The heterogeneity of pore distribution is of great significance to reveal the occurrence state and transmission characteristics of tight sandstone gas reservoir. Based on the NMR saturation and centrifugal T2 spectrum distribution curves of middle and high rank coal samples in Qinshui Basin, the middle and high rank coal samples are divided into three types. Based on this data, the applicability of single fractal and multifractal models to the quantitative characterization of pore size distribution of middle and high-order coal samples is analyzed, and the pore fractal characteristics are revealed by integrating pore structure and reservoir physical parameters. The results show that the T2 value of class A samples is between 1 ~ 1000ms, and the saturated T2 spectrum distribution shows a "single peak", which is dominated by the development of macropores, with good physical conditions. The porosity is mostly 4.04 ~ 6.16%, and the permeability of each sample is greater than 0.1md. The T2 value of class B samples is mainly 0.1 ~ 300ms, the T2 spectrum is symmetrical "three peaks", the irreducible water saturation is relatively high, the pore development is relatively small under the influence of compaction, and the average porosity and permeability are less than that of class A. The T2 values of C and D samples are between 0.01 ~ 200 and 0.01 ~ 10ms respectively. The saturated T2 spectrum distribution shows "single peak state", and the pore permeability structure is the worst. The single fractal dimension has a good linear relationship with porosity, T2 cut off and other physical parameters. It is mainly suitable for type B, C and D samples with relatively developed micropores. At the same time, there is a good negative correlation between multifractal parameters and single fractal parameters. Affected by the difference of calculation principles, small and large pores are the key pore sizes affecting the change of single fractal parameters, while mesoporous pore distribution is the key pore size affecting the change of multifractal parameters.