## 5 Discussion
### Relationships between Fractal Dimensions and Pore Structure Parameters  
The average shape factor was 0.56 for organic pores and 0.54 for inorganic pores (Table 1). These indicate that both the organic pores and inorganic pores in the shale of K\({}_{2}\)n have similar near-square pore shapes. The average probability entropy was about 0.6 for \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **TOC** & **T\({}_{\text{max}}\)** & **S1** & **S2** & **HI** & **OSI** \\  & **(\%)** & **(\({}^{\circ}\)C)** & **(mg/g)** & **(mg/g)** & **(mg/g TOC)** & **(mg/g TOC)** \\ \hline SK1-S-1 & 1.68 & 435 & 0.14 & 4.59 & 273 & 8.33 \\ SK1-S-2 & 1.46 & 438 & 0.15 & 5.41 & 371 & 10.27 \\ SK1-S-3 & 4.94 & 442 & 0.60 & 42.83 & 867 & 12.15 \\ SK1-S-4 & 1.70 & 436 & 0.31 & 9.16 & 539 & 18.24 \\ SK1-S-5 & 2.73 & 439 & 0.55 & 18.58 & 681 & 20.15 \\ SK1-S-6 & 1.91 & 439 & 0.28 & 12.18 & 638 & 14.66 \\ SK1-S-7 & 2.10 & 441 & 0.31 & 13.22 & 630 & 14.76 \\ SK1-S-8 & 2.01 & 438 & 0.30 & 12.70 & 632 & 14.93 \\ SK1-S-9 & 1.93 & 434 & 0.41 & 11.57 & 599 & 21.24 \\ SK1-S-10 & 3.92 & 439 & 0.94 & 29.05 & 741 & 23.98 \\ SK1-S-11 & 8.74 & 441 & 2.88 & 75.41 & 863 & 32.95 \\ SK1-S-12 & 1.75 & 439 & 0.26 & 9.48 & 542 & 14.86 \\ SK1-S-13 & 0.30 & 439 & 0.04 & 0.39 & 131 & 13.42 \\ SK1-S-14 & 0.64 & 441 & 0.05 & 1.55 & 244 & 7.87 \\ SK1-S-15 & 7.70 & 441 & 3.38 & 75.05 & 975 & 43.90 \\ SK1-S-16 & 7.85 & 443 & 2.06 & 69.78 & 889 & 26.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Rock-Eval data of K\({}_{2}\)n\({}^{1+2}\) shale, Songliao Basin. Figure 7: Relationship between TOC content and hydrocarbon generation potential of K\({}_{2}\)n\({}^{1+2}\) shale. (**a**) S2 versus TOC plot showing the quantity and quality of the organic matter, kerogen type, trend HI (HIL), and dead carbon content. (**b**) Relationship between TOC content and S1. the organic pores and about 0.9 for the inorganic pores (Table 2). These indicate that more than half of the pores in the shale of K\({}_{2}\)n have same directional property. This is consistent with the fracture pores shown by the hysteresis loop of the nitrogen adsorption isotherm. The fractal dimension D1 ranged from 2.4406 to 2.6174, with a mean value of 2.5308. The fractal dimension D2 ranged from 2.5036 to 2.7197, with a mean value of 2.6556. The fractal dimensions indicate that the shale pores have good fractal properties in both internal structure and surface, the internal structure of the pores has stronger complexity and non-homogeneity than the surface of the pores, and the smaller pores have stronger complexity and non-homogeneity than the larger ones. The BET specific surface area of the samples ranged from 9.69 to 65.91 m\({}^{2}\)/g, the pore volume ranged from 0.0444 to 0.1187 cm\({}^{3}\)/g (average 0.0768 cm\({}^{3}\)/g), and the average pore size was 8.22-15.40 nm (average 10.10 nm). The average pore diameter of the shale of K\({}_{2}\)n was negatively correlated with the fractal dimensions D1 (R\({}^{2}\) = 0.5948, T \(>\) 2.58, \(p\) < 0.01) and D2 (R\({}^{2}\) = 0.9716, T \(>\) 2.58, \(p\) < 0.01), indicating that the fractal dimension increases with the decrease in the average pore diameter (Figure 8). This trend is consistent with the shale data of the Qingshankou Formation recorded by [PERSON] et al. and [PERSON] et al. [51; 78]. The lacustrine shale samples with higher D2 values had a more complex pore structure, which may be due to the fact that the shale samples with a smaller average pore size also contained more micropores. The fractal dimensions D1 and D2 increased with the increase in the BET surface area. The correlation coefficient between D2 and the BET surface area (R\({}^{2}\) = 0.8002, T \(>\) 2.58, \(p\) < 0.01) was slightly higher than that between D1 and the BET surface area (R\({}^{2}\) = 0.7757, T \(>\) 2.58, \(p\) < 0.01, Figure 8).