# Analysis and Characterization of Micro-Nano Pores in Coal Reservoirs of Different Coal Ranks
## 3 Results and Discussion
### Pore Network Stick Model  
The PNM stick model refers to simplified pore and throat structures with parameterized geometry and connectivity. It is extracted from a binarized 3D core pore model to accurately reflect the pore structure and its connectivity [35]. In this study, the maximum ball method was employed to extract the PNM from the 3D pore structure of the core sample. This method involves filling the pore space with spheres of different sizes. Upon identifying the local maximum ball within this spere set, the pore and throat structures within the pore network were established, with the smallest ball between the two largest balls forming the \"pore-throat-pore\" relationship [36; 37; 38; 39]. The quantitative characterization of reservoir space was achieved through the extraction of pore throat parameters such as pore volume, pore area, pore equivalent radius, throat area, throat equivalent radius, and throat length [40]. The visualization results of the pore throat analysis of the coal samples using the Avizo software are shown in Figure 10.  
The figure illustrates that the pores in the middle-rank coal LL were the most developed, followed by the high-rank coal ZZ, with the low-rank coal XJ exhibiting the least number of pores. This indicates that the micro-nano pores were more developed in the middle-rank and high-rank coals, while the micro-scale pores in the low-rank coal and nano-scale pores exceeding 200 nm were relatively weak. The ball-stick model diagram indicates relatively poor pore connectivity in coal samples XJ and ZZ, while the topological relationship of the pores in coal sample LL was complex, with more connected pores. Table 5 presents the pore characteristic parameters of the three coal samples. A notable difference in the number of connected pores between the different coal samples was observed. Figure 10: PNM structure of coal samples. (**a**) PNM structure of micro-CT sample; (**b**) PNM structure of nano-CT sample. The blue part of the figure represents the pore space. The pores in the figure are equivalent to spheres. The color from green to red represents that the pores are getting larger and larger. In Table 5, under micro-CT scanning, LL exhibited the largest total number of pores (193,056), while XJ exhibited the least (59,998), which contributed to the higher porosity of LL compared with XJ. Similar trends were observed under nano-CT scanning. The coordination number reflected the connectivity of the pore network, with higher values indicating superior connectivity and permeability. Under micro-CT scanning, the overall connectivity was XJ \(>\) LL \(>\) ZZ, while, under nano-CT scanning, it was LL \(>\) ZZ \(>\) XJ, with LL exhibiting excellent overall connectivity. The average surface area of the micro-nano pores varied significantly among the three coal samples, contributing to differences in the pore structures. Among these, the average surface area of the micro-nano pores was large in the low-rank coal XJ, indicating larger pore sizes and exceptional connectivity compared with the high-rank coal ZZ. However, the high moisture content in the low-rank coal XJ hindered the coal methane adsorption channels, resulting in weaker adsorption capacity. It was observed that the pore equivalent radius distribution of each sample was unimodal. Specifically, under micro-CT scanning, the pore equivalent radius was predominantly concentrated between 100 \(\upmu\)m and 400 \(\upmu\)m, while, under nano-CT scanning, it was primarily concentrated between 500 nm and 2500 nm, indicating excellent homogeneity within each sample. Notably, the micro-CT scan revealed a significantly higher number of medium-rank coal LL pore equivalents in the range of 100-200 \(\upmu\)m compared with the low-rank coal XJ and high-rank coal ZZ. Thus, the nano-CT scans yielded consistent results across all the samples.