## 2 Experiments
The temperatures of the flow loop and (\(T_{S1}\), \(T_{S2}\), \(T_{T}\)), chilling water baths, and R134a storage tank were measured with T-type thermocouples having an uncertainty of \(\pm\)0.3 K after calibration. Pressure and temperature data were processed and recorded by data logger (Agilent, 34970A) and software program HP-VEE. R134a hydrate is a nonstoichiometric inclusion solid compound formed from guest gas molecules and host water molecules under sufficiently high-pressure condition at a given temperature. The hydration number of gas hydrate is defined as the average number of water molecules per unit cell that contains one gas molecule. As the measured average hydration number (\(r\)) of R134a hydrate is 17 [52], the fraction of water molecule (x\({}_{H_{2}O}\)) is 73.86 wt.%, and that of R134a molecule (x\({}_{R}\)) is 26.14 wt.%, considering that the molecular weight of water (\(M_{H_{2}O}\)) is 18.02 kg/kmol, and that of R134a (\(M_{R}\)) is 102.03 kg/kmol:  
\[x_{H_{2}O}=\frac{rM_{H_{2}O}}{rM_{H_{2}O}+M_{R}} \tag{1}\]  
\[x_{R}=1-x_{H_{2}O} \tag{2}\]  
The rheological characteristics of two-phase flow strongly depend on the solid volume fraction, especially in the laminar regime [39]. In order to obtain the valid empirical correlation for the pressure difference across the orifice, the solid volume fraction needs to be precisely acquired or evaluated. In the present work, hydrate slurry having the prespecified solid volume fraction of (15, 20, 25, 28, or 30)% was formed within the flow loop. Considering the difference in liquid water density and hydrate density [33; 34] shown in Table 1, the net amount of water to be removed from the flow loop (\(H_{2}O\),_remove_) and the amount of R134a to be injected (\(M_{R}\)) to attain specific hydrate solid fractions (\(\phi_{s}\)) can be calculated as follows:  
\[m_{H_{2}O,remove}=(\rho_{H_{2}O}-x_{H_{2}O}\rho_{S})\phi_{S}V_{T} \tag{3}\]  
\[m_{R}=x_{R}\rho_{S}\phi_{S}V_{T} \tag{4}\]  
where, \(V_{T}\) ( = 5.68 L) is the total volume of the flow loop. Table 2 presents the mass of water that needs to be removed from the flow loop, and the mass of the R134a that needs to be injected into the flow loop for each specific hydrate volume fraction. In order to prepare for an experimental run, the flow loop was completely filled with water. At the same time, air bubbles were eliminated through the bubble removal chamber, while the pump was running with a volume flow rate of 15.8 LPM, which is equivalent to a flow velocity of 0.73 m/s. When the removal of air bubble was complete, the pump was paus \begin{table}
\begin{tabular}{c c c} \hline \hline
**Phase** & \(\rho_{sat}\) **at 2 °C [kg/m\({}^{3}\)]** & \(\Delta\)**H [kj/kg]** \\ \hline Liquid H\({}_{2}\)O & 999.9 & 0 \\ Liquid R134a & 1288 & \(-\)197.1 \\ Vapor R134a & 15.46 & 0 \\ Hydrate & 1047 & \(-\)342.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Densities and formation enthalpies of relevant phases. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Hydrate Volume Fraction** & **15\%** & **20\%** & **25\%** & **28\%** & **30\%** \\ \hline Mass of removed water [g] & 195 & 260 & 325 & 364 & 390 \\ Mass of injected R134a [g] & 235.4 & 313.9 & 392.4 & 439.4 & 470.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The amounts of removed water from the flow loop and of injected R134a to the flow loop for each predetermined hydrate volume fraction. the air removing chamber to the flow loop were closed. Then, the gas supply port was opened to pressurize the flow loop to help push the water out. The calculated amount of water in Table 2 was withdrawn. During the intermittent manual withdrawal of liquid water, the loop pressure fluctuated as shown in Figure 2 The peak pressures were less than 400 kPa, due to the dissolution of R134a gas. After water removal, the gas supply port was closed, and the pump operation was resumed to check the stabilized loop pressure. The flow loop pressure after 40 s of stabilization was about 120 kPa.