# Formation Kinetics and Morphology Characteristics of Natural Gas Hydrates in Sandstone Fractures
## 3 Results and Discussion  
### Hydrate Formation  
#### 3.1.1 Effect of Fracture Width  
Figure 5a presents a comparison of hydrate induction times under varying fracture width conditions. As shown in the figure, under identical pressure conditions, the hydrate induction time for Type I fractures with a 3 mm width is longer than for the other two widths. The hydrate induction time for the 3 mm fracture width is 0.539 h, whereas for the 10 mm fracture width, the induction time decreases to 0.428 h, reflecting a 20.59% reduction. This phenomenon may be attributed to the fact that the fracture width affects the gas diffusion rate and fluid flow within the fracture. In smaller widths, both gas diffusion and \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number**} & **Pressure** & **Fracture** & **Fracture** & **Roughness** & **Note** \\  & **[MPa]** & **Shape** & **Width [mm]** & **[mm]** & **Note** \\ \hline
1 & & I & 3/6/10 & / & 3 groups \\
2 & & X & 3/6/10 & / & 3 groups \\
3 & & I & 10 & 2.5/3.5 & 2 groups \\
4 & & X & 10 & 2.5/3.5 & 2 groups \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental parameters and conditions of CH\({}_{4}\) hydrate under sandstone fracture environments. Figure 4: Selection of temperature and pressure. fluid flow are restricted, impeding the gas mass transfer process, which consequently affects the hydrate induction time. Furthermore, the crystal growth of the hydrate is restricted, resulting in smaller crystal volumes and higher specific surface areas. Under constant liquid surface tension, the more pronounced the interface interactions, the less stable the formed hydrate. However, under identical pressure conditions, the hydrate induction times for fractures with 6 mm and 10 mm widths are almost identical. This suggests that as the fracture width increases, the space required for hydrate crystal nucleation is sufficiently provided. At this point, gas diffusion is more likely to reach a balanced state, resulting in a more uniform distribution of gas and liquid within the fracture, thereby minimizing the effect of fracture width on the hydrate induction time once the threshold (6 mm) is surpassed. Furthermore, fluctuations in induction times for the 6 mm and 10 mm widths may primarily be due to the randomness of hydrate nucleation and the effect of pressure on gas solubility. Figure 5: Type I fracture under different widths: (**a**) hydrate induction time; (**b**) total formation duration. Figure 5b illustrates the total formation duration for different fracture widths. It demonstrates a trend of initially increasing, followed by a decrease as the fracture width increases. This phenomenon may be attributed to the fact that under lower pressures, the hydrate phase equilibrium is only reached, and the formation rate is inherently slower. In fractures with smaller widths (3 mm), capillary forces are more pronounced, leading to a larger gas-liquid contact area, which facilitates the gas mass transfer process, thereby promoting hydrate formation. In contrast, in fractures with larger widths, the increased fracture radius diminishes the capillary force. In this case, the total formation duration is primarily governed by gas diffusion. This hypothesis can be validated by Figure 6, where, under lower pressures, the gas consumption in the 3 mm width fracture is the highest among the three fractures, at 3.82 \(\times\) 10\({}^{-1}\) mol, whereas the gas consumption in the 6 mm width fracture is the lowest, at 3.48 \(\times\) 10\({}^{-1}\) mol. However, the difference in gas consumption among the three widths is relatively small. As illustrated in Figure 7, the hydrate growth process in fractures with varying widths is quite similar. Hydrates initially form at the fracture wall and subsequently expand toward the left and right sidewalls. The hydrates come into contact, collide, and aggregate, ultimately filling the entire fracture. This occurs because, within the fissures, hydrate growth is significantly influenced by capillary effects.