## 6 Conclusions  
This study employs XRD, FE-SEM, NMR, and fractal dimension theory to assess the heterogeneity of pore structures in three-dimensional space. Additionally, an investigation is conducted on the correlation between the fractal dimension obtained from NMR analysis and various factors such as the TOC content, mineral composition, geochemical parameters, and physical parameters. In general, the relationship between the fractal dimension obtained from NMR measurements and the physical properties of reservoirs can be utilized as a means of assessing the quality of shale reservoirs. Furthermore, the presence of shale pores is intricately linked to the sedimentary environment, mineral composition, and diagenesis. The diverse nature of shale is frequently ascribed to disparities in the sedimentary milieu and diagenetic mechanisms. Hence, the determination of fractal dimensions in individual well profiles and planes facilitates the investigation of the impact of a sedimentary environment and burial history on porosity heterogeneity and reservoir quality. At the same time, attention should also be paid to avoiding environmental pollution during shale-oil exploration and development. Figure 12: Relationship between the shale NMR fractal dimension and reservoir physical properties. 1. The Funing Formation shale is presently considered to be in a mature stage, as evidenced by the majority of samples displaying a total organic carbon (TOC) content surpassing 1%. This suggests the presence of favorable organic geochemical conditions. The shale samples from the Funing Formation exhibit a dominant mineral composition, with quartz comprising an average of 25.53% and dolomite comprising an average of 24.23%. Clay minerals follow closely, with an average composition of 20.77%, while feldspar constitutes an average of 13.80%. Nevertheless, it is worth noting that there is no single mineral that demonstrates a distinct dominance, as each average content remains below 40%. 2. The primary pore classifications observed in the Funing Formation shale within the Gaoyou Sag consist of inorganic matrix pores. These pores encompass dissolution pores, intergranular pores formed by clay minerals, and a limited quantity of intergranular pores associated with pyrite. The range of the pore-size distribution is extensive, spanning from a few nanometers to hundreds of nanometers, with a minority extending into the micron range. On average, the pore size measures in the tens of nanometers. 3. The Funing formation's NMR fractal dimension displays a notable two-segment configuration, wherein the fractal dimension \(\mathrm{D}_{\mathrm{Min}}\), which characterizes the pore structure of bound fluid, spans 0.5795 to 1.3813 (with a mean value of 0.8110). Furthermore, the fractal dimension \(\mathrm{D}_{\mathrm{Max}}\), which serves as an indicator of the pore structure of fluid that can be displaced, exhibits a range of values from 2.9592 to 2.9793, with an average value of 2.9651. 4. The organic geochemical characteristics and mineral composition of shale exert varying degrees of influence on the NMR fractal dimensions characterizing the two pore structures. Specifically, TOC, quartz, calcite, illite-smectite, illite, and chlorite impact \(\mathrm{D}_{\mathrm{Min}}\), with all except calcite and illite-smectite showing negative correlations. Organic matter content and mineral composition play a significant role in controlling the fractal dimension. 5. The evaluation of reservoir performance relies heavily on the assessment of porosity and permeability, which are considered to be vital parameters. There exists a noteworthy correlation between the physical parameters and the fractal dimensions of both bound-fluid pores and movable-fluid pores. This implies that the utilization of NMR fractal dimensions can be advantageous in assessing physical properties, thereby enhancing the characterization of reservoirs. Data curation, Y.Z. ; methodology, Y.Z. ; project administration, Z.J. ; resources, Z.J. ; writing--original draft, Z.W.