## 4 Results
### 2D Pore Structure
#### 4.1.2 PCAS Analysis  
The pore (particle) and fracture image identification and analysis system (PCAS) is professional software for the quantitative analysis of the pore system and fracture system. The software can automatically obtain geometric and statistical parameters and calculate the depth, area, and fractal dimensions of individual pores. The pores are identified by importing the SEM pictures of the core samples into the software and adjusting the grayscale threshold of the pictures. In the SEM pictures, the areas with pores have a darker color compared to other areas, and the adjustment process can make the darker parts of the pictures appear darker and the brighter parts appear brighter, thus identifying the physical parameters of the pores [63]. In this study, the probability entropy and shape factor obtained were mainly calculated by PCAS software [63]. The probability entropy is mainly used to describe the directionality of the 2D structure of the pores, which is calculated as follows (Equation (1)):  
\[H=-\sum_{i=1}^{n}P_{i}\text{log}_{n}\,P_{i} \tag{1}\]  
where \(H\) is the probability entropy; \(P_{i}\) denotes the percentage of pores in a specific range, for example, between 0\({}^{\circ}\) and 10\({}^{\circ}\) when \(i=1\), in the 2D direction ranging from 0\({}^{\circ}\) to 180\({}^{\circ}\), and divided into eighteen parts, i.e., \(n=18\), the probability entropy has values between 0 (all pores are arranged in the same orientation) and 1 (pores have random orientation). The shape factor (_ff_) is a descriptor of the characteristic shape and reflects the roundness and roughness of the hole edges. It has a maximum value of 1.0 (for a circle) or 0.785 (for a square). Its calculation formula is as follows (Equation (2)):  
\[ff=4\pi S/C^{2} \tag{2}\]  
where \(S\) is the area of the pore, and \(C\) is the perimeter of the pore. The scanning electron microscope images of the shale samples from K\({}_{2}\)n\({}^{1+2}\) were imported into PCAS software, and the organic and inorganic pores could be identified by adjusting the gray level of the images. Taking SEM images of sample SK1-S-1 as an example, the gray level of the SEM images was adjusted to identify the organic pores. Each organic pore was colored with different colors, and the other inorganic pores were eliminated. Then some parameters of each organic pore with different colors were obtained by further calculation in the software (Figure 3) [63]. Using PCAS software, the scanning electron microscope images were divided into organic and inorganic pores, the probability entropy and shape factors of different types of pores were analyzed separately, and the distribution of the pore size were analyzed at the same time (Table 1). By processing 31 scanned images of K\({}_{2}\)n\({}^{1+2}\) with PCAS software, and rejecting the unqualified images and obtaining each parameter of the pores, the following results were obtained by comprehensive analysis: (i) The shape factor of the organic pores was mainly concentrated between 0.3 and 0.7. The average shape factor was 0.56. The average probability entropy of the organic pores was \(\sim\)0.6 (Table 2). (ii) The shape factor of the inorganic pores was mainly concentrated between 0.5 and 0.6. The average shape factor was 0.54. The average probability entropy of the inorganic pores was \(\sim\)0.9 (Table 2). (iii) As a whole, the number of inorganic pores was much larger than the number of organic pores. The use of backscattered electron imaging is beneficial to observe the shape, size, and distribution pattern of nanoscale pores on the smooth and flat surface of the sample after argon ion polishing [10; 15; 16; 17; 18]. SEM analysis and PCAS analysis showed the 2D pore structure characteristics. As image-processing tests on the number of pores have some limitations, these were specific analyses of typical micro-regions, aiming to complement the information on pore characteristics.