# Effect of Parameters on Vapor Generation in Ship-to-Ship Liquefied Natural Gas Bunkering
## 4 Results and Discussions
### Effect of Bunkering Flow Rate  
The effects of varying the bunkering flow rates (300, 500, and 1000 m\({}^{3}\)/h) on the vapor generation and vapor return were studied. Figure 5 shows the T-s diagram corresponding to each location of the bunkering system at different bunkering flow rates. It can be seen that the LNG temperature increased at the pump outlet, and the degree of temperature rise was larger at higher bunkering flow rates. This was because some of the mechanical energy transferred from the pump shaft was lost in the form of heat, and the other was converted into pressure for the LNG. The relationship between the temperature rise (\(\Delta T_{\text{\it pump}}\)) at the pump outlet, shaft power, and flow rate can be expressed as follows:  
\[\Delta T_{\text{\it pump,in-out}}=\frac{\dot{Q}_{\text{\it shaff}}(1-\eta)}{ \dot{m}\text{-}C_{p}} \tag{10}\]  
In the above, \(\Delta T_{\text{\it pump,}}\)\(\dot{Q}_{\text{\it shaff}}\), \(\dot{m}\), \(\eta\), and \(C_{p}\) represent the temperature increase of the LNG through the pump, shaft power at the corresponding efficiency, mass flow rates through the pump, efficiency of the pump, and specific heat of the liquid in the pump, respectively. In addition, Figure 5 indicates that the LNG temperature in the receiving tank inlet (\(T_{\text{\it receiving\, tank\, inlet}}\)) was slightly higher than that of \(T_{\text{\it pump\, outlet}}\). This is mainly due to heat ingress through the pipes and friction losses in the pipes during bunkering. Table 5 shows the types and amounts of heat ingress to the system during bunkering, according to different bunkering flow rates. In the case of a bunkering flow rate of 300 m\({}^{3}\)/h, the total amount of heat ingress through the pipe and tank was larger than that of other cases due to the longer bunkering time; however, the amount of pump power converted to heat was relatively small. In contrast, in a case of a bunkering flow rate of 1000 m\({}^{3}\)/h, the amount of heat ingress through the pipe and tank was  
Figure 5: T–s diagram at bunkering flow rates of 300, 500, and 1000 m\({}^{3}\)/h. relatively small, due to the short bunkering time; however, a relatively large amount of the pump's shaft power was converted to heat. The variations of the vapor return flow rates differing at various bunkering flow rates are shown in Figure 6. The total amounts of vapor return at bunkering flow rates of 300, 500, and 1000 m\({}^{3}\)/h were approximately 3963, 4017, and 3955 kg respectively, and the net vapor generation values in the receiving tank were 391, 417, and 388 kg, respectively. This indicates that the bunkering flow rate does not significantly influence the amount of vapor return and net vapor generation. It also implies that the factors affecting vapor generation and vapor return at different bunkering flow rates includes not only heat ingress, but also other factors according to the change in the bunkering flow rate, such as the pressure variation in the receiving tank, as can be seen in Figure 7.  
For example, in the case of a bunkering flow rate of 1000 m\({}^{3}\)/h, as bunkering progressed, the pressure in the receiving tank was significantly increased because the vapor return flow rate was relatively small as a fixed C\({}_{\rm v}\) value (compared to the bunkering flow rate). As a result, owing to the pressure exerted by the vapor over the LNG surface, a reduced amount of LNG flashed into vapor, and the heat entering the system mainly raised the temperature of the LNG. Although the largest amount of heat ingress occurred at a bunkering flow rate of 1000 m\({}^{3}\)/h, due to the pressure effect from pumping, the amount of vapor generation is similar to that of the others. With the heat ingress and pressure by the pump in play, an optimum bunkering flow rate may exist. The optimum bunkering flow rate should be determined considering the amount of vapor generation and vapor return, operating pressure of the tank, and bunkering time limit, which may affect the operation schedule of the receiving ship.