## 4 Discussion  
Frail geometric theory plays a vital role in exploring objects from similar structures and morphological phenomena. Due to the complexity and irregularity of the pore structure \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Pressure/MP** & **Spectrum Peak Start and End Time/ms (Polymark/\%)** \\ \hline
0 & 0.163–7.925 & 12.916–205.651 \\
0 & (88.256) & (11.744) \\
1 & 0.163–7.925 & 12.916–205.651 \\
1 & (88.446) & (11.454) \\
3 & 0.163–7.925 & 12.916–205.651 \\
5 & 0.163–7.925 & 12.916–205.651 \\  & (90.618) & (9.382) \\
8 & 0.163–7.925 & 12.916–205.651 \\  & (91.429) & (8.571) \\
11 & 0.163–7.925 & 12.916–205.651 \\  & (91.893) & (8.107) \\
15 & 0.163–7.925 & 12.916–205.651 \\  & (92.132) & (7.868) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: T2 spectrum peak distribution under different pressures of sandstone. Figure 5: T2 spectrum under different fences 1 test piece No. 2.3.  
and pore diameter distribution, the traditional Eueli is difficult to accurately quantify it. Since [PERSON] has introduced fractal theory, it has become a powerful tool describing porous medium physical geometric properties, pore structure and surface characteristics, which are usually expressed in fractal dimensions D, and the number of fractal dimensions is 2-3 [24]. Nuclear magnetic resonance technology can effectively reveal the distribution characteristics of coal rock microscopic pores. Through this technology, we can get the T2 map of the test piece. It is worth noting that the T2 spectrum has the fractal characteristics of porous media, which provides us with a new perspective to interpret the micro-structure of coal rocks. According to the T2 spectrum distribution curve characteristics, we proposed a unique NBR fractal dimension algorithm. This algorithm enables us to in-depth research on the fractal characteristics of the pore structure at different standards, thereby understanding the micro-structure characteristics of coal rocks more accurately. According to the theory of fractal geometry [25], if the distribution of the pores of the reservoir meets the fractal structure, the number N with a radius of the rock pores is greater than R and the pore radius R meets the power of the power function. \[N(>r)=\int\limits_{r}^{r_{\max}}P(r)dr=ar^{-D} \tag{1}\]  
Nuci magnetic resonance total horizontal relaxation mechanism is  
\[\frac{1}{T_{2}}=\frac{1}{T_{2B}}+\frac{1}{T_{2S}}+\frac{1}{T_{2D}}\approx\frac {1}{T_{2B}}=P\bigg{(}\frac{S}{V}\bigg{)}=F_{S}\frac{P}{r} \tag{2}\]  
The T2B in the formula represents the inherent attributes of hydrogen fluids, which can usually be ignored; T2S represents the horizontal relaxation time caused by the surface relaxation; the T2D is the horizontal relaxation time of the pore fluid caused by diffusion under magnetic gradients. It can be ignored in a uniform magnetic field environment. Parameter P represents the surface relaxation strength; S refers to the pore surface area, the unit is a square centimeter; V is the pore volume, the unit is cubic centimeter; R represents the pore radius; FS is a geometric shape factor. For cylindrical pipes, FS is equal to 2. Therefore, the cumulative pore volume SV in the MRI measurement measurement can be expressed as:  
\[S_{\textit{D}}=\bigg{(}\frac{T_{\max}}{T_{2}}\bigg{)}^{D-3} \tag{3}\]  
Get the two sides of the two sides:  
\[\text{lg}(S_{\textit{D}})=(3-D)\text{lg}(T_{2})+(D-3)\text{lg}T_{\text{2 max}} \tag{4}\]  
Then the nuclear magnetic pores are divided with the number of dimensions:  
\[D=3-K \tag{5}\]  
The above formula reveals the existence of linear correlation between LG (SV) and LOG (T2). Through the linear fitting analysis of the NMR T2 spectrum, we can obtain the fractal dimensions of the rock pore structure. From the nuclear magnetic data, it can be seen that the sandstone in the region has a clear double peak form. It is inappropriate to comprehensively describe the complex pore structure with a single fractal dimension. Two differential dimensions, namely large and small holes fractal dimensions.