# Experimental Analysis of Pore and Permeability Characteristics of Coal by Low-Field NMR
## 3 Discussion
### NMR Pore Structure
#### 3.3.2 NMR Permeability
The relationship between porosity and tortuosity can be expressed as follows [36]:  
\[\tau=0.8(1-\varphi_{\text{FFI}})+1. \tag{15}\]  
The \(T_{2}\) is linearly related to the pore size, and the geometrical fractal relation of NMR pores can be expressed as follows [13]:  
\[V_{\text{c}}=\frac{T_{2}^{3-D_{\text{NMR}}}}{T_{\text{2 max}}^{3-D_{\text{NMR }}}} \tag{16}\]  
where \(V_{\text{c}}\) is the percentage of pore accumulation volume occupied by the total volume, %; and \(T_{\text{2 max}}\) is the maximum transverse relaxation time, ms. Using logarithms for Equation (16), we obtained the following:  
\[\text{lg}V_{\text{c}}=(3-D_{\text{NMR}})\text{lg}T_{2}+(D_{\text{NMR}}-3)\text{ lg}T_{2\text{max}} \tag{17}\]  
Based on the NMR experimental data and Equation (17), the relationship between \(\text{lg}(V_{\text{c}})\) and \(\text{lg}(T_{2})\) was obtained, and then, the fractal dimension of seepage fissures can be calculated. Using Equations (9)-(11) and (13), the permeability of NMR in each coal sample was calculated, and the results are shown in Figure 8:0  
Table 4 showed that \(T_{\text{2,log mean}}\), \(D_{\text{NMR}}\), and \(S_{\text{p}}\) are between 0.83-2.18 ms, 2.9434-2.9940, 0.48-450.66 m\({}^{-1}\), respectively, which indicated that the pore structures of the coal samples from different mining areas were different. There were noticeable differences in the permeability results calculated by different models, and no one model results were basically consistent with the results of the laboratory tests. It was worth noting that the porosity and structural parameters of the bedding and vertical layers of the same seam were very close, but their permeability determined in the laboratory differed greatly. The above fact shows that the permeability of the coal seam is not only closely related to the porosity but also to the pore connectivity. The pores and fissures in the coal seam are controlled by the maceral, coalification, and tectonic movement, and the heterogeneity of pore structure and connectivity is much higher than that of porosity, so their influence on permeability is often more significant. Therefore, it is very difficult to establish a model of the relationship between porosity and permeability of different reservoirs, especially for coal samples from different mining areas, and the relationship between them is more complex and changeable. The NMR porosity determined in the laboratory can basically represent the porosity of the coal reservoir. The structure and connectivity of the pores in the coal are typically heterogeneous, and the permeability of the coal samples from the same mining area differs, so they cannot represent the permeability of the coal reservoir. Therefore, it is difficult to establish an exact relation equation between the NMR porosity and the permeability of the reservoir only through the laboratory work. The study of the correlation between the MNR porosity and permeability of 51 coal samples drilled from 16 wells in southern Sichuan Basin by [PERSON] et al. (2017) also proved this opinion.