## 6 The Case Study and Simulation Results
### Simulation Results: Not Adiabatic Processes  
The heat exchange between the pressure vessels and the nitrogen of the holds has been calculated at each time step. The overall heat transfer coefficient has been obtained calculating the internal and external convective heat exchange coefficients according to Section 4.1, while the heat conduction through the composite wall of the GASVESSEL cylinders has been obtained on the basis of the specifications given in Table 3.  
From the temperature trends in the pressure vessels obtained in the previous case of adiabatic loading and unloading, it can be deduced that the heat exchange with the environment should allow improving both the filling of the cylinder during the loading phase and the emptying during the unloading phase. In fact, the heat exchange with the environment contrasts both the heating of the accumulated gas in the first case and the cooling of the residual one in the second. However, it is  
Figure 16: Compressor power (adiabatic unloading). Figure 15: Compression ratio (adiabatic unloading). evident that the improvement will be less significant in the loading phase during the summer and in the unloading phase during the winter. The results obtained with the simulations under these two conditions, which can be considered of greater operational interest, are presented below. In the case of summer loading, the loaded mass was 7290 ton, with an increment of 8% with respect to the adiabatic case. However, the duration of the process is extended by 45%, from 35 h to about 51 h. The increment of 16 h is almost entirely due to the greater mass loaded during the forced phase (39 h instead of 24 h) at high compression ratios. Figure 17 shows the trend as a function of time of pressure and temperature in the pressure vessels. By comparing the temperature trend with those of Figure 7, it can be observed that the initial cooling of the CNG in the vessels disappears, that the maximum temperature is 70 \({}^{\circ}\)C instead of 78 \({}^{\circ}\)C, and that it occurs at about half the duration of the process. Most importantly, the final temperature reduces to 60 \({}^{\circ}\)C, giving the cited increment of the loaded mass. The compressor power trend reported in Figure 18 is quite similar to that of the adiabatic case of Figure 17 until time 35 h; then, the reduction of temperature  
As a whole, the mean flow rate decreases from 192 to 143 ton/h, the fuel consumption increases from 36 to 51 ton (\(\simeq\) 0.6% of the total cargo), and the specific energy consumption reaches 134 kJ/kg, instead of 96 kJ/kg. As far as the heat exchange is concerned, the peak power dispersed by the single cylinder is equal to 32 kW, and the energy dispersed in the hold is 658 kWh. Considering that there are 256 cylinders in the hold, which are filled at the same time, there is a total maximum dispersed power of 8.2 MW and a total dispersed energy of 168.448 kWh. In the case of winter unloading, the unloaded mass is 7025 ton, with an increment of about 14% in comparison with the adiabatic case. The residual mass is reduced of 265 ton with respect to the adiabatic calculation, due to the higher final temperature. Figure 19 shows the trend as a function of time of pressure and temperature in the pressure vessels: the minimum temperature is \(-25\)\({}^{\circ}\)C, which is reached at about two-thirds of the unloading time, while the final temperature is \(-17\)\({}^{\circ}\)C (remember that in the adiabatic case, the minimum was \(-60\)\({}^{\circ}\)C at the end of the process). The unloading process lasts 55 h, 44 of which are due to the forced phase. The increments with respect to the adiabatic case are of 9 and 10 h, respectively. The mean flow rate is about 119 ton/h against 135 ton/h. The fuel consumption goes from 51 ton to 67 ton (\(\simeq\)1% of the total cargo), and the specific energy consumption goes from 151 kJ/kg to 183 kJ/kg.