## 2 Materials and Techniques
### Experimental Procedures
#### 2.3.3 NMR Pore Size Distribution Calibration  
The techniques for measuring nuclear magnetic resonance (NMR) spectroscopy enable the rapid acquisition of reservoir properties, such as porosity, permeability, oil saturation, and water saturation, by analyzing the volume, properties, and NMR T\({}_{2}\) relaxation time  
Figure 3: The process of rock quality evaluation. distribution spectrum characteristics of fluids within rock core pores. The transverse relaxation time, T\({}_{2}\), of the fluid in the rock core can be determined via surface relaxation, bulk relaxation, and diffusion relaxation [50; 51], as illustrated in Equation (1):  
\[\frac{1}{\text{T}_{2}}=\frac{1}{\text{T}_{2\text{S}}}+\frac{1}{\text{T}_{2\text {D}}}+\frac{1}{\text{T}_{2\text{B}}} \tag{1}\]  
where T\({}_{2}\) is the transverse relaxation time in milliseconds (ms), T\({}_{2\text{S}}\) denotes the surface relaxation time in ms, T\({}_{2\text{B}}\) stands for the bulk relaxation time in ms, and T\({}_{2\text{D}}\) represents the diffusion relaxation time in ms.  
[PERSON] et al. discovered that in scenarios where the pore fluid is water, the contribution of T\({}_{2\text{B}}\) is typically insignificant. Conversely, in cases where the pore fluid consists of a viscous oil or a solution with a high concentration of paramagnetic ions, bulk relaxation mechanisms may predominate [52]. When the pore fluid is a single-phase wetting fluid, the bulk relaxation time T\({}_{2\text{B}}\) is much larger than the surface relaxation time T\({}_{2\text{S}}\), which can be neglected in Equation (1). In an NMR system utilizing a homogeneous magnetic field, the effect of diffusion relaxation becomes negligible. Furthermore, when the gradient of the magnetic field is minimal and the echo time in the Carr-Purcell-Meiboom-Gill (CPMG) sequence is adequately brief (less than 1 ms), diffusion effects can also be effectively ignored [53]. The expression for the transverse relaxation time, T\({}_{2}\), of porous media can then be expressed to Equation (2), as per references [31; 54]  
\[\frac{1}{\text{T}_{2}}\approx\frac{1}{\text{T}_{2\text{S}}}=\rho_{2}(\frac{ \text{S}}{\text{V}})_{\text{pore}} \tag{2}\]  
where \(\rho_{2}\) is the transverse relaxation rate, which characterizes the strength of fluid relaxation at the pore surface, in \(\upmu\)m/ms. S/V denotes the specific surface area of a single pore, in \(\upmu\)m\({}^{2}\)/\(\upmu\)m\({}^{3}\). Equation (2) suggests that the transverse relaxation time T\({}_{2}\) is related to the specific surface area of the porous medium. If we simplify the pore structure to be either spherical or cylindrical, then Equation (2) can be transformed into Equation (3):  
\[\text{T}_{2}=\frac{1}{\rho_{2}}(\frac{\text{V}}{\text{S}})_{\text{pore}}= \frac{\text{r}}{\rho_{2}\text{F}_{\text{S}}} \tag{3}\]  
where F\({}_{\text{S}}\) is the pore shape factor (F\({}_{\text{S}}\) is 3 for spherical pores and 2 for tubular pores, dimensionless), and r represents the pore radius, measured in micrometers (\(\upmu\)m). According to Equation (3), the transverse relaxation time T\({}_{2}\) of the rock core is linearly proportional to pore radius r. However, after extensive experimental matching, it has been observed that due to the complexity of the formation pore structure, T\({}_{2}\) is proportional to the pore radius r with a power index (n) [26; 33; 55]. Therefore, Equation (3) is modified to obtain Equations (4) and (5):  
\[\text{T}_{2}=\frac{\text{r}^{\text{n}}}{\rho_{2}\text{F}_{\text{S}}} \tag{4}\]  
\[\text{r}=(\rho_{2}\text{F}_{\text{S}}\text{T}_{2})^{\frac{1}{\text{n}}} \tag{5}\]  
In experimental settings, obtaining definitive values for \(\rho_{2}\) and F\({}_{\text{S}}\) is complex. Consequently, converting the transverse relaxation time T\({}_{2}\) distribution into a pore diameter distribution curve by determining the values of \(\rho_{2}\) and F\({}_{\text{S}}\) presents significant challenges.