## 4 Result
### NMR Experiment and Its Fractal Characteristics  
#### 4.3.1 NMR Experimental Results and Physical Properties  
The \(T_{2}\) spectrum distribution of the saturated water sample and the centrifuged shale exhibits a similar pattern, characterized by a double-peak shape in which the left peak is higher than the right peak. (Figure 7). The \(T_{2}\) spectral distribution of sample L-1 in the water-saturated state, along with the centrifuged samples L-5 and L-6, exhibited distinct double peaks that were discontinuous in nature. In contrast, the \(T_{2}\) spectra of the remaining samples displayed a consistent pattern of dual peaks. Significantly, the peak area observed in sample L-1 is considerably greater in magnitude when compared to that of sample L-2. Based on the \(T_{2}\) spectral distribution illustrated in Figure 7, it can be categorized into two distinct types. Samples L-1, L-3, L-5, and L-6 are classified as Type I based on their unique double-peak characteristics. The significant disparity observed in relaxation times between the centrifuged samples and the saturated-water state suggests a substantial abundance of mobile fluids within the pores, leading to a high saturation of mobile fluids and favorable conditions for percolation.  
The second category comprises samples L-2 and L-4, both of which demonstrate bimodal characteristics. Nevertheless, the difference in relaxation-time distributions between the centrifuged samples and those in the saturated-water state is relatively insignificant. This observation suggests the presence of a significant volume of fluids that is confined within the pores, a low saturation of fluid that is capable of movement, and unfavorable conditions for fluid seepage.  
The \(T_{2}\) cut-off value is an effective boundary for identifying movable-fluid pores and bound-fluid pores. The procedure involves identifying the maximum porosity signal value following centrifugation and representing it as a line parallel to the horizontal axis. Subsequently, a vertical line is drawn from the intersection of this line and the porosity value corresponding to saturated water. The corresponding relaxation time is the \(T_{2}\) cut-off value [21; 34; 35]. The distinction between cumulative saturated porosity and cumulative porosity post-centrifugation lies in the presence of movable fluid, with the porosity of the centrifugal sample representing the irreducible fluid saturation. The total porosity, movable fluid porosity, bound fluid porosity, permeability and other physical parameters were calculated from the \(T_{2}\) spectrum of the NMR experiment (Table 2). The calculation results show that the total porosity of Funing Formation shale in the Gaoyou Sag of Subei basin is 4.28-7.68%, with an average of 5.67%; the porosity of movable fluid is 1.10-3.78%, with an average of 2.80%, while the bound-fluid porosity is 1.60-3.90%, with an average of 2.87%.  
Figure 7: \(T_{2}\) Spectra of NMR experiments on the Funing Formation shale in the Gaoyou Depression.  
In this paper, Coates model is used to calculate the permeability of shale samples, and the formula is as follows:  
\[K_{C}=\frac{\varphi}{c}\left(\frac{S_{FFI}}{S_{BVI}}\right)^{2} \tag{3}\]  
where \(K_{C}\) is the permeability calculated by the Coates model; \(\varphi\) is the porosity; \(C\) is the coefficient; \(S_{FFI}\) is the movable fluid saturation; and \(S_{BVI}\) is the irreducible fluid saturation.  
According to Formula (3), the permeability of the Funing Formation continental shale in the Gaoyou Sag of Subei basin is 0.00083 md-0.06981 md, with an average of 0.03747 md.