## 2 Materials and Methods
### Saturated Methane NMR of Plug-Sized Shale Samples  
Due to the large amount of methane adsorption in shale, the \"saturated methane\" mentioned in this experiment includes both adsorbed methane and free methane injected into the core pores under certain pressure conditions. A \({}^{1}\)H-NMR Rock Core Analyzer manufactured by the Suzhou Niumag Analytical Instrument Corporation in China was employed in this study, which has a magnetic field of 0.3 \(\pm\) 0.05 T and a frequency of 12 MHz. In order to verify whether the NMR technique can measure adsorbed gas, the original methane intake gas system was improved before this experimental test. A reference chamber with a known volume has been added between the sample chamber and the high-pressure methane cylinder (Figure 2) to record the pressure changes during the experiment and calculate the total methane mass injected into the sample chamber. This study used plug samples (diameter \(\times\) height: 25.5 mm \(\times\) 30 mm) that were saturated with methane for the NMR T\({}_{2}\) spectrum testing, which has two advantages: one is to maintain the integrity of the micro-scale pore structure of shale reservoirs; the other is to effectively deduct the annular volume between the plug sample and sample chamber, achieving the monitoring of NMR signals for both adsorbed and free gases in the plug sample. Before each experiment, the chamber volume of the experimental equipment was calibrated using methane gas to avoid the impact of temperature changes on the experimental results. The methane in the sample chamber of the NMR system can be divided into three categories: free methane in the shale pores, adsorbed methane in the shale pores, and bulk methane that is free in the void space of the sample chamber and not related to the sample. The specific procedures for methane-saturated NMR T\({}_{2}\) spectrum tests are as follows: (1) Sample pretreatment: the shale samples are dried at 110 \({}^{\circ}\)C for 24 h and the mass of the dried core is recorded for gas content calculation. (2) Test-parameter setting: the echo interval (TE) is set to 0.1 ms, the number of echoes (NECH) is set to 12,000, the cumulative scanning number (NS) is set to 128 times, and the waiting time (TW) is set to 3000 ms.  
(3) Calibration between the methane mass and the NMR signal is conducted in an empty sample chamber with different pressures and temperatures: for this work, we tested the NMR T\({}_{2}\) spectra at different temperatures (40 \({}^{\circ}\)C, 60 \({}^{\circ}\)C, 80 \({}^{\circ}\)C, and 100 \({}^{\circ}\)C) and pressures (2 MPa, 4 MPa, 6 MPa, 8 MPa, 10 MPa, and 12 MPa). (4) Sample-testing steps: the dried sample is placed in the sample chamber for vacuum extraction and loading the peripheral pressure of the core (approximate formation pressure);  
Figure 2: Schematic of the experimental apparatus used in the NMR measurements. the entire testing system is heated to the required temperature; a certain pressure of methane gas is injected into the reference chamber, and the pressure data (P\({}_{1}\)) are recorded after equilibrium; the valve between the reference chamber and the sample chamber is opened to allow methane gas to expand into the sample chamber; after the system pressure is balanced, the NMR T\({}_{2}\) spectrum is tested and the pressure data (P\({}_{2}\)) are recorded. The criterion for determining the saturated methane equilibrium of shale is to test the NMR T\({}_{2}\) spectrum every 1 h after methane adsorption for a set period of time until three consecutive NMR T\({}_{2}\) spectra remain unchanged, indicating full saturation of the sample. (5) Results processing: the saturated methane NMR signal intensity calculation is tested in the above steps.