## 3 Results and Discussion
### For Evaluation of Gas Hydrates Kinetics
#### 3.3.2 Calculation of Kinetic Parameters  
The induction time of the gas hydrate formation was taken as the time needed to start the formation of decent amounts of hydrates. It can be detected as the point when a sudden pressure drop with an increase in temperature was observed, as illustrated in Figure 7. The plot of pressure and temperature vs. time has been drawn, and from the sudden change of temperature, as the gas hydrate formation is an exothermic reaction for decreasing pressure, triggered as induction time.  
The initial rate of gas consumption is the foremost constraint for the study of the kinetics of gas hydrates. It represents the rate of the multiphase carbon dioxide (CO\({}_{2}\)) hydrate formation, and is calculated as follows, in Equation (1):  
\[r(t)=-\frac{n_{i}^{i-1}-n_{i}^{i+1}}{t_{i-1}-t_{i+1}}\ n_{w_{0}}^{-1} \tag{1}\]  
where, \(n_{i}^{i-1}\) and \(n_{i}^{i+1}\) are the mole numbers of gas in the gas phase at time intervals \(t_{i-1}\) and \(t_{i+1}\) respectively, and \(n_{w_{0}}\) is the initial mole number of water [20]. The initial rate of gas consumption from the system can be observed from Figure 8 gas consumption (CO\({}_{2}\)) curve vs. time (t), in which the time vs. mole consumption plot is available.  
Figure 7: Pressure/Temperature vs. Time (t) curve to find Induction time.  
CO\({}_{2}\) Gas Consumption and Gas Uptake  
The amount of carbon dioxide (CO\({}_{2}\)) consumed to experiment with maximum hydrate formation is a vital constraint to bring gas hydrate technology to the industrial scale. The gas consumption is calculated using Equation (2). An assumption is made that there is no change in the volume of water during the gas hydrate formation. This is because of the closed system in the experimental setup, and the volume change due to the temperature effect is minimal on the volume of the water [23; 24; 25]. Therefore, the following equation is used for the isothermal experiment:  
\[\Delta n_{g}=\frac{V}{R}\left[\left(\frac{P}{ZT}\right)_{0}-\left(\frac{P}{ZT }\right)_{t}\right] \tag{2}\]  
where \(P\) and \(T\) are the pressure and temperature of the multiphase system, respectively. The volume of the gas-phase is \(V\), and \(R\) is the universal Gas constant. \(Z\) is the compressibility factor, which is calculated using the Peng\(-\)Robinson equation of state. Subscripts 0 and \(t\) stands for the starting time of the experiment and the experimental conditions at time \(t\), respectively.  
To normalize the amount of gas consumption and eliminate the size of the sample, the gas uptake is calculated, as shown in Equation (3). It represents the amount of gas trapped in one mole of a water sample:  
\[U=\frac{\Delta n_{g}}{n_{w}} \tag{3}\]  
The graphical representation of mole consumption to time is displayed in Figure 8.  
The experimental results to determine the rate of formation of gas hydrates in the multiphase system is stated in Figure 9. When the multiphase system with gasoline is observed, it can be noted clearly that the rate of formation is lower compared to deionized water, which is because of the chemical inhibitors that are added during the processing of gasoline from crude oil. For instance, gasoline consists of oxygenates like ethylene glycol, which is a good gas hydra  
Figure 8: Gas consumption (CO\({}_{2}\)) curve vs. time (t).  
similarly, when the crude oil multiphase system is observed, the rate of formation is higher because of the presence of long carbon chains and impurities. The presence of longer carbon chains affects the kinetics of the gas hydrates formation [21; 22].