slightly higher than the experimental values. This is due to the target pressure being set at 250 bar in the simulation, compared to 240 bar in the experimental setup. The real gas model again yielded results closer to the experimental curve, confirming its higher accuracy under dynamic filling conditions. This target pressure difference also accounted for the small deviation observed during the flow decline stage, as the simulation continued for a longer duration to reach 250 bar, leading to slightly higher mass flow values near the end of the process. The experimental flow rate deviation was approximately \(\pm\)0.015 kg/s, as also reported by [PERSON] et al. [47] and [PERSON] et al. [27]. Similarly, the pressure deviation between the simulation and experiment was approximately 10 bar (4.2%), consistent with the target pressure difference observed in George [54]. The total filling time deviation between the simulation and experiment was around 2 s, corresponding to about 5.5% of the total duration.