## 1 Introduction  
As conventional oil and gas fields gradually enter the late stage of development, low-permeability, ultra-low-permeability, and other unconventional oil and gas reservoirs with permeability of less than 10 mD have steadily become the focus of growth [1; 2; 3]. In the process of the water drive development of such reservoirs, the injection pressure is high, the sweep efficiency is low, and the development effect is poor [4; 5; 6]. Compared with water, supercritical CO\({}_{2}\) has low viscosity, strong diffusivity, and a strong extraction effect. It is able to easily enter tiny pores, which helps to improve the swept area and microscopic oil displacement efficiency and is more suitable for the development of low permeability reservoirs [7; 8; 9; 10; 11; 12; 13; 14; 15]. As a high-precision nondestructive measurement method, nuclear magnetic resonance is widely used in the detection of the microscopic pore structure of rocks, and the total pore diameter of cores can be effectively characterized by the transverse relaxation time (T\({}_{2}\)) of nuclear magnetic resonance [16; 17]. The smaller the T\({}_{2}\) is, the smaller the pore-throat size of the core. However, it can only be qualitatively analyzed in actual use according to the T\({}_{2}\) distribution and its frequency changes, which has significant limitations. Therefore, it must be converted into a rock pore-throat radius (r) to quantitatively analyze the degree of pore-throat utilization [18; 19; 20]. As a measurement method of pore-throat size, HPMI can obtain the percentage content of each pore-throat size according to the mercury inlet curve [21; 22]. However, the measurement points are relatively few (no more than 30), and the pore-throat distribution curve is rough. Due to the advantages and disadvantages of the two-pore-throat characterization methods, HPMI and nuclear magnetic resonance are often combined to characterize pore structures in actual use [23; 24; 25; 26; 27]. Many studies have shown a certain correspondence between T\({}_{2}\) and r, and previous studies on the conversion relationship between the two have made noticeable progress [28; 29; 30; 31; 32; 33]. [PERSON] et al. proposed a linear transformation formula. Still, the parameters related to core properties are involved in the formula, and significant parameter differences between different cores may affect the formula's accuracy [34; 35; 36; 37]. [PERSON] et al. used the similarity between the T\({}_{2}\) spectrum and capillary force curve to establish a transformational relationship, eliminating the influence caused by different characteristic parameters [38; 39]. According to the existing research results, the accuracy of the linear relationship between T\({}_{2}\) and r is low, and the conversion results of some cores will have large deviations. Later, it was found that only spherical or columnar pore-throats are suitable for linear conversion, while other pore-throats with complex shapes are entirely unsuitable [35]. After many experiments, statistics, and a theoretical derivation verification, people found that the relationship between T\({}_{2}\) and r presents a power function; the shape of the pore-throat has no restriction on this transformation mode, which becomes the most widely used transformation relationship [40; 41; 42; 43; 44]. However, the matching relationship between r and T\({}_{2}\) is also different under different pore-throat sizes, so applying a matching relationship to the entire aperture range is unsuitable, and the pore-throats must be segmented in treatment [45; 46; 47; 48]. Some scholars use the peak value of the T\({}_{2}\) spectrum for segmentation and find that the power function relationship of large, medium, and small pores is very different [49; 50; 51; 52]. After the fractal theory was proposed in the 1970s, it was widely used to characterize pore structure.