# Experimental Analysis of Pore and Permeability Characteristics of Coal by Low-Field NMR
## 3 Discussion
### Pore Type of NMR
#### 3.1.2 Pore Types and Development Characteristics  
There are multi-shape and multi-scale pores and fissures in coal. When NMR is used for PSD analysis, it is necessary to convert the NMR signal into the equivalent pore size. According to the morphological changes of the \(T_{2}\) spectra before and after centrifugation, combined with the size, shape, and distribution of the pores and fissures in the coal observed by SEM, the contribution to gas adsorption, diffusion and seepage, and the pores and fissures in the coal can be classified. According to the NMR theory, there is an intrinsic relationship between the pore size and \(T_{2}\). It is assumed that there exists very long free relaxation rate and ignores the effects of free and diffusion relaxation. In porous materials, the hydrogen proton is mainly affected by the surface diffusion relaxation, and the surface relaxation time is related to the surface relaxation rate and pores shape [10; 21]. \[\frac{1}{T_{2}}=\rho_{\mathrm{s}}\frac{S}{V}=\rho_{\mathrm{s}}\frac{F}{r_{ \mathrm{p}}} \tag{1}\]  
Figure 2: \(T_{2}\) distribution of the coal samples of different ranks: (**a**) CZ-1 and CZ-4; (**b**) CZ-2 and CZ-3; (**c**) WY-1 and WY-2; (**d**) YJL-1 and YJL-2. where \(T_{2}\) is the transverse relaxation time, ms; \(\rho_{\rm s}\) is the surface relaxation rate, cm/ms; \(S\) is the pore surface area, m\({}^{2}\); \(V\) is the pore volume, cm\({}^{3}\); \(r_{\rm p}\) is the pore radius, nm; \(F\) is the geometrical shape factor of the pore, and the value of the spherical, cylindrical, and plate pore is 3, 2, 1, respectively. The surface relaxation rate is a characteristic parameter of the interaction of the magnetic material in the solid-liquid interface, which is closely related to the surface properties. For a certain coal sample, the surface relaxation rate is a constant. Assuming that the structure and composition of pores in a certain aperture are very similar, the \(F\) in Equation (1) is also a constant, and then, the \(T_{2}\) is linearly related to the equivalent pore size. Figure 2 shows that the development of the pores and fissures from the coal samples of CZ, WY, and YJL differed greatly. In general, both the pores and fissures are developed in coal, and they are all reflected in the \(T_{2}\) spectra, so \(r_{\rm p}\) in Equation (1) is equivalent to the pore radius. The \(T_{2}\) spectra can only reflect the relative proportions of the pore volume in different pore sizes, without any information regarding pore morphology. Figure 3a-e are the SEM images of the pores and fissures of the YJL coal samples after argon ion polishing. The fissures, micro-fissures, and nanopores are all developed in the YJL coal samples. The fissures were randomly distributed in the coal matrix, their length often exceeded the visual range of the SEM image, and the width was generally greater than 2.5 \(\upmu\)m (Figure 3a). Micro-fissures were often developed in some special macroals, their width was hundreds of nanometers, and the length was hundreds of microns (Figure 3b,c). The nanopores were distributed on some small macroal particles with the aperture between dozens of and hundreds of nanometers (Figure 3d,e). Based on the morphology of the \(T_{2}\) spectra and the size and shape of the pores and fissures observed by SEM, the pores and fissures in the YJL coal samples can be divided into three types: nanopores, micro-fissures, and fissures. Comparing the \(T_{2}\) spectra of the samples from different mining areas (Figure 2), it was found that their characteristics were obviously different. The three types of pores in the YJL coal samples were all developed, the nanopore peaks were the strongest, the second was the micro-fissures peak, and the fissure peaks were the weakest, which was consistent with the distribution and development characteristics of the pores observed by SEM.