## 4 Discussion
### Comparison of the Total Gas Content Tests Using Different Methods
#### 4.1.2 NMR Method  
This study used plug sample nuclear magnetic resonance technology to test the free gas in shale reservoirs. Calculating the total gas content by the NMR method includes measuring the adsorption gas volume using an isothermal adsorption experiment and measuring the free gas volume using NMR. The temperature and pressure of the shale reservoirs in the Zhaotong and Weiyuan areas are 60 \({}^{\circ}\)C and 15 MPa, as well as 90 \({}^{\circ}\)C and 35 MPa, respectively. The free gas contents of shale reservoirs can be directly measured through NMR experiments. Due to the burial depth of the shale reservoirs in the Luzhou area exceeding 4000 m and the experimental pressure and temperature reaching 60 MPa and 130 \({}^{\circ}\)C, respectively, nuclear magnetic resonance equipment cannot meet the experimental requirements of formation conditions. Therefore, it is necessary to establish corresponding geological models for extrapolation. The method of extrapolation will be explained in detail in the following paragraphs.  
The saturated methane NMR signal intensity of the L214 samples under different temperature and pressure conditions was tested and plotted into the corresponding plates (Figure 8a). We can see that there is a good linear relationship between the NMR signal intensity and pressure under the same temperature conditions, which also indicates that the methane in shale cores exists in the form of free gas. Meanwhile, it should be pointed out that the NMR response characteristics of all samples under different temperature and pressure conditions are consistent with those of the L214 sample. These will not be explained individually in this work. The slope (K) of the straight line varies at different temperatures and decreases in a negative logarithmic form as the temperature increases (Figure 8b). Whether it is in the form of free methane in the shale pores or bulk relaxation methane in the MF and sample cells, the NMR signal intensity will decrease with increasing temperature. As temperature mainly affects the K value on the basis of pressure linearity, Equation (1) can be rewritten as:  
\[\mathrm{m}_{\mathrm{free}}=\mathrm{K}\times\mathrm{T}_{\mathrm{2 free}}=[ \mathrm{a}\times\mathrm{LN(T)}+\mathrm{b}]\times\mathrm{T}_{\mathrm{2 free}} \tag{8}\]  
where a and b are constants. T is the experimental temperature, in \({}^{\circ}\)C. The NMR signal intensity of actual shale samples at different temperatures and pressures can be fitted using multivariate nonlinear regression, based on the experimental results and the correlation in Figure 8. The specific expression is as follows:  
\[\mathrm{T}_{\mathrm{2 free}}=[\mathrm{A}\times\mathrm{LN(T)}+\mathrm{B}]\times \mathrm{P}+\mathrm{C} \tag{9}\]  
where A, B, and C are constants; T is the experimental temperature, in \({}^{\circ}\)C.  
Figure 8: (**a**) The relationship between NMR signal intensity and pressure in the L214 shale samples at different temperatures; (**b**) the relationship between the linear slope (K: between pressure and signal intensity at different temperatures) and temperature.  
We organized the NMR signal intensity of the same sample, tested it under different temperature and pressure conditions, recorded it in Microsoft Excel, and imported it into the Origin function analysis software. We then used Equation (9) in tens of thousands of iterations to ensure the convergence and strong correlation of the function. After fitting the actual experimental data, the values of A, B, and C were 3.57, 3.20, and 4552, respectively. The square of the correlation coefficient was 0.86. Then, the NMR signal intensity of the L214 sample at 130 \({}^{\circ}\)C and 60 MPa was calculated to be 5787 a.u. Therefore, the free gas content at STP was 16.38 m\({}^{3}\)/t and the total gas content was 18.88 m\({}^{3}\)/t.