# Formation Kinetics and Morphology Characteristics of Natural Gas Hydrates in Sandstone Fractures
## 2 Methodology
### Experimental Procedures  
The steps for hydrate formation and observation are outlined as follows in this study. (1) Pre-treatment of the reaction vessel: To minimize the impact of impurities during the experiment, de-aerated water is injected into the reaction vessel 3 times prior to the start of the experiment, for cleaning and drying. (2) Determination of shooting conditions: Through multiple pre-experiments, it was found that a liquid phase volume of 45 mL is the optimal condition. (3) Fracture pre-fabrication and filling: The pre-fabricated fractures are positioned within the vessel to ensure their bottoms are in full contact with the liquid surface. A high-definition camera is adjusted accordingly. The liquid is slowly directed into the fractures using a glass rod to prevent bubble formation, which could interfere with the camera's recording. (4) Sealing integrity testing and the preparation of experimental conditions: After sealing the reaction vessel, N\({}_{2}\) gas is introduced for a sealing integrity test to confirm that no gas leakage occurs during the experiment. After the test, the N\({}_{2}\) is discharged through the back pressure valve, and the vessel is treated under vacuum using a vacuum pump. Subsequently, the pressure inside the reaction vessel is maintained at 0.1 MPa by adjusting the SPVC piston pump, and the dehumidifier and water bath are set to the required temperature and humidity. (5) Experiment starts: Pre-cooled CH\({}_{4}\) gas is slowly injected into the reaction vessel, and the internal pressure is controlled to reach the desired testing pressure. The moment when both the temperature and pressure conditions are met is designated as the zero-time point of the experiment. (6) Observation and recording: The CH\({}_{4}\) gas consumption curve is recorded using the SPVC piston pump, while the formation of CH\({}_{4}\) hydrate within the fractures is observed using the high-definition camera. The experiment ends when gas consumption ceases. The quantity of hydrate formation is calculated using Equation (1). (7) Hydrate dissociation and yield calculation: After closing the reaction vessel's adjustment valve and discharging the remaining gas from the SPVC piston pump, the back-pressure valve is opened, and the pressure is rapidly reduced until the internal pressure of the vessel reaches 2 MPa. Once the volume of the SPVC piston pump remains stable for 30 min, it is confirmed that the hydrate has completely dissociated, and the experiment is concluded. The gas production is calculated using Equation (1). (8) Hydrate reformation: The pressure is adjusted above the hydrate phase equilibrium, promoting hydrate reformation until gas consumption ceases, marking the end of the experiment. \[n=(\frac{P_{0}}{Z_{0}}-\frac{P_{\mathrm{t}}}{Z_{\mathrm{t}}})\times\frac{V_{ \mathrm{g}}}{RT} \tag{1}\]  
where \(n\) denotes the gas consumption; \(P_{0}\) and \(P_{\mathrm{t}}\) representst the initial system pressure and the system pressure at time \(t\), respectively; \(Z_{0}\) and \(Z_{\mathrm{t}}\) correspond to the gas compressibility factors at \(P_{0}\) and \(P_{\mathrm{t}}\), respectively, computed in accordance with the national standard GB/T 17747.3-2011 [52], utilizing a Matlab programming model; \(T\) denotes the experimental temperature; \(R\) represents the molar gas constant (8.314 J/(mol\(\cdot\)K)); and \(V_{\mathrm{g}}\) denotes the gas volume within the reaction vessel, which is 6.98 \(\times\) 10\({}^{-5}\) m\({}^{3}\). In the experiment, the primary factors considered are the fracture width, fracture shape, and roughness. The fracture widths employed are 3 mm, 6 mm, and 10 mm. The fracture shapes are Type I and Type X. The pore pressure is set at 5 MPa, and the fracture roughness is controlled by attaching glass beads to the fracture walls, with roughness values of 2.5 mm and 3.5 mm employed. The temperature gradient during formation and the CH\({}_{4}\) hydrate phase equilibrium conditions are considered (as shown in Figure 4).