# Effect of Parameters on Vapor Generation in Ship-to-Ship Liquefied Natural Gas Bunkering
## 3 Simulation and Input Preparation
The overall heat transfer coefficients of the bunker tanks and fuel tank were determined based on normal BORs of 0.25% and 0.35% respectively, at an ambient air temperature of 25 \({}^{\circ}\)C and an LNG temperature of \(-\)162 \({}^{\circ}\)C. These were assumed as constants in all simulations. The overall heat transfer coefficient of the bunker tank could be calculated as follows [15]:  
\[ \begin{array}{l}\dot{Q}=\frac{BOR\left(\frac{\omega_{c}}{\omega_{d}}\right)} {24\times 3600\times 100}\rho_{LNG}\cdot V_{net,bt,fl}\cdot h_{tap}\\ =\frac{0.25}{24\times 3600\times 100}\times 425\left(\frac{k_{B}}{m^{3}} \right)\times 3185\left(m^{3}\right)\times 512,590\left(\frac{l}{k_{S}} \right)=20,077\ W\end{array}  \tag{2}\]  
\[ \begin{array}{l}(ULA)_{bt}=\frac{\dot{Q}}{T_{ambient}-T_{LNG}}=\frac{20,076 \left(W\right)}{25-\left(-162\right)}=107.36\ W/K\end{array}  \tag{3}\]  
\[U_{bt}=\frac{\left(ULA\right)_{bt}}{A_{bt}}=\frac{106.8\ \left(W/K\right)}{932.5\ \left(m^{2} \right)}=0.414\ kJ/hr\cdot m^{2}\cdot K \tag{4}\]  
In the above, \(\dot{Q}\) is the heat transfer rate to the tank during normal storage, and \(\rho_{LNG}\) and \(h_{tap}\) are the LNG density and heat of vaporization at \(-\)162 \({}^{\circ}\)C and 1 atm. \(V_{net,bt,fl}\) is 98% of the tank net volume, and that is the filling limit. \(\left(ULA\right)_{bt}\) is the thermal conductance of the bunker tank, and \(A_{bt}\) is the total surface area of the bunker tank. The overall heat transfer coefficient of the fuel tank was calculated using the same procedure. The overall heat transfer coefficient of the insulated pipes was calculated as follows:  
\[U_{pipe}=\frac{1}{\frac{D_{positional,\ O,D}}{D_{pipe,\ LD}\cdot h_{in}}+\frac{D_{ transitional,\ O,D}\cdot h\left(\frac{D_{pipe,\ O}}{D_{pipe,\ LD}}\right)}{2k_{pipe}}+\frac{D_{ transitional,\ O,D}\cdot h\left(\frac{D_{positional,\ O,D}}{D_{pipe,\ O}}\right)}{2k_{insulation}}+\frac{1}{h_{air}}} \tag{5}\]  
Here, \(D_{insulation\ O,D}\), \(D_{pipe\ O,D}\), and \(D_{pipe\ I,D}\) represent the outer diameter of the insulation, outer diameter of the pipe, and inner diameter of the pipe, respectively. \(k_{pipe}\) and \(k_{insulation}\) are the thermal conductivity of the pipe and insulation, \(h_{in}\) is the convective heat transfer coefficient of the LNG in the pipe, and \(h_{air}\) is the convective heat transfer coefficient of air. In the present study, the flow rate-related friction effect associated with the pipe wall, the gravity effect, and the Joule-Thomson effect associated with the pressure change in the pipe with phase transition were not taken into account. This approach can be reasonable considering that the length of bunkering pipeline and duration of bunkering are relatively short. The isothermal flash process for phase transitions are well described in Reference [28]. The input parameters for simulation are summarized in Tables 2-4. In addition, to effectively compare the amounts of vapor produced during bunkering, the following formulas were applied:  
\[\Delta m_{y,b}=m_{i,y,b}-m_{f,y,b} \tag{6}\]